Basic Single-Variable Algebra - Algebra 2
Card 1 of 3288
If 
and 
, what is the value of 
?
If
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Substitute the values into the expression.
In order to evaluate this expression, we will need to rewrite the negative exponents into fractions.
Simplify the fractions.
Reduce this fraction.
The answer is: 
Substitute the values into the expression.
In order to evaluate this expression, we will need to rewrite the negative exponents into fractions.
Simplify the fractions.
Reduce this fraction.
The answer is:
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If 
and 
, what is the value of 
?
If
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Substitute the values in the expression.
Rationalize the denominator by multiplying square root of three on the top and bottom of the fraction.
Simplify the top and bottom.
The answer is: 
Substitute the values in the expression.
Rationalize the denominator by multiplying square root of three on the top and bottom of the fraction.
Simplify the top and bottom.
The answer is:
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The quantity x varies directly with y. If x is 26 when y is 100, find x when y is 200.
The quantity x varies directly with y. If x is 26 when y is 100, find x when y is 200.
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We must set up a proportion. Since x varies directly with y, when y is multiplied by 2, x is also multiplied by 2. 26 times 2 is 52.
Direct variation: 
We must set up a proportion. Since x varies directly with y, when y is multiplied by 2, x is also multiplied by 2. 26 times 2 is 52.
Direct variation:
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Set up the inequality: Seven less than twice a number exceeds eleven.
Set up the inequality: Seven less than twice a number exceeds eleven.
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Break up the statement into parts.
Twice a number: 
Seven less than twice a number: 
Exceeds eleven cannot be 11: 
Combine the parts to form the inequality.
The answer is: 
Break up the statement into parts.
Twice a number:
Seven less than twice a number:
Exceeds eleven cannot be 11:
Combine the parts to form the inequality.
The answer is:
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Set up the inequality: Four less than three times a number cannot exceed five.
Set up the inequality: Four less than three times a number cannot exceed five.
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Split the statement into parts.
Three times a number: 
Four less than three times a number: 
Cannot exceed five: 
Cannot exceed five means that it can be five, but no more than five.
Combine the parts to form the inequality.
The answer is: 
Split the statement into parts.
Three times a number:
Four less than three times a number:
Cannot exceed five:
Cannot exceed five means that it can be five, but no more than five.
Combine the parts to form the inequality.
The answer is:
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Sunshine paint is made by mixing three parts yellow paint and one part red paint. How many gallons of yellow paint should be mixed with two quarts of red paint?
(1 gallon = 4 quarts)
Sunshine paint is made by mixing three parts yellow paint and one part red paint. How many gallons of yellow paint should be mixed with two quarts of red paint?
(1 gallon = 4 quarts)
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First set up the proportion:
x = 
Then convert this to gallons:
First set up the proportion:
x =
Then convert this to gallons:
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Set up the inequality:
Four times the quantity of seven less than three times a number cannot exceed eight.
Set up the inequality:
Four times the quantity of seven less than three times a number cannot exceed eight.
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Break up the sentence into parts.
Three times a number: 
Seven less than three times a number: 
Four times the quantity of seven less than three times a number: 
Cannot exceed eight: 
Combine the parts to form the inequality.
The answer is: 
Break up the sentence into parts.
Three times a number:
Seven less than three times a number:
Four times the quantity of seven less than three times a number:
Cannot exceed eight:
Combine the parts to form the inequality.
The answer is:
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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?
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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
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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?
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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?
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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)?
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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?
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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
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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
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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
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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.
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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.
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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
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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
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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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