Single-Variable Algebra - GED Math
Card 0 of 840
Sixty-four coins, all dimes and nickels, total $5.15. How many of the coins are dimes?
Sixty-four coins, all dimes and nickels, total $5.15. How many of the coins are dimes?
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Let 
be the number of dimes. Then there are 
nickels.
An equation can be set up and solved for 
for the amount of money:
, the number of dimes.
Let
An equation can be set up and solved for
Sixty-four coins, all dimes and quarters, total $8.95. How many quarters are there?
Sixty-four coins, all dimes and quarters, total $8.95. How many quarters are there?
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Let 
be the number of quarters. Then there are 
dimes.
An equation can be set up and solved for 
for the amount of money in dollars:
Let
An equation can be set up and solved for
Marge and William are running away from each other in opposite directions. Marge is running at a rate of 
, while William is running at a rate of 
. In how many minutes will they be 
from each other?
Marge and William are running away from each other in opposite directions. Marge is running at a rate of 
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Every second, you know that Marge and William will become a total of 
or 
. Now, you can use the simple work formula for distance:
or, for our data, 
(Remember 
kilometers is 
meters.)
Thus, solving for 
you get:
This is in seconds, though. You need minutes. To convert, you need to divide by 
:
Every second, you know that Marge and William will become a total of 
(Remember 
Thus, solving for
This is in seconds, though. You need minutes. To convert, you need to divide by
Timmy works at a fast food chain retail store five days a week, eight hours a day. Suppose it costs him $2.00 everyday to drive to and from work. He makes $10.00 per hour. How much will Timmy have at the end of the week, before applicable taxes?
Timmy works at a fast food chain retail store five days a week, eight hours a day. Suppose it costs him $2.00 everyday to drive to and from work. He makes $10.00 per hour. How much will Timmy have at the end of the week, before applicable taxes?
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Timmy makes ten dollars per hour for eight hours.
For five days: 
Timmy also will pay 
for the week to get to work and back.
Subtract his expense from his earnings for the week.
Timmy will have 
by the end of the week.
Timmy makes ten dollars per hour for eight hours.
For five days:
Timmy also will pay
Subtract his expense from his earnings for the week.
Timmy will have
Multiply:
Multiply:
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Factor:
Factor:
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where
The numbers 
and 
fit those criteria. Therefore,
You can double check the answer using the FOIL method
where
The numbers
You can double check the answer using the FOIL method
Which of the following is a factor of the polynomial 
?
Which of the following is a factor of the polynomial
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Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states that 
is a factor of polynomial 
if and only if 
. We substitute 1, 2, 4, and 9 for 
in the polynomial to identify the factor.
:
:
:
:
Only 
makes the polynomial equal to 0, so among the choices, only 
is a factor.
Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states that
Only
Which of the following is a factor of the polynomial 
Which of the following is a factor of the polynomial
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Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states that is a factor of polynomial if and only if . We substitute 
and 
for in the polynomial to identify the factor.
:
:
:
:
Only 
makes the polynomial equal to 0, so of the four choices, only 
is a factor of the polynomial.
Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states that
Only
Which of the following is not a prime factor of 
?
Which of the following is not a prime factor of
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Factor 
all the way to its prime factorization.
can be factored as the difference of two perfect square terms as follows:
is a factor, and, as the sum of squares, it is a prime. 
is also a factor, but it is not a prime factor - it can be factored as the difference of two perfect square terms. We continue:
Therefore, all of the given polynomials are factors of 
, but 
is the correct choice, as it is not a prime factor.
Factor
Therefore, all of the given polynomials are factors of
Which of the following is a prime factor of 
?
Which of the following is a prime factor of
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is the sum of two cubes:
As such, it can be factored using the pattern
where 
;
The first factor,as the sum of squares, is a prime.
We try to factor the second by noting that it is "quadratic-style" based on 
. and can be written as
;
we seek to factor it as 
We want a pair of integers whose product is 1 and whose sum is 
. These integers do not exist, so 
is a prime.
is the prime factorization and the correct response is 
.
As such, it can be factored using the pattern
where
The first factor,as the sum of squares, is a prime.
We try to factor the second by noting that it is "quadratic-style" based on
we seek to factor it as
We want a pair of integers whose product is 1 and whose sum is
Which of the following is a prime factor of 
?
Which of the following is a prime factor of
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This can be most easily solved by first substituting 
for 
, and, subsequently, 
for 
:
This becomes quadratic in the new variable, and can be factored as
,
filling out the blanks with two numbers whose sum is 
and whose product is 
. Through some trial and error, the numbers can be seen to be 
.
Therefore, after factoring and substituting back,
The first factor, the sum of squares, is prime. The second factors as the difference of squares, so the final factorization is
.
Of the choices given, 
is correct.
This can be most easily solved by first substituting
This becomes quadratic in the new variable, and can be factored as
filling out the blanks with two numbers whose sum is
Therefore, after factoring and substituting back,
The first factor, the sum of squares, is prime. The second factors as the difference of squares, so the final factorization is
Of the choices given,
Which of the following is a prime factor of 
?
Which of the following is a prime factor of
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can be seen to fit the pattern
:
where 
can be factored as 
, so
.
does not fit into any factorization pattern, so it is prime, and the above is the complete factorization of the polynomial. Therefore, 
is the correct choice.
where
A triangle has a base of 
ft and height of 
ft. What is the area (in square feet) of the triangle?
A triangle has a base of
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The area of a triangle is: 
Use the FOIL Method to simplify.
The area of a triangle is:
Use the FOIL Method to simplify.
Express 286 in base five.
Express 286 in base five.
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To convert a base ten number to base five, divide the number by five, with the remainder being the digit in the units place; continue, dividing each successive quotient by five and putting the remainder in the next position to the left until the final quotient is less than five.
- 1 is the last digit.
- 2 is the second-to-last digit.
- 1 is the third-to-last digit; 2 is the first digit.
286 is equal to 
.
To convert a base ten number to base five, divide the number by five, with the remainder being the digit in the units place; continue, dividing each successive quotient by five and putting the remainder in the next position to the left until the final quotient is less than five.
286 is equal to
Increase 
by 20%. Which of the following will this be equal to?
Increase
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A number increased by 20% is equivalent to 100% of the number plus 20% of the number. This is taking 120% of the number, or, equivalently, multiplying it by 1.2.
Therefore, 
increased by 20% is 1.2 times this, or
.
A number increased by 20% is equivalent to 100% of the number plus 20% of the number. This is taking 120% of the number, or, equivalently, multiplying it by 1.2.
Therefore,
Divide:
Divide:
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Divide termwise:
Divide termwise:
Multiply:
Multiply:
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This product fits the difference of cubes pattern, where 
:
so
This product fits the difference of cubes pattern, where
so
Give the value of 
that makes the polynomial 
the square of a linear binomial.
Give the value of
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A quadratic trinomial is a perfect square if and only if takes the form
for some values of 
and 
.
, so
and 
.
For 
to be a perfect square, it must hold that
,
so 
. This is the correct choice.
A quadratic trinomial is a perfect square if and only if takes the form
For
so
Simplify the following: 
Simplify the following:
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Group all like terms by their order:
Simplify:
Group all like terms by their order:
Simplify:
Simplify the following: 
Simplify the following:
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This can be solved using the FOIL method. The steps are shown below.
Therefore, after reordering, the answer is: 
This can be solved using the FOIL method. The steps are shown below.
Therefore, after reordering, the answer is: