Expressions - PSAT Math
Card 0 of 406
Which of the following phrases can be written as the algebraic expression
?
Which of the following phrases can be written as the algebraic expression ?
is the cube of
, which is the difference of a number and nineteen; therefore,
is "the cube of the difference of a number and nineteen."
is the cube of
, which is the difference of a number and nineteen; therefore,
is "the cube of the difference of a number and nineteen."
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Which of the following phrases can be written as the algebraic expression
?
Which of the following phrases can be written as the algebraic expression ?
is seventeen decreased by
, which is the cube of a number; therefore,
is "seventeen decreased by the cube of a number."
is seventeen decreased by
, which is the cube of a number; therefore,
is "seventeen decreased by the cube of a number."
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Increase
by 70%. Which of the following will this be equal to?
Increase by 70%. Which of the following will this be equal to?
A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.
Therefore,
increased by 70% is 1.7 times this, or

A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.
Therefore, increased by 70% is 1.7 times this, or
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Which of the following operations could represent the expression
?
Which of the following operations could represent the expression ?
Begin by putting the equation given into your own words. It might sound something similar to:
2 times x squared plus 7
Now, go through each answer choice and see if any of them are similar to this. We immediately see that the answer "7 more than 2 times the square of x" is similar to what we came up with. Let's do a quick run through of the other choices to be sure of our choice:
"2 times 7 more than the square of x" is equal to
, which is equivalent to
.
"2 times 7 less than the square of x" is equal to
, which is equivalent to
.
"7 more than the square of 2x" is equal to
, which is equivalent to
.
"7 less than the square of 2x" is equal to
, which is equivalent to
.
The only answer that works is "7 more than 2 times the square of x". This is the correct answer.
Begin by putting the equation given into your own words. It might sound something similar to:
2 times x squared plus 7
Now, go through each answer choice and see if any of them are similar to this. We immediately see that the answer "7 more than 2 times the square of x" is similar to what we came up with. Let's do a quick run through of the other choices to be sure of our choice:
"2 times 7 more than the square of x" is equal to , which is equivalent to
.
"2 times 7 less than the square of x" is equal to , which is equivalent to
.
"7 more than the square of 2x" is equal to , which is equivalent to
.
"7 less than the square of 2x" is equal to , which is equivalent to
.
The only answer that works is "7 more than 2 times the square of x". This is the correct answer.
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What does
equal?
What does equal?
When solving a complex expression, remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Reading left to right, begin by doing all operations within the innermost Parentheses first:



Continue simplifying using the acronym PEMDAS:


The expression is equal to -63.
When solving a complex expression, remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Reading left to right, begin by doing all operations within the innermost Parentheses first:
Continue simplifying using the acronym PEMDAS:
The expression is equal to -63.
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If √(ab) = 8, and _a_2 = b, what is a?
If √(ab) = 8, and _a_2 = b, what is a?
If we plug in _a_2 for b in the radical expression, we get √(_a_3) = 8. This can be rewritten as a_3/2 = 8. Thus, log_a 8 = 3/2. Plugging in the answer choices gives 4 as the correct answer.
If we plug in _a_2 for b in the radical expression, we get √(_a_3) = 8. This can be rewritten as a_3/2 = 8. Thus, log_a 8 = 3/2. Plugging in the answer choices gives 4 as the correct answer.
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Simplify (4x)/(x2 – 4) * (x + 2)/(x2 – 2x)
Simplify (4x)/(x2 – 4) * (x + 2)/(x2 – 2x)
Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.
Factor first. The numerators will not factor, but the first denominator factors to (x – 2)(x + 2) and the second denomintaor factors to x(x – 2). Multiplying fractions does not require common denominators, so now look for common factors to divide out. There is a factor of x and a factor of (x + 2) that both divide out, leaving 4 in the numerator and two factors of (x – 2) in the denominator.
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what is 6/8 X 20/3
what is 6/8 X 20/3
6/8 X 20/3 first step is to reduce 6/8 -> 3/4 (Divide top and bottom by 2)
3/4 X 20/3 (cross-cancel the threes and the 20 reduces to 5 and the 4 reduces to 1)
1/1 X 5/1 = 5
6/8 X 20/3 first step is to reduce 6/8 -> 3/4 (Divide top and bottom by 2)
3/4 X 20/3 (cross-cancel the threes and the 20 reduces to 5 and the 4 reduces to 1)
1/1 X 5/1 = 5
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Which of the following is equivalent to
? Assume that denominators are always nonzero.
Which of the following is equivalent to ? Assume that denominators are always nonzero.
We will need to simplify the expression
. We can think of this as a large fraction with a numerator of
and a denominator of
.
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator.
has a denominator of
, and
has a denominator of
. The least common denominator that these two fractions have in common is
. Thus, we are going to write equivalent fractions with denominators of
.
In order to convert the fraction
to a denominator with
, we will need to multiply the top and bottom by
.

Similarly, we will multiply the top and bottom of
by
.

We can now rewrite
as follows:
= 
Let's go back to the original fraction
. We will now rewrite the numerator:
= 
To simplify this further, we can think of
as the same as
. When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words,
.
= 


Lastly, we will use the property of exponents which states that, in general,
.

The answer is
.
We will need to simplify the expression . We can think of this as a large fraction with a numerator of
and a denominator of
.
In order to simplify the numerator, we will need to combine the two fractions. When adding or subtracting fractions, we must have a common denominator. has a denominator of
, and
has a denominator of
. The least common denominator that these two fractions have in common is
. Thus, we are going to write equivalent fractions with denominators of
.
In order to convert the fraction to a denominator with
, we will need to multiply the top and bottom by
.
Similarly, we will multiply the top and bottom of by
.
We can now rewrite as follows:
=
Let's go back to the original fraction . We will now rewrite the numerator:
=
To simplify this further, we can think of as the same as
. When we divide a fraction by another quantity, this is the same as multiplying the fraction by the reciprocal of that quantity. In other words,
.
=
Lastly, we will use the property of exponents which states that, in general, .
The answer is .
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Which of the following phrases can be written as the algebraic expression
?
Which of the following phrases can be written as the algebraic expression ?
is seventeen decreased by
, which is the cube of a number; therefore,
is "seventeen decreased by the cube of a number."
is seventeen decreased by
, which is the cube of a number; therefore,
is "seventeen decreased by the cube of a number."
Compare your answer with the correct one above
Increase
by 70%. Which of the following will this be equal to?
Increase by 70%. Which of the following will this be equal to?
A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.
Therefore,
increased by 70% is 1.7 times this, or

A number increased by 70% is equivalent to 100% of the number plus 70% of the number. This is taking 170% of the number, or, equivalently, multiplying it by 1.7.
Therefore, increased by 70% is 1.7 times this, or
Compare your answer with the correct one above
Which of the following phrases can be written as the algebraic expression
?
Which of the following phrases can be written as the algebraic expression ?
is the cube of
, which is the difference of a number and nineteen; therefore,
is "the cube of the difference of a number and nineteen."
is the cube of
, which is the difference of a number and nineteen; therefore,
is "the cube of the difference of a number and nineteen."
Compare your answer with the correct one above
Which of the following operations could represent the expression
?
Which of the following operations could represent the expression ?
Begin by putting the equation given into your own words. It might sound something similar to:
2 times x squared plus 7
Now, go through each answer choice and see if any of them are similar to this. We immediately see that the answer "7 more than 2 times the square of x" is similar to what we came up with. Let's do a quick run through of the other choices to be sure of our choice:
"2 times 7 more than the square of x" is equal to
, which is equivalent to
.
"2 times 7 less than the square of x" is equal to
, which is equivalent to
.
"7 more than the square of 2x" is equal to
, which is equivalent to
.
"7 less than the square of 2x" is equal to
, which is equivalent to
.
The only answer that works is "7 more than 2 times the square of x". This is the correct answer.
Begin by putting the equation given into your own words. It might sound something similar to:
2 times x squared plus 7
Now, go through each answer choice and see if any of them are similar to this. We immediately see that the answer "7 more than 2 times the square of x" is similar to what we came up with. Let's do a quick run through of the other choices to be sure of our choice:
"2 times 7 more than the square of x" is equal to , which is equivalent to
.
"2 times 7 less than the square of x" is equal to , which is equivalent to
.
"7 more than the square of 2x" is equal to , which is equivalent to
.
"7 less than the square of 2x" is equal to , which is equivalent to
.
The only answer that works is "7 more than 2 times the square of x". This is the correct answer.
Compare your answer with the correct one above
What does
equal?
What does equal?
When solving a complex expression, remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Reading left to right, begin by doing all operations within the innermost Parentheses first:



Continue simplifying using the acronym PEMDAS:


The expression is equal to -63.
When solving a complex expression, remember the acronym PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction). Reading left to right, begin by doing all operations within the innermost Parentheses first:
Continue simplifying using the acronym PEMDAS:
The expression is equal to -63.
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A rowing team paddles upstream at a rate of 10 miles every 2 hours and downstream at a rate of 27 miles every 3 hours. Assuming they are paddling at the same rate up and downstream, what is the speed of the water?
A rowing team paddles upstream at a rate of 10 miles every 2 hours and downstream at a rate of 27 miles every 3 hours. Assuming they are paddling at the same rate up and downstream, what is the speed of the water?
Upstream: p – w = (10/2) or p – w = 5 miles/hour
Downstream: p + w = (27/3) or p + w = 9 miles/hour
Then we add the two equations together to cancel out the w's. After adding we see
2p = 14
p = 7 miles/hour where p is the rate of the paddling. We plug p into the equation to find
w = 2 miles/hour where w is the rate of the stream's water.
Upstream: p – w = (10/2) or p – w = 5 miles/hour
Downstream: p + w = (27/3) or p + w = 9 miles/hour
Then we add the two equations together to cancel out the w's. After adding we see
2p = 14
p = 7 miles/hour where p is the rate of the paddling. We plug p into the equation to find
w = 2 miles/hour where w is the rate of the stream's water.
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If ab - bc + d = d2 - c2, then what is the value of a when b is two, c is negative one, and d is zero?
If ab - bc + d = d2 - c2, then what is the value of a when b is two, c is negative one, and d is zero?
ab - bc + d = d2 - c2
We need to substitute values in for b, c, and d, and then solve the equation for a.
a(2) - 2(-1) + 0 = 02 - (-1)2
2a +2 + 0 = 0 - (1)
2a + 2 = -1
2a = -3
a = -3/2
The answer is -3/2.
ab - bc + d = d2 - c2
We need to substitute values in for b, c, and d, and then solve the equation for a.
a(2) - 2(-1) + 0 = 02 - (-1)2
2a +2 + 0 = 0 - (1)
2a + 2 = -1
2a = -3
a = -3/2
The answer is -3/2.
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If 11x + 4 = 19x – 12, then what is 2x – 4?
If 11x + 4 = 19x – 12, then what is 2x – 4?
First solve for x. The first equation would simplify as:
16 = 8x
x = 2
If we plug x = 2 into the second expression:
2(2) – 4 = 0
0 is the correct answer.
First solve for x. The first equation would simplify as:
16 = 8x
x = 2
If we plug x = 2 into the second expression:
2(2) – 4 = 0
0 is the correct answer.
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If x = 2 and y = 3, then evaluate 2(x – 3) + 5y2
If x = 2 and y = 3, then evaluate 2(x – 3) + 5y2
To evaluate an expression we make substitutions into the expression
2(x – 3) + 5y2 becomes 2(2 – 3) + 5 * 32 = –2 + 45 = 43
To evaluate an expression we make substitutions into the expression
2(x – 3) + 5y2 becomes 2(2 – 3) + 5 * 32 = –2 + 45 = 43
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IF 5x3 = 40, then what is the value of 12x – (x/2)?
IF 5x3 = 40, then what is the value of 12x – (x/2)?
Use the first equation to solve for x, then plug into the 2nd equation to find a value.
5x3 = 40
x3 = 8
x = 2
12(2) – (2/2) = 24 – 1 = 23
Use the first equation to solve for x, then plug into the 2nd equation to find a value.
5x3 = 40
x3 = 8
x = 2
12(2) – (2/2) = 24 – 1 = 23
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