line - an infinitely long one-dimensional object with no width, depth, or curvature

(3,-4) lies on the line with equation 3x-2y=k, find k

(3,-4) lies on the line with equation 3x-2y=k, find k
Plug in our values:
3(3) -2(-4) = k
9 + 8 = k
k = [B]17[/B]

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]

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

225 lines per second how many per minute

225 lines per second how many per minute
There are 60 seconds in 1 minute, so we have:
225 lines 60 seconds
---------- * --------------
1 second 1 minute
Cancel the second from top and bottom, and we have:
[B]13,500 lines
---------------
1 minute[/B]

A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation

A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 654,000 ? 1800x dollars. After how many months will the value of the building be $409,200?
We want to know x for the equation:
654000 - 1800x = 409200
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=654000-1800x%3D409200&pl=Solve']type it in our math engine[/URL] and we get:
x = [B]136 months[/B]

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6

A 1.5 inch tall preying mantis will sometimes hold its ground and attempt to fight a person who is 6 feet tall. If a person who is 6 feet tall is engaged in a battle with an animal that was proportionally as tall as the person is to the preying mantis, how tall would the animal be?
In terms of inches, [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']6 feet = 72 inches[/URL]
Set up a proportion of height of smaller creature to larger creature where h is the heigh of the animal
1.5/72 = 72/h
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=1.5&num2=72&den1=72&den2=h&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator[/URL], we get:
h = 3456 inches
In terms of feet, we have [URL='https://www.mathcelebrity.com/linearcon.php?quant=3456&pl=Calculate&type=inch']3456 inches[/URL] = [B]288 feet[/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 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of t

A 50-foot pole and a 70-foot pole are 30 feet apart. If you were to run a line between the tops of the two poles, what is the minimum length of cord you would need?
The difference between the 70 foot and 50 foot pole is:
70 - 50 = 20 foot height difference.
So we have a right triangle, with a height of 20, base of 30. We want to know the hypotenuse.
Using our [URL='https://www.mathcelebrity.com/pythag.php?side1input=20&side2input=30&hypinput=&pl=Solve+Missing+Side']Pythagorean theorem calculator to solve for hypotenuse[/URL], we get:
hypotenuse = [B]36.06 feet[/B]

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch?

A 7-foot piece of cotton cloth costs $3.36. What is the price per inch?
Using [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']our length converter[/URL], we see that:
7 feet = 84 inches
So $3.36 for 84 inches. We [URL='https://www.mathcelebrity.com/perc.php?num=3.36&den=84&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']divide $3.36 by 84[/URL] to get the cost per inch:
$3.36/84 = [B]0.04 per inch[/B]

A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model tha

A bakery sells 5800 muffins in 2010. The bakery sells 7420 muffins in 2015. Write a linear model that represents the number y of muffins that the bakery sells x years after 2010.
Find the number of muffins sold after 2010 through 2015:
7,420 - 5,800 = 1,620
Now, since the problem states a linear sales model, we need to determine the sales per year:
1,620 muffins sold since 2010 / 5 years = 324 muffins per year.
Build our linear model:
[B]y = 5,800 + 324x
[/B]
Reading this out loud, we start with 5,800 muffins at the end of 2010, and we add 324 more muffins for each year after 2010.

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many dif

A baseball team has 25 total players consisting of 15 position players and 10 pitchers. How many different ways are there to arrange the batting order of 9 starting players if only one pitcher is used at a time and the pitcher always bats last.
(This means that 8 players are taken from the position players and one pitcher is then added at the end of the lineup.)
First 8 positions:
[URL='https://www.mathcelebrity.com/permutation.php?num=15&den=8&pl=Permutations']15P8[/URL] = 259,459,200
For the pitcher, we can have 10 different possibilities for the 9th player:
259,459,200 x 10 = [B]2,594,592,000 ways[/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 Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The b

A Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The bouquet costs $32. Write and solve a system of linear equations to find the number of lillies and tulips in the bouquet.
Let l be the number of lillies and t be the number of tulips. We're given 2 equations:
[LIST=1]
[*]l + t = 12
[*]3l + 2t = 32
[/LIST]
With this system of equations, we can solve it 3 ways.
[LIST]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Substitution']Substitution Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Elimination']Elimination Method[/URL]
[*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Cramers+Method']Cramers Rule[/URL]
[/LIST]
No matter which method we choose, we get:
[LIST]
[*][B]l = 8[/B]
[*][B]t = 4[/B]
[/LIST]
[B]Now Check Your Work For Equation 1[/B]
l + t = 12
8 + 4 ? 12
12 = 12
[B]Now Check Your Work For Equation 2[/B]
3l + 2t = 32
3(8) + 2(4) ? 32
24 + 8 ? 32
32 = 32

A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the can

A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the candlestick is 13.4 inches tall. Write and solve a linear equation to find the original height of the candle.
Let h equal the number of hours the candlestick burns. We have a candlestick height equation of C.
C = 13.4 + 0.2(8) <-- We need to add back the 8 hours of candlestick burning
C = 13.4 + 1.6
C = [B]15 inches[/B]

A certain race is a distance of 26 furlongs. How far is the race in (a) miles? (b) yards?

A certain race is a distance of 26 furlongs. How far is the race in (a) miles? (b) yards?
[URL='https://www.mathcelebrity.com/linearcon.php?quant=26&pl=Calculate&type=furlong']We type in [I]26 furlongs[/I] into our search engine[/URL] and we get:
[LIST]
[*][B]3.25 miles[/B]
[*][B]5,720 yards[/B]
[/LIST]

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 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 is planning to manufacture a certain product. The fixed costs will be $474778 and it will

A company is planning to manufacture a certain product. The fixed costs will be $474778 and it will cost $293 to produce each product. Each will be sold for $820. Find a linear function for the profit, P , in terms of units sold, x .
[U]Set up the cost function C(x):[/U]
C(x) = Cost per product * x + Fixed Costs
C(x) = 293x + 474778
[U]Set up the Revenue function R(x):[/U]
R(x) = Sale Price * x
R(x) = 820x
[U]Set up the Profit Function P(x):[/U]
P(x) = Revenue - Cost
P(x) = R(x) - C(x)
P(x) = 820x - (293x + 474778)
P(x) = 820x - 293x - 474778
[B]P(x) = 527x - 474778[/B]

A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with

A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket that costs $19 per ticket. The Web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy?
Let t be the number of tickets. We have the following equation with ticket price, insurance, and flat fee:
167t + 19t + 16 = 1132
Combine like terms:
186t + 16 = 1132
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=186t%2B16%3D1132&pl=Solve']equation calculator[/URL], we have:
[B]t = 6[/B]

a family went to a baseball game. the cost to park the car was $5 AND THE COST PER TICKET WAS $21. W

a family went to a baseball game. the cost to park the car was $5 AND THE COST PER TICKET WAS $21. WRITE A LINEAR FUNCTION IN THE FORM Y=MX+B, FOR THE TOTAL COST OF GOING TO THE BASEBALL GAME,Y, AND THE TOTAL NUMBER PEOPLE IN THE FAMILY,X.
We have:
[B]y = 21x + 5[/B]
Since the cost of each ticket is $21, we multiply this by x, the total number of people in the family.
We add 5 as the cost to park the car, which fits the entire family, and is a one time cost.

A gasoline tank is leaking at a rate of n gallons in t hours. If the gasoline cost $2 per gallon, wh

A gasoline tank is leaking at a rate of n gallons in t hours. If the gasoline cost $2 per gallon, what is the value of the gasoline that will be lost in m minutes?
n gallons / t hours = n/t gallons per hour are leaking
The value of the gas that leaks each hour is $2, so we have:
2n/t dollar per hour is leaking
Value per minute means we divide by 60:
2n/60t
Dividing top and bottom by 2 to simplify, we have:
n/30t
Given m minutes, we multiply to get:
[B]nm/30t[/B]

A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it

A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it take them to eat the food. Write your answer in a linear equation.
Let the number of days be d. We have the following equation:
12d = 250
To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=12d%3D250&pl=Solve']type this equation in our search engine[/URL] and we get:
d = [B]20.833[/B]

A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives

A house valued at 70,000 in 1989 increased in value to 125,000 in 2000. Find a function which gives the value of the house, v, as a function of y, the number of years after 1989.
Let's determine the years:
2000 - 1989 = 11
Let's determine the change in value:
125,000 - 70,000 = 55,000
Assuming a linear progression, we have:
55,000/11 = 5,000 per year increase
[B]y = 70,000 + 5,000v[/B] where v is the number of years after 1989
Plug in 11 to check our work
y = 70,000 + 5,000(11)
y = 70,000 + 55,000
y = 125,000

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 line has a slope of 1/2 and a run of 50. Find the rise of the line.

A line has a slope of 1/2 and a run of 50. Find the rise of the line.
Slope = Rise/Run
We're given a run of 50, so let the rise be r. We have:
r/50 = 1/2
To solve this proportion, we [URL='https://www.mathcelebrity.com/prop.php?num1=r&num2=1&den1=50&den2=2&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get:
r = [B]25[/B]

A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form

A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form
The slope-intercept equation for a line:
y = mx + b where m is the slope
Given m = 7, we have:
y = 7x + b
The y-intercept is found by setting x to 0:
y = 7(0) + b
y = 0 + b
y = b
We're given the y-intercept is -4, so we have:
b = -4
So our slope-intercept equation is:
[B]y = 7x - 4[/B]

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 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 machine has a first cost of 13000 an estimated life of 15 years and an estimated salvage value of

a machine has a first cost of 13000 an estimated life of 15 years and an estimated salvage value of 1000.what is the book value at the end of 9 years?
Using [URL='https://www.mathcelebrity.com/depsl.php?d=&a=13000&s=1000&n=15&t=9&bv=&pl=Calculate']our straight line depreciation calculator[/URL], we get a book value at time 9, B9 of:
[B]5,800[/B]

A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up

A mother duck lines her 13 ducklings up behind her. In how many ways can the ducklings line up?
In position one, we can have any of the 13 ducks.
In position two, we can have 12 ducks, since one has to occupy position one.
We subtract 1 each time until we fill up all 13 positions.
We have:
13 * 12 * 11 * ... * 2 * 1
Or, 13!. [URL='https://www.mathcelebrity.com/factorial.php?num=13!&pl=Calculate+factorial']Typing 13! into our search engine[/URL], we get [B]6,227,020,800[/B] ways the ducklings can line up behind the mother duck.

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age o

A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.
If the baby gains 5 pounds every 2 months, then they gain 5/2 = 2.5 pounds per month. Let x be the number of months old for the baby, we have:
The baby starts at 10 pounds. And every month (x), the baby's weight increases 2.5 pounds. Our equation is:
[B]y = 2.5x + 10[/B]

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of

A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx b that describes the baby's weight.
The baby gains 4 pounds every month, where x is the number of months since birth. The baby boy starts life (time 0) at 6 pounds. So we have
[B]y = 4x + 6[/B]

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of

A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight.
Every month, the baby gains 2/3 of a pound. So we have:
[B]y = 2/3x + 7
[/B]
The baby starts off with 7 pounds. So we add 7 pounds + 2/3 times the number of months passed since birth.

A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear eq

A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear equation to find the total cost to download 30 songs
Set up the cost function C(s) where s is the number of songs:
C(s) = cost per song * s + download fee
Plugging in our numbers for s = 30 and a download fee of $2 and s = 1.29, we have:
C(30) = 1.29(30) + 2
C(30) = 38.7 + 2
C(30) = [B]40.7[/B]

A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear

A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear equation to find the total cost to download 30 songs.
Let the number of songs be s. And the cost function be C(s). We have:
C(s) = Price per song downloaded * s + app download charge
C(s) = 1.29s + 2
The problem asks for C(30):
C(3) = 1.29(30) + 2
C(3) = 38.7 +2
C(3) = $[B]40.7[/B]

a music app charges $5 to download the app plus $1.25 per song downloaded. write linear equation to

a music app charges $5 to download the app plus $1.25 per song downloaded. write linear equation to calculate the cost for x number of songs
With x songs, our Cost equation C(x) is:
C(x) = cost per download * x downloads + app download fee
[B]C(x) = 1.25x + 5[/B]

A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equa

A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equation and a linear equation to find the total cost to download 30 songs
Set up the equation C(d) where d is the number of downloads:
C(d) = cost per download * d + download fee
Plugging in our numbers, we get:
C(d) = 1.29d + 2
The problem asks for C(30):
C(30) = 1.29(30) + 2
C(30) = 38.7 + 2
C(30) = [B]40.70[/B]

A park bench is 6 feet long. Convert the length to inches

A park bench is 6 feet long. Convert the length to inches
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=6&pl=Calculate&type=foot']type in 6 feet into our search engine[/URL]. We get:
6 feet = [B]72 inches[/B]

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample stan

A random sample of n = 10 flash light batteries with a mean operating life X=5 hr. And a sample standard deviation S = 1 hr. is picked from a production line known to produce batteries with normally distributed operating lives. What's the 98% confidence interval for the unknown mean of the working life of the entire population of batteries?
[URL='http://www.mathcelebrity.com/normconf.php?n=10&xbar=5&stdev=1&conf=98&rdig=4&pl=Small+Sample']Small Sample Confidence Interval for the Mean test[/URL]
[B]4.1078 < u < 5.8922[/B]

A roller coaster car carriers 32 people every 10 minutes there are 572 people in line in front of Ru

A roller coaster car carriers 32 people every 10 minutes there are 572 people in line in front of Ruben how long will it take for Ruben to ride the roller coaster
527/32 = 17.875
Which means on the 18th ride, Ruben will get a seat.
18 rides * 10 minutes per ride = [B]180 minutes, or 3 hours.[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis?
Slope is y/x,so we have 27/36.
[URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']Using our fraction simplifier[/URL], we can reduce 27/36 to 3/4. So this is our slope.
[B]3/4[/B]

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis?
Slope = Rise/Run or y/x
Since tests are on the y-axis and time is on the x-axis, we have:
Slope = 27/36
We can simplify this, so we [URL='https://www.mathcelebrity.com/fraction.php?frac1=27%2F36&frac2=3%2F8&pl=Simplify']type in 27/36 into our search engine[/URL], and get:
[B]Slope = 3/4[/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 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 survey of 75 people found 45 like rabbits, 32 like hamsters, and 15 like both animals. How many pe

A survey of 75 people found 45 like rabbits, 32 like hamsters, and 15 like both animals. How many people like neither animal?
People who like either rabbits or hamsters = Rabbit liners + hamster likes - both likers
People who like either rabbits or hamsters = 45 + 32 - 15
People who like either rabbits or hamsters = 62
People who like neither = 75 - People who like either rabbits or hamsters
People who like neither = 775 - 62
People who like neither = [B]13[/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 yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost

A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost of a yoga membership?
Set up the cost function M(c) for classes (c)
[B]M(c) = 16 + 7c[/B]

Additive Identity Property

Free Additive Identity Property Calculator - Displays the line by line proof for the additive identity property
Numerical Properties

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Ke

Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Kenny buys 1 software package and 1 month of game play. Each software package costs $25. If their total cost is $155, what is the cost of one month of game play.
Let s be the cost of software packages and m be the months of game play. We have:
[LIST]
[*]Angie: 2s + 4m
[*]Kenny: s + m
[/LIST]
We are given each software package costs $25. So the revised equations above become:
[LIST]
[*]Angie: 2(25) + 4m = 50 + 4m
[*]Kenny: 25 + m
[/LIST]
Finally, we are told their combined cost is 155. So we add Angie and Kenny's costs together:
4m + 50 + 25 + m = 155
Combine like terms:
5m + 75 = 155
[URL='http://www.mathcelebrity.com/1unk.php?num=5m%2B75%3D155&pl=Solve']Typing this into our search engine[/URL], we get [B]m = 16[/B]

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, ab

Bangladesh, a country about the size of the state of Iowa, but has about half the U.S population, about 170 million. The population growth rate in Bangladesh is assumed to be linear, and is about 1.5% per year of the base 170 million. Create a linear model for population growth in Bangladesh. Assume that y is the total population in millions and t is the time in years.
At any time t, the Bangladesh population at year t is:
[B]y = 170,000,000(1.015)^t[/B]

Below are data showing the results of six subjects on a memory test. The three scores per subject ar

Below are data showing the results of six subjects on a memory test. The three scores per subject are their scores on three trials (a, b, and c) of a memory task. Are the subjects getting better each trial? Test the linear effect of trial for the data.
A score trial B score trial 2 C Score trial 3
4 6 7
3 7 8
2 8 5
1 4 7
4 6 9
2 4 2
(a) Compute L for each subject using the contrast weights -1, 0, and 1. That is, compute (-1)(a) + (0)(b) + (1)(c) for each subject.
(b) Compute a one-sample t-test on this column (with the L values for each subject) you created. Formula t = To computer a one-sample t-test first know the meaning of each letter
(a) Each L column value is just -1(Column 1) + 0(Column2) + 1(Column 3)
A score trial B score trial 2 C Score trial 3 L = (-1)(a) + (0)(b) + (1)(c)
4 6 7 3
3 7 8 5
2 8 5 3
1 4 7 6
4 6 9 5
2 4 2 0
(b) Mean = (3 + 5 + 3 + 6 + 5 + 0)/6 = 22/6 = 3.666666667
Standard Deviation = 2.160246899
Use 3 as our test mean
(3.666667 - 3)/(2.160246899/sqrt(6)) = 0.755928946

Budget Line Equation

Free Budget Line Equation Calculator - Solves for any one of the 5 items in the standard budget line equation:

Income (I)

Quantity of x = Q_{x}

Quantity of y = Q_{y}

Price of x = P_{x}

Price of y = P_{y}

Income (I)

Quantity of x = Q

Quantity of y = Q

Price of x = P

Price of y = P

Caleb has a complicated and difficult research paper due soon. What should he do to keep from feelin

Caleb has a complicated and difficult research paper due soon. What should he do to keep from feeling overwhelmed and procrastinating? A. work on the paper every day but save the bulk of the work for the night before it's due B. break down the paper into several small steps and start with the smallest one C. write down the deadline for the paper where he can see it every day so he doesn't forget D. work on the hardest parts of the paper first and take multiple breaks until he's finished
Caleb wants to avoid both overwhelm and procrastination. Let's review each option:
[LIST]
[*]A is out because saving a majority of the work will cause overwhelm [U]and[/U] demonstrates procrastination
[*]B is a good option as small steps reduce overwhelm
[*]C looks nice on paper, but will he follow through with seeing the deadline everyday?
[*]D is a good option as well. Finishing the tough parts first makes the rest of the journey seem like a downhill cruise
[/LIST]
Based on these, I'd take [B]B or D[/B]

Can a coefficient of determination be negative? Why or why not?

Can a coefficient of determination be negative? Why or why not?
[B]Yes, reasons below[/B]
[LIST]
[*] predictions that are being compared to the corresponding outcomes have not been derived from a model-fitting procedure using those data
[*] where linear regression is conducted without including an intercept
[*] Yes, negative values of R2 may occur when fitting non-linear functions to data
[/LIST]

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she

Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Let m be the number of months. We have the pages written function P(m) as:
P(m) = 12m + 35
The problem asks for P(5):
P(5) = 12(5) + 35
P(5) = 60 + 35
P(5) = [B]95[/B]

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month unti

Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months.
Set up the equation where m is the number of months:
pages per month * m + pages written already
12m + 35
The problems asks for m = 5:
12(5) + 35
60 + 35
[B]95 pages[/B]

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]

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.

Complex Number Operations

Free Complex Number Operations Calculator - Given two numbers in complex number notation, this calculator:

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

1) Adds (complex number addition), Subtracts (complex number subtraction), Multiplies (complex number multiplication), or Divides (complex number division) any 2 complex numbers in the form a + bi and c + di where i = √-1.

2) Determines the Square Root of a complex number denoted as √a + bi

3) Absolute Value of a Complex Number |a + bi|

4) Conjugate of a complex number a + bi

Compound Interest and Annuity Table

Free Compound Interest and Annuity Table Calculator - Given an interest rate (i), number of periods to display (n), and number of digits to round (r), this calculator produces a compound interest table. It shows the values for the following 4 compound interest annuity functions from time 1 to (n) rounded to (r) digits:

v^{n}

d

(1 + i)^{n}

a_{n|}

s_{n|}

ä_{n|i}

s_{n|i}

Force of Interest δ^{n}

v

d

(1 + i)

a

s

ä

s

Force of Interest δ

Consecutive Interior Angles

Free Consecutive Interior Angles Calculator - Shows you a proof of consecutive interior angles using parallel lines and a transversal

Consider a firm that has two assembly lines, 1 and 2, both producing calculator. Assume that you hav

Consider a firm that has two assembly lines, 1 and 2, both producing calculator. Assume that you have purchased a calculator and it turns out to be defective. And the line 1 produces 60% of all calculators produced.
L1: event that the calculator is produced on line 1
L2: event that the calculator is produced on line 2
Suppose that your are given the conditional information:
10% of the calculator produced on line 1 is defective
20% of the calculator produced on line 2 is defective
Q: If we choose one defective, what is the probability that the defective calculator comes from Line 1 and Line2?
L1 = event that the calculator is produced on line 1 = 0.6
L2 = event that the calculator is produced on line 2 = 1 - 0.6 = 0.4
D = Defective
D|L1 Defective from Line 1 = 0.1
D|L2 = Defective from Line 2 = 0.20
[U]Defective from Line 1[/U]
P(L1|D) = P(L1)P(D/L1) / [ P(L1)P(D/L1) + P(L2)P(D/L2)]
P(L1|D) = (.60)(.10) /[(.60)(.10)+ (.40)(.20)]
[B]P(L1|D) = 0.4286[/B]
[U]Defective from Line 2[/U]
P(L2|D) = P(L2)P(D/L2) / [ P(L1)P(D/L1) + P(L2)P(D/L2)]
P(L2|D) = (.40)(.20) /[(.60)(.10)+ (.40)(.20)]
[B]P(L2|D) = 0.5714[/B]

Counting on a Number Line

Free Counting on a Number Line Calculator - Shows addition or subtraction by moving left or right on a number line.

Covariance and Correlation coefficient (r) and Least Squares Method and Exponential Fit

Free Covariance and Correlation coefficient (r) and Least Squares Method and Exponential Fit Calculator - Given two distributions X and Y, this calculates the following:

* Covariance of X and Y denoted Cov(X,Y)

* The correlation coefficient r.

* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)

Exponential Fit

* Coefficient of Determination r squared r^{2}

* Spearmans rank correlation coefficient

* Wilcoxon Signed Rank test

* Covariance of X and Y denoted Cov(X,Y)

* The correlation coefficient r.

* Using the least squares method, this shows the least squares regression line (Linear Fit) and Confidence Intervals of α and Β (90% - 99%)

Exponential Fit

* Coefficient of Determination r squared r

* Spearmans rank correlation coefficient

* Wilcoxon Signed Rank test

distance between -2 and 9 on the number line

distance between -2 and 9 on the number line
Distance on the number line is the absolute value of the difference:
D = |9 - -2|
D = |11|
D = [B]11[/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

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and

Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and sharing the same y-intercept
Get this in slope-intercept form by adding 5y to each side:
4x - 5y + 5y = 5y + 20
Cancel the 5y's on the left side and we get:
5y + 20 = 4x
Subtract 20 from each side
5y + 20 - 20 = 4x - 20
Cancel the 20's on the left side and we get:
5y = 4x - 20
Divide each side by 5:
5y/5 = 4x/5 - 4
y = 4x/5 - 4
So we have a slope of 4/5
to find our y-intercept, we set x = 0:
y = 4(0)/5 - 4
y = 0 - 4
y = -4
If we want a line perpendicular to the line above, our slope will be the negative reciprocal:
The reciprocal of 4/5 is found by flipping the fraction making the numerator the denominator and the denominator the numerator:
m = 5/4
Next, we multiply this by -1:
-5/4
So our slope-intercept of the perpendicular line with the same y-intercept is:
[B]y = -5x/4 - 4[/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 the difference between a mountain with an altitude of 1,684 feet above sea level and a valley

find the difference between a mountain with an altitude of 1,684 feet above sea level and a valley 216 feet below sea level.
Below sea level is the same as being on the opposite side of zero on the number line. To get the difference, we do the following:
1,684 - (-216)
Since subtracting a negative is a positive, we have:
1,684 + 216
[B]1,900 feet[/B]

Find the gradient of the the line with the equation 8x - 4y =12

Find the gradient of the the line with the equation 8x - 4y =12
[URL='https://www.mathcelebrity.com/parperp.php?line1=8x-4y%3D12&line2=6x+-+3y+%3D+18&pl=Slope']Type this equation into our search engine[/URL] and choose "slope" and we get:
Slope (gradient) = [B]2[/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]

Find y if the line through (1,y) and (4,5) has a slope of 3

Find y if the line through (1,y) and (4,5) has a slope of 3.
Slope formula is:
m = (y2 - y1)/(x2 - x1)
With m = 3, we have:
3 = (5 - y)/(4 - 1)
3 = (5 - y)/3
Cross multiply:
5 - y = 9
Subtract 5 from each side
-y = 4
Multiply each side by -1
[B]y = -4[/B]

Five one -foot rulers laid end to end reach how many inches?

Five one -foot rulers laid end to end reach how many inches?
Since [URL='https://www.mathcelebrity.com/linearcon.php?quant=5&pl=Calculate&type=foot']1 foot = 12 inches from our conversion calculator[/URL], we have:
5 feet = [B]60 inches[/B]

Frank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find

Frank is a plumber who charges a $35 service charge and $15 per hour for his plumbing services. Find a linear function that expresses the total cost C for plumbing services for h hours.
Cost functions include a flat rate and a variable rate. The flat rate is $35 and the variable rate per hour is 15. The cost function C(h) where h is the number of hours Frank works is:
[B]C(h) = 15h + 35[/B]

Function

Free Function Calculator - Takes various functions (exponential, logarithmic, signum (sign), polynomial, linear with constant of proportionality, constant, absolute value), and classifies them, builds ordered pairs, and finds the y-intercept and x-intercept and domain and range if they exist.

If MN is perpendicular to PQ and the slope of PQ is -4 what is the slope for MN

If MN is perpendicular to PQ and the slope of PQ is -4 what is the slope for MN
the slope of a line perpendicular to another line is the negative reciprocal. Therefore:
Slope of MN = -1/Slope of PQ
Slope of MN = -1/-4
Slope of MN = [B]1/4[/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 slope is 6 what would the slope of a line parallel to it be?

If the slope is 6 what would the slope of a line parallel to it be?
Our rule for the relation of second lines to first lines with regards to slope is this:
[LIST]
[*]Parallel lines have the [U]same[/U] slope
[*]Perpendicular lines have the [U]negative reciprocal[/U] slope
[/LIST]
So the slope of the line parallel would also be [B]6[/B]

Imaginary Numbers

Free Imaginary Numbers Calculator - Calculates the imaginary number i where i = √-1 raised to any integer power as well as the product of imaginary numbers of quotient of imaginary numbers

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]

In 2010 a algebra book cost $125. In 2015 the book cost $205. Whats the linear function since 2010?

In 2010 a algebra book cost $125. In 2015 the book cost $205. Whats the linear function since 2010?
In 5 years, the book appreciated 205 - 125 = 80 in value.
80/5 = 16.
So each year, the book increases 16 in value. Set up the cost function:
[B]C(y) = 16y where y is the number of years since 2010[/B]

In 2016, National Textile installed a new textile machine in one of its factories at a cost of $300,

In 2016, National Textile installed a new textile machine in one of its factories at a cost of $300,000. The machine is depreciated linearly over 10 years with a scrap value of $10,000. (a) Find an expression for the textile machines book value in the t?th year of use (0 ? t ? 10)
We have a straight line depreciation. Book Value is shown on the [URL='http://www.mathcelebrity.com/depsl.php?d=&a=300000&s=10000&n=10&t=3&bv=&pl=Calculate']straight line depreciation calculator[/URL].

In simple linear regression the slope and the correlation coefficient will have the same signs True

In simple linear regression the slope and the correlation coefficient will have the same signs
True
False
[B]FALSE[/B] - Only if they are normalized

Interpolation

Free Interpolation Calculator - Given a set of data, this interpolates using the following methods:

* Linear Interpolation

* Nearest Neighbor (Piecewise Constant)

* Polynomial Interpolation

* Linear Interpolation

* Nearest Neighbor (Piecewise Constant)

* Polynomial Interpolation

It is estimated that weekly demand for gasoline at new station is normally distributed, with an aver

It is estimated that weekly demand for gasoline at new station is normally distributed, with an average of 1,000 and standard deviation of 50 gallons. The station will be supplied with gasoline once a week. What must the capacity of its tank be if the probability that its supply will be exhausted in a week is to be no more than 0.01?
0.01 is the 99th percentile
Using our [URL='http://www.mathcelebrity.com/percentile_normal.php?mean=+1000&stdev=50&p=99&pl=Calculate+Percentile']percentile calculator[/URL], we get [B]x = 1116.3[/B]

James is ordering action figures online. Each action figure is $9. Shipping cost $10 per order. Jame

James is ordering action figures online. Each action figure is $9. Shipping cost $10 per order. James does not want to spend over $154. How many action figures can he order?
Step 1: Subtract the cost of shipping from the spend
$154 - $10 = $144
Step 2: Divide $144 to spend after shipping by $9 action figures
144/9 = [B]$16 action figures[/B]

Jayden spent $46.20 on 12 galllons of gasoline. What was the price per gallon?

Jayden spent $46.20 on 12 galllons of gasoline. What was the price per gallon?
Price per gallon = Total spend / number of gallons
Price per gallon = $46.20/12
Price per gallon = $[B]3.85[/B]

Jazmin is a hairdresser who rents a station in a salon for daily fee. The amount of money (m) Jazmin

Jazmin is a hairdresser who rents a station in a salon for daily fee. The amount of money (m) Jazmin makes from any number of haircuts (n) a day is described by the linear function m = 45n - 30
A) A haircut costs $30, and the station rent is $45
B) A haircut costs $45, and the station rent is $30.
C) Jazmin must do 30 haircuts to pay the $45 rental fee.
D) Jazmin deducts $30 from each $45 haircut for the station rent.
[B]Answer B, since rent is only due once. Profit is Revenue - Cost[/B]

Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which

Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which system of linear equations represents the given situation?
Let a be the number of the $13 book, and b equal the number of $17 books. We have the following system of linear equations:
[LIST=1]
[*][B]a + b = 88[/B]
[*][B]13a + 17b = 128[/B]
[/LIST]
To solve this system, use our calculator for the following methods:
[LIST]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Substitution']Substitution[/URL]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Elimination']Elimination[/URL]
[*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Cramers+Method']Cramers Method[/URL]
[/LIST]

Julius Caesar was born and 100 BC and was 66 years old when he died in which year did he die?

Julius Caesar was born and 100 BC and was 66 years old when he died in which year did he die?
BC means "Before Christ". On a timeline, it represents a negative number, where year 0 is the birth of Christ. So we have -100 + 66 = -34
-34 means [B]34 BC[/B].

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $

kim and jason just had business cards made. kim’s printing company charged a one time setup fee of $8 and then $20 per box of cards. jason,meanwhile ordered his online. they cost $8 per box. there was no setup fee, but he had to pay $20 to have his order shipped to his house. by coincidence, kim and jason ended up spending the same amount on their business cards. how many boxes did each buy? how much did each spend?
Set up Kim's cost function C(b) where b is the number of boxes:
C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee
C(b) = 20c + 8 + 0
Set up Jason's cost function C(b) where b is the number of boxes:
C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee
C(b) = 8c + 0 + 20
Since Kim and Jason spent the same amount, set both cost equations equal to each other:
20c + 8 = 8c + 20
[URL='https://www.mathcelebrity.com/1unk.php?num=20c%2B8%3D8c%2B20&pl=Solve']Type this equation into our search engine[/URL] to solve for c, and we get:
c = 1
How much did they spend? We pick either Kim's or Jason's cost equation since they spent the same, and plug in c = 1:
Kim:
C(1) = 20(1) + 8
C(1) = 20 + 8
C(1) = [B]28
[/B]
Jason:
C(1) = 8(1) + 20
C(1) = 8 + 20
C(1) = [B]28[/B]

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying fo

Kimberly is taking three online classes during the summer. She spends 10 hours each week studying for her marketing class, 12 hours studying for her statistics class, and 8 hours studying for her business law class. What percent of her study time does she spend for her statistics class?
The percentage equals hours spent on statistics divided by total hours spent studying for everything.
[U]Calculate total study hours:[/U]
Total Study Hours = Marketing Class Study Hours + Statistics Class Study Hours + Business Law Study Hours
Total Study Hours = 10 + 8 + 12
Total Study Hours = [B]30[/B]
[U]Calculate Statistics Study Hours Percentage:[/U]
Statistics Study Hours Percentage = Statistics Class Study Hours / Total Study Hours
Statistics Class Study Hours = 8/30
Using our [URL='https://www.mathcelebrity.com/perc.php?num=8&den=30&pcheck=1&num1=16&pct1=80&pct2=70&den1=80&idpct1=10&hltype=1&idpct2=90&pct=82&decimal=+65.236&astart=12&aend=20&wp1=20&wp2=30&pl=Calculate']fraction to decimal calculator[/URL], we get
Statistics Class Study Hours = [B]26.67%[/B]

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]

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]

Linear Algebra Summary

Free Linear Algebra Summary Calculator - This is a list of notes, tips, and tricks involving Linear Algebra

Linear Congruence

Free Linear Congruence Calculator - Given an modular equation ax ≡ b (mod m), this solves for x if a solution exists

Linear Congruential Generator

Free Linear Congruential Generator Calculator - Using the linear congruential generator algorithm, this generates a list of random numbers based on your inputs

Linear Conversions

Free Linear Conversions Calculator - Converts to and from the following linear measurements for a given quantity:

Inches

Feet

Yards

Miles

Micrometer

Millimeters

Centimeters

Meters

Kilometers

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Inches

Feet

Yards

Miles

Micrometer

Millimeters

Centimeters

Meters

Kilometers

Furlongs

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]

Madeline’s science quiz consists of 10 questions, all of which are true or false. How many different

Madeline’s science quiz consists of 10 questions, all of which are true or false. How many different choices for answering the 10 questions are possible?
2 ways of answering each True or False Question ^ (10 different ways to answer each question)
2^10 = [B]1,024 ways[/B]

Marcus drives a machine that paints lines along the highway. He needs to paint a line that is 9/10 o

Marcus drives a machine that paints lines along the highway. He needs to paint a line that is 9/10 of a mile long. He is 2/3 of the way done when he runs out of paint. What fraction of a mile has he painted?
Marcus has painted 2/3 of 9/10.
If we [URL='https://www.mathcelebrity.com/fraction.php?frac1=2%2F3&frac2=9%2F10&pl=Multiply']type 2/3 of 91/20 in our search engine[/URL], we get:
[B]3/5[/B]

Match each variable with a variable by placing the correct letter on each line.

Match each variable with a variable by placing the correct letter on each line.
a) principal
b) interest
c) interest rate
d) term/time
2 years
1.5%
$995
$29.85
[B]Principal is $995
Interest is $29.85 since 995 * .0.15 * 2 = 29.85
Interest rate is 1.5%
Term/time is 2 year[/B]s

Mental Models of Math Book

Calculation Domination: How Anybody Can Explode Their Math Scores Using the Mental Magic of Elon Musk and Warren Buffett.
[MEDIA=youtube]RclG-k6itpk[/MEDIA]
This audiobook shows you various mental models of the top 5% of math students. Mental models come from the following disciplines: Math Anxiety Science Problem Solving Probability Decision Making Metaphysics Persuasion Math Testing

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 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]

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 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]

Represent the number of inches in 7 feet

Represent the number of inches in 7 feet
We [URL='https://www.mathcelebrity.com/linearcon.php?quant=7&pl=Calculate&type=foot']type in 7 feet to our search engine and we get[/URL]:
7 feet = [B]84 inches[/B]

Sarah starts with $300 in her savings account. She babysits and earns $30 a week to add to her accou

Sarah starts with $300 in her savings account. She babysits and earns $30 a week to add to her account. Write a linear equation to model this situation? Enter your answer in y=mx b form with no spaces.
Let x be the number of hours Sarah baby sits. Then her account value y is:
y = [B]30x + 300[/B]

Security Market Line and Treynor Ratio

Free Security Market Line and Treynor Ratio Calculator - Solves for any of the 4 items in the Security Market Line equation, Risk free rate, market return, Β, and expected return as well as calculate the Treynor Ratio.

slope is 0 and whose y-intercept is 9.

slope is 0 and whose y-intercept is 9.
The standard line equation is y = mx + b where m is the slope and b is the y-intercept is b.
Plugging in our numbers, we get:
y = 0x + 9
y = [B]9[/B]

Solve for x

[IMG]https://mathcelebrity.com/community/data/attachments/0/supp-angles.jpg[/IMG]
The angle with measurements of 148 degrees lies on a straight line, which means it's supplementanry angle is:
180 - 148 = 32
Since the angle of 2x - 16 and 32 lie on a straight line, their angle sum equals 180:
2x + 16 + 32 = 180
To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B16%2B32%3D180&pl=Solve']type it in our math engine [/URL]and we get:
x = [B]66[/B]

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Square Roots and Exponents

Free Square Roots and Exponents Calculator - Given a number (n), or a fraction (n/m), and/or an exponent (x), or product of up to 5 radicals, this determines the following:

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x^{th} power denoted as n^{x} (Write without exponents)

* n raised to the x^{th} power raised to the yth power denoted as (n^{x})^{y} (Write without exponents)

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

* The square root of n denoted as √n

* The square root of the fraction n/m denoted as √n/m

* n raised to the x

* n raised to the x

* Product of up to 5 square roots: √a√b√c√d√e

* Write a numeric expression such as 8x8x8x8x8 in exponential form

Straight Line Depreciation

Free Straight Line Depreciation Calculator - Solves for Depreciation Charge, Asset Value, Salvage Value, Time, N, and Book Value using the Straight Line Method.

Suppose that J and K are on the number line. If JK=9 and J lies at 4 where could K be located?

Suppose that J and K are on the number line. If JK=9 and J lies at 4 where could K be located?
We'd need 9 spaces to the right of 4 or 9 spaces to the left of 4 to have JK be 9.
To the right:
K = 4 + 9
K = [B]13[/B]
K = 4 - 9
K = [B]-5[/B]

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in ga

Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel?
Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have:
W(g) = gx + c where c is a constant
We are given:
[LIST]
[*]W(20) = 2012
[*]W(55) = 2208
[/LIST]
We want to know W(65)
Using our givens, we have:
W(20) = 20x + c = 2012
W(55) = 55x + c = 2208
Rearranging both equations, we have:
c = 2012 - 20x
c = 2208 - 55x
Set them both equal to each other:
2012 - 20x = 2208 - 55x
Add 55x to each side:
35x + 2012 = 2208
Using our [URL='http://www.mathcelebrity.com/1unk.php?num=35x%2B2012%3D2208&pl=Solve']equation solver[/URL], we see that x is 5.6
Plugging x = 5.6 back into the first equation, we get:
c = 2012 - 20(5.6)
c = 2012 - 112
c = 2900
Now that we have all our pieces, find W(65)
W(65) = 65(5.6) + 2900
W(65) = 264 + 2900
W(65) = [B]3264[/B]

Target Heart Rate

Free Target Heart Rate Calculator - Given an age, this calculator determines the following 5 target heart rate zones:

Healthy Heart Zone (Warm up) 50 - 60%

Fitness Zone (Fat Burning) 60 - 70%

Aerobic Zone (Endurance Training) 70 - 80%

Anaerobic Zone (Performance Training) 80 - 90%

Red Line (Maximum Effort) 90 - 100%

Healthy Heart Zone (Warm up) 50 - 60%

Fitness Zone (Fat Burning) 60 - 70%

Aerobic Zone (Endurance Training) 70 - 80%

Anaerobic Zone (Performance Training) 80 - 90%

Red Line (Maximum Effort) 90 - 100%

The coach writes the batting order on a piece of paper. How many different ways could the list be wr

The coach writes the batting order on a piece of paper. How many different ways could the list be written?
We have 9 people in a line up. The total lineups are shown by:
9 * 8 * 7 * ... * 2 * 1
Or, 9!. [URL='https://www.mathcelebrity.com/factorial.php?num=9!&pl=Calculate+factorial']Typing 9! in our search engine[/URL] and we get [B]362,880[/B]

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base

The distance between consecutive bases is 90 feet. An outfielder catches the ball on the third base line about 40 feet behind third base. How far would the outfielder have to throw the ball to first base?
We have a right triangle. From home base to third base is 90 feet. We add another 40 feet to the outfielder behind third base to get: 90 + 40 = 130
The distance from home to first is 90 feet.
Our hypotenuse is the distance from the outfielder to first base.
[URL='https://www.mathcelebrity.com/pythag.php?side1input=130&side2input=90&hypinput=&pl=Solve+Missing+Side']Using our Pythagorean theorem calculator[/URL], we get:
d = [B]158.11 feet[/B]

the equation of a line is y = mx + 4. find m if the line passes through (-5,0)

the equation of a line is y = mx + 4. find m if the line passes through (-5,0)
Plug in our numbers of x = -5, and y = 0:
-5m + 4 = 0
To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=-5m%2B4%3D0&pl=Solve']plug in this equation into our search engine[/URL] and we get:
[B]m = 0.8 or 4/5[/B]
so our line equation becomes:
[B]y = 4/5x + 4[/B]

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 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 price of a gallon of gasoline is $3.15. The price when Ryan’s mother started driving was 1/7 of

The price of a gallon of gasoline is $3.15. The price when Ryan’s mother started driving was 1/7 of the current price. What was the price of gasoline when Ryan’s mother started driving?
$3.15/7 = [B]$0.45[/B]

The slope of a line is 7/6. What is the slope of any line parallel to this line?

The slope of a line is 7/6. What is the slope of any line parallel to this line?
Parallel lines have the same slope, because they never touch.
So the slope of the parallel line is [B]7/6[/B]

The world record for the mile in the year 1865 was held by Richard Webster of England when he comple

The world record for the mile in the year 1865 was held by Richard Webster of England when he completed a mile in 4 minutes and 36.5 seconds. The world record in 1999 was set by Hicham El Guerrouj when he ran a mile in 3 minutes and 43.13 seconds.
If both men ran the mile together, how many feet behind would Richard Webster be when Hichem El Guerrouj crossed the finish line?
Change times to seconds:
[LIST]
[*]4 minutes and 36.5 seconds = 4*60 + 36.5 = 240 + 36.5 = 276.5 seconds
[*]3 minute and 43.13 seconds = 3*60 + 43.13 = 180 + 43.13 = 223.13 seconds
[/LIST]
Now, find the distance Richard Webster travelled in 3 minutes and 43.13 seconds which is when Hiram El Guerrouj crossed the finish line.
1 mile = 5280 feet:
Set up a proportion of distance in feet to seconds where n is the distance Richard Webster travelled
5280/276.5 = n/223.13
Using our [URL='https://www.mathcelebrity.com/proportion-calculator.php?num1=5280&num2=n&den1=276.5&den2=223.13&propsign=%3D&pl=Calculate+missing+proportion+value']proportion calculator,[/URL] we get:
n = 4260.85 feet
Distance difference = 5280 - 4260.85 = [B]1019.15 feet[/B]

There are 12 inches per foot. How many inches are there in 14 feet?

There are 12 inches per foot. How many inches are there in 14 feet?
Two ways to solve this. Plug in [URL='http://www.mathcelebrity.com/linearcon.php?quant=14&pl=Calculate&type=foot']14 feet [/URL]into the search engine to get [B]168 inches.[/B]
Or, we do proportions:
12 inches / 1 foot * 14 feet = 12 * 14 = 168 inches per 14 feet.

There were 286,200 graphic designer jobs in a country in 2010. It has been projected that there will

There were 286,200 graphic designer jobs in a country in 2010. It has been projected that there will be 312,500 graphic designer jobs in 2020. (a) Using the data, find the number of graphic designer jobs as a linear function of the year.
[B][U]Figure out the linear change from 2010 to 2020[/U][/B]
Number of years = 2020 - 2010
Number of years = 10
[B][U]Figure out the number of graphic designer job increases:[/U][/B]
Number of graphic designer job increases = 312,500 - 286,200
Number of graphic designer job increases = 26,300
[B][U]Figure out the number of graphic designer jobs added per year[/U][/B]
Graphic designer jobs added per year = Total Number of Graphic Designer jobs added / Number of Years
Graphic designer jobs added per year = 26,300 / 10
Graphic designer jobs added per year = 2,630
[U][B]Build the linear function for graphic designer jobs G(y) where y is the year:[/B][/U]
G(y) = 286,200 + 2,630(y - 2010)
[B][U]Multiply through and simplify:[/U][/B]
G(y) = 286,200 + 2,630(y - 2010)
G(y) = 286,200 + 2,630y - 5,286,300
[B]G(y) = 2,630y - 5,000,100[/B]

Using a number line how far is - 2 from 6

Using a number line how far is - 2 from 6
We use [URL='https://www.mathcelebrity.com/mptnline.php?ept1=-2&empt=+&ept2=6&pl=Calculate+missing+Number+Line+item']our number line calculator[/URL] and we get:
Distance is [B]8[/B]

Vectors

Free Vectors Calculator - Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

Walking Distance (Pedometer)

Free Walking Distance (Pedometer) Calculator - Given a number of steps and a distance per stride in feet, this calculator will determine how far you walk in other linear measurements.

What is a Line

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

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 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 number is the same distance from 0 on the number line as 4

which number is the same distance from 0 on the number line as 4
We use absolute value for distance.
Since 4 is 4 units right of 0 on the number line, we can also move 4 units left of 0 on the number line and we land on [B]-4[/B]

Which of the following equations represents a line that is parallel to the line with equation y = -3

Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4?
A) 6x + 2y = 15
B) 3x - y = 7
C) 2x - 3y = 6
D) x + 3y = 1
Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line.
If we rearrange A) by subtracting 6x from each side, we get:
2y = -6x + 15
Divide each side by 2, we get:
y = -3x + 15/2
This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].

Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7

Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7
The standard equation for slope (m) and y-intercept (b) is given as:
y = mx + b
We're given m = 4 and y-intercept = -7, so we have:
[B]y = 4x - 7[/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]