165cm in ft

Using our [URL='http://www.mathcelebrity.com/linearcon.php?quant=165&pl=Calculate&type=centimeter#foot']linear conversion calculator[/URL], we get:
[B]5.41339 feet[/B]

35 m/s for 40 s. how far does it travel?

35 m/s for 40 s. how far does it travel?
This is a distance problem. The formula to relate, distance, rate, and time is:
d = rt
We are given r = 35 m/s and t = 40s. We want d
d = 35 m/s * 40s
d = [B]1,400 meters[/B]

50 meters in 21.81 seconds

Set up a proportion, with meters to seconds:
50 meters/21.81 seconds = x meters / 1 second
50/21.81 = x/1
Using our proportion calculator, we have:
[B]x = 2.293 meters per second[/B]

A 7 by 5 photo was enlarged. The length and width were enlarged 125%. Find the perimeter of the phot

A 7 by 5 photo was enlarged. The length and width were enlarged 125%. Find the perimeter of the photo.
Enlarge length 125%: 7 * 1.25 = 8.75
Enlarge width 125%: 5 * 1.25 = 6.25
Perimeter of the enlarged photo is 2l + 2w, so we have:
P = 2(8.75) + 2(6.25)
P = 17.5 + 12.5
P = [B]30[/B]

A beach volleyball court is 10 yards wide and 17 yards long. The rope used for the boundary line cos

A beach volleyball court is 10 yards wide and 17 yards long. The rope used for the boundary line costs $2.00 per yard. How much would it cost to buy a new boundary line for the court?
[U]Approach:[/U]
[LIST]
[*]A volleyball court is shaped as a rectangle.
[*]And the boundary line runs on the perimeter of the rectangle.
[*]So we want the perimeter of the rectangle
[/LIST]
Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=17&w=10&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 17 and width = 10[/URL], we have:
P = [B]54[/B]

A bicycle wheel is one meter around. If the spikes are 4 centimeters apart, how many spokes are on t

A bicycle wheel is one meter around. If the spikes are 4 centimeters apart, how many spokes are on the wheel altogether?
1 meter = 100 cm per our [URL='https://www.mathcelebrity.com/linearcon.php?quant=1&pl=Calculate&type=meter']conversions calculator[/URL]
100 cm for the whole circle / 4 cm for each spike = [B]25 spikes[/B]

A binomial probability experient is conducted with the given parameters. Compute the probability of

A binomial probability experient is conducted with the given parameters. Compute the probability of x successes in the n independent trials of the experiment.
n = 40, p = 0.05, x = 2
P(2) =
Answer is [B]0.2777[/B]. Using Excel formula of =BINOMDIST(2,40,0.05,FALSE) or using our [URL='http://www.mathcelebrity.combinomial.php?n=+40&p=0.05&k=2&t=+5&pl=P%28X+%3D+k%29']binomial probability calculator[/URL]

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the

A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree?
So we have a [U]right triangle[/U]. Hypotenuse is 15. Base is 12. We want the length of the leg.
The formula for a right triangle relation of sides is a^2 + b^2 = c^2 where c is the hypotenuse and a, b are the sides
Rearranging this equation to isolate a, we get a^2 = c^2 - b^2
Taking the square root of both sides, we get a = sqrt(c^2 - b^2)
a = sqrt(15^2 - 12^2)
a = sqrt(225 - 144)
a = sqrt(81)
a = [B]9 meters[/B]

A boat traveled at a constant speed for 32 hours, covering a total distance of 597 kilometers. To th

A boat traveled at a constant speed for 32 hours, covering a total distance of 597 kilometers. To the nearest hundredth of a kilometer per hour, how fast was it going?
Distance = Rate * Time
We're given t = 32, and d = 597. Using our [URL='https://www.mathcelebrity.com/drt.php?d=+597&r=+&t=32&pl=Calculate+the+missing+Item+from+D%3DRT']distance, rate, and time calculator[/URL], we get:
r = [B]18.656 km/hr[/B]

a car is traveling 75 kilometers per hour. How many meters does the car travel in one minute

a car is traveling 75 kilometers per hour. How many meters does the car travel in one minute
convert from Kilometers to meters
1 kilometer = 1000 meters
75 kilometers = 1000 meters * 75 = 75000 meters
convert from hours to minutes
1 hour = 60 minutes, the car travels:
75,000 meters / 60 minutes = [B]1,250 meters / minute[/B]

A car travels at 40 kilometers per hour. Write an expression for the distance traveled after h hours

A car travels at 40 kilometers per hour. Write an expression for the distance traveled after h hours.
Distance = rate * time, so we have:
Distance = 40km/h * h
Distance = [B]40h[/B]

A carpenter bought a piece of wood that was 43.32 centimeters long. Then she sawed 5.26 centimeters

A carpenter bought a piece of wood that was 43.32 centimeters long. Then she sawed 5.26 centimeters off the end. How long is the piece of wood now?
When you saw off the end, the length decrease. So we subtract:
New length = Original length - Sawed piec
New length = 43.32 - 5.26
New length = [B]38.06[/B]

A chalkboard is 3 feet tall and 4 feet long. What is its perimeter

A chalkboard is 3 feet tall and 4 feet long. What is its perimeter
A chalkboard is a rectangle. So the perimeter is:
2l + 2w
Using [URL='https://www.mathcelebrity.com/rectangle.php?l=4&w=3&a=&p=&pl=Calculate+Rectangle']our rectangle calculator[/URL], we get:
P = [B]14[/B]

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallp

A child's bedroom is rectangular in shape with dimensions 17 feet by 15 feet. How many feet of wallpaper border are needed to wrap around the entire room?
A rectangle has an Perimeter (P) of:
P = 2l + 2w
We're given l = 17 and w = 15. So we have:
P = 2(17) + 2(15)
P = 34 + 30
P = [B]64[/B]

A construction crew has just built a new road. They built 43.75 kilometers of road at a rate of 7 ki

A construction crew has just built a new road. They built 43.75 kilometers of road at a rate of 7 kilometers per week. How many weeks did it take them?
Let w = weeks
7 kilometers per week * w = 43.75
To solve for w, we divide each side of the equation by 7:
7w/7 = 43.75/7
Cancel the 7's, we get:
w = [B]6.25 [/B]

A construction crew has just built a new road. They built 8.75 kilometers of road in 7 weeks. At wha

A construction crew has just built a new road. They built 8.75 kilometers of road in 7 weeks. At what rate did they build the road?
Rate = Km of road / weeks
Rate = 8.75 km / 7 weeks
Rate = [B]1.25 km per week[/B]

A cube is 1 meter long.What is the total length of all its edges?

A cube is 1 meter long.What is the total length of all its edges?
A cube has 12 edges.
12 edges x 1 meter for each edge = [B]12 meters[/B]

A dresser has a length of 24 inches. What is the length of the dresser in centimeters?

A dresser has a length of 24 inches. What is the length of the dresser in centimeters?
[SIZE=5][B]Convert 24 inches to centimeters[/B][/SIZE]
centimeters = 2.54 x inches
centimeters = 2.54 x 24
centimeters = [B]60.96[/B]

A Fahrenheit thermometer shows that the temperature is 15 degrees below zero. Enter the integer that

A Fahrenheit thermometer shows that the temperature is 15 degrees below zero. Enter the integer that represents the temperature in degrees Fahrenheit.
Below zero means negative in Fahrenheit, so we have:
[B]-15[/B]

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants t

A farmer has 165 feet of fencing material in which to enclose a rectangular grazing area. He wants the length x to be greater than 50 feet and the width y to be no more than 20 feet. Write a system to represent this situation.
Perimeter of a rectangle:
P = 2l + 2w
We have P = 165 and l = x --> x>50 and width y <= 20. Plug these into the perimeter formula
[B]165 = 2x + 2y where x > 50 and y <= 20[/B]

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per

A garden has a length that is three times its width. If the width is n feet and fencing cost $8 per foot, what is the cost of the fencing for the garden?
Garden is a rectangle which has Perimeter P of:
P = 2l + 2w
l = 3w
P = 2(3w) + 2w
P = 6w + 2w
P = 8w
Width w = n, so we have:
P = 8n
Cost = 8n * 8 = [B]64n dollars[/B]

A gardener wants to fence a circular garden of diameter 21cm. Find the length of the rope he needs t

A gardener wants to fence a circular garden of diameter 21cm. Find the length of the rope he needs to purchase, if he makes 2round of fence Also find the cost of the rope, if it costs Rs4 per meter (take pie as 22/7)
Circumference of a circle = Pi(d).
Given Pi = 22/7 for this problem, we have:
C = 22/7(21)
C = 22*3
[B]C = 66[/B]

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 2

A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 20 feet less than 3 times the width, what are the dimensions of the rectangular plot?
[U]Set up equations:[/U]
(1) 2l + 2w = 800
(2) l = 3w - 20
[U]Substitute (2) into (1)[/U]
2(3w - 20) + 2w = 800
6w - 40 + 2w = 800
[U]Group the w terms[/U]
8w - 40 = 800
[U]Add 40 to each side[/U]
8w = 840
[U]Divide each side by 8[/U]
[B]w = 105
[/B]
[U]Substitute w = 105 into (2)[/U]
l = 3(105) - 20
l = 315 - 20
[B]l = 295[/B]

A lead pipe 20 ft long is 3/8 inch thick and has an inner diameter of 3 inches. Find the volume of l

A lead pipe 20 ft long is 3/8 inch thick and has an inner diameter of 3 inches. Find the volume of lead in it.
A lead pipe is a cylinder. We want the volume of a cylinder.
Convert 20ft to inches:
20ft = 12(20) = 240 inches
Find the inner radius:
1/2 * inner diameter
1/2 * 3 = 3/2
Now add the thickness for the total radius
3/2 + 3/8 = 12/8 + 3/8 = 15/8
Find volume of the lead where volume = pi r^2 h
Lead vol (V) = Overall volume - inner volume
Lead Vol = pi(15/8)^2(240) - pi(3/2)^2(240)
Lead Vol = 240pi(225/64 - 9/4)
9/4 = 144/64
Lead Vol = 240pi(225/64 - 144/64)
Lead Vol = 240pi(81/64)
[B]Lead Vol = 303.75pi[/B]

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line s

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line segment remains?
This means the leftover segment has a length of:
[B]26 - x[/B]

A meter is defined as the distance light travels in 1/299,792,458 of a second. How many meters does

A meter is defined as the distance light travels in 1/299,792,458 of a second. How many meters does light travel in 1/8 of a second?
1/8 second / 1/299,792,458
299,792,458/8 = [B]37,474,057.25 meters[/B]

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going dow

A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current?
[U]Assumptions:[/U]
[LIST]
[*]B = the speed of the boat in still water.
[*]S = the speed of the stream
[/LIST]
Relative to the bank, the speeds are:
[LIST]
[*]Upstream is B - S.
[*]Downstream is B + S.
[/LIST]
[U]Use the Distance equation: Rate * Time = Distance[/U]
[LIST]
[*]Upstream: (B-S)6 = 258
[*]Downstream: (B+S)6 = 330
[/LIST]
Simplify first by dividing each equation by 6:
[LIST]
[*]B - S = 43
[*]B + S = 55
[/LIST]
Solve this system of equations by elimination. Add the two equations together:
(B + B) + (S - S) = 43 + 55
Cancelling the S's, we get:
2B = 98
Divide each side by 2:
[B]B = 49 mi/hr[/B]
Substitute this into either equation and solve for S.
B + S = 55
49 + S = 55
To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=49%2Bs%3D55&pl=Solve']type it in our search engine[/URL] and we get:
S = [B]6 mi/hr[/B]

A mug has 3 inch diameter and is 3.5 inches tall how much water can it hold

A mug has 3 inch diameter and is 3.5 inches tall how much water can it hold
A mug is a cylinder. If the diameter is 3, then the radius is 3/2 = 1.5.
Using our cylinder volume calculator, we get:
[B]V = 7.875pi or 24.74 cubic inches[/B]

a painter is painting a circular sculpture. The sculpture has a radius of 5 meters. How much paint s

a painter is painting a circular sculpture. The sculpture has a radius of 5 meters. How much paint should she use to paint the sculpture
Area of a circle (A) is:
A = ?r˛
Substituting r = 5 into this formula, we get:
A = ? * 5˛
A = [B]25?[/B]

A parallelogram has a perimeter of 48 millimeters. Two of the sides are each 20 millimeters long. Wh

A parallelogram has a perimeter of 48 millimeters. Two of the sides are each 20 millimeters long. What is the length of each of the other two sides?
2 sides * 20 mm each is 40 mm
subtract this from the perimeter of 48:
48 - 40 = 8
Since the remaining two sides equal each other, their length is:
8/2 = [B]4mm[/B]

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. Wh

A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. What is the length of each of the other two sides?
A parallelogram is a rectangle bent on it's side. So we have the perimeter formula P below:
P = 2l + 2w
We're given w = 17 and P = 54. So we plug this into the formula for perimeter:
2l + 2(17) = 54
2l + 34 = 54
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B34%3D54&pl=Solve']equation calculator[/URL], we get [B]l = 10[/B].

A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of

A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of each coin are there?
Let d = the number of dimes and q = the number of quarters. We have two equations:
(1) d + q = 146
(2) 0.1d + 0.25q = 27.05
Rearrange (1) into (3) solving for d
(3) d = 146 - q
Substitute (3) into (2)
0.1(146 - q) + 0.25q = 27.05
14.6 - 0.1q + 0.25q = 27.05
Combine q's
0.15q + 14.6 = 27.05
Subtract 14.6 from each side
0.15q = 12.45
Divide each side by 0.15
[B]q = 83[/B]
Plugging that into (3), we have:
d = 146 - 83
[B]d = 63[/B]

A penny has a diameter of 19 millimeters. What is the radius of the penny.

A penny has a diameter of 19 millimeters. What is the radius of the penny.
D = 2r
To solve for r, we divide each side by 2:
r = D/2
Plugging in D = 19, we get:
r = [B]19/2 or 9.5[/B]

A playing card is 7 centimeters wide and 10 centimeters tall. What is its area?

A playing card is 7 centimeters wide and 10 centimeters tall. What is its area?
A playing card has a rectangle shape, so the area is l x w.
A = l x w
A = 10 cm x 7 cm
A =[B] 70 cm^2[/B]

A pool is 5 meters wide and 21 meter long what is the area of the pool?

A pool is 5 meters wide and 21 meter long what is the area of the pool?
A pool is a rectangle. So the area for a rectangle is:
A = lw [I]where l is the length and w is the width.[/I]
[URL='https://www.mathcelebrity.com/rectangle.php?l=21&w=5&a=&p=&pl=Calculate+Rectangle']Plugging in our width of 5 and length of 21 to our rectangle calculator[/URL], we get:
A = [B]105 m^2[/B]

A rectangle has a length that is 8.5 times its width. IF the width is n, what is the perimeter of th

A rectangle has a length that is 8.5 times its width. IF the width is n, what is the perimeter of the rectangle.
w = n
l = 8.5n
P = 2(8.5n) + 2n
P = 17n + 2n
P = [B]19n[/B]

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSION

A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSIONS OF THE RECTANGLE?
Whoa... stop screaming with those capital letters! But I digress...
The perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]P = 196
[*]l = 6w
[/LIST]
Plug these into the perimeter formula:
2(6w) + 2w = 196
12w + 2w = 196
[URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B2w%3D196&pl=Solve']Plugging this equation into our search engine[/URL], we get:
[B]w = 14[/B]
Now we put w = 14 into equation (2) above:
l = 6(14)
[B]l = 84
[/B]
So our length (l), width (w) of the rectangle is (l, w) = [B](84, 14)
[/B]
Let's check our work by plugging this into the perimeter formula:
2(84) + 2(14) ? 196
168 + 28 ? 196
196 = 196 <-- checks out

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?

a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?
We know the rectangle has the following formulas:
Area = lw
Perimeter = 2l + 2w
Given an area of 238 and a perimeter of 62, we have:
[LIST=1]
[*]lw = 238
[*]2(l + w) = 62
[/LIST]
Divide each side of (1) by w:
l = 238/w
Substitute this into (2):
2(238/w + w) = 62
Divide each side by 2:
238/w + w = 31
Multiply each side by w:
238w/w + w^2 = 31w
Simplify:
238 + w^2 = 31w
Subtract 31w from each side:
w^2 - 31w + 238 = 0
We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get:
w = (14, 17)
We take the lower amount as our width and the higher amount as our length:
[B]w = 14
l = 17
[/B]
Check our work for Area:
14(17) = 238 <-- Check
Check our work for Perimeter:
2(17 + 14) ? 62
2(31) ? 62
62 = 62 <-- Check

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards b

A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards because of a building code, what will the length need to be?
Perimeter of a rectangle (P) with length (l) and width (w) is:
2l + 2w = P
We're given P = 506 and w = 100. We plug this in to the perimeter formula and get:
2l + 2(100) = 506
To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B2%28100%29%3D506&pl=Solve']type it in our search engine[/URL] and we get:
l = [B]153[/B]

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 fe

A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 feet longer than the width, then how wide is the field?
We're given:
[LIST=1]
[*]l = w + 40
[/LIST]
And we know the perimeter of a rectangle is:
P = 2l + 2w
Substitute (1) into this formula as well as the given perimeter of 1120:
2(w + 40) + 2w = 1120
Multiply through and simplify:
2w + 80 + 2w = 1120
Group like terms:
4w + 80 = 1120
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B80%3D1120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 260[/B]

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?

A rectangular field is twice as long as it is wide. If the perimeter is 360 what are the dimensions?
We are given or know the following about the rectangle
[LIST]
[*]l = 2w
[*]P = 2l + 2w
[*]Since P = 360, we have 2l + 2w = 360
[/LIST]
Since l = 2w, we have 2l + (l) = 360
3l = 360
Divide by 3, we get [B]l = 120[/B]
Which means w = 120/2
[B]w = 60[/B]

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find i

A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find its length and width.
The area of a rectangle (A) is:
A = lw --> where l is the length and w is the width
We're given l = 2w, so we substitute this into the Area equation:
A = (2w)w
A = 2w^2
We're given the area of the pitch is 360, so we set:
2w^2 = 360
We [URL='https://www.mathcelebrity.com/1unk.php?num=2w%5E2%3D360&pl=Solve']type this equation into our search engine[/URL], follow the links, and get:
w = [B]6*sqrt(5)
[/B]
Now we take this, and substitute it into this equation:
6*sqrt(5)l = 360
Dividing each side by 6*sqrt(5), we get:
l = [B]60/sqrt(5)[/B]

A rectangular house is 68 yards wide and 112 yards long. What is its perimeter?

A rectangular house is 68 yards wide and 112 yards long. What is its perimeter?
The perimeter of a rectangle is:
P = 2l + 2w
Plugging in our length of 112 and our width of 68, we get:
P = 2(112) + 2(68)
P = 224 + 136
P = [B]360[/B]

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards

A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards greater than the width. What is the width of the parking lot?
The perimeter of a rectangle is: 2l + 2w = P.
We're given 2 equations:
[LIST=1]
[*]2l + 2w = 152
[*]l = w + 12
[/LIST]
Substitute equation (2) into equation (1) for l:
2(w + 12) + 2w = 152
2w + 24 + 2w = 152
Combine like terms:
4w + 24 = 152
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B24%3D152&pl=Solve']type this equation into our search engine[/URL] and we get:
w =[B] 32[/B]

A rectangular piece of paper has the dimensions of 10 inches by 7 inches.What is the perimeter of th

A rectangular piece of paper has the dimensions of 10 inches by 7 inches.What is the perimeter of the piece of paper
Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=10&w=7&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get perimeter P:
P = [B]34[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters
Given l = length and w = width, The perimeter of a rectangle is 2l + 2w, we have:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 56
[/LIST]
Substitute equation (1) into equation (2) for l:
2(3w) + 2w = 56
6w + 2w = 56
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our math engine[/URL] and we get:
w = [B]7
[/B]
To solve for l, we substitute w = 7 into equation (1):
l = 3(7)
l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters.

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters.
We're given the following:
[LIST]
[*]l = 3w
[/LIST]
We know the Perimeter (P) of a rectangle is:
P = 2l + 2w
Substituting l = 3w and P = 56 into this equation, we get:
2(3w) + 2w = 56
Multiplying through, we get:
6w + 2w = 56
(6 +2)w = 56
8w = 56
[URL='https://www.mathcelebrity.com/1unk.php?num=8w%3D56&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 7[/B]
Substitute w = 7 into l = 3w, we get:
l = 3(7)
[B]l = 21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimensions of the room.
We're given two items:
[LIST]
[*]l = 3w
[*]P = 56
[/LIST]
We know the perimeter of a rectangle is:
2l + 2w = P
We plug in the given values l = 3w and P = 56 to get:
2(3w) + 2w = 56
6w + 2w = 56
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']plug this equation into our search engine[/URL] and we get:
w = [B]7
[/B]
To solve for l, we plug in w = 7 that we just found into the given equation l = 3w:
l = 3(7)
l = [B]21
[/B]
So our dimensions length (l) and width (w) are:
(l, w) = [B](21, 7)[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimension of the room.
We're given:
l = 3w
The Perimeter (P) of a rectangle is:
P = 2l + 2w
With P = 56, we have:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 56
[/LIST]
Substitute equation (1) into equation (2) for l:
2(3w) + 2w = 56
6w + 2w = 56
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]7
[/B]
Now we plug w = 7 into equation (1) above to solve for l:
l = 3(7)
l = [B]21[/B]

A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimens

A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimension of the room.
We're given:
[LIST]
[*]l = 3w
[*]P = 64
[/LIST]
We also know the perimeter of a rectangle is:
2l + 2w = P
We plugin l = 3w and P = 64 into the perimeter equation:
2(3w) + 2w = 64
Multiply through to remove the parentheses:
6w + 2w = 64
To solve this equation for w, we type it in our search engine and we get:
[B]w = 8[/B]
To solve for l, we plug w = 8 into the l = 3w equation above:
l = 3(8)
[B]l = 24[/B]

A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimens

A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimension of the room
The perimeter of a rectangle is P = 2l + 2w. We're given two equations:
[LIST=1]
[*]l = 4w
[*]2l + 2w = 80. <-- Since perimeter is 80
[/LIST]
Plug equation (1) into equation (2) for l:
2(4w) + 2w = 80
8w + 2w = 80
[URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B2w%3D80&pl=Solve']Plugging this equation into our search engine[/URL], we get:
w = [B]10[/B]
To get l, we plug w = 10 into equation (1):
l = 4(10)
l = [B]40[/B]

A rocket travels at a rate of 160 meters in 3 seconds. What is the speed of the rocket in meters per

A rocket travels at a rate of 160 meters in 3 seconds. What is the speed of the rocket in meters per second?
160 meters /3 seconds = [B]53.333333333 meters per second[/B]

A spherical water tank holds 11,500ft^3 of water. What is the diameter?

A spherical water tank holds 11,500ft^3 of water. What is the diameter?
The tank holding amount is volume. And the volume of a sphere is:
V = (4pir^3)/3
We know that radius is 1/2 of diameter:
r =d/2
So we rewrite our volume function:
V = 4/3(pi(d/2)^3)
We're given V = 11,500 so we have:
4/3(pi(d/2)^3) = 11500
Multiply each side by 3/4
4/3(3/4)(pi(d/2)^3) = 11,500*3/4
Simplify:
pi(d/2)^3 = 8625
Since pi = 3.1415926359, we divide each side by pi:
(d/2)^3 = 8625/3.1415926359
(d/2)^3 = 2745.42
Take the cube root of each side:
d/2 = 14.0224
Multiply through by 2:
[B]d = 28.005[/B]

A sprinter runs 400 meters in 54 seconds. What is the runners average running rate in meters per sec

A sprinter runs 400 meters in 54 seconds. What is the runners average running rate in meters per second?
400 meters/54 seconds = [B]7.407 meters per second[/B].

A square has a perimeter of 24 inches. What is the area of the square?

A square has a perimeter of 24 inches. What is the area of the square?
Perimeter of a square = 4s where s = the length of a side. Therefore, we have:
4s = P
4s = 24
Using our equation solver, [URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D24&pl=Solve']we type in 4s = 24[/URL] and get:
s = 6
The problems asks for area of a square. It's given by
A = s^2
Plugging in s = 6, we get:
A = 6^2
A = 6 * 6
A = [B]36
[/B]
Now if you want a shortcut in the future, type in the shape and measurement you know. Such as:
[I][URL='https://www.mathcelebrity.com/square.php?num=24&pl=Perimeter&type=perimeter&show_All=1']square perimeter = 24[/URL][/I]
From the link, you'll learn every other measurement about the square.

A student walks 1500 meters to school in 30 minutes. What is their average speed in meters per minut

A student walks 1500 meters to school in 30 minutes. What is their average speed in meters per minute?
1500 meters / 30 minutes
Divide top and bottom by 30
[B]50 meters / minute[/B]

A submarine at an elevation of -185 meters descends to 3 times that elevation. Then, it elevates 90

A submarine at an elevation of -185 meters descends to 3 times that elevation. Then, it elevates 90 meters. What is the submarines new elevation?
3 times the current elevation is:
3 * -185 = -555
Elevating 90 meters means we have a positive change:
-555 + 90 = [B]-465[/B]

A submarine dove 132.58 meters to reach a resting depth of 700 meter below sea level. What was it's

A submarine dove 132.58 meters to reach a resting depth of 700 meter below sea level. What was it's original depth
Below sea level is a negative amount. So they end up at -700.
To go back up toward sea level, we'd be at:
-700 + 132.58 = -567.42
Negative numbers mean below sea level, so the original depth was [B]567.42 meters below sea level[/B]

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 met

A submarine hovers at 240 meters below sea level. If it descends 160 meters and then ascends 390 meters, what is its new position?
240 meters below sea level means a negative number, so we start with:
-240
Descending 160 meters means our depth decreases, so we subtract:
-240 - 160 = -400
Ascends means our depth increases, so we add:
-400 + 390 = [B]-10 or 10 feet below sea level[/B]

A submarine sits at –300 meters in relation to sea level. Then it descends 115 meters. What is its n

A submarine sits at –300 meters in relation to sea level. Then it descends 115 meters. What is its new position in relation to sea level?
Descending means we go down in sea level, so we subtract:
-300 - 115 = [B]-415 or 415 meters below sea level[/B]

A thermometer has a range of 1.5 degrees of the temperature, what is the maximum and minimum at 87.4

A thermometer has a range of 1.5 degrees of the temperature, what is the maximum and minimum at 87.4 degrees
Range = Max - Min
Divide this by 2 to get the lesser half and larger half:
Half-Range = 1.5/2
Half-Range = 0.75
[U]Our Maximum temperature is:[/U]
Max Temp = Current Temp + Half-Range
Max Temp = 87.4 + 0.75
Max Temp = [B]88.15
[/B]
[U]Our Minimum temperature is:[/U]
Min Temp = Current Temp - Half-Range
Min Temp = 87.4 - 0.75
Min Temp = [B][B]86.65[/B][/B]

A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For

A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For how many minutes does it walk?
Distance formula (d) for a rate (r) and time (t) is:
d = rt
We're given d = 12.5 and r = 5
12.5 = 5t
5t = 12.5
Solve for t. Divide each side of the equation by 5:
5t/5 = 12.5/5
Cancel the 5's on left side and we get:
t = [B]2.5[/B]

A train ticket is 8 centimeters tall and 10 centimeters long. What is its area?

A train ticket is 8 centimeters tall and 10 centimeters long. What is its area?
The ticket is a rectangle. The area is:
A = lw
Plugging in our numbers, we get:
A = (8)(10)
A = 80

A trapezoid has one base that is 120% of the length of the other base. The two sides are each 1/2 th

A trapezoid has one base that is 120% of the length of the other base. The two sides are each 1/2 the length of the smaller base. If the perimeter of the trapezoid is 54.4 inches, what is the length of the smaller base of the trapezoid?
Setup measurements:
[LIST]
[*]Small base = n
[*]Large base = 1.2n
[*]sides = n/2
[*]Perimeter = n + 1.2n + 0.5n + 0.5n = 54.4
[/LIST]
Solve for [I]n[/I] in the equation n + 1.2n + 0.5n + 0.5n = 54.4
[SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE]
(1 + 1.2 + 0.5 + 0.5)n = 3.2n
[SIZE=5][B]Step 2: Form modified equation[/B][/SIZE]
3.2n = + 54.4
[SIZE=5][B]Step 3: Divide each side of the equation by 3.2[/B][/SIZE]
3.2n/3.2 = 54.4/3.2
n = [B]17[/B]
[URL='https://www.mathcelebrity.com/1unk.php?num=n%2B1.2n%2B0.5n%2B0.5n%3D54.4&pl=Solve']Source[/URL]

A tree is 23.1 feet tall. What is its height in meters ? Use the following conversion: 1 meter is 3.

A tree is 23.1 feet tall. What is its height in meters ? Use the following conversion: 1 meter is 3.3 feet
23.1 feet * 1 meter / 3.3 feet = [B]7 meters[/B]

a triangle has side lengths of 12,16, and 20 centimeters. is it a right triangle?

a triangle has side lengths of 12,16, and 20 centimeters. is it a right triangle?
First, we see if we can simplify. So we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=12&num2=16&num3=20&pl=GCF']type GCF(12,16,20) [/URL]and we get 4.
We divide the 3 side lengths by 4:
12/4 = 3
16/4 = 4
20/4 = 5
And lo and behold, we get a Pythagorean Triple of 3, 4, 5. So [B]yes, this is a right triangle[/B].

A triangular garden has base of 6 meters amd height of 8 meters. Find its area

A triangular garden has base of 6 meters amd height of 8 meters. Find its area
Area (A) of a triangle is:
A = bh/2
Plugging in our numbers, we get:
A = 6*8/2
A = [B]24 square meters[/B]

A yard is 33.21 meters long and 17.6 meters wide. What length of fence must be purchased to enclose

A yard is 33.21 meters long and 17.6 meters wide. What length of fence must be purchased to enclose the entire yard?
The yard is a rectangle. The perimeter of a rectangle is:
P = 2l + 2w where l is the length and w is the width.
Evaluating, using our [URL='https://www.mathcelebrity.com/rectangle.php?l=33.21&w=17.6&a=&p=&pl=Calculate+Rectangle']rectangle calculator[/URL], we get P = [B]101.62[/B]

A young snake measures 0.23 meters long. During the course of his lifetime,he will grow to be 13 tim

A young snake measures 0.23 meters long. During the course of his lifetime,he will grow to be 13 times his current length what will be his length be when he is full grown
Full Grown Length = Current Length * Growth Multiplier
Full Grown Length = 0.23 * 13
Full Grown Length = [B]2.99 meters[/B]

A ________ ________ is the value of a statistic that estimates the value of a parameter.

A ________ ________ is the value of a statistic that estimates the value of a parameter.
[B]Point Estimate[/B].
A point [B]estimate[/B] is a single [B]value[/B] (statistic) used to [B]estimate[/B] a population [B]value[/B]([B]parameter[/B])

Allan built an additional room onto his house. The length of the room is 3 times the width. The peri

Allan built an additional room onto his house. The length of the room is 3 times the width. The perimeter of the room is 60 feet. What is the length of the room
A room is a rectangle. We know the perimeter of a rectangle is:
P = 2l + 2w
We're given two equations:
[LIST=1]
[*]l = 3w
[*]P = 60
[/LIST]
Plug (1) and (2) into our rectangle perimeter formula:
2(3w) + w = 60
6w + w = 60
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2Bw%3D60&pl=Solve']Type this equation into our search engine[/URL] to solve for w:
w = 8.5714
Now plug w = 8.5714 into equation 1 to solve for l:
l = 3(8.5714)
l = [B]25.7142[/B]

An equilateral triangle has three sides of equal length. What is the equation for the perimeter of a

An equilateral triangle has three sides of equal length. What is the equation for the perimeter of an equilateral triangle if P = perimeter and S = length of a side?
P = s + s + s
[B]P = 3s[/B]

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three tim

An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three times as long as the shortest side. The remaining two sides are each 8m longer than the shortest side. The perimeter of the Pentagon is 79m. Find the length of each side of the Pentagon.
Let long sides be l. Let short sides be s. Let medium sides be m. We have 3 equations:
[LIST=1]
[*]2l + 2m + s = 79
[*]m = s + 8
[*]l = 3s
[/LIST]
Substitute (2) and (3) into (1):
2(3s) + 2(s + 8) + s = 79
Multiply through and simplify:
6s + 2s + 16 + s = 79
9s + 16 = 79
[URL='https://www.mathcelebrity.com/1unk.php?num=9s%2B16%3D79&pl=Solve']Using our equation calculator[/URL], we get [B]s = 7[/B].
This means from Equation (2):
m = 7 + 8
[B]m = 15
[/B]
And from equation (3):
l = 3(7)
[B]l = 21[/B]

Area Conversions

This calculator converts between the following area measurements:

acre

hectare

square inch

square foot

square yard

square mile

square millimeter

square meter

square kilometer

acre

hectare

square inch

square foot

square yard

square mile

square millimeter

square meter

square kilometer

Barbara bought a piece of rope that was 7 1/3 meters long. She cut the rope into 3 equal pieces. How

Barbara bought a piece of rope that was 7 1/3 meters long. She cut the rope into 3 equal pieces. How long is each piece of rope?
Using our mixed number converter, we see that:
[URL='https://www.mathcelebrity.com/fraction.php?frac1=7%261%2F3&frac2=3%2F8&pl=Simplify']7&1/3[/URL] = 22/3
Split into [URL='https://www.mathcelebrity.com/fraction.php?frac1=22%2F9&frac2=3&pl=Simplify']3 equal pieces[/URL], we have:
22/3 / 3 = 22/9 or 2&4/9

Basal Metabolic Rate (BMR)

Given a gender, an age, and a height/weight in inches/pounds or meters/kilograms, this will calculate the Basal Metabolic Rate (BMR)

Bike rental shop A charges $20 per kilometre travelled with no additional fee. Bike rental shop B ch

Bike rental shop A charges $20 per kilometre travelled with no additional fee. Bike rental shop B charges only $8 per kilometre travelled, but has a starting charge of $35. If Bob plans to travel 7km by bike, which rental shop should he choose for a better price
[U]Shop A Cost function C(k) where k is the number of kilometers used[/U]
C(k) = Cost per kilometer * k + Starting Charge
C(k) = 20k
With k = 7, we have:
C(7) = 20 * 7
C(7) = 140
[U]Shop B Cost function C(k) where k is the number of kilometers used[/U]
C(k) = Cost per kilometer * k + Starting Charge
C(k) = 8k + 35
With k = 7, we have:
C(7) = 8 * 7 + 35
C(7) = 56 + 35
C(7) = 91
Bog should choose [B]Shop B[/B] since they have the better price for 7km

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 fe

Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W.
Plugging our numbers in for P = 22 and L = 5, we get:
22 = 2(5) + 2W
22 = 10 + 2w
Rewritten, we have:
10 + 2w = 22
[URL='https://www.mathcelebrity.com/1unk.php?num=10%2B2w%3D22&pl=Solve']Plug this equation into the search engine[/URL], we get:
[B]w = 6[/B]

Body Mass Index (BMI)

Solves for the popular health measurement of Body Mass Index or Weight using inches and pounds input or meters and kilos input.

Also calculates the estimated surface area of the body using the Mosteller Formula

Also calculates the estimated surface area of the body using the Mosteller Formula

Brenda has already knit 4 centimeters of scarf, and can knit 1 centimeter each night. After 43 night

Brenda has already knit 4 centimeters of scarf, and can knit 1 centimeter each night. After 43 nights of knitting, how many centimeters of scarf will Brenda have knit in total?
1 centimeter per night * 43 nights = 43 centimeters knitted.
Add that to the 4 centimeters she started with, and we have:
43 + 4 = [B]47 centimeters[/B]

can someone help me with how to work out this word problem?

Consider a paper cone, pointing down, with the height 6 cm and the radius 3 cm; there is currently 9/4 (pie) cubic cm of water in the cone, and the cone is leaking at a rate of 2 cubic centimeters of water per second. How fast is the water level changing, in cm per second?

Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long

Charrie found a piece of 8 meters rope. She cuts it into equal length. She made three cuts. How long is each piece of the rope?
Equal length means we divide the length of the rope by the number of equal cuts
[B]8/3 or 2 & 2/3 meters[/B]

Circle Equation

This calculates the standard equation of a circle and general equation of a circle from the following given items:

* A center (h,k) and a radius r

* A diameter A(a_{1},a_{2}) and B(b_{1},b_{2})

This also allows you to enter a standard or general form equation so that the center (h,k) and radius r can be determined.

* A center (h,k) and a radius r

* A diameter A(a

This also allows you to enter a standard or general form equation so that the center (h,k) and radius r can be determined.

Circles

Calculates and solves for Radius, Diameter, Circumference, and Area of a Circle.

Compare a decimeter to a meter using percents. (A decimeter is what percent of a meter?)

Compare a decimeter to a meter using percents. (A decimeter is what percent of a meter?)
1 decimeter = 0.1 meters, so [B]10%[/B]

Cylinders

Calculates and solves for Radius, Diameter, Volume (Capacity), Lateral Area, and Surface Area of a Cylinder.

Danna walked along a road. Starting from her house she walked 14 meters due south then walked 8 mete

Danna walked along a road. Starting from her house she walked 14 meters due south then walked 8 meters due north and finally walked 20 meters due south. how far away was Danna from her hours
14 - 8 + 20 = [B]26 miles due south[/B]

Decagon

Solves for the side, perimeter, and area of a decagon.

Determine ux and sigma(x) from the given parameters of the population and sample size u = 76, sigma

Determine ux and sigma(x) from the given parameters of the population and sample size
u = 76, sigma = 28, n = 49
ux = ?
sigma(x) = ?
[B]u = ux = 76[/B]
sigma(x) = sigma/sqrt(n) so we have
28/sqrt(49) = 28/7 = [B]4[/B]

Equilateral Triangle

Given a side (a), this calculates the following items of the equilateral triangle:

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h_{a},h_{b},h_{c})

* medians (m_{a},m_{b},m_{c})

* angle bisectors (t_{a},t_{b},t_{c})

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h

* medians (m

* angle bisectors (t

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in

Fantasia decided to paint her circular room which had a diameter of 25 feet. She started painting in the center and when she had painted a circle with a 5-foot diameter, she used one quart of paint. How many more quarts of paint must Fantasia buy to finish her room?
The area formula for a circle is:
Area = pir^2
Area of full room
Radius = D/2
Radius = 25/2
Radius = 12.5
Area = 3.1415 * 12.5 * 12.5
Area = 490.625
Area of 5-foot diameter circle
Radius = D/2
Radius = 5/2
Radius = 2.5
Area = 3.1415 * 2.5 * 2.5
Area = 19.625
So 1 quart of paint covers 19.625 square feet
Area of unpainted room = Area of Room - Area of 5-foot diameter circle
Area of unpainted room = 490.625 - 19.625
Area of unpainted room = 471
Calculate quarts of paint needed:
Quarts of paint needed = Area of unpainted Room / square feet per quart of paint
Quarts of paint needed = 471/19.625
Quarts of paint needed = [B]24 quarts[/B]

For the normal distribution with parameters ? = 4, ? = 3 ; calculate P(x > 1)

For the normal distribution with parameters ? = 4, ? = 3 ; calculate P(x > 1)
[URL='https://www.mathcelebrity.com/probnormdist.php?xone=1&mean=4&stdev=3&n=1&pl=P%28X+%3E+Z%29']Using our calculator[/URL], we get P(x > 1) = [B]0.841345[/B]

Frequency and Wavelength and Photon Energy

Provides the following 3 items using the speed of light and Plancks constant (h):

- Given a frequency of centimeters, feet, meters, or miles the calculator will determine wavelength in Hz, KHz, MHz, GHz

- Given a wavelength of Hz, KHz, MHz, GHz, the calculator will determine frequency in centimeters, feet, meters, or miles

- Calculates photon energy

- Given a frequency of centimeters, feet, meters, or miles the calculator will determine wavelength in Hz, KHz, MHz, GHz

- Given a wavelength of Hz, KHz, MHz, GHz, the calculator will determine frequency in centimeters, feet, meters, or miles

- Calculates photon energy

From 199 meters above sea level, Linda took off in her helicopter and descended 296 meters. What is

From 199 meters above sea level, Linda took off in her helicopter and descended 296 meters. What is Lindas elevation now?
[I]Descended[/I] means we subtract 296 meters from 199 meters.
Elevation Now = 199 - 296
Elevation Now = -97
Negative elevation means [I]below sea level[/I]. So our answer is:
[B]97 meters [I]below sea level[/I][/B]

Goal is to take at least 10,000 steps per day. According to your pedometer you have walked 5,274 ste

Goal is to take at least 10,000 steps per day. According to your pedometer you have walked 5,274 steps. Write and solve an inequality to find the possible numbers of steps you can take to reach your goal.
[U]
Subtract off the existing steps (s) from your goal of 10,000[/U]
g >= 10000 - 5274
[B]g >= 4726[/B]
[I]Note: we use >= since 10,000 steps meets the goal as well as anytihng above it[/I]

Gravitational Force

Using Sir Isaac Newtons Law of Gravitational Force, this calculator determines the force between two objects with mass in kilograms at a distance apart in meters using the constant of gravity.

Greg runs 120 m in 20 seconds. How far can he run in one minute?

Greg runs 120 m in 20 seconds. How far can he run in one minute?
We want to compare seconds to seconds.
[URL='https://www.mathcelebrity.com/timecon.php?quant=1&pl=Calculate&type=minute']1 minute[/URL] = 60 seconds
Set up a proportion of meters to seconds where m is the meters ran in 60 seconds:
120/20 = m/60
To solve this proportion for m, we [URL='https://www.mathcelebrity.com/prop.php?num1=120&num2=m&den1=20&den2=60&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
m. = [B]360 meters[/B]

He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the deli

He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the delivery address. Write an equation that can be used to calculate the delivery price and the distance between the kitchen and the delivery address. Use your equation to calculate the total cost to deliver to someone 2.4km away
Let k be the number of kilometers between the kitchen and delivery address. Our Delivery equation D(k) is:
[B]D(k) = 2k + 1.50[/B]
The problem wants to know D(2.4):
D(2.4) = 2(2.4) + 1.50
D(2.4) = 4.8 + 1.50
D(2.4) = [B]$6.30[/B]

Help on problem

[B]I need 36 m of fencing for my rectangular garden. I plan to build a 2m tall fence around the garden. The width of the garden is 6 m shorter than twice the length of the garden. How many square meters of space do I have in this garden?
List the answer being sought (words) ______Need_________________________
What is this answer related to the rectangle?_Have_________________________
List one piece of extraneous information____Need_________________________
List two formulas that will be needed_______Have_________________________
Write the equation for width_____________Have_________________________
Write the equation needed to solve this problem____Need____________________[/B]

Heptagon

Solves for side length, perimeter, and area of a heptagon.

Hexagon

This calculator solves for side length (s), Area (A), and Perimeter (P) of a hexagon given one of the 3 entries.

Hong is riding his bicycle. He rides for 22.5 kilometers at a speed of 9 kilometers per hour. For ho

Hong is riding his bicycle. He rides for 22.5 kilometers at a speed of 9 kilometers per hour. For how many hours does he ride?
Distance = Rate * Time
The problem asks for time.
[URL='https://www.mathcelebrity.com/drt.php?d=+22.5&r=+9&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator[/URL], we get:
t = [B]2.5 hours[/B]

How many microns are in a meter?

How many microns are in a meter?
1 meter = [B]1,000,00 microns[/B]

How many millimeters are in a meter?

How many millimeters are in a meter?
1 meter = [B]1,000 millimeters[/B]

How much sand is needed to fill a pit that measures 8 meters deep, 10 meters wide, and 15 meters lon

How much sand is needed to fill a pit that measures 8 meters deep, 10 meters wide, and 15 meters long? Explain your answer.
The pit is a rectangular solid. The volume is:
V = l * w * h
V = 15 * 10 * 8
V = [B]1,200 cubic meters[/B]

If 2 inches is about 5 centimeters, how many inches are in 25 centimeters? Choose the proportions th

If 2 inches is about 5 centimeters, how many inches are in 25 centimeters? Choose the proportions that accurately represent this scenario.
We set up a proportion of inches to centimeters where i is the number of inches in 25 centimeters:
2/5 = i/25
To solve this proportion for i, we [URL='https://www.mathcelebrity.com/prop.php?num1=2&num2=i&den1=5&den2=25&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
i = [B]10[/B]

If 800 feet of fencing is available, find the maximum area that can be enclosed.

If 800 feet of fencing is available, find the maximum area that can be enclosed.
Perimeter of a rectangle is:
2l + 2w = P
However, we're given one side (length) is bordered by the river and the fence length is 800, so we have:
So we have l + 2w = 800
Rearranging in terms of l, we have:
l = 800 - 2w
The Area of a rectangle is:
A = lw
Plug in the value for l in the perimeter into this:
A = (800 - 2w)w
A = 800w - 2w^2
Take the [URL='https://www.mathcelebrity.com/dfii.php?term1=800w+-+2w%5E2&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']first derivative[/URL]:
A' = 800 - 4w
Now set this equal to 0 for maximum points:
4w = 800
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%3D800&pl=Solve']Typing this equation into the search engine[/URL], we get:
w = 200
Now plug this into our perimeter equation:
l = 800 - 2(200)
l = 800 - 400
l = 400
The maximum area to be enclosed is;
A = lw
A = 400(200)
A = [B]80,000 square feet[/B]

If a rock rolled n meters, how many decimeters did it roll?

If a rock rolled n meters, how many decimeters did it roll?
Setup conversion
1 meter = 10 decimeters
Therefore, n meters is [B]10n[/B] decimeters

If a snail crawled n millimeters, how many kilometers did it travel?

If a snail crawled n millimeters, how many kilometers did it travel?
1 millimeter = 1/1000 of a meter
1 meter = 1/1000 of a kilometer
1/1000 * 1/1000 = 0.000001
So our kilometers value is
[B]0.000001n[/B]

If a soccer ball was kicked at a distance of n decimeters, how many meters did it travel?

If a soccer ball was kicked at a distance of n decimeters, how many meters did it travel?
Meters = Decimeters/10
Meters = [B]n/10[/B]

If a speedometer indicates that a car is traveling at 65 kilometers per hour, how fast is the car tr

If a speedometer indicates that a car is traveling at 65 kilometers per hour, how fast is the car traveling in miles per hour? (Round to the nearest tenth.)
Set up a proportion of miles per kilometers:
0.621/1 = n/65
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=0.621&num2=n&den1=1&den2=65&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = [B]40.365[/B]

If Colton ran n kilometers, how many millimeters did he run?

If Colton ran n kilometers, how many millimeters did he run?
1 kilometer = 1,000,000 millimeters
n kilometers = [B]1,000,000n [/B]millimeters

if my diameter is 19 inches, what is my radius?

if my diameter is 19 inches, what is my radius?
Radius = Diameter/2
Radius = [B]19/2[/B]

If the diameter of a circle is n, what is the circumference?

If the diameter of a circle is n, what is the circumference?
Diameter of a circle = pi(d)
Given d = n, we have:
Diameter = pi(n)

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide

If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide must the field be?
The perimeter of a rectangle P, is denoted as:
P = 2l + 2w
We're given l = 25, and P = 120, so we have
2(25) + 2w = 120
Simplify:
2w + 50 = 120
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B50%3D120&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 35[/B]

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, th

If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, then what are the length and width?
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given P = 44, so we substitute this into the rectangle perimeter equation:
2l + 2w = 44
We're also given w = 0.5l - 2. Substitute the into the Perimeter equation:
2l + 2(0.5l - 2) = 44
Multiply through and simplify:
2l + l - 4 = 44
Combine like terms:
3l - 4 = 44
[URL='https://www.mathcelebrity.com/1unk.php?num=3l-4%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get:
[B]l = 16[/B]
Substitute this back into the equation w = 0.5l - 2
w = 0.5(16) - 2
w = 8 - 2
[B]w = 6[/B]

In 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose S

In 1996 Ato Boldon of UCLA ran the 100-meter dash in 9.92 seconds. In 1969 John Carlos of San Jose State ran the 100-yard dash in 9.1 seconds. Which runner had the faster average speed?
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=100&type=yard&pl=Calculate']convert yards to meters using our conversion calculator[/URL] and we get:
100 yards = 91.44 meters
Now we set up a proportion of time per meter:
[LIST]
[*]Ato Boldon: 9.92/100 = 0.992 per meter
[*]John Carlos: 9.1/91.44 = 0.995 per meter
[/LIST]
[B]Since Ato Boldon's time was [I]less per meter[/I], he had the faster average speed[/B]

Isosceles Triangle

Given a long side (a) and a short side (b), this determines the following items of the isosceles triangle:

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?

Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?
Distance = Rate * Time
We're given D = 395 and t = 5
We want Rate. We divide each side of the equation by time:
Distance / Time = Rate * Time / Time
Cancel the Time's on each side and we get:
Rate = Distance / Time
Plugging our numbers in, we get:
Rate = 395/5
Rate = [B]79 kilometers[/B]

Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined

Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined distance thrown by the 3 friends is 124 metres, how far did Angus throw the javelin?
Assumptions and givens:
[LIST]
[*]Let a be the distance Angus threw the javelin
[*]Let c be the distance Cameron threw the javelin
[*]Let j be the distance Jenny threw the javelin
[/LIST]
We're given 3 equations:
[LIST=1]
[*]j = a + 4
[*]j = c - 5
[*]a + c + j = 124
[/LIST]
Since j is the common variable in all 3 equations, let's rearrange equation (1) and equation (2) in terms of j as the dependent variable:
[LIST=1]
[*]a = j - 4
[*]c = j + 5
[*]a + c + j = 124
[/LIST]
Now substitute equation (1) and equation (2) into equation (3) for a and c:
j - 4 + j + 5 + j = 124
To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=j-4%2Bj%2B5%2Bj%3D124&pl=Solve']type it in our math engine[/URL] and we get:
j = 41
The question asks how far Angus (a) threw the javelin. Since we have Jenny's distance j = 41 and equation (1) has j and a together, let's substitute j = 41 into equation (1):
a = 41 - 4
a = [B]37 meters[/B]

Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he ru

Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he run in 500 seconds? Round to one decimal place.
Set up the distance equation:
Distance = Rate * Time
300 = 90r
Solving this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=300%3D90r&pl=Solve']type it in our search engine[/URL] and we get:
r = 3.333
For 500 seconds, we set up our distance equation again:
Distance = 500 * 3.333333
Distance = [B]1666.7 meters[/B]

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft

Kamara has a square fence kennel area for her dogs in the backyard. The area of the kennel is 64 ft squared. What are the dimensions of the kennel? How many feet of fencing did she use? Explain.
Area of a square with side length (s) is:
A = s^2
Given A = 64, we have:
s^2 = 64
[URL='https://www.mathcelebrity.com/radex.php?num=sqrt(64%2F1)&pl=Simplify+Radical+Expression']Typing this equation into our math engine[/URL], we get:
s = 8
Which means the dimensions of the kennel are [B]8 x 8[/B].
How much fencing she used means perimeter. The perimeter P of a square with side length s is:
P = 4s
[URL='https://www.mathcelebrity.com/square.php?num=8&pl=Side&type=side&show_All=1']Given s = 8, we have[/URL]:
P = 4 * 8
P = [B]32[/B]

Keith is cutting two circular table tops out of a piece of plywood. the plywood is 4 feet by 8 feet

Keith is cutting two circular table tops out of a piece of plywood. the plywood is 4 feet by 8 feet and each table top has a diameter of 4 feet. If the price of a piece of plywood is $40, what is the value of the plywood that is wasted after the table tops are cut?
Area of the plywood = 4 * 8 = 32 square feet
[U]Calculate area of 1 round top[/U]
Diameter = 2
Radius = Diameter/2 = 4/2 = 2
Area of each round top = pir^2
Area of each round top = 3.14 * 2 * 2
Area of each round top = 12.56 square feet
[U]Calculate area of 2 round tops[/U]
Area of 2 round tops = 12.56 + 12.56
Area of 2 round tops = 25.12 sq feet
[U]Calculate wasted area:[/U]
Wasted area = area of the plywood - area of 2 round tops
Wasted area = 32 - 25.12
Wasted area = 6.88 sq feet
[U]Calculate cost per square foot of plywood:[/U]
Cost per sq foot of plywood = Price per plywood / area of the plywood
Cost per sq foot of plywood = 40/32
Cost per sq foot of plywood = $1.25
[U]Calculate the value of the plywood:[/U]
Value of the plywood = Wasted Area sq foot * Cost per sq foot of plywood
Value of the plywood = 6.88 * 1.25
Value of the plywood = [B]$8.60[/B]

Kites

This calculates perimeter and/or area of a kite given certain inputs such as short and long side, short and long diagonal, or angle between short and long side

Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10

Kris wants to fence in her square garden that is 40 feet on each side. If she places posts every 10 feet, how many posts will she need?
Perimeter (P) of a square with side s:
P = 4s
Given s = 40, we have:
P = 4(40)
P = 160 feet
160 feet / 10 foot spaces = [B]16 posts[/B]

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden

Laura found a roll of fencing in her garage. She couldn't decide whether to fence in a square garden or a round garden with the fencing.
Laura did some calculations and found that a circular garden would give her 1380 more square feet than a square garden. How many feet of fencing were in the roll that Laura found? (Round to the nearest foot.)
Feet of fencing = n
Perimeter of square garden = n
Each side of square = n/4
Square garden's area = (n/4)^2 = n^2/16
Area of circle garden with circumference = n is:
Circumference = pi * d
n = pi * d
Divide body tissues by pi:
d = n/pi
Radius = n/2pi
Area = pi * n/2pi * n/2pi
Area = pin^2/4pi^2
Reduce by canceling pi:
n^2/4pi
n^2/4 * 3.14
n^2/12.56
The problem says that the difference between the square's area and the circle's area is equal to 1380 square feet.
Area of Circle - Area of Square = 1380
n^2/12.56 - n^2/16 = 1380
Common denominator = 200.96
(16n^2 - 12.56n^2)/200.96 = 1380
3.44n^2/200.96 = 1380
Cross multiply:
3.44n^2 = 277,324.8
n^2 = 80,617.7
n = 283.9
Nearest foot = [B]284[/B]

Linear Conversions

Converts to and from the following linear measurements for a given quantity:

Inches

Feet

Yards

Miles

Micrometer

Millimeters

Centimeters

Meters

Kilometers

Furlongs

Inches

Feet

Yards

Miles

Micrometer

Millimeters

Centimeters

Meters

Kilometers

Furlongs

Liquid Conversions

Takes a liquid measurement as seen in things like recipes and performs the following conversions: ounces, pints, quarts, gallons, teaspoon (tsp), tablespoon (tbsp), microliters, milliliters, deciliters, kiloliters,liters, bushels, and cubic meters.

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is

Marco orders a large pizza, with a diameter of 14 inches. It is cut into 8 congruent pieces. what is the area of one piece?
A pizza is a circle. If the diameter of the pizza is 14 inches, the radius is 14/2 = 7 inches.
Area of a circle is pi(r^2). With r = 7, we have:
A =7^2(pi)
A = 49pi
Area of a slice of pizza is the area of the full pizza divided by 8
A(Slice) = [B]49pi/8[/B]

Mr. Jimenez has a pool behind his house that needs to be fenced in. The backyard is an odd quadrilat

Mr. Jimenez has a pool behind his house that needs to be fenced in. The backyard is an odd quadrilateral shape and the pool encompasses the entire backyard. The four sides are 1818a, 77b, 1111a, and 1919b in length. How much fencing? (the length of the perimeter) would he need to enclose the pool?
The perimeter P is found by adding all 4 sides:
P = 1818a + 77b + 1111a + 1919b
Group the a and b terms
P = (1818 + 1111)a + (77 + 1919b)
[B]P = 2929a + 1996b[/B]

Nonagon

Calculates the side, perimeter, and area of a nonagon

Octagon

Calculate side, area, and perimeter of an octagon based on inputs

On a map, every 5 cm represents 250 kilometres. What distance would be represented by a 3 cm line?

On a map, every 5 cm represents 250 kilometres. What distance would be represented by a 3 cm line?
We set up a proportion of map cm distance to kilometers where k is the kilometers represented by a 3cm line
5/250 = 3/k
To solve this proportion for k, we [URL='https://www.mathcelebrity.com/prop.php?num1=5&num2=3&den1=250&den2=k&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
k = [B]150[/B]

On a trip, a family drove 270 kilometers in 3 hours. how many kilometers were traveled in one hour.

On a trip, a family drove 270 kilometers in 3 hours. how many kilometers were traveled in one hour. Express this as a rate per hour.
270 kilometers per 3 hours
270/3
Divide top and bottom by 3 to get km/hr
[B]90 kilometers per hour[/B]

Pentagons

Given a side length and an apothem, this calculates the perimeter and area of the pentagon.

Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?

Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?
The perimeter P of a rectangle with length l and width w is:
2l + 2w = P
We're given P = 372 and l = 99, so we have:
2(99) + 2w = 372
2w + 198 = 372
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 198 and 372. To do that, we subtract 198 from both sides
2w + 198 - 198 = 372 - 198
[SIZE=5][B]Step 2: Cancel 198 on the left side:[/B][/SIZE]
2w = 174
[SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE]
2w/2 = 174/2
w = [B]87[/B]

please answer my second word problem

A tortoise is walking in the desert. It walks at a speed of
4
meters per minute for
6.4
meters. For how many minutes does it walk?

please answer my second word problem

Distance = Rate x Time
6.4 meters = 4 meters/minute * t
Divide each side by 4
[B]t = 1.6 minutes[/B]

Please help me!! I don't understand!

I don't understand this word problem: If each of these shapes in Figure 1 were separated and filled with water, could the sphere that contains the cube hold all of the water? [I]Assume in the second image the corners of the cube touch the sphere so the diagonal from one corner of the cube to the opposite diagonal corner is the diameter of the sphere. [IMG]https://classroom.ucscout.org/courses/1170/files/191225/preview?verifier=mT7v59BhdVHalyprWq0KmBEItbf4CPWFqOgwoEa8[/IMG][IMG]https://classroom.ucscout.org/courses/1170/files/191494/preview?verifier=nsLscsxToebAVXTSYsoMr7rwIl536LrCJSDGPaHp[/IMG][/I]
Could you guys help me please?

Polygons

Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Quadrilateral

Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.

Rectangle Word Problem

Solves word problems based on area or perimeter and variable side lengths

Rectangles and Parallelograms

Solve for Area, Perimeter, length, and width of a rectangle or parallelogram and also calculates the diagonal length as well as the circumradius and inradius.

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacie

Researchers in Antarctica discovered a warm sea current under the glacier that is causing the glacier to melt. The ice shelf of the glacier had a thickness of approximately 450 m when it was first discovered. The thickness of the ice shelf is decreasing at an average rate if 0.06 m per day.
Which function can be used to find the thickness of the ice shelf in meters x days since the discovery?
We want to build an function I(x) where x is the number of days since the ice shelf discovery.
We start with 450 meters, and each day (x), the ice shelf loses 0.06m, which means we subtract this from 450.
[B]I(x) = 450 - 0.06x[/B]

Rhombus

Given inputs of a rhombus, this calculates the following:

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

Perimeter of a Rhombus

Area of a Rhombus

Side of a Rhombus

Running from the top of a flagpole to a hook in the ground there is a rope that is 9 meters long. If

Running from the top of a flagpole to a hook in the ground there is a rope that is 9 meters long. If the hook is 4 meters from the base of the flagpole, how tall is the flagpole?
We have a right triangle, with hypotenuse of 9 and side of 4.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=4&hypinput=9&pl=Solve+Missing+Side']Using our Pythagorean Theorem calculator[/URL], we get a flagpole height of [B]8.063[/B].

Sections of a rail way are 66m in length. What is the length of 81 placed to end to end?

Sections of a rail way are 66m in length. What is the length of 81 placed to end to end?
We have 81 sections x 66 meters per section = [B]5,346[/B]

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants i

Sheila wants build a rectangular play space for her dog. She has 100 feet of fencing and she wants it to be 5 times as long as it is wide. What dimensions should the play area be?
Sheila wants:
[LIST=1]
[*]l =5w
[*]2l + 2w = 100 <-- Perimeter
[/LIST]
Substitute (1) into (2)
2(5w) + 2w = 100
10w + 2w = 100
12w = 100
Divide each side by 12
[B]w = 8.3333[/B]
Which means l = 5(8.3333) -->[B] l = 41.6667[/B]

Simple and Compound and Continuous Interest

Calculates any of the four parameters of the simple interest formula or compound interest formula or continuous compound formula

1) Principal

2) Accumulated Value (Future Value)

3) Interest

4) Time.

1) Principal

2) Accumulated Value (Future Value)

3) Interest

4) Time.

Sound travels about 340 m/s. The function d(t) = 340t give the distance d(t),in meters., that sound

Sound travels about 340 m/s. The function d(t) = 340t give the distance d(t),in meters., that sound travel in T seconds. How far goes sound traveling 59s?
What we want is d(59)
d(59) = 340m/s(59s) = [B]20,060m[/B]

Squares

Solve for Area of a square, Perimeter of a square, side of a square, diagonal of a square.

Suppose Rocky Mountain have 72 centimeters of snow. Warmer weather is melting at the rate of 5.8 cen

Suppose Rocky Mountain have 72 centimeters of snow. Warmer weather is melting at the rate of 5.8 centimeters a day. If snow continues to melt at this rate, after seven days of warm weather, how much snow will be left?
Snow remaining = Starting snow - melt rate * days
Snow remaining = 72 - 5.8(7)
Snow remaining = 72 - 40.6
Snow remaining = [B]31.4 cm[/B]

The button on Alice's shirt has a diameter of 8 millimeters. What is the button's radius?

The button on Alice's shirt has a diameter of 8 millimeters. What is the button's radius?
Radius = Diameter / 2
Radius = 8/2
Radius = [B]4[/B]

The cost of hiring a car for a day is $60 plus 0.25 cents per kilometer. Michelle travels 750 kilome

The cost of hiring a car for a day is $60 plus 0.25 cents per kilometer. Michelle travels 750 kilometers. What is her total cost
Set up the cost function C(k) where k is the number of kilometers traveled:
C(k) = 60 + 0.25k
The problem asks for C(750)
C(750) = 60 + 0.25(750)
C(750) = 60 + 187.5
C(750) = [B]247.5[/B]

The fastest student in gym class runs 50 meters in 7.4 seconds. The slowest time in the class was 4.

The fastest student in gym class runs 50 meters in 7.4 seconds. The slowest time in the class was 4.36 seconds slower than the fastest time.
Slowest time = 7.4 - 4.36
Slowest time = [B]3.04[/B]

the grass in jamie’s yard grew 16 centimeters in 10 days. how many days did it take for the grass to

the grass in jamie’s yard grew 16 centimeters in 10 days. how many days did it take for the grass to grow 1 centimeter
We set up a proportion of centimeters to days where d is the number of days it takes for the grass to grow 1 centimeter:
16/10 = 1/d
To solve this proportion for d, [URL='https://www.mathcelebrity.com/prop.php?num1=16&num2=1&den1=10&den2=d&propsign=%3D&pl=Calculate+missing+proportion+value']we type it in our search engine[/URL] and we get:
d = [B]0.625 or 5/8[/B]

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +3

The height of an object t seconds after it is dropped from a height of 300 meters is s(t)=-4.9t^2 +300. Find the average velocity of the object during the first 3 seconds? (b) Use the Mean value Theorem to verify that at some time during the first 3 seconds of the fall the instantaneous velocity equals the average velocity. Find that time.
Average Velocity:
[ f(3) - f(0) ] / ( 3 - 0 )
Calculate f(3):
f(3) = -4.9(3^2) + 300
f(3) = -4.9(9) + 300
f(3) = -44.1 + 300
f(3) = 255.9
Calculate f(0):
f(0) = -4.9(0^2) + 300
f(0) = 0 + 300
f(0) = 300
So we have average velocity:
Average velocity = (255.9 - 300)/(3 - 0)
Average velocity = -44.1/3
Average velocity = -[B]14.7
[/B]
Velocity is the first derivative of position
s(t)=-4.9t^2 +300
s'(t) = -9.8t
So we set velocity equal to average velocity:
-9.8t = -14.7
Divide each side by -9.8 to solve for t, we get [B]t = 1.5[/B]

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find th

The largest American flag ever flown had a perimeter of 1,520 feet and a length of 505 feet. Find the width of the flag.
for a rectangle, the Perimeter P is given by:
P = 2l + 2w
P[URL='https://www.mathcelebrity.com/rectangle.php?l=505&w=&a=&p=1520&pl=Calculate+Rectangle']lugging in our numbers for Perimeter and width into our rectangle calculator[/URL], we get:
l =[B] 255[/B]

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the peri

The length of a rectangle is equal to triple the width. Find the length of the rectangle if the perimeter is 80 inches.
The perimeter (P) of a rectangle is:
2l + 2w = P
We're given two equations:
[LIST=1]
[*]l = 3w
[*]2l + 2w = 80
[/LIST]
We substitute equation 1 into equation 2 for l:
2(3w) + 2w = 80
6w + 2w = 80
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D80&pl=Solve']type it in our search engine[/URL] and we get:
w = 10
To solve for the length (l), we substitute w = 10 into equation 1 above:
l = 3(10)
l = [B]30[/B]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
P = 2l + 2w
Since P = 120, we have:
(1) 2l + 2w = 120
We are also given:
(2) l = 3w - 6
Substitute equation (2) into equation (1)
2(3w - 6) + 2w = 120
Multiply through:
6w - 12 + 2w = 120
Combine like terms:
8w - 12 = 120
Add 12 to each side:
8w = 132
Divide each side by 8 to isolate w:
w =16.5
Now substitute w into equation (2)
l = 3(16.5) - 6
l = 49.5 - 6
l = 43.5
So (l, w) = (43.5, 16.5)

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangular word problem calculator[/URL], we have:
[LIST]
[*][B]l = 43.5[/B]
[*][B]w = 16.5[/B]
[/LIST]

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building.
Using our [URL='http://www.mathcelebrity.com/rectangle-word-problems.php?t1=perimeter&v1=120&t2=length&v2=6&op=less&v3=3&t4=times&t5=width&pl=Calculate']rectangle word problem calculator[/URL], we get:
[LIST]
[*][B]w = 16.5[/B]
[*][B]l = 43.5[/B]
[/LIST]

the length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width

The length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width.
Using our r[URL='http://www.mathcelebrity.com/rectangle.php?l=3&w=&a=&p=50&pl=Calculate+Rectangle']ectangle solver[/URL], we get [B]w = 10[/B].

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally’s garden.
Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given:
[LIST=1]
[*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I]
[*]2l + 2w = 72
[/LIST]
We substitute equation (1) into equation (2) for l:
2(3w + 4) + 2w = 72
Multiply through and simplify:
6w + 8 + 2w = 72
(6 +2)w + 8 = 72
8w + 8 = 72
To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B8%3D72&pl=Solve']type it in our search engine[/URL] and we get:
w = [B]8
[/B]
To solve for l, we substitute w = 8 above into Equation (1):
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden

The length of Sally’s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters
A garden is a rectangle, which has perimeter P of:
P = 2l + 2w
With P = 72, we have:
2l + 2w = 72
We're also given:
l = 3w + 4
We substitute this into the perimeter equation for l:
2(3w + 4) + 2w = 72
6w + 8 + 2w = 72
To solve this equation for w, we t[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B8%2B2w%3D72&pl=Solve']ype it in our search engine[/URL] and we get:
w =[B] 8[/B]
Now, to solve for l, we substitute w = 8 into our length equation above:
l = 3(8) + 4
l = 24 + 4
l = [B]28[/B]

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length a

The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width.
A flag is a rectangle shape. So we have the following equations
Since P = 2l + 2w, we have 2l + 2w = 60
l = 7w - 2
Substitute Equation 1 into Equation 2:
2(7w -2) + 2w = 60
14w - 4 + 2w = 60
16w - 4 = 60
Add 4 to each side
16w = 64
Divide each side by 16 to isolate w
w = 4
Which means l = 7(4) - 2 = 28 - 2 = 26

The moon's diameter is 2,159 miles. What is the surface area of the moon? Round to the nearest mile.

The moon's diameter is 2,159 miles. What is the surface area of the moon? Round to the nearest mile.
The moon is a sphere. So our Surface Area formula is:
S =4pir^2
If diameter is 2,159, then radius is 2,159/2 = 1079.5. Plug this into the Surface Area of a sphere formula:
S = 4 * pi * 1079.5^2
S = 4 * pi *1165320.25
S = 4661281 pi
S = [B]14,643,846.15 square miles[/B]

The perimeter of a bedroom door is 28 feet. It is 4 feet wide. How tall is it?

The perimeter of a bedroom door is 28 feet. It is 4 feet wide. How tall is it?
Using our[URL='https://www.mathcelebrity.com/rectangle.php?l=&w=4&a=&p=28&pl=Calculate+Rectangle'] rectangle calculator[/URL], we get:
l = [B]10[/B]

The perimeter of a college basketball court is 102 meters and the length is twice as long as the wid

The perimeter of a college basketball court is 102 meters and the length is twice as long as the width. What are the length and width?
A basketball court is a rectangle. The perimeter P is:
P = 2l + 2w
We're also given l = 2w and P = 102. Plug these into the perimeter formula:
2(2w) + 2w = 102
4w + 2w = 102
6w = 102
[URL='https://www.mathcelebrity.com/1unk.php?num=6w%3D102&pl=Solve']Typing this equation into our calculator[/URL], we get:
[B]w = 17[/B]
Plug this into the l = 2w formula, we get:
l = 2(17)
[B]l = 34[/B]

The perimeter of a garden is 70 meters. Find its actual dimensions if its length is 5 meters longer

The perimeter of a garden is 70 meters. Find its actual dimensions if its length is 5 meters longer than twice its width.
Let w be the width, and l be the length. We have:
P = l + w. Since P = 70, we have:
[LIST=1]
[*]l + w = 70
[*]l = 2w + 5
[/LIST]
Plug (2) into (1)
2w + 5 + w = 70
Group like terms:
3w + 5 = 70
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=3w%2B5%3D70&pl=Solve']equation calculator[/URL], we get [B]w = 21.66667[/B]. Which means length is:
l = 2(21.6667) + 5
l = 43.33333 + 5
[B]l = 48.3333[/B]

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?

The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?
[U]Assumptions and givens:[/U]
[LIST]
[*]The poster has a rectangle shape
[*]l = 6
[*]P = 20
[*]The perimeter of a rectangle (P) is: 2l + 2w = P
[/LIST]
Plugging in our l and P values, we get:
2(6) + 2w = 20
Multiplying through and simplifying, we get:
12 + 2w = 20
To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B2w%3D20&pl=Solve']type this equation into our search engine [/URL]and we get:
w = [B]4[/B]

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Fin

The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Find the length and the width of the rectangle.
l = 4w - 15
Perimeter = 2l + 2w
Substitute, we get:
400 = 2(4w - 15) + 2w
400 = 8w - 30 + 2w
10w - 30 = 400
Add 30 to each side
10w = 370
Divide each side by 10 to isolate w
w = 37
Plug that back into our original equation to find l
l = 4(37) - 15
l = 148 - 15
l = 133
So we have (l, w) = (37, 133)

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is

The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is it’s width?
The formula for a rectangles perimeter P, is:
P = 2l + 2w where l is the length and w is the width.
Plugging in our P = 340 and l = 97, we have:
2(97) + 2w = 340
Multiply through, we get:
2w + 194 = 340
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B194%3D340&pl=Solve']Type this equation into our search engine[/URL], we get:
[B]w = 73[/B]

The perimeter of a rectangular backyard is 162 feet. It is 52 feet long. How wide is it?

The perimeter of a rectangular backyard is 162 feet. It is 52 feet long. How wide is it?
We [URL='https://www.mathcelebrity.com/rectangle.php?l=52&w=&a=&p=162&pl=Calculate+Rectangle']use our rectangle solver to solve for w[/URL]. We get:
[B]w = 29[/B]

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?

The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?
Set up the perimeter equation:
2l + 2w = P
Given P = 204 and l = 66, we have:
2(66) + 2w = 204
2w + 132 = 204
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B132%3D204&pl=Solve']equation solver,[/URL] we get w = [B]36[/B].

The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the

The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the dimensions
We are given the following equations:
[LIST=1]
[*]220 = 2l + 2w
[*]l = w + 30
[/LIST]
Plug (1) into (2)
2(w + 30) + 2w = 220
2w + 60 + 2w = 220
Combine like terms:
4w + 60 = 220
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B60%3D220&pl=Solve']Plug 4w + 60 = 220 into the search engine[/URL], and we get [B]w = 40[/B].
Now plug w = 40 into equation (2)
l = 40 + 30
[B]l = 70[/B]

The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is

The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is its width?
Set up the rectangle perimeter equation:
P = 2l + 2w
For l = 69 and P = 250, we have:
250= 2(69) + 2w
250 = 138 + 2w
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B138%3D250&pl=Solve']equation solver[/URL], we get:
[B]w = 56 [/B]

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length

The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it’s length?
Set up the perimeter (P) of a rectangle equation given length (l) and width (w):
2l + 2w = P
We're given P = 300 and w = 59. Plug these into the perimeter equation:
2l + 2(59) = 300
2l + 118 = 300
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B118%3D300&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]l = 91[/B]

The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it?

The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it?
Perimeter of a rectangle P is:
P = 2l + 2w
We have:
2l + 2w = 16
We are given w = 5, so we have:
2l + 2(5) = 16
2l + 10 = 16
[URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B10%3D16&pl=Solve']Plugging this into our equation calculator[/URL], we get [B]l = 3[/B].

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. Wh

The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio?
Perimeter of a rectangle is:
P = 2l + 2w
We're given l = w + 3 and P = 54. So plug this into our perimeter formula:
54= 2(w + 3) + 2w
54 = 2w + 6 + 2w
Combine like terms:
4w + 6 = 54
[URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B6%3D54&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 12[/B]
Plug this into our l = w + 3 formula:
l = 12 + 3
[B]l = 15[/B]

The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, wh

The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, what is its width?
The perimeter for a rectangle (P) is given as:
2l + 2w = P
We're given P = 258 and l = 71. Plug these values in:
2(71) + 2w = 258
142 + 2w = 258
[URL='https://www.mathcelebrity.com/1unk.php?num=142%2B2w%3D258&pl=Solve']Typing this equation into our search engine[/URL], we get:
[B]w = 58[/B]

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?

The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?
The perimeter for a rectangle is given below:
P = 2l + 2w
We're given l = 7 and P = 60. Plug this into the perimeter formula:
60 = 2(7) + 2w
60 = 14 + 2w
Rewritten, it's 2w + 14 = 60.
[URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B14%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get [B]w = 23[/B].

The perimeter of a square with side a

The perimeter of a square with side a
Perimeter of a square is 4s where s is the side length.
With s = a, we have:
P = [B]4a[/B]

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimete

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000.
[LIST]
[*]h = b + 70
[*]A = 1/2bh = 3000
[/LIST]
Substitute the height equation into the area equation
1/2b(b + 70) = 3000
Multiply each side by 2
b^2 + 70b = 6000
Subtract 6000 from each side:
b^2 + 70b - 6000 = 0
Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=b%5E2%2B70b-6000%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get:
b = 50 and b = -120
Since the base cannot be negative, we use b = 50.
If b = 50, then h = 50 + 70 = 120
The perimeter is b + h + hypotenuse
Using the [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=70&angle_b=&b=50&c=&pl=Calculate+Right+Triangle']right-triangle calculator[/URL], we get hypotenuse = 86.02
Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/B]

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the

The sides of a triangle are consecutive numbers. If the perimeter of the triangle is 240 m, find the length of each side
Let the first side be n.
Next side which is consecutive is n + 1
Next side which is consecutive is n + 1 + 1 = n + 2
So we have the sum of 3 consecutive numbers is 240.
We type in [I][URL='https://www.mathcelebrity.com/sum-of-consecutive-numbers.php?num=sumof3consecutivenumbersis240&pl=Calculate']sum of 3 consecutive numbers is 240[/URL][/I] into our search engine and we get:
[B]79, 80, 81[/B]

The slope of a roof is called its pitch. The Parthenon, an ancient Greek temple, has a roof with a r

The slope of a roof is called its pitch. The Parthenon, an ancient Greek temple, has a roof with a rise of 3.6 meters and a run of 12 meters. What is the pitch of the roof? Enter your answer in the box.
Slope is rise over run.
Slope = 3.6/12
Slope = [B]0.3[/B]

The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters

The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters as dimes. What is the total number of dimes in the parking meter?
Let q be the number of quarters. Let d be the number of dimes. We're given:
[LIST=1]
[*]q = 2d
[*]0.10d + 0.25q = 18
[/LIST]
Substitute (1) into (2):
0.10d + 0.25(2d) = 18
0.10d + 0.5d = 18
[URL='https://www.mathcelebrity.com/1unk.php?num=0.10d%2B0.5d%3D18&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 30[/B].

Three tennis balls each have a radius of 2 inches. They are put into a 12 inch high cylinder with a

Three tennis balls each have a radius of 2 inches. They are put into a 12 inch high cylinder with a 4 inch diameter. What is the volume of the space remaining in the cylinder?
Volume of each ball is 4/3 ?r^3
V = 4/3 * 3.1415 * 2^3
V = 1.33 * 3.1415 * 8 = 33.41 cubic inches
The volume of 3 balls is:
V = 3(33.41)
V = 100.23
Volume of the cylinder is area of circle times height:
V = 3.14 * 2 * 2 * 1 = 150.72
Volume of remaining space is:
V = Volume of cylinder - Volume of 3 balls
V = 150.72 - 100.23
V = [B]50.49[/B]

To rent a car it costs $12 per day and $0.50 per kilometer traveled. If a car were rented for 5 days

To rent a car it costs $12 per day and $0.50 per kilometer traveled. If a car were rented for 5 days and the charge was $110.00, how many kilometers was the car driven?
Using days as d and kilometers as k, we have our cost equation:
Rental Charge = $12d + 0.5k
We're given Rental Charge = 110 and d = 5, so we plug this in:
110 = 12(5) + 0.5k
110 = 60 + 0.5k
[URL='https://www.mathcelebrity.com/1unk.php?num=60%2B0.5k%3D110&pl=Solve']Plugging this into our equation calculator[/URL], we get:
[B]k = 100[/B]

Trapezoids

This calculator determines the following items for a trapezoid based on given inputs:

* Area of trapezoid

* Perimeter of a Trapezoid

* Area of trapezoid

* Perimeter of a Trapezoid

Triangle with perimeter

A triangle with a perimeter of 120.
What degree are the three sides?

Use the information below to determine the weight of 500 gallons of water. a) There are 1.057 quart

Use the information below to determine the weight of 500 gallons of water.
a) There are 1.057 quarts in a liter and 4 quarts in a gallon
b) A cubic decimeter of water is a liter of water
c) A cubic decimeter of water weighs one kilogram
d) There are 2.2 pounds in a kilogram
[LIST]
[*]500 gallons = 2000 quarts
[*]2000 quarts / 1.057 quarts in a liter = 1892.15 liters
[*]1892.15 liters weight 1892.15 kilograms
[*]1892.15 kilograms x 2.2 pounds = [B]4163 pounds[/B]
[/LIST]

What is the area of a triangular parking lot with a width of 200m and a length of 100m?What is the a

What is the area of a triangular parking lot with a width of 200m and a length of 100m?
Area of a Triangle = bh/2
Plugging in our numbers, we get:
Area of Parking Lot = 200(100)/2
Area of Parking Lot = 100 * 100
Area of Parking Lot = [B]10,000 sq meters[/B]

What is the formula for the circumference of a circle?

What is the formula for the circumference of a circle?
Given radius r and diameter d, the circumference C is:
[B]C = 2?r or ?d[/B]

What is the weight of a cubic meter of water? Express your answer in kilograms?

What is the weight of a cubic meter of water? Express your answer in kilograms?
1 kilogram per cubic decimeter and 1000 cubic decimeters in a cubic meter = [B]1000 kilograms[/B]

When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at

When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at a speed of 750 meters per minute. The fox started to run away at a speed of 720 meters per minute. How soon will the dog catch the fox?
The dog sits a position p.
Distance = Rate x Time
The dogs distance in minutes is D = 720t
The fox sits at position p + 60
Distance = Rate x Time
The fox's distance in minutes is D = 750t - 60 <-- Subtract 60 since the fox is already ahead 60 meters.
We want to know when their distance (location) is the same. So we set both distance equations equal to each other:
720t = 750t - 60
[URL='https://www.mathcelebrity.com/1unk.php?num=720t%3D750t-60&pl=Solve']Using our equation calculator[/URL], we get [B]t = 2[/B].
Let's check our work:
Dog's distance is 720(2) = 1440
Fox's distance is 750(2) - 60 = 1,440

Which of the following descriptions of null hypothesis are correct? (Select all that apply) a. A nu

Which of the following descriptions of null hypothesis are correct? (Select all that apply)
a. A null hypothesis is a hypothesis tested in significance testing.
b. The parameter of a null hypothesis is commonly 0.
c. The aim of all research is to prove the null hypothesis is true
d. Researchers can reject the null hypothesis if the P-value is above 0.05
[B]a. A null hypothesis is a hypothesis tested in significance testing.
[/B]
[I]b. is false because a parameter can be anything we choose it to be
c. is false because our aim is to disprove or fail to reject the null hypothesis
d. is false since a p-value [U]below[/U] 0.05 is often the rejection level.[/I]

while scuba diving jerey rose directly toward the surface of the water at a constant velocity for 2.

while scuba diving jerey rose directly toward the surface of the water at a constant velocity for 2.0 minutes. he rose 9.0 meters in that time. what was his velocity?
9 meters / 2 minutes = [B]4.5 meters / minute[/B]

Yolanda is riding her bicycle. She rides for 5 hours at a speed of 12.5 kilometers per hours. For ho

Yolanda is riding her bicycle. She rides for 5 hours at a speed of 12.5 kilometers per hours. For how many kilometers does she ride?
This is a distance problem, where distance = rate * time. We are given time of 5 hours, at a rate of 12.5km/hour.
Using our [URL='http://www.mathcelebrity.com/drt.php?d=+&r=12.5&t=5&pl=Calculate+the+missing+Item+from+D%3DRT']distance calculator[/URL], we get D = [B]62.5km[/B].

You have $20 to spend on a taxi fare. The ride costs $5 plus $2.50 per kilometer.

You have $20 to spend on a taxi fare. The ride costs $5 plus $2.50 per kilometer.
Let k be the number of kilometers.
Total Cost = Cost per kilometer * number of kilometers + Fixed Cost
With k for kilometers, 2.5 as cost per kilometer, and 5 as fixed cost, and 20 on total cost, we have:
2.5k + 5 = 20
To solve this equation for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5k%2B5%3D20&pl=Solve']type it in our math engine [/URL]and we get
k = [B]6[/B]

You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per kilometer. Write the inequality

You have $20 to spend on taxi fare. The ride costs $5 plus $2.50 per kilometer. Write the inequality.
Let k be the number of kilometers. We want our total to be $20 [I]or less. [/I]We have the following inequality:
[B]2.50k + 5 <= 20[/B]