Expressions - Algebra II
Card 0 of 596
Simply: 
Simply:
In this form, the exponents are multiplied: 
.
In multiplication problems, the exponents are added.
In division problems, the exponents are subtracted.
It is important to know the difference.
In this form, the exponents are multiplied:
In multiplication problems, the exponents are added.
In division problems, the exponents are subtracted.
It is important to know the difference.
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Simplify the expression.
Simplify the expression.
When multiplying exponential components, you must add the powers of each term together.
When multiplying exponential components, you must add the powers of each term together.
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Expand:
Expand:
First, FOIL:
Simplify:
Distribute the 
through the parentheses:
Rewrite to make the expression look like one of the answer choices:
First, FOIL:
Simplify:
Distribute the
Rewrite to make the expression look like one of the answer choices:
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Multiply, expressing the product in simplest form:
Multiply, expressing the product in simplest form:
Cross-cancel the coefficients by dividing both 15 and 25 by 5, and both 14 and 21 by 7:
Now use the quotient rule on the variables by subtracting exponents:
Cross-cancel the coefficients by dividing both 15 and 25 by 5, and both 14 and 21 by 7:
Now use the quotient rule on the variables by subtracting exponents:
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Simplify the following expression:
Simplify the following expression:
Step 1: A power raised to a power can be simplified by multiplying the two powers.
Step 2: When a fraction is raised to a power, it applies to both the top and bottom. Again, you multiply the powers.
Step 3: When dividing exponents with the same base, you subtract the power of the bottom from the power of the top.
Step 1: A power raised to a power can be simplified by multiplying the two powers.
Step 2: When a fraction is raised to a power, it applies to both the top and bottom. Again, you multiply the powers.
Step 3: When dividing exponents with the same base, you subtract the power of the bottom from the power of the top.
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The sum of three consecutive even integers equals 72. What is the product of these integers?
The sum of three consecutive even integers equals 72. What is the product of these integers?
Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.
x + (x + 2) + (x + 4) = 72
3x + 6 = 72
3x = 66
x = 22.
This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.
The answer is 13728.
Let us call x the smallest integer. Because the next two numbers are consecutive even integers, we can call represent them as x + 2 and x + 4. We are told the sum of x, x+2, and x+4 is equal to 72.
x + (x + 2) + (x + 4) = 72
3x + 6 = 72
3x = 66
x = 22.
This means that the integers are 22, 24, and 26. The question asks us for the product of these numbers, which is 22(24)(26) = 13728.
The answer is 13728.
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We have three cats, Chai, Sora, and Newton. Chai is 3 years old. Sora two years older than twice Chai's age. Newton is one year younger than one-fourth of Sora's age. How old are Sora and Newton?
We have three cats, Chai, Sora, and Newton. Chai is 3 years old. Sora two years older than twice Chai's age. Newton is one year younger than one-fourth of Sora's age. How old are Sora and Newton?
To make this much easier, translate the word problem into a system of three equations.
We have C for Chai, S for Sora, and N for Newton. To find Sora's age, plug in 
into 
.
Sora is 8 years old. Use this to find Newton's age.
Newton is one year old. So the answer is:
Sora, 8 years
Newton, 1 year
To make this much easier, translate the word problem into a system of three equations.
We have C for Chai, S for Sora, and N for Newton. To find Sora's age, plug in
Sora is 8 years old. Use this to find Newton's age.
Newton is one year old. So the answer is:
Sora, 8 years
Newton, 1 year
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Carla wants to sell stickers to advertise her website. The machine that makes stickers costs $22, and each sticker costs $2 to make. She plans to sell these stickers for $3 each.
Write an equation that describes the number of stickers Carla would have to sell in order to break even.
Carla wants to sell stickers to advertise her website. The machine that makes stickers costs $22, and each sticker costs $2 to make. She plans to sell these stickers for $3 each.
Write an equation that describes the number of stickers Carla would have to sell in order to break even.
Here, we can see that the independent variable is the number of stickers, so we'll call that 
. Each sticker costs $2 to make, so we'll write that as 
. The cost of the machine is always the same ($22), so we call that a constant.
So far, we have 
as the cost of making 
number of stickers.
Now, we need to describe the revenue gained by selling 
number of stickers. We know that Carla wants to sell the stickers at $3 each, which we can write as 
.
"Breaking even" means that your costs equal your income. In other words, it's the point at which Carla's sold exactly enough stickers to make all of her initial investment back. In math, we use an equal sign to describe this. Hence, we end up with the equation:
Here, we can see that the independent variable is the number of stickers, so we'll call that
So far, we have
Now, we need to describe the revenue gained by selling
"Breaking even" means that your costs equal your income. In other words, it's the point at which Carla's sold exactly enough stickers to make all of her initial investment back. In math, we use an equal sign to describe this. Hence, we end up with the equation:
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Express as a mathematical expression.
more than 
Express as a mathematical expression.
Take every word and translate into math.
more than means that you need to add 
to something.
That something is 
so just combine them to have an expression of 
.
Take every word and translate into math.
That something is
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A car dealer receives 
commission on his total sales amount when he sells less than 
cars per month. If he sells over 
cars per month, he receives 
commision.
If each cars sells for 
, which expression set correctly repressent the salesman's earnings per month, 
and the amount of cars sold, 
?
A car dealer receives
If each cars sells for
The salesman will sell either more than 5 cars or less than 5.
Therefore, only one set of the equations will be true for any one month.
The word between the expressions needs to be "or."
The total profit is expressed by 30,000x.
The commision can be calculated as 
.
The higher commision must be matched to the equation for greater amount of cars sold, 
.
The salesman will sell either more than 5 cars or less than 5.
Therefore, only one set of the equations will be true for any one month.
The word between the expressions needs to be "or."
The total profit is expressed by 30,000x.
The commision can be calculated as
The higher commision must be matched to the equation for greater amount of cars sold,
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Sally has 3 dollars saved. She works at the ice cream shop where she earns 5 dollars an hour. How many hours does she need to work to have enough money to buy a doll that is 23 dollars?
Sally has 3 dollars saved. She works at the ice cream shop where she earns 5 dollars an hour. How many hours does she need to work to have enough money to buy a doll that is 23 dollars?
To set up this equation we need to put the amount of money she needs on one side of the equation and the amount of money she earns on the other side of the equation. It looks like the following
where 
represents the number of hours Sally works. To get the dollar amount she earns for the hours she works, we mulitply it by 5. The 3 represents the amount of money she already has saved. These two added together needs to equal 23 dollars, the amount for the doll.
From here we solve for 
:
To set up this equation we need to put the amount of money she needs on one side of the equation and the amount of money she earns on the other side of the equation. It looks like the following
where
From here we solve for
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Set up the expression to solve the following word problem:
Annie, Josh, and Brenda each have a certain number of cards. Josh has twice as many cards as Annie, and Brenda has three times as many cards as Josh. They have 
cards in total.
Set up the expression to solve the following word problem:
Annie, Josh, and Brenda each have a certain number of cards. Josh has twice as many cards as Annie, and Brenda has three times as many cards as Josh. They have
Let us call the number of cards Annie has 
Josh has twice as many so we can call the number of cards Josh has 
Brenda has 3 times as many cards as Josh so we can call the number of cards Brenda has 
The total is 90 so we have 
Which we simplify by adding all the x terms: 
Let us call the number of cards Annie has
Josh has twice as many so we can call the number of cards Josh has
Brenda has 3 times as many cards as Josh so we can call the number of cards Brenda has
The total is 90 so we have
Which we simplify by adding all the x terms:
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Jacob just opened a soda bottling factory. His starting costs were 
. For each soda he bottles, he will make 
. Which of the following expressions shows how much money 
Jacob will make in terms of 
, the number of sodas he bottles.
Jacob just opened a soda bottling factory. His starting costs were
The $10,000 that Jacob invested can be considered as a negative starting value, which will be the y-intercept in the equation.
The total money Jacob makes depends on how many bottles he sells.
If each bottle earns Jacob 50 cents, then the correct equation is 
.
The $10,000 that Jacob invested can be considered as a negative starting value, which will be the y-intercept in the equation.
The total money Jacob makes depends on how many bottles he sells.
If each bottle earns Jacob 50 cents, then the correct equation is
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Express as a mathematical expression.
less than 
Express as a mathematical expression.
Take every word and translate into math.
less than means that you need to subtract 
from something.
That something is 
so just combine them to have an expression of 
.
Take every word and translate into math.
That something is
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Express as a mathematical expression.
times 
Express as a mathematical expression.
Take every word and translate into math.
times something means that you need to multiply 
to something.
That something is 
so just combine them to have an expression of 
Take every word and translate into math.
That something is
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Express as a mathematical expression.
The quotient of 
and 
Express as a mathematical expression.
The quotient of
Take every word and translate it into math.
Anytime you take a quotient of 
and 
, 
is the in the numerator and 
is in the denominator.
Therefore expression is 
Take every word and translate it into math.
Anytime you take a quotient of
Therefore expression is
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Express as a mathematical expression.
more than 
times 
Express as a mathematical expression.
Take every word and translate it into math.
more than means that you need to add 
to something.
times something means that you need to multiply 
to something.
That something is 
so just combine them to have an expression of 
.
Take every word and translate it into math.
That something is
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Express as a mathematical expression.
is less than the quotient of 
and 
Express as a mathematical expression.
Take every word and translate into math.
less than means that you need to subtract 
from something.
Anytime you take a quotient of 
and 
, 
is the in the numerator and 
is in the denominator. Therefore expression is 
.
Let's combine to create the expression of 
.
Take every word and translate into math.
Anytime you take a quotient of
Let's combine to create the expression of
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Lisa has $6. She wants to buy some apples and bananas, but wants exactly ten fruits total. If bananas cost 50 cents each and apples cost $1 each, how many apples and bananas should she get?
Let 
represent bananas and 
represent apples. Set up the system of two equations but do not solve them.
Lisa has $6. She wants to buy some apples and bananas, but wants exactly ten fruits total. If bananas cost 50 cents each and apples cost $1 each, how many apples and bananas should she get?
Let
We need to write two equations, one for the total cost of all the fruits, and one for the total number of fruits.
If 
represents the number of bananas, and 
represents the number of apples, then from the problem statement we know that
must be equal to 
because Lisa wants 
total fruits.
For the other equation we know the price of each fruit and the total amount she wants to spend.
We have now identified the two equations. If you were to solve them, you would see that 
and 
, so she should get 
apples and 
bananas.
We need to write two equations, one for the total cost of all the fruits, and one for the total number of fruits.
If
For the other equation we know the price of each fruit and the total amount she wants to spend.
We have now identified the two equations. If you were to solve them, you would see that
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Set up the following expression: Twenty less than eight times a number.
Set up the following expression: Twenty less than eight times a number.
To set up the expression, evaluate part by part. Let 
be the unknown number.
Eight times a number: 
Twenty less than eight times the number means that this product is subtracted twenty. The final answer must be less than eight times the unknown number by twenty.
The correct answer is: 
To set up the expression, evaluate part by part. Let
Eight times a number:
Twenty less than eight times the number means that this product is subtracted twenty. The final answer must be less than eight times the unknown number by twenty.
The correct answer is:
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