Equations - Algebra II
Card 0 of 1868
The monthly cost to insure your cars varies directly with the number of cars you own. Right now, you are paying $420 per month to insure 3 cars, but you plan to get 2 more cars, so that you will own 5 cars. How much does it cost to insure 5 cars monthly?
The monthly cost to insure your cars varies directly with the number of cars you own. Right now, you are paying $420 per month to insure 3 cars, but you plan to get 2 more cars, so that you will own 5 cars. How much does it cost to insure 5 cars monthly?
The statement, 'The monthly costly to insure your cars varies directly with the number of cars you own' can be mathematically expressed as 
. M is the monthly cost, C is the number of cars owned, and k is the constant of variation.
Given that it costs $420 a month to insure 3 cars, we can find the k-value.
Divide both sides by 3.
Now, we have the mathematical relationship.
Finding how much it costs to insure 5 cars can be found by substituting 5 for C and solving for M.
The statement, 'The monthly costly to insure your cars varies directly with the number of cars you own' can be mathematically expressed as
Given that it costs $420 a month to insure 3 cars, we can find the k-value.
Divide both sides by 3.
Now, we have the mathematical relationship.
Finding how much it costs to insure 5 cars can be found by substituting 5 for C and solving for M.
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If the roots of a function are 
, what does the function look like in 
format?
If the roots of a function are
This is a FOIL problem. First, we must set up the problem in a form we can use to create the function. To do this we take the opposite sign of each of the numbers and place them in this format: 
.
Now we can FOIL.
First: 
Outside: 
Inside: 
Last: 
Then add them together to get 
.
Combine like terms to find the answer, which is 
.
This is a FOIL problem. First, we must set up the problem in a form we can use to create the function. To do this we take the opposite sign of each of the numbers and place them in this format:
Now we can FOIL.
First:
Outside:
Inside:
Last:
Then add them together to get
Combine like terms to find the answer, which is
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Tom is painting a fence 
feet long. He starts at the West end of the fence and paints at a rate of 
feet per hour. After 
hours, Huck joins Tom and begins painting from the East end of the fence at a rate of 
feet per hour. After 
hours of the two boys painting at the same time, Tom leaves Huck to finish the job by himself.
If Huck completes painting the entire fence after Tom leaves, how many more hours will Huck work than Tom?
Tom is painting a fence
If Huck completes painting the entire fence after Tom leaves, how many more hours will Huck work than Tom?
Tom paints for a total of 
hours (2 on his own, 2 with Huck's help). Since he paints at a rate of 
feet per hour, use the formula
(or 
)
to determine the total length of the fence Tom paints.
feet
Subtracting this from the total length of the fence 
feet gives the length of the fence Tom will NOT paint: 
feet. If Huck finishes the job, he will paint that 
feet of the fence. Using 
, we can determine how long this will take Huck to do:
hours.
If Huck works 
hours and Tom works 
hours, he works 
more hours than Tom.
Tom paints for a total of
to determine the total length of the fence Tom paints.
Subtracting this from the total length of the fence
If Huck works
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Two numbers have a ratio of 5:6 and half of their sum is 22. What are the numbers?
Two numbers have a ratio of 5:6 and half of their sum is 22. What are the numbers?
Set up the equation:
Solve the equation:
Find the two numbers:
The two numbers have a ratio of 5:6, therefore the ratio can also be represented as:
The two numbers are 20 and 24.
Set up the equation:
Solve the equation:
Find the two numbers:
The two numbers have a ratio of 5:6, therefore the ratio can also be represented as:
The two numbers are 20 and 24.
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What is the equation of the line that has a slope of 3 and passes through the point (3,-6)?
What is the equation of the line that has a slope of 3 and passes through the point (3,-6)?
The equation for a line in slope-intercept form is:
where 
and 
are the known coordinates (3,-6).
Substituting gives
,
and simplifying gives the final answer:
The equation for a line in slope-intercept form is:
where
Substituting gives
and simplifying gives the final answer:
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Set up an equation that properly displays the information given.
Suzanne has a pack of multi-colored jelly beans. She wants to sort them into equal amounts to give out to her four friends, but not until she eats eight of them. If the total pack contains 60 jelly beans, then how many is each friend going to get?
Set up an equation that properly displays the information given.
Suzanne has a pack of multi-colored jelly beans. She wants to sort them into equal amounts to give out to her four friends, but not until she eats eight of them. If the total pack contains 60 jelly beans, then how many is each friend going to get?
Let 
be the number of jelly beans that each friend will receive. She has four friends, so the total number of jelly beans her friends will receive is 
. Suzanne eats another eight, so the equation can be written as 
.
Let
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A circular tower stands surrounded by a circular moat. A bridge provides a passage over the moat to the tower. The distance from the outer edge of the moat to the center of the tower is 
meters. The area of the floor of tower is 
. How long is the bridge over the moat?
A circular tower stands surrounded by a circular moat. A bridge provides a passage over the moat to the tower. The distance from the outer edge of the moat to the center of the tower is
The distance from the outer edge of the moat to the center of the castle is the radius (100 m) of the larger circle formed by the outer edge of the circular moat.
The radius of the tower's floor (found using the area of the floor), needs to be subracted from 100 m to find the distance fo the bridge.
The distance from the outer edge of the moat to the center of the castle is the radius (100 m) of the larger circle formed by the outer edge of the circular moat.
The radius of the tower's floor (found using the area of the floor), needs to be subracted from 100 m to find the distance fo the bridge.
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Your friend goes on a diet to lose a little weight. He starts at 
pounds and cuts his calories by 
a day. Write a linear equation to express your friend's weight in pounds as a function of weeks on the diet. Hint: there are 
,
calories in a pound.
Your friend goes on a diet to lose a little weight. He starts at
The question asks for a relation between pounds lost and weeks on the diet. If each day your friend cuts 500 calories, the number of pounds he is losing per week is 1:
The rate of change, or slope, is therefore -1. The slope is negative because the independent variable (weight in pounds) is decreases as the dependent variable (time in weeks) increases. The y-intercept is 180, because that is how much your friend weighs at the start, when time = 0. Plugging these values into 
form, we end up with:
The question asks for a relation between pounds lost and weeks on the diet. If each day your friend cuts 500 calories, the number of pounds he is losing per week is 1:
The rate of change, or slope, is therefore -1. The slope is negative because the independent variable (weight in pounds) is decreases as the dependent variable (time in weeks) increases. The y-intercept is 180, because that is how much your friend weighs at the start, when time = 0. Plugging these values into
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Solve for 
in the following equation: 
Solve for
Starting with the equation 
, you want to collect like terms.
Put all of the numbers on one side, and leave only the variable on the other side.
The first step is to subtract 
from both sides.
You get 
.
The next step is to divide both sides by 
to get the final answer, 
.
Starting with the equation
Put all of the numbers on one side, and leave only the variable on the other side.
The first step is to subtract
You get
The next step is to divide both sides by
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Express as an equation.
more than 
is 
Express as an equation.
Take every word and translate into math.
more than means that you need to add 
to something which is 
.
Anytime you see "is" means equal.
Now let's combine and create an expression of 
Take every word and translate into math.
Anytime you see "is" means equal.
Now let's combine and create an expression of
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Express as an equation.
times 
is 
less than 
Express as an equation.
Take every word and translate into math.
times something means that you need to multiply 
to something which is 
.
less than means that you need to subtract 
from 
.
Anytime you see "is" means equal.
Let's combine to get 
.
Take every word and translate into math.
Anytime you see "is" means equal.
Let's combine to get
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If Bob's age is 
years old and Jack is 
more than 
times Bob's age, then express Jack's age in terms of 
.
If Bob's age is
Take every word and translate into math.
more than means that you need to add 
to something.
times something means that you need to multiply 
to Bob's age which is 
.
Now we can combine them to have an expression of 
.
Take every word and translate into math.
Now we can combine them to have an expression of
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There are 
marbles in a jar. There are 
types of color: red, blue, green and yellow. There are 
red marbles, 
blue marbles, 
green marbles. Find an equation to represent the number of yellow marbles.
There are
We have 
known values and 
unknown value. We have a total and that these 
colors add up to 
.
Let's represent the colors with variables corresponding to the first letter of the color. 
.
Now, plug in the values that are known. Final answer is 
.
To simplify we add the constants which results in:
We have
Let's represent the colors with variables corresponding to the first letter of the color.
Now, plug in the values that are known. Final answer is
To simplify we add the constants which results in:
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Express as an equation.
Difference between 
times 
and the quotient of 
and 
is 
more than 
times 
.
Express as an equation.
Difference between
Take every word and translate into math. What a difference means, is that 
is the first number subtracting 
.
The 
part is 
times something means that you need to multiply 
to something which is .
The 
part is quotient.
Anytime you take a quotient of 
and 
, 
is the in the numerator and 
is in the denominator. Therefore the expression is 
.
Anytime you see "is" means equal.
more than means that you need to add 
to something.
That something is 
multipled by 
or 
.
Let's just combine them to have an expression of 
.
Take every word and translate into math. What a difference means, is that
The
The
Anytime you take a quotient of
Anytime you see "is" means equal.
That something is
Let's just combine them to have an expression of
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Jon needs to make four monthly deposits. The first month, he deposits 
dollars. Each month after he adds 
dollars to the previous month's deposit. Find an equation to solve for 
if the total amount of money deposited for the four months is 
Jon needs to make four monthly deposits. The first month, he deposits
Let's translate into math equations.
First month is 
Then for the next month, he adds 
to the previous month or 
Then, for the next month, he adds another 
to the previous month which was 
By adding another 
, this month becomes 
For the fourth month, it's just another 
added to the previous month which was 
The fourth month becomes 
.
With the total given, lets combine the expressions to get 
.
Simplifying this we get:
Let's translate into math equations.
First month is
With the total given, lets combine the expressions to get
Simplifying this we get:
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Express as an equation.
The sum of 
and 
is 
.
Express as an equation.
The sum of
Take every word and translate into math. The sum of something means adding. So that would be 
. Is means equals something. Putting it all together, we get 
.
Take every word and translate into math. The sum of something means adding. So that would be
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Express as an equation.
The difference between 
and 
is 
Express as an equation.
The difference between
Take every word and translate into math. Difference means subtracting. So we are subtracting 
and 
. Is means equal something. Putting it all together, we have 
.
Take every word and translate into math. Difference means subtracting. So we are subtracting
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Express as an equation. The product of 
and 
is the sum of 
and 
.
Express as an equation. The product of
Take every word and translate into math. The product of something means multiplying. So we have 
. The sum of something means adding. So that would be 
. Is means equals something. Putting it together, we have 
.
Take every word and translate into math. The product of something means multiplying. So we have
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Express as an equation. The quotient of 
and 
is the difference of 
and 
times sum of 
and 
.
Express as an equation. The quotient of
Take every word and translate into math. Quotient means dividing, so we have 
. When it's 
and 
, 
will always be at the numerator of the fraction. Is means equal something. Difference is subtracting and we are subtracting 
with 
times sum of 
and 
. Times means multiplying and sum means addition. We are multiplying 
with 
. There must be parentheses as the sum of 
and 
is an expression. Putting it all together, we get 
.
Take every word and translate into math. Quotient means dividing, so we have
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Express as an equation.
The square root of 
is the sum of 
and 
squared.
Express as an equation.
The square root of
Take every word and translate into math. Square root means using a radical sign. So we have 
. Is means equal something. Next, sum is addition so we have 
. Since it's squared, we have the whole thing in parentheses raised to the second power like so: 
. It is tempting to think it's 
but if it was, then it should say sum of 
and 
square. So final answer is 
.
Take every word and translate into math. Square root means using a radical sign. So we have
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