point - an exact location in the space, and has no length, width, or thickness

-11, -9, -7, -5, -3 What is the next number? What is the 200th term in this sequence?

-11, -9, -7, -5, -3 What is the next number? What is the 200th term in this sequence?
We see that Term 1 is -11, Term 2 is -9, so we do a point slope equation of (1,-11)(2,-9) to get the [URL='https://www.mathcelebrity.com/search.php?q=%281%2C-11%29%282%2C-9%29']nth term of the formula[/URL]
f(n) = 2n - 13
The next number is the 6th term:
f(6) = 2(6) - 13
f(6) = 12 - 13
f(6) = [B]-1
[/B]
The 200th term is:
f(200) = 2(200) - 13
f(200) = 400 - 13
f(200) = [B]387[/B]

100, 75, 50, 25, 0, -25 What is the next number? What is the 100th term?

100, 75, 50, 25, 0, -25 What is the next number? What is the 100th term?
Using point slope, we get (1, 100)(2, 75)
Our [URL='https://www.mathcelebrity.com/search.php?q=%281%2C+100%29%282%2C+75%29&x=0&y=0']series function becomes[/URL]
f(n) = -25n + 125
The next term is the 7th term:
f(7) = -25(7) + 125
f(7) = -175 + 125
f(7) = [B]-50
[/B]
The 100th term is found by n = 100:
f(100) = -25(100) + 125
f(100) = -2500 + 125
f(100) = [B]-2375[/B]

2 Lines Intersection

Free 2 Lines Intersection Calculator - Enter any 2 line equations, and the calculator will determine the following:

* Are the lines parallel?

* Are the lines perpendicular

* Do the lines intersect at some point, and if so, which point?

* Is the system of equations dependent, independent, or inconsistent

* Are the lines parallel?

* Are the lines perpendicular

* Do the lines intersect at some point, and if so, which point?

* Is the system of equations dependent, independent, or inconsistent

3 Point Equation

Free 3 Point Equation Calculator - Forms a quadratic from 3 points that are entered.

3-dimensional points

Free 3-dimensional points Calculator - Calculates distance between two 3-dimensional points

(x_{1}, y_{1}, z_{1}) and (x_{2}, y_{2}, z_{2}) as well as the parametric equations and symmetric equations

(x

5, 14, 23, 32, 41....1895 What term is the number 1895?

5, 14, 23, 32, 41....1895 What term is the number 1895?
Set up a point slope for the first 2 points:
(1, 5)(2, 14)
Using [URL='https://www.mathcelebrity.com/search.php?q=%281%2C+5%29%282%2C+14%29&x=0&y=0']point slope formula, our series function[/URL] is:
f(n) = 9n - 4
To find what term 1895 is, we set 9n - 4 = 1895 and solve for n:
9n - 4 = 1895
Using our [URL='https://www.mathcelebrity.com/1unk.php?num=9n-4%3D1895&pl=Solve']equation solver[/URL], we get:
n = [B]211[/B]

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points

A 100 point test contains a total of 20 questions. The multiple choice questions are worth 3 points each and short response questions are worth 8 points each. Write a system of linear equations that represents this situation
Assumptions:
[LIST]
[*]Let m be the number of multiple choice questions
[*]Let s be the number of short response questions
[/LIST]
Since total points = points per problem * number of problems, we're given 2 equations:
[LIST=1]
[*][B]m + s = 20[/B]
[*][B]3m + 8s = 100[/B]
[/LIST]
We can solve this system of equations 3 ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+s+%3D+20&term2=3m+%2B+8s+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[B]m = 12, s = 8[/B]

A car is traveling 60 km per hour. How many hours will it take for the car to reach a point that is

A car is traveling 60 km per hour. How many hours will it take for the car to reach a point that is 180 km away?
Rate * Time = Distance so we have t for time as:
60t = 180
To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=60t%3D180&pl=Solve']type it in the search engine[/URL] and we get:
t = [B]3[/B]

A chest of treasure was hidden in the year 64 BC and found in 284 AD. For how long was the chest hid

A chest of treasure was hidden in the year 64 BC and found in 284 AD. For how long was the chest hidden
BC stands for Before Christ. Year 0 is when Christ was born. AD stands for After Death
On a number line, the point of Christ's birth is 0.
So BC is really negative
AD is positive
So we have:
284 - -64
284 + 64
[B]348 years[/B]

A circle has a center at (6, 2) and passes through (9, 6)

A circle has a center at (6, 2) and passes through (9, 6)
The radius (r) is found by [URL='https://www.mathcelebrity.com/slope.php?xone=6&yone=2&slope=+2%2F5&xtwo=9&ytwo=6&pl=You+entered+2+points']using the distance formula[/URL] to get:
r = 5
And the equation of the circle is found by using the center (h, k) and radius r as:
(x - h)^2 + (y - k)^2 = r^2
(x - 6)^2 + (y - 2)^2 = 5^2
[B](x - 6)^2 + (y - 2)^2 = 25[/B]

A company had sales of $19,808 million in 1999 and $28,858 million in 2007. Use the Midpoint Formula

A company had sales of $19,808 million in 1999 and $28,858 million in 2007. Use the Midpoint Formula to estimate the sales in 2003
2003 is the midpoint of 1999 and 2007, so we use our [URL='https://www.mathcelebrity.com/mptnline.php?ept1=19808&empt=&ept2=28858&pl=Calculate+missing+Number+Line+item']midpoint calculator[/URL] to get:
[B]24,333[/B] sales in 2003

A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each l

A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lamp, and the selling price is $150 per lamp.
Set up the Cost Equation C(l) where l is the price of each lamp:
C(l) = Variable Cost x l + Fixed Cost
C(l) = 90l + 1800
Determine the revenue function R(l)
R(l) = 150l
Determine the profit function P(l)
Profit = Revenue - Cost
P(l) = 150l - (90l + 1800)
P(l) = 150l - 90l - 1800
[B]P(l) = 60l - 1800[/B]
Determine the break even point:
Breakeven --> R(l) = C(l)
150l = 90l + 1800
[URL='https://www.mathcelebrity.com/1unk.php?num=150l%3D90l%2B1800&pl=Solve']Type this into the search engine[/URL], and we get [B]l = 30[/B]

A direct variation includes the points ( – 5, – 20) and (n,8). Find n.

A direct variation includes the points ( – 5, – 20) and (n,8). Find n.
Slopes are proportional for rise over run. Set up a proportion of x's to y's:
-5/n = -20/8
To solve this proportion for n, we [URL='https://www.mathcelebrity.com/prop.php?num1=-5&num2=-20&den1=n&den2=8&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get:
n = [B]2[/B]

A game show has 74 categories. There are 9,785 points in each category. How many points are there in

A game show has 74 categories. There are 9,785 points in each category. How many points are there in total on the game show?
Total points = Total categories * points per category
Total points = 9785 * 74
Total points = [B]724,090[/B]

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s sta

A helicopter rose vertically 300 m and then flew west 400 m how far was the helicopter from it’s starting point?
The distance forms a right triangle. We want the distance of the hypotenuse.
Using our [URL='http://www.mathcelebrity.com/pythag.php?side1input=300&side2input=400&hypinput=&pl=Solve+Missing+Side']right triangle calculator[/URL], we get a distance of [B]500[/B].
We also could use a shortcut on this problem. If you divide 300 and 400 by 100, you get 3 and 4. Since we want the hypotenuse, you get the famous 3-4-5 triangle ratio. So the answer is 5 * 100 = 500.

A is 0 and AR=19 what is the midpoint

A is 0 and AR=19 what is the midpoint
[URL='https://www.mathcelebrity.com/mptnline.php?ept1=0&empt=&ept2=19&pl=Calculate+missing+Number+Line+item']Using our midpoint calculator, with one point at 0, and the other point at 19[/URL], we get the midpoint M:
M = [B]19/2 or 9.5[/B]

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hour

A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hours head start. How far from the starting point are the planes?
Use the formula D = rt where
[LIST]
[*]D = distance
[*]r = rate
[*]t = time
[/LIST]
The plan traveling 150 mph for 3 hours:
Time 1 = 150
Time 2 = 300
Time 3 = 450
Now at Time 3, the other plane starts
Time 4 = 600
Time 5 = 750
Time 6 =
450 + 150t = 550t
Subtract 150t
400t = 450
Divide each side by 400
t = 1.125
Plug this into either distance equation, and we get:
550(1.125) = [B]618.75 miles[/B]

A lady walks into a store and steals $100 bill from the register without the owners knowledge. She c

A lady walks into a store and steals $100 bill from the register without the owners knowledge. She comes back 5 minutes later and buys $70 worth of goods with the $100 bill. The owner gives her $30 in change. How much did the owner lose?
[LIST=1]
[*]After the lady steals $100, the owner is down -$100.
[*]The lady comes back, and buys $70 worth of goods. At this point, the owner has -$100 + $70 = $-30.
[*]Next, the owner gives the lady another $30 in change, making the owner's loss -$30 - $30 = [B]-$60[/B].
[/LIST]

A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that lin

A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that line.
Our line equation is:
y = mx + b
We're given:
m = 4/5
(x, y) = (0, 0)
So we have:
0 = 4/5(0) + b
0 = 0 + b
b = 0
Therefore, our line equation is:
y = 4/5x
[URL='https://www.mathcelebrity.com/function-calculator.php?num=y%3D4%2F5x&pl=Calculate']Start plugging in values here to get a list of points[/URL]

A line joins A (1, 3) to B (5, 8). (a) (i) Find the midpoint of AB.

A line joins A (1, 3) to B (5, 8). (a) (i) Find the midpoint of AB.
We type in (1,3),(5,8) to our search engine. We [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=3&slope=+2%2F5&xtwo=5&ytwo=8&pl=You+entered+2+points']choose our midpoint of 2 points calculator,[/URL] and we get:
[B](3, 11/2)[/B]

A line passes through the point -3,4 and has a slope of -5

A line passes through the point -3,4 and has a slope of -5
Using our [URL='http://A line passes through the point -3,4 and has a slope of -5']point slope calculator[/URL], we get a line equation of:
y = -5x - 11

A line segment has the endpoints S(10, 7) and T(2, 7). Find the coordinates of its midpoint M.

A line segment has the endpoints S(10, 7) and T(2, 7). Find the coordinates of its midpoint M.
[URL='https://www.mathcelebrity.com/slope.php?xone=2&yone=7&slope=+&xtwo=10&ytwo=7&bvalue=+&pl=You+entered+2+points']Using our midpoint calculator[/URL], we get:
M = [B](6, 7)[/B]

A man stands at point p, 45 metres from the base of a building that is 20 metres high. Find the angl

A man stands at point p, 45 metres from the base of a building that is 20 metres high.
Find the angle of elevation of the top of the building from the man.
Draw a right triangle ABC where Side A is from the bottom of the building to the man and Side B is the bottom of the building to the top of the building. Using right triangle calculations, we want Angle A which is the angle of elevation.
[URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=20&angle_b=&b=45&c=&pl=Calculate+Right+Triangle']Angle of Elevation[/URL] which is [B]23.9625°[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produced. The product sells for $22/unit.
The cost function for each unit u is:
C(u) = Variable Cost * Units + Fixed Cost
C(u) = 10u + 100000
The revenue function R(u) is:
R(u) = 22u
We want the break-even point, which is where:
C(u) = R(u)
10u + 100000 = 22u
[URL='https://www.mathcelebrity.com/1unk.php?num=10u%2B100000%3D22u&pl=Solve']Typing this equation into our search engine[/URL], we get:
u =[B]8333.33[/B]

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produ

A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produced. The product sells for $20/unit
[U]Cost Function C(u) where u is the number of units:[/U]
C(u) = cost per unit * u + fixed cost
C(u) = 12u + 100000
[U]Revenue Function R(u) where u is the number of units:[/U]
R(u) = Sale price * u
R(u) = 20u
Break even point is where C(u) = R(u):
C(u) = R(u)
12u + 100000 = 20u
To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=12u%2B100000%3D20u&pl=Solve']type this equation into our search engine[/URL] and we get:
u = [B]12,500[/B]

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 poin

A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test?
Let's call the 5 point questions m for multiple choice. Let's call the 2 point questions t for true-false. We have two equations:
[LIST=1]
[*]m + t = 38
[*]5m + 2t = 100
[/LIST]
Rearrange (1) to solve for m - subtract t from each side:
3. m = 38 - t
Now, substitute (3) into (2)
5(38 - t) + 2t = 100
190 - 5t + 2t = 100
Combine like terms:
190 - 3t = 100
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=190-3t%3D100&pl=Solve']equation solver[/URL], we get [B]t = 30[/B].
Plugging t = 30 into (1), we get:
30 + t = 38
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=m%2B30%3D38&pl=Solve']equation solver[/URL] again, we get [B]m = 8[/B].
Check our work for (1)
8 + 30 = 38 <-- Check
Check our work for (2)
5(8) + 2(30) ? 100
40 + 60 ? 100
100 = 100 <-- Check
You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+38&term2=5m+%2B+2t+%3D+100&pl=Cramers+Method']simultaneous equations calculator[/URL]

A plane is flying at an altitude of 45,000 feet. It begins to drop in altitude 3,000 feet per minute

A plane is flying at an altitude of 45,000 feet. It begins to drop in altitude 3,000 feet per minute. What is the slope in this situation?
Set up a graph where minutes is on the x-axis and altitude is on the y-axis.
[LIST=1]
[*]Minute 1 = (1, 42,000)
[*]Minute 2 = (2, 39,000)
[*]Minute 3 = (3, 36,000)
[*]Minute 4 = (4, 33,000)
[/LIST]
You can see for every 1 unit move in x, we get a -3,000 unit move in y.
Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=42000&slope=+2%2F5&xtwo=2&ytwo=39000&bvalue=+&pl=You+entered+2+points']use our slope calculator[/URL] to get:
Slope = -[B]3,000[/B]

A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation t

A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation to determine the break even point?
Set up the cost functions for Rental Truck 1 (R1) and Rental Truck 2 (R2) where m is the number of miles
R1(m) = 0.59m + 49.95
R2(m) = 0.99m + 39.95
Break even is when we set the cost functions equal to one another:
0.59m + 49.95 = 0.99m + 39.95
[URL='https://www.mathcelebrity.com/1unk.php?num=0.59m%2B49.95%3D0.99m%2B39.95&pl=Solve']Typing this equation into the search engine[/URL], we get [B]m = 25[/B].

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment

A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $584. What was the simple interest rate of the bonds?
For simple interest, we have:
Balance * interest rate = Interest payment
8000i = 584
Divide each side of the equation by 8000 to isolate i:
8000i/8000 = 584/8000
Cancelling the 8000's on the left side, we get:
i = 0.073
Most times, interest rates are expressed as a percentage.
Percentage interest = Decimal interest * 100%
Percentage interest = 0.073 * 100%
Multiplying by 100 is the same as moving the decimal point two places right:
Percentage interest = [B]7.3%[/B]

A revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is

A revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is
Break even is when C(x) = R(x). So we set them equal and solve for x:
-9x + 341 = 22x
Typing[URL='https://www.mathcelebrity.com/1unk.php?num=-9x%2B341%3D22x&pl=Solve'] this equation into our search engine[/URL], we get:
x = [B]11[/B]

A scuba diver swam 96ft under the sea and then went back up 34ft. What is the depth of the diver at

A scuba diver swam 96ft under the sea and then went back up 34ft. What is the depth of the diver at this point?
96 - 34 = [B]62 ft[/B]

A segment has an endpoint at (2, 1). The midpoint is at (5, 1). What are the coordinates of the othe

A segment has an endpoint at (2, 1). The midpoint is at (5, 1). What are the coordinates of the other endpoint?
The other endpoint is (8,1) using our [URL='http://www.mathcelebrity.com/mptnline.php?ept1=2&empt=5&ept2=&pl=Calculate+missing+Number+Line+item']midpoint calculator.[/URL]

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 w

A spinner has 3 equal sections labelled A, B, C. A bag contains 3 marbles: 1 grey, 1 black, and 1 white. The pointer is spun and a marble is picked at random.
a) Use a tree diagram to list the possible outcomes.
[LIST=1]
[*][B]A, Grey[/B]
[*][B]A, Black[/B]
[*][B]A, White[/B]
[*][B]B, Grey[/B]
[*][B]B, Black[/B]
[*][B]B, White[/B]
[*][B]C, Grey[/B]
[*][B]C, Black[/B]
[*][B]C, White[/B]
[/LIST]
b) What is the probability of:
i) spinning A?
P(A) = Number of A sections on spinner / Total Sections
P(A) = [B]1/3[/B]
---------------------------------
ii) picking a grey marble?
P(A) = Number of grey marbles / Total Marbles
P(A) = [B]1/3[/B]
---------------------------------
iii) spinning A and picking a white marble?
Since they're independent events, we multiply to get:
P(A AND White) = P(A) * P(White)
P(A) was found in i) as 1/3
Find P(White):
P(White) = Number of white marbles / Total Marbles
P(White) = 1/3
[B][/B]
Therefore, we have:
P(A AND White) = 1/3 * 1/3
P(A AND White) = [B]1/9[/B]
---------------------------------
iv) spinning C and picking a pink marble?
Since they're independent events, we multiply to get:
P(C AND Pink) = P(C) * P(Pink)
Find P(C):
P(C) = Number of C sections on spinner / Total Sections
P(C) = 1/3
[B][/B]
Find P(Pink):
P(Pink) = Number of pink marbles / Total Marbles
P(Pink) = 0/3
[B][/B]
Therefore, we have:
P(C AND Pink) = 1/3 * 0
P(C AND Pink) = [B]0[/B]

A straight line has the equation ax + by=23. The points (5,-2) and (1,-5) lie on the line. Find the

A straight line has the equation ax + by=23. The points (5,-2) and (1,-5) lie on the line. Find the values of a and b.
plug in both points and form 2 equations:
[LIST=1]
[*]5a - 2b = 23
[*]1x - 5b = 23
[/LIST]
We can solve this simultaneous equations any one of three ways:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the same answer:
[LIST]
[*][B]a = 3[/B]
[*][B]b = -4[/B]
[/LIST]

A test has twenty questions worth 100 points . The test consist of true/false questions worth 3 poin

A test has twenty questions worth 100 points . The test consist of true/false questions worth 3 points each and multiple choice questions worth 11 points each . How many multiple choice questions are on the test?
Set up equations where t = true false and m = multiple choice:
[LIST=1]
[*]t + m = 20
[*]3t + 11m = 100
[/LIST]
Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=t+%2B+m+%3D+20&term2=3t+%2B+11m+%3D+100&pl=Cramers+Method']simultaneous equation calculator[/URL]:
[B]t = 15, m = 5[/B]

A test has twenty questions worth 100 points total. the test consists of true/false questions worth

A test has twenty questions worth 100 points total. the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many true/false questions are on the test?
Let m be the number of multiple choice questions and t be the number of true/false questions. We're given:
[LIST=1]
[*]m + t = 20
[*]11m + 3t = 100
[/LIST]
We can solve this system of equations 3 ways below:
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we choose, we get the following answers:
[LIST]
[*][B]m = 5[/B]
[*][B]t = 15[/B]
[/LIST]
Check our work in equation 1:
5 + 15 ? 20
[I]20 = 20[/I]
Check our work in equation 2:
11(5) + 3(15) ? 100
55 + 45 ? 100
[I]100 = 100[/I]

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 poin

A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?
Let the number of true/false questions be t. Let the number of multiple choice questions be m. We're given two equations:
[LIST=1]
[*]m + t = 20
[*]11m + 3t = 100
[/LIST]
We have a set of simultaneous equations. We can solve this using 3 methods:
[LIST=1]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL]
[/LIST]
No matter which method we pick, we get the same answer:
[LIST]
[*][B]m = 5[/B]
[*][B]t = 15[/B]
[/LIST]

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle

A turtle and rabbit are in a race to see who is the first to reach a point 100 feet away. The turtle travels at a constant speed of 20 feet per minute for the entire 100 feet. The rabbit travels at a constant speed of 40 feet per minute for the first 50 feet, stops for 3 minutes, and then continuous at a constant speed of 40 feet per minute for the last 50 feet.
(i) Determine which animal won the race.
(ii). By how much time the animal won the race.
(iii) Explain one life lesson from the race.
We know the distance formula is:
d = rt
For the turtle, he has a rate (r) of 20 feet / minute and distance (d) of 100. We want to solve for time:
[URL='https://www.mathcelebrity.com/drt.php?d=+100&r=+20&t=&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 5
The rabbit has 3 parts of the race:
Rabbit Part 1: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Rabbit Part 2: The rabbit stops for 3 minutes (t = 3)
Rabbit Part 3: Distance (d) = 50 and rate (r) = 40
[URL='https://www.mathcelebrity.com/drt.php?d=50&r=40&t=+&pl=Calculate+the+missing+Item+from+D%3DRT']Using our distance rate time calculator solving for t[/URL], we get:
t = 1.25
Total time for the rabbit from the 3 parts is (t) = 1.25 + 3 + 1.25
Total time for the rabbit from the 3 parts is (t) = 5.5
[LIST]
[*](i) The [B]turtle won[/B] the race because he took more time to finish and they both started at the same time
[*](ii) We subtract the turtles time from the rabbit's time: 5.5 - 5 = [B]0.5 minutes which is also 30 seconds[/B]
[*](iii) [B]Slow and Steady wins the race[/B]
[/LIST]

A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selec

A typical adult has an average IQ score of 105 with a standard deviation of 20. If 20 randomly selected adults are given an IQ test, what is the probability that the sample mean scores will be between 85 and 125 points?
For x = 125, our z-score and probability is seen [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+125&mean=+105&stdev=+20&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
Z = 1
P(x < 1) = 0.841345
For x = 85, our z-score and probability is seen [URL='http://www.mathcelebrity.com/probnormdist.php?xone=+85&mean=+105&stdev=+20&n=+1&pl=P%28X+%3C+Z%29']here[/URL]
Z = -1
P(x < -1) = 0.158655
So what we want is the probability between these values:

0.841345 - 0.158655 = [B]0.68269[/B]

0.841345 - 0.158655 = [B]0.68269[/B]

A vertical line that passes through the point (3, -2). Identify TWO additional points on the line.

A vertical line that passes through the point (3, -2). Identify TWO additional points on the line.
A vertical line runs straight up, so the x-coordinate is always the same.
We use x = 3 and any y point:
(3, -1)
(3, 0)
(3, 1)

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and

A woman walked for 5 hours, first along a level road, then up a hill, and then she turned around and walked back to the starting point along the same path. She walks 4mph on level ground, 3 mph uphill, and 6 mph downhill. Find the distance she walked.
Hint: Think about d = rt, which means that t = d/r. Think about each section of her walk, what is the distance and the rate. You know that the total time is 5 hours, so you know the sum of the times from each section must be 5.
Let Level distance = L and hill distance = H. Add the times it took for each section of the walk:
L/4 + H /3 + H/6 + L/4 = 5
The LCD of this is 12 from our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=6&pl=LCM']LCD Calculator[/URL]
[U]Multiply each side through by our LCD of 12[/U]
3L + 4H + 2H + 3L = 60
[U]Combine like terms:[/U]
6L + 6H = 60
[U]Divide each side by 3:[/U]
2L + 2H = 20
The woman walked [B]20 miles[/B]

A young dad, who was a star football player in college, set up a miniature football field for his fi

A young dad, who was a star football player in college, set up a miniature football field for his five-year-old young daughter, who was already displaying an unusual talent for place-kicking. At each end of the mini-field, he set up goal posts so she could practice kicking extra points and field goals. He was very careful to ensure the goalposts were each straight up and down and that the crossbars were level. On each set, the crossbar was six feet long, and a string from the top of each goalpost to the midpoint between them on the ground measured five feet. How tall were the goalposts? How do you know this to be true?
The center of each crossbar is 3 feet from each goalpost. We get this by taking half of 6, since midpoint means halfway.
Imagine a third post midway between the two goal posts. It has the same height as the two goalposts.
From the center post, the string from the top of a goalpost to the base of the center post, and half the crossbar form and right triangle with hypotenuse 5 feet and one leg 3 feet.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=&side2input=3&hypinput=5&pl=Solve+Missing+Side']Using the Pythagorean Theorem[/URL], the other leg -- the height of each post -- is 4 feet.

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])

After a long journey, you finally arrive at the edge o a deep gorge where there are two identical br

After a long journey, you finally arrive at the edge o a deep gorge where there are two identical bridges from which to choose your path to the other side.
One bridge is safe, while the other is very dangerous and has caused the deaths of hundreds of travelers. The owner of the first bridge is a talking rat, while the owner of the second bridge is a talking frog. Friends told you before you left that one of the bridge owners always tells the truth, while the other always lies.
You are allowed one question to ask of either the frog or the rat to find out which bridge is the safe bridge. What is the question that you would ask?
[B]Ask the frog the following question: "If I were to ask the rat which bridge is the same bridge, which one would he point to?"
[/B]
If the frog is the truth teller, he would tell you that the rat would point to the dangerous bridge.
If the frog is the liar, the truth telling rat would point out the safe bridge, but the lying frog would tell you he said the dangerous bridge.
In both situations, the dangerous bridge would be pointed to. Take the other bridge.

An air horn goes off every 48 seconds,another every 80 seconds. At 5:00 pm the two go off simultaneo

An air horn goes off every 48 seconds,another every 80 seconds. At 5:00 pm the two go off simultaneously. At what time will the air horns blow again at the same time?
We want to find the least common multiple of (48, 80). So we [URL='https://www.mathcelebrity.com/gcflcm.php?num1=48&num2=80&num3=&pl=GCF+and+LCM']type this in our search engine[/URL], and we get:
240.
So 240 seconds is our next common meeting point for each air horn.
When we [URL='https://www.mathcelebrity.com/timecon.php?quant=240&pl=Calculate&type=second']type 240 seconds into our search engine[/URL], we get 4 minutes.
We add the 4 minutes to the 5:00 pm time to get [B]5:04 pm[/B].

An analysis of the final test scores for Managerial Decision Making Tools reveals the scores follow

An analysis of the final test scores for Managerial Decision Making Tools reveals the scores follow the normal probability distribution. The mean of the distribution is 75 and the standard deviation is 8. The instructor wants to award an "A" to students whose score is in the highest 10 percent. What is the dividing point for those students who earn an "A"?
Top 10% is equivalent to the 90th percentile.
Using our [URL='http://www.mathcelebrity.com/percentile_normal.php?mean=+75&stdev=8&p=+90&pl=Calculate+Percentile']percentile calculator[/URL], the 90th percentile cutoff point is [B]85.256[/B]

Annie got a new video game. She scored 152 points on the first level, 170 points on the second level

Annie got a new video game. She scored 152 points on the first level, 170 points on the second level, 188 points on the third level, and 206 points on the fourth level. What kind of sequence is this?
This is an [URL='https://www.mathcelebrity.com/sequenceag.php?num=152%2C170%2C188%2C206&n=10&pl=Calculate+Series&a1=&d=']arithmetic series as seen on our calculator[/URL]:

B is the midpoint of AC and BC=5

B is the midpoint of AC and BC=5
Since the midpoint divides a segment into two equal segments, we know that:
AB = BC
So AB =[B] 5[/B]
And AC = 5 + 5 = [B]10[/B]

b more points than 75

b more points than 75
Let b be the number of points
b + 75

Bearing

Free Bearing Calculator - Takes a bearing and lists the steps needed to get from Point A to Point B using that bearing.

Break Even

Free Break Even Calculator - Given a fixed cost, variable cost, and revenue function or value, this calculates the break-even point

C is the midpoint of BD then BC congruent CD

C is the midpoint of BD then BC congruent CD
[URL='https://www.mathcelebrity.com/proofs.php?num=cisthemidpointofbd&pl=Prove']True using this proof[/URL]

Caleb earns points on his credit card that he can use towards future purchases.

Caleb earns points on his credit card that he can use towards future purchases. He earns four points per dollar spent on flights, two points per dollar spent on hotels, and one point per dollar spent on all other purchases. Last year, he charged a total of $9,480 and earned 14,660 points. The amount of money spent on flights was $140 money than twice the amount of money spent on hotels. Find the amount of money spent on each type of purchase.

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?

Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to

Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to 4x + y = 8 through (4, 3).
Step 1: Find the slope of the line 4x + y = 8.
In y = mx + b form, we have y = -4x + 8.
The slope is -4.
To be perpendicular to a line, the slope must be a negative reciprocal of the line it intersects with.
Reciprocal of -4 = -1/4
Negative of this = -1(-1/4) = 1/4
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=4&yone=3&slope=+0.25&xtwo=3&ytwo=2&bvalue=+&pl=You+entered+1+point+and+the+slope']slope calculator[/URL], we get [B]y = 1/4x + 2[/B]

Chord

Free Chord Calculator - Solves for any of the 3 items in the Chord of a Circle equation, Chord Length (c), Radius (r), and center to chord midpoint (t).

Collinear Points that form Unique Lines

Free Collinear Points that form Unique Lines Calculator - Solves the word problem, how many lines can be formed from (n) points no 3 of which are collinear.

Corvettes are known as sporty cars that can travel at high rates of speed. It is therefore assumed t

Corvettes are known as sporty cars that can travel at high rates of speed. It is therefore assumed that they are much more dangerous than minivans. An owner of a Corvette points out that when statistics are studied, there are far more deaths each year from crashes that involve minivans than crashes that involve Corvettes, so Corvettes, so Corvettes must be safer than minivans. The statistics the Covert owner sites are correct. Is his logic faulty? Why or why not?
[B]Faulty.[/B]
There are hundreds of times more minivans on the road than Corvettes, so we expect more deaths even if they are the safest car on the road.

Does the point (0, 3) satisfy the equation y = x?

Does the point (0, 3) satisfy the equation y = x?
Plug in our values of x = 0 and y = 3:
3 = 0
This is false, so the point (0,3) does [B]not satisfy[/B] the equation y = x

Does the point (2, 4) satisfy the equation y = 2x?

Does the point (2, 4) satisfy the equation y = 2x?
Plug in x = 2 to y = 2x:
y = 2(2)
y = 4
[B]Yes, the point (2,4) satisfies the equation y = 2x[/B]

Does the point (3, 0) satisfy the equation y = x?

Does the point (3, 0) satisfy the equation y = x?
plug in x = 3 and y = 0 into y = x
0 = 3 which is [B]false. No, it doesn't satisfy the equation[/B]

does the point (3,0) line on the line y=3x

does the point (3,0) line on the line y=3x
Substitute the x value of (x,y) = (3,0) into y = 3x:
y = 3(3)
y = 9
Since y = 9 and y <> 0, then no, this point [B]does not[/B] lie on the line

During a game, a basketball team scored 38 points worth of two-pointers, 33 points worth of three-po

During a game, a basketball team scored 38 points worth of two-pointers, 33 points worth of three-pointers, and 8 points worth of free throws. How many shots did the basketball team make during the game? shots (Hint: A free throw is worth one point).
[U]Calculate two-point shots:[/U]
Two-point shots = Two Pointers / 2
Two-point shots = 38/2
Two-point shots = 19
[U]Calculate three-point shots:[/U]
Three-point shots = Three Pointers / 2
Three-point shots = 33/3
Three-point shots = 11
[U]Calculate free-throw shots:[/U]
Free throw shots = Free throws / 1
Free throw shots = 8/1
Free throw shots = 8
[U]Calculate total shots:[/U]
Total shots = Two-point shots + three-point shots + free throws
Total shots = 19 + 11 + 8
Total shots = [B]38[/B]

Each unit on a map of a forest represents 1 mile. To the nearest tenth of a mile, what is the distan

Each unit on a map of a forest represents 1 mile. To the nearest tenth of a mile, what is the distance from a ranger station at (1, 2) on the map to a river crossing at (2, 4) ?
We use our 2 point calculator and we get a distance of 2.2361.
Since each unit represents 1 mile, we have:
2.2361 units * 1 mile per unit = [B]2.2361 miles[/B]

Ellipses

Free Ellipses Calculator - Given an ellipse equation, this calculates the x and y intercept, the foci points, and the length of the major and minor axes as well as the eccentricity.

Equation of a Plane

Free Equation of a Plane Calculator - Given three 3-dimensional points, this calculates the equation of a plane that contains those points.

Evan scored 34 points in a basketball game. 21 of the points were from 3-point shots and the rest we

Evan scored 34 points in a basketball game. 21 of the points were from 3-point shots and the rest were free-throws. What expression shows the points scored from free-throws?
Calculate the points from free throws (f):
f = 34 - 21
f = [B]13[/B]

Find a linear function f, given f(16)=-2 and f(-12)=-9. Then find f(0)

Find a linear function f, given f(16)=-2 and f(-12)=-9. Then find f(0).
We've got 2 points:
(16, -2) and (-12, -9)
Calculate the slope (m) of this line using:
m = (y2 - y1)/(x2 - x1)
m = (-9 - -2)/(-12 - 16)
m = -7/-28
m = 1/4
The line equation is denoted as:
y = mx + b
Let's use the first point (x, y) = (16, -2)
-2 = 1/4(16) + b
-2 = 4 + b
Subtract 4 from each side, and we get:
b = -6
So our equation of the line is:
y = 1/4x - 6
The questions asks for f(0):
y = 1/4(0) - 6
y = 0 - 6
[B]y = -6[/B]

Find an equation of the line containing the given pair of points (1,5) and (3,6)

Find an equation of the line containing the given pair of points (1,5) and (3,6).
Using our[URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=5&slope=+2%2F5&xtwo=3&ytwo=6&pl=You+entered+2+points'] point slope calculator[/URL], we get:
[B]y = 1/2x + 9/2[/B]

Find Requested Value

Physiologists often use the forced vital capacity as a way to assess a person's ability to move air in and out of their lungs. A researcher wishes to estimate the forced vital capacity of people suffering from asthma. A random sample of 15 asthmatics yields the following data on forced vital capacity, in liters.
5.2 4.9 2.9 5.3 3.0
4.0 5.2 5.2 3.2 4.7
3.2 3.5 4.8 4.0 5.1
Use the data to obtain a point estimate of the mean forced vital capacity for all asthmatics

Find the distance between (1,2,3) and (7,5,5)

[URL='https://www.mathcelebrity.com/3dist.php?xone=1&yone=2&zone=3&xtwo=7&ytwo=5&ztwo=5&pl=Distance+between+3-D+points']Use our distance calculator[/URL]
[MEDIA=youtube]BbU23Cz1nAE[/MEDIA]

Find the distance between the points (10,7) and (6,10)

Find the distance between the points (10,7) and (6,10).
[URL='https://www.mathcelebrity.com/slope.php?xone=10&yone=7&slope=+2%2F5&xtwo=6&ytwo=10&pl=You+entered+2+points']Using our two-points calculator[/URL], we get a distance of [B]5[/B].

Find the midpoint of the set of points (4,4) and (0,6)

Find the midpoint of the set of points (4,4) and (0,6)
We [URL='https://www.mathcelebrity.com/slope.php?xone=4&yone=4&slope=+2%2F5&xtwo=0&ytwo=6&pl=You+entered+2+points']type in (4,4) and (0,6) into our search engine [/URL]and we get:
Midpoint = [B](2, 5)[/B]

Find y if the line through (1, y) and (2, 7) has a slope of 4.

Find y if the line through (1, y) and (2, 7) has a slope of 4.
Given two points (x1, y1) and (x2, y2), Slope formula is:
slope = (y2 - y1)/(x2 - x1)
Plugging in our coordinates and slope to this formula, we get:
(7 - y)/(2 - 1) = 4
7 - y/1 = 4
7 - y = 4
To solve this equation for y, w[URL='https://www.mathcelebrity.com/1unk.php?num=7-y%3D4&pl=Solve']e type it in our search engine[/URL] and we get:
y = [B]3[/B]

Functions-Derivatives-Integrals

Free Functions-Derivatives-Integrals Calculator - Given a polynomial expression, this calculator evaluates the following items:

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1^{st} Derivative ƒ'(x) The derivative of your expression will also be evaluated at a point, i.e., ƒ'(1)

3) 2^{nd} Derivative ƒ''(x) The second derivative of your expression will be also evaluated at a point, i.e., ƒ''(1)

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

1) Functions ƒ(x). Your expression will also be evaluated at a point, i.e., ƒ(1)

2) 1

3) 2

4) Integrals ∫ƒ(x) The integral of your expression will also be evaluated on an interval, i.e., [0,1]

5) Using Simpsons Rule, the calculator will estimate the value of ≈ ∫ƒ(x) over an interval, i.e., [0,1]

Grade Point Average (GPA)

Free Grade Point Average (GPA) Calculator - Calculates Grade Point Average (GPA) based on letter grades entered.

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took

Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took four tests. She scored 10 points better on the second test than she did on the first, 20 points better on the third test than on the first, and 30 points better on the fourth test than on the first. If the mean of these four tests was 70, what was her score on the third test?
Givens:
[LIST]
[*]Let the first test score be s:
[*]The second test score is: s + 10
[*]The third test score is: s + 20
[*]The fourth test score is: s + 30
[/LIST]
The mean of the four tests is 70, found below:
Sum of test scores / Number of Tests = Mean
Plugging in our number, we get:
(s + s + 10 + s + 20 + s + 30) / 4 = 70
Cross multiply and simplify:
4s + 60 = 70 * 4
4s + 60 = 280
To [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D280&pl=Solve']solve this equation for s, we type it in our search engine[/URL] and we get:
s = 55
So the third test score:
s + 20 = 55 + 20
[B]75[/B]

Hyperbola

Free Hyperbola Calculator - Given a hyperbola equation, this calculates:

* Equation of the asymptotes

* Intercepts

* Foci (focus) points

* Eccentricity ε

* Latus Rectum

* semi-latus rectum

* Equation of the asymptotes

* Intercepts

* Foci (focus) points

* Eccentricity ε

* Latus Rectum

* semi-latus rectum

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 approximately 68% of the scores lie between 40.7 and 59.9 , then the approximate value of the sta

If approximately 68% of the scores lie between 40.7 and 59.9 , then the approximate value of the standard deviation for the distribution, according to the empirical rule, is
The empirical rule states 68% of the values lie within 1 standard deviation of the mean. The mean is the midpoint of the interval above:
(59.9 + 40.7)/2 = 50.3
Standard deviation is the absolute value of the mean - endpoint
|59.9 - 50.3| = [B]9.6[/B]

If the equation of a line passes through the points (1, 3) and (0, 0), which form would be used to w

If the equation of a line passes through the points (1, 3) and (0, 0), which form would be used to write the equation of the line?
[URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=3&slope=+&xtwo=0&ytwo=0&bvalue=+&pl=You+entered+2+points']Typing (1,3),(0,0) into the search engine[/URL], we get a point-slope form:
[B]y - 3 = 3(x - 1)[/B]
If we want mx + b form, we have:
y - 3 = 3x - 3
Add 3 to each side:
[B]y = 3x[/B]

if the point (.53,y) is on the unit circle in quadrant 1, what is the value of y?

if the point (.53,y) is on the unit circle in quadrant 1, what is the value of y?
Unit circle equation:
x^2 + y^2 = 1
Plugging in x = 0.53, we get
(0.53)^2 + y^2 = 1
0.2809 + y^2 = 1
Subtract 0.2809 from each side:
y^2 = 0.7191
y = [B]0.848[/B]

In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two

In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two grades was 180.
Let the high grade be h and the low grade be l. We're given:
[LIST=1]
[*]h = l + 50
[*]h + l = 180
[/LIST]
Substitute equation (1) into equation (2) for h
l + 50 + l = 180
To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B50%2Bl%3D180&pl=Solve']we type it in our search engine[/URL] and we get:
l = [B]65
[/B]
Now, we take l = 65 and substitute it into equation (1) to solve for h:
h = 65 + 50
h = [B]115[/B]

In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing

In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game?
Let w be the winning team's points, and l be the losing team's points. We have two equations:
[LIST=1]
[*]w + l = 41
[*]w - l = 27
[/LIST]
Add the two equations:
2w = 68
Divide each side by 2
[B]w = 34[/B]
Substitute this into (1)
34 + l = 41
Subtract 34 from each side
[B]l = 7[/B]
Check your work:
[LIST=1]
[*]34 + 7 = 41 <-- check
[*]34 - 7 = 27 <-- check
[/LIST]
The final score of the game was [B]34 to 7[/B].
You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=w+%2B+l+%3D+41&term2=w+-+l+%3D+27&pl=Cramers+Method']simultaneous equation solver[/URL].

In which quadrant is the point (2,negative 6) located?

In which quadrant is the point (2,negative 6) located?
We have the point (2, -6). It lies in Quadrant IV.
to get this, [URL='https://www.mathcelebrity.com/polrectcord.php?num=2%2C-6&pl=Show+Detail#Quadrant']type in (2, -6) to the search engine[/URL], and click "Quadrant".

Is the point (4,7) a solution of the equation yequals15xminus8?

Is the point (4,7) a solution of the equation y equals 15x minus 8?
Plug in x = 4:
15(4) - 8
60 - 8
52
Since 52 <> 4, (4,7) is [U][B]not[/B][/U] a solution of the equation y equals 15x minus 8

Jack scored a mean of 15 points per game in his first 3 basketball games. In his 4th grade, he score

Jack scored a mean of 15 points per game in his first 3 basketball games. In his 4th grade, he scored 27 points. What was Jack's mean score for the four games?
The mean is the average:
Mean = (15 + 15 + 15 + 27)/4
Mean = 72/4
[B]Mean = 18[/B]

Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 point

Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 points
The phrase [I]total[/I] means a sum, so we have the following equation:
15 + p = 34
To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=15%2Bp%3D34&pl=Solve']type this equation into our search engine [/URL]and we get:
p = [B]19[/B]

jane has 55$ to spend at cedar point. the admission price is 42$ and each soda is 4.25. write an ine

jane has 55$ to spend at cedar point. the admission price is 42$ and each soda is 4.25. write an inequality to show how many sodas he can buy.
Let s be the number of sodas.
Cost for the day is:
Price per soda * s + Admission Price
4.25s + 42
We're told that Jane has 55, which means Jane cannot spend more than 55. Jane can spend up to or less than 55. We write this as an inequality using <= 55
[B]4.25s + 42 <= 55[/B]
[B][/B]
If the problems asks you to solve for s, we type it in our math engine and we get:
Solve for [I]s[/I] in the inequality 4.25s + 42 ? 55
[SIZE=5][B]Step 1: Group constants:[/B][/SIZE]
We need to group our constants 42 and 55. To do that, we subtract 42 from both sides
4.25s + 42 - 42 ? 55 - 42
[SIZE=5][B]Step 2: Cancel 42 on the left side:[/B][/SIZE]
4.25s ? 13
[SIZE=5][B]Step 3: Divide each side of the inequality by 4.25[/B][/SIZE]
4.25s/4.25 ? 13/4.25
[B]s ? 3.06[/B]

Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in

Jessica has 16 pairs of shoes. She buys 2 additional pair of shoes every month. What is the slope in this situation?
Set up a graph where months is on the x-axis and number of shoes Jessica owns is on the y-axis.
[LIST=1]
[*]Month 1 = (1, 18)
[*]Month 2 = (2, 20)
[*]Month 3 = (3, 22)
[*]Month 4 = (4, 24)
[/LIST]
You can see for every 1 unit move in x, we get a 2 unit move in y.
Pick any of these 2 points, and [URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=22&slope=+2%2F5&xtwo=4&ytwo=24&pl=You+entered+2+points']use our slope calculator[/URL] to get:
Slope = [B]2[/B]

Jina's test score average decreased by 10 points this semester. Write a signed number to represent t

Jina's test score average decreased by 10 points this semester. Write a signed number to represent this change in average.
Let A be the original average. The new average is:
A + (-10)

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth

Jinas final exam has true/false questions, worth 3 points each, and multiple choice questions, worth 4 points each. Let x be the number of true/false questions she gets correct, and let y be the number of multiple choice questions she gets correct. She needs at least 76 points on the exam to get an A in the class. Using the values and variables given, write an inequality describing this.
At least means greater than or equal to, so we have:
[B]3x + 4y >= 76[/B]

Joanie multiplied 0.78 times 0.34 and got the product 26.52. What error did she make

Joanie multiplied 0.78 times 0.34 and got the product 26.52. What error did she make
[B]She didn't move the decimal point over 2 spots[/B]:
0.78 * 0.34 = 0.2652

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which

Jordan has already scored 153 points this basketball season. If he scores 17 points per game, which inequality represents the number of addional games he needs to play in order to score at least 255 points for the season?
Let g be the number of games Jordan plays. Total points per game is 17g. And he’s already scored 153. So we need 17g + 153 to be [I]at least [/I]255. The phrase at least means greater than or equal to, so we use the >= operator for our inequality:
[B]17g + 153 >= 255[/B]

Jose earned 60 points on a game show. In the next round he lost 64 points then gained 12 points and

Jose earned 60 points on a game show. In the next round he lost 64 points then gained 12 points and at last lost 28 points. What was his score at the end of the show?
Start with 60 points:
60
lose 64 means we subtract 64 from our points
60 - 64 = -4
Gained 12 means we add 12 to our points:
-4 + 12 = 8
Lost 28 means we subtract 28 from our points:
8 - 28 = [B]-20 points[/B]

Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he

Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he must score at least 660 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests, n, in order to get an A.
We want to know n, such that 556 + n >= 660. <-- We use >= symbol since at least means greater than or equal to.
556 + n >= 660
Use our [URL='http://www.mathcelebrity.com/1unk.php?num=556%2Bn%3E%3D660&pl=Solve']equation/inequality calculator[/URL], we get [B]n >= 104[/B]

Juan runs out of gas in a city. He walks 30yards west and then 16 yards south looking for a gas stat

Juan runs out of gas in a city. He walks 30yards west and then 16 yards south looking for a gas station. How far is he from his starting point?
Juan is located on a right triangle. We calculate the hypotenuse:
30^2 + 16^2 = Hypotenuse^2
900 + 256 = Hypotenuse^2
Hypotenuse^2 = 1156
Take the square root of each side:
[B]Hypotenuse = 34 yards[/B]

kelly's test score is 6 points higher than Mike's

kelly's test score is 6 points higher than Mike's
Assumptions:
[LIST]
[*]Let Kelly's test score be k
[*]Let Mike's test score be m
[/LIST]
Higher means we add, so we have
[B]k = m + 6[/B]

Lanette walked forward 9 steps, backward 15 steps, forward 7 steps, and backward 8 steps. How many s

Lanette walked forward 9 steps, backward 15 steps, forward 7 steps, and backward 8 steps. How many steps is lanette from where she started?
We use (+) for forward steps and (-) for backward steps
[LIST]
[*]Forward 9, backward 15 is: +9 - 15 = -6
[*]Forward 7 steps is: -6 + 7 = +1
[*]Backward 8 steps = +1 - 8 = -7
[/LIST]
Since negative is backward and positive is forward, we see Lanette is [B]7 steps backwards [/B]from her starting point.

Lebron James scored 288 points in 9 games this season. Assuming he continues to score at this consta

Lebron James scored 288 points in 9 games this season. Assuming he continues to score at this constant rate, write a linear equation that represents the scenario.
288 points / 9 games = 32 points per game
Let g be the number of games Lebron plays. We build an equation for his season score:
Lebron's Season Score = Points per game * number of games
Lebron's Season Score = [B]32g[/B]

Let A = (-4,5) and B = (1,3) Find the distance from A to B

Let A = (-4,5) and B = (1,3) Find the distance from A to B
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=-4&yone=5&slope=+&xtwo=1&ytwo=3&bvalue=+&pl=You+entered+2+points']distance between two points calculator[/URL], we get:
[B]5.3852[/B]

Line Equation-Slope-Distance-Midpoint-Y intercept

Free Line Equation-Slope-Distance-Midpoint-Y intercept Calculator - Enter 2 points, and this calculates the following:

* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points

* Midpoint of the two points

* Distance between the 2 points

* 2 remaining angles of the rignt triangle formed by the 2 points

* y intercept of the line equation

* Point-Slope Form

* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points

* Midpoint of the two points

* Distance between the 2 points

* 2 remaining angles of the rignt triangle formed by the 2 points

* y intercept of the line equation

* Point-Slope Form

* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

Line m passes through points (3, 16) and (8, 10). Line n is perpendicular to m. What is the slope of

Line m passes through points (3, 16) and (8, 10). Line n is perpendicular to m. What is the slope of line n?
First, find the slope of the line m passing through points (3, 16) and (8, 10).
[URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=16&slope=+2%2F5&xtwo=8&ytwo=10&pl=You+entered+2+points']Typing the points into our search engine[/URL], we get a slope of:
m = -6/5
If line n is perpendicular to m, then the slope of n is denote as:
n = -1/m
n = -1/-6/5
n = -1*-5/6
n = [B]5/6[/B]

Line m passes through points (7, 5) and (9, 10). Line n passes through points (3, 1) and (7, 10). Ar

Line m passes through points (7, 5) and (9, 10). Line n passes through points (3, 1) and (7, 10). Are line m and line n parallel or perpendicular
[U]Slope of line m is:[/U]
(y2 - y1)/(x2 - x1)
(10 - 5)/(9 - 7)
5/2
[U]Slope of line n is:[/U]
(y2 - y1)/(x2 - x1)
(10 - 1)/(7 - 3)
9/4
Run 3 checks on the slopes:
[LIST=1]
[*]Lines that are parallel have equal slopes. Since 5/2 does not equal 9/4, these lines [B]are not parallel[/B]
[*]Lines that are perpendicular have negative reciprocal slopes. Since 9/4 is not equal to -2/5 (the reciprocal of the slope of m), these lines [B]are not perpendicular[/B]
[*][B]Therefore, since the lines are not parallel and not perpendicular[/B]
[/LIST]

M is the midpoint of AB. Prove AB = 2AM

M is the midpoint of AB. Prove AB = 2AM
M is the midpoint of AB (Given)
AM = MB (Definition of Congruent Segments)
AM + MB = AB (Segment Addition Postulate)
AM + AM = AB (Substitution Property of Equality)
2AM = AB (Distributive property)
[MEDIA=youtube]8BNo_4kvBzw[/MEDIA]

m is the midpoint of cf for points c(3,4) and f(9,8). Find MF

m is the midpoint of cf for points c(3,4) and f(9,8). Find MF
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=4&slope=+2%2F5&xtwo=9&ytwo=8&pl=You+entered+2+points']line equation and midpoint calculator[/URL], we get:
MF = [B](6, 6)[/B]

Midpoint formula

Midpoint formula
Given two points (x1, y1) and (x2, y2), the midpoint is found as the average distance between the 2 points:
[LIST]
[*]x value is: (x1 + x2)/2
[*]y value is: (y1 + y2)/2
[/LIST]
So our midpoint is:
((x1 + x2)/2, (y1 + y2)/2)

Mount McKinley in Alaska, the highest mountain in North America, is 20,320 feet above sea level. Dea

Mount McKinley in Alaska, the highest mountain in North America, is 20,320 feet above sea level. Death Valley, the lowest point, is 280 feet below sea level. What is the difference in height between Mount McKinley and Death Valley?
Regarding height with respect to sea level...
[LIST]
[*]Above sea level is written as positive height
[*]Below sea level is written as negative height
[/LIST]
So we have:
+20,320 - -280
+20,320 + 280
[B]20,600[/B]

Noah scores 20 points. Mai’s score was 30 points. The mean for Noah’s, Mia’s, and Clare’s was 40 poi

Noah scores 20 points. Mai’s score was 30 points. The mean for Noah’s, Mia’s, and Clare’s was 40 points. What was Clare’s score?
[URL='https://www.mathcelebrity.com/missingaverage.php?num=20%2C30&avg=40&pl=Calculate+Missing+Score']Using our missing average calculator[/URL], Claire's score was [B]70[/B].

Number Line

Free Number Line Calculator - Counts from a point going left and right on a number line

Number Line Midpoint

Free Number Line Midpoint Calculator - Calculates a midpoint between 2 points on a number line or finds the second endpoint if one endpoint and midpoint are given.

On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two

On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. Find the lowest grade.
[U]Let h be the highest grade and l be the lowest grade. Set up the given equations:[/U]
(1) h = l + 42
(2) h + l = 138
[U]Substitute (1) into (2)[/U]
l + 42 + l = 138
[U]Combine l terms[/U]
2l + 42 = 138
[U]Enter that equation into our [URL='http://www.mathcelebrity.com/1unk.php?num=2l%2B42%3D138&pl=Solve']equation calculator[/URL] to get[/U]
[B]l = 48
[/B]
[U]Substitute l = 48 into (1)[/U]
h = 48 + 42
[B]h = 90[/B]

Ordered Pair

Free Ordered Pair Calculator - This calculator handles the following conversions:

* Ordered Pair Evaluation and symmetric points including the abcissa and ordinate

* Polar coordinates of (r,θ°) to Cartesian coordinates of (x,y)

* Cartesian coordinates of (x,y) to Polar coordinates of (r,θ°)

* Quadrant (I,II,III,IV) for the point entered.

* Equivalent Coordinates of a polar coordinate

* Rotate point 90°, 180°, or 270°

* reflect point over the x-axis

* reflect point over the y-axis

* reflect point over the origin

* Ordered Pair Evaluation and symmetric points including the abcissa and ordinate

* Polar coordinates of (r,θ°) to Cartesian coordinates of (x,y)

* Cartesian coordinates of (x,y) to Polar coordinates of (r,θ°)

* Quadrant (I,II,III,IV) for the point entered.

* Equivalent Coordinates of a polar coordinate

* Rotate point 90°, 180°, or 270°

* reflect point over the x-axis

* reflect point over the y-axis

* reflect point over the origin

Pick's Theorem

Free Pick's Theorem Calculator - This calculator determines the area of a simple polygon using interior points and boundary points using Pick's Theorem

Plane and Parametric Equations in R

Free Plane and Parametric Equations in R^{3} Calculator - Given a vector A and a point (x,y,z), this will calculate the following items:

1) Plane Equation passing through (x,y,z) perpendicular to A

2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

1) Plane Equation passing through (x,y,z) perpendicular to A

2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A

Point and a Line

Free Point and a Line Calculator - Enter any line equation and a 2 dimensional point. The calculator will figure out if the point you entered lies on the line equation you entered. If the point does not lie on the line, the distance between the point and line will be calculated.

Point Estimate and Margin of Error

Free Point Estimate and Margin of Error Calculator - Given an upper bound and a lower bound and a sample size, this calculate the point estimate, margin of error.

Point P is located at -15 and point Q is located at 6 on a number line. Which value would represent

Point P is located at -15 and point Q is located at 6 on a number line. Which value would represent point T, the midpoint of PQ?
Using our [URL='https://www.mathcelebrity.com/mptnline.php?ept1=-15&empt=&ept2=6&pl=Calculate+missing+Number+Line+item']midpoint calculator[/URL], we get:
T = [B]-4.5[/B]

Points A, B, and C are collinear. Point B is between A and C. Find AB if AC=15 and BC=7.

Points A, B, and C are collinear. Point B is between A and C. Find AB if AC=15 and BC=7.
Collinear means on the same line.
By segment subtraction, we have:
AB = AC - BC
AB = 15 - 7
AB = [B]8[/B]

PRIVATE SAT TUTORING - LIVE FACE-TO-FACE SKYPE TUTORING

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Every SAT expert scored at least a 1500/1600 on the SAT and comes from the country’s top schools like Princeton, Johns Hopkins, and Georgetown. After only 10 sessions our average student improves 120 points.
Our success comes from the individual attention we give our students. Our strategies give them confidence to succeed, plus we coach them through the SAT by creating a structured study plan. Working with our expert tutors, our students achieve amazing SAT success.
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Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?

Q is a point on segment PR. If PQ = 2.7 and PR = 6.1, what is QR?
From segment addition, we know that:
PQ + QR = PR
Plugging our given numbers in, we get:
2.7 + QR = 6.1
Subtract 2.7 from each side, and we get:
2.7 - 2.7 + QR = 6.1 - 2.7
Cancelling the 2.7 on the left side, we get:
QR = [B]3.4[/B]

Quadrilateral

Free Quadrilateral Calculator - 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.

Relative Coordinates

Free Relative Coordinates Calculator - Given a starting point (x_{1},y_{1}), this will determine your relative coordinates after moving up, down, left, and right.

Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more poi

Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more points than Eleanor. What were Eleanor and Rigby's scores?
Let Rigby's score be r
Let Eleanor's score be e
We're given two equations:
[LIST=1]
[*]r = e + 9
[*]e + r = 181
[/LIST]
Substitute equation (1) into equation (2):
e + (e + 9) = 181
Group like terms:
2e + 9 = 181
To solve this equation for e, we [URL='https://www.mathcelebrity.com/1unk.php?num=2e%2B9%3D181&pl=Solve']type it in our search engine[/URL] and we get:
e = [B]86[/B]

Six less than twice a number is at least -1 and at most 1

First, the phrase [I]a number[/I] means we choose an arbitrary variable, let's call it x.
Twice a number means we multiply it by 2.
2x
Six less than that means we subtract 6
2x - 6
Now, the last piece, we set up an inequality. At least -1 means greater than or equal to 1. At most 1 means less than or equal to 1. Notice, for both points, we include the number.
-1 <= 2x - 6 <= 1

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 c

Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point.
Calculate the revenue function R(c) where s is the number of sodas sold:
R(s) = Sale Price * number of units sold
R(s) = 50s
Calculate the cost function C(s) where s is the number of sodas sold:
C(s) = Variable Cost * s + Fixed Cost
C(s) = 0.25s + 900
Our break-even point is found by setting R(s) = C(s):
0.25s + 900 = 50s
We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get:
s = [B]18.09[/B]

Statistics Summary

Free Statistics Summary Calculator - This is a summary of formulas, pointers, and decision trees for statistics.

Stop Your Math Homework at THIS moment

Use the Ziegarnik Effect to find the perfect breaking point for your math homework.
[MEDIA=youtube]PtllyMvRE6M[/MEDIA]

Suppose that the manager of the Commerce Bank at Glassboro determines that 40% of all depositors hav

Suppose that the manager of the Commerce Bank at Glassboro determines that 40% of all depositors have a multiple accounts at the bank. If you, as a branch manager, select a random sample of 200 depositors, what is the probability that the sample proportion of depositors with multiple accounts is between 35% and 50%?
[URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=50&n=+100&ptype==&p=+0.4&alpha=+0.05&pl=Proportion+Hypothesis+Testing']50% proportion probability[/URL]: z = 2.04124145232
[URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+35&n=+100&ptype==&p=+0.4&alpha=+0.05&pl=Proportion+Hypothesis+Testing']35% proportion probability[/URL]: z = -1.02062072616
Now use the [URL='http://www.mathcelebrity.com/zscore.php?z=p%28-1.02062072616

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognit

The brand manager for a brand of toothpaste must plan a campaign designed to increase brand recognition. He wants to first determine the percentage of adults who have heard of the bran. How many adults must he survey in order to be 90% confident that his estimate is within seven percentage points of the true population percentage?
[IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5
1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] = 0.5
margin of error (E) = 0.07
At 90% confidence level the t is,
alpha = 1 - 90%
alpha = 1 - 0.90
alpha = 0.10
alpha / 2 = 0.10 / 2 = 0.05
Zalpha/2 = Z0.05 = 1.645
sample size = n = (Z[IMG]https://ci4.googleusercontent.com/proxy/mwhpkw3aM19oMNA4tbO_0OdMXEHt9juW214BnNpz4kjXubiVJgwolO7CLbmWXXoSVjDPE_T0CGeUxNungBjN=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Calpha[/IMG] / 2 / E )2 * [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] * (1 - [IMG]https://ci5.googleusercontent.com/proxy/kc6cjrLvUq64guMaArhfiSR0mOnTrBwB9iFM9u9VaZ5YYn86CSDWXr1FNyqxylwytHdbQ3iYsUDnavt-zvt-OK0=s0-d-e1-ft#http://latex.codecogs.com/gif.latex?%5Chat%20p[/IMG] )
= (1.645 / 0.07)^2 *0.5*0.5
23.5^2 * 0.5 * 0.5
552.25 * 0.5 * 0.5
= 138.06
[B]sample size = 138[/B]
[I]He must survey 138 adults in order to be 90% confident that his estimate is within seven percentage points of the true population percentage.[/I]

The distance between X and 8 is less than 14

Distance implies the positive difference between 2 points. Therefore, we use absolute value:
|x - 8| < 14
Note, we use less than since 14 is not included.

The function f(x) = e^x(x - 3) has a critical point at x =

The function f(x) = e^x(x - 3) has a critical point at x =
The critical point is where the derivative equals 0.
We multiply through for f(x) to get:
f(x) = xe^x - 3e^x
Using the product rule on the first term f'g + fg', we get:
f'(x) = xe^x + e^x - 3e^x
f'(x) = xe^x -2e^x
f'(x) = e^x(x - 2)
We want f'(x) = 0
e^x(x - 2) = 0
When [B]x = 2[/B], then f'(x) = 0

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 mon

The graph shows the average length (in inches) of a newborn baby over the course of its first 15 months. Interpret the RATE OF CHANGE of the graph.
[IMG]http://www.mathcelebrity.com/community/data/attachments/0/rate-of-change-wp.jpg[/IMG]
Looking at our graph, we have a straight line. For straight lines, rate of change [U][I]equals[/I][/U] slope.
Looking at a few points, we have:
(0, 20), (12, 30)
Using our [URL='https://www.mathcelebrity.com/slope.php?xone=0&yone=20&slope=+2%2F5&xtwo=12&ytwo=30&pl=You+entered+2+points']slope calculator for these 2 points[/URL], we get a slope (rate of change) of:
[B]5/6[/B]

The Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39

The Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39 baskets total, how many of each basket did they make?
Let x = 2 point baskets and y = 3 point baskets. We have the following given equations:
[LIST=1]
[*]x + y = 39
[*]2x + 3y = 81
[/LIST]
Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=x%2By%3D39&term2=2x+%2B+3y+%3D+81&pl=Cramers+Method']simultaneous equations calculator[/URL], we get:
[B]x = 36 <-- 2 point baskets
y = 3 <-- 3[B] point baskets
[/B][/B]
To confirm our work:
[LIST=1]
[*]36 + 3 = 39
[*]2(36) + 3(3) = 72 + 9 = 81
[/LIST]

the midpoint between m and n

the midpoint between m and n
The [I]midpoint is halfway between[/I] m and n:
[B](m + n)/2[/B]

The point (1,5) is a solution to the equation 2y - x = 9

The point (1,5) is a solution to the equation 2y - x = 9
[B]Yes[/B], because:
2(5) - 1 ? 9
10 - 1 ? 9
9 = 9

The points -5, -24 and 5,r lie on a line with slope 4. Find the missing coordinate r. Slope = (y2 -

The points -5, -24 and 5,r lie on a line with slope 4. Find the missing coordinate r.
Slope = (y2 - y1)/(x2 - x1)
Plugging in our numbers, we get:
4 = (r - -24)/(5 - -5)
4 = (r +24)/10
Cross multiply:
r + 24 = 40
Subtract 24 from each side:
[B]r = 16[/B]

The points 6,4 and 9,r lie on a line with slope 3. Find the missing coordinate r.

The points 6,4 and 9,r lie on a line with slope 3. Find the missing coordinate r.
Slope = (y2 - y1)/(x2 - x1)
Plugging in our numbers, we get:
3 = (r - 4)/(9 - 6)
3 = (r - 4)/3
Cross multiply:
r - 4 = 9
Add 4 to each side:
[B]r = 13[/B]

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for

The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point.
[U]Calculate cost function C(b) with b as the number of books:[/U]
C(b) = Cost per book * b + Overhead
[B]C(b) = 15b + 5500[/B]
[U]Calculate Revenue Function R(b) with b as the number of books:[/U]
R(b) = Sales Price per book * b
[B]R(b) = 40b[/B]
[U]Calculate break even function E(b):[/U]
Break-even Point = Revenue - Cost
Break-even Point = R(b) - C(b)
Break-even Point = 40b - 15b - 5500
Break-even Point = 25b - 5500
[U]Calculate break even point:[/U]
Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0
25b - 5500 = 0
To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-5500%3D0&pl=Solve']type this equation into our search engine[/URL] and we get:
[B]b = 220[/B]

The team A scored 13 more points than Team B. The total of their score was 47. How many points did t

The team A scored 13 more points than Team B. The total of their score was 47. How many points did team A score?
Let a be the amount of points A scored, and b be the amount of points B scored. We're given:
[LIST=1]
[*]a = b + 13
[*]a + b = 47
[/LIST]
Plug (1) into (2)
(b + 13) + b = 47
Combine like terms:
2b + 13 = 47
[URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B13%3D47&pl=Solve']Typing this equation into our search engine[/URL], we get:
b = 17
Now plug this into (1):
a = 17 + 13
a = [B]30[/B]

Triangle Coordinate Items

Free Triangle Coordinate Items Calculator - Enter 3 points for the vertices of a triangle, and this will calculate the area of that triangle and the centroid.

Triangle KLM has vertices at . k(-2,-2), l(10,-2), m(4,4) What type of triangle is KLM?

Triangle KLM has vertices at . k(-2,-2), l(10,-2), m(4,4) What type of triangle is KLM?
[URL='https://www.mathcelebrity.com/slope.php?xone=-2&yone=-2&slope=+2%2F5&xtwo=10&ytwo=-2&pl=You+entered+2+points']Side 1: KL[/URL] = 12
[URL='https://www.mathcelebrity.com/slope.php?xone=10&yone=-2&slope=+2%2F5&xtwo=4&ytwo=4&pl=You+entered+2+points']Side 2: LM[/URL] = 8.4853
[URL='https://www.mathcelebrity.com/slope.php?xone=-2&yone=2&slope=+2%2F5&xtwo=4&ytwo=4&pl=You+entered+2+points']Side 3: KM[/URL] = 6.3246
Then, we want to find the type of triangle. Using our [URL='https://www.mathcelebrity.com/tribasic.php?side1input=12&side2input=8.4853&side3input=6.3246&angle1input=&angle2input=&angle3input=&pl=Solve+Triangle']triangle solver with our 3 sides[/URL], we get:
[B]Obtuse, Scalene[/B]

what is 828 rounded to the nearest hundred

what is 828 rounded to the nearest hundred
828 lies between 800 and 900.
The halfway point is 850, so 828 rounds down to [B]800[/B]

What is a Point

Free What is a Point Calculator - This lesson walks you through what a point is and the various implications of a point in geometry

What is a Segment

Free What is a Segment Calculator - This lesson walks you through what a segment is and the various implications of a segment in geometry including the midpoint of a segment.

What is the slope of the line through (1,9) and (5,3)

What is the slope of the line through (1,9) and (5,3)
[URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=9&slope=+2%2F5&xtwo=5&ytwo=3&pl=You+entered+2+points']We run this through our slope calculator[/URL], and get an initial slope of 6/4.
But this is not in simplest form. So we type 6/4 into our calculator, and s[URL='https://www.mathcelebrity.com/fraction.php?frac1=6%2F4&frac2=3%2F8&pl=Simplify']elect the simplify option[/URL].
We get [B]3/2[/B]

What is the X coordinate of the point (6, 19)

What is the X coordinate of the point (6, 19)
Using our [URL='https://www.mathcelebrity.com/ordered-pair.php?num=6%2C19&pl=Show+Detail']ordered pair calculator[/URL], we see that the x coordinate is [B]6[/B]

What number is half between 1.24 and 1.8?

What number is half between 1.24 and 1.8?
Halfway between two points is called the midpoint.
Using out [URL='http://www.mathcelebrity.com/mptnline.php?ept1=1.24&empt=&ept2=1.8&pl=Calculate+missing+Number+Line+item']midpoint calculator[/URL], we get 1.52:

Which of the following descriptions of confidence interval is correct? (Select all that apply) a. I

Which of the following descriptions of confidence interval is correct? (Select all that apply)
a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
b. If a 95% confidence interval contains 0, then the 99% confidence interval contains 0
c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
d. If a 95% confidence interval contains 1, then the 99% confidence interval contains 1
[B]a. If a 99% confidence interval contains 0, then the 95% confidence interval contains 0
c. If a 99% confidence interval contains 1, then the 95% confidence interval contains 1
[/B]
[I]The lower the confidence interval, the wider the range, so if a higher confidence interval contains a point, a lower confidence interval will contain that point as well.[/I]

You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $1

You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $15 each and you paid $6.50 a piece plus a $50 set-up fee and $25 for shipping. How many shirts do you have to sell to break even? Round to the nearest whole number.
[U]Step 1: Calculate Your Cost Function C(s) where s is the number of t-shirts[/U]
C(s) = Cost per Shirt * (s) Shirts + Set-up Fee + Shipping
C(s) = $6.50s + $50 + $25
C(s) = $6.50s + 75
[U]Step 2: Calculate Your Revenue Function R(s) where s is the number of t-shirts[/U]
R(s) = Price Per Shirt * (s) Shirts
R(s) = $15s
[U]Step 3: Calculate Break-Even Point[/U]
Break Even is where Cost = Revenue. Set C(s) = R(s)
$6.50s + 75 = $15s
[U]Step 4: Subtract 6.5s from each side[/U]
8.50s = 75
[U]Step 5: Solve for s[/U]
[URL='https://www.mathcelebrity.com/1unk.php?num=8.50s%3D75&pl=Solve']Run this through our equation calculator[/URL] to get s = 8.824. We round up to the next integer to get [B]s = 9[/B].
[B][URL='https://www.facebook.com/MathCelebrity/videos/10156751976078291/']FB Live Session[/URL][/B]

You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $

You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $2 for a ticket. Write an expression for the total cost of going to Cedar Point where r is the number of rides.
Set up the cost equation C(r):
C(r) = Cost per ride * r rides + Park Fee
[B]C(r) = 2r + 50[/B]

You are using a spinner with the numbers 1-10 on it. Find the probability that the pointer will sto

You are using a spinner with the numbers 1-10 on it. Find the probability that the pointer will stop on an odd number or a number less than 4.
We want P(odd number) or P(n<4).
[LIST]
[*]Odd numbers are {1, 3, 5, 7, 9}
[*]n < 4 is {1, 2, 3}
[/LIST]
We want the union of these 2 sets:
{1, 2, 3, 5, 7, 9}
We have 6 possible pointers in a set of 10.
[B]6/10 = 3/5 = 0.6 or 60%[/B]

you start at a point on the number line and move 4 units left. If you are now at 10, then what was y

you start at a point on the number line and move 4 units left. If you are now at 10, then what was your original point?
Work backwards. If we're at 10, and we moved left, this means we add 4 to get back to our starting point:
10 + 4 = [B]14[/B]