Concepts - HSPT Math
Card 0 of 8060
Simplify the following expression: x3 - 4(x2 + 3) + 15
Simplify the following expression: x3 - 4(x2 + 3) + 15
To simplify this expression, you must combine like terms. You should first use the distributive property and multiply -4 by x2 and -4 by 3.
x3 - 4x2 -12 + 15
You can then add -12 and 15, which equals 3.
You now have x3 - 4x2 + 3 and are finished. Just a reminder that x3 and 4x2 are not like terms as the x’s have different exponents.
To simplify this expression, you must combine like terms. You should first use the distributive property and multiply -4 by x2 and -4 by 3.
x3 - 4x2 -12 + 15
You can then add -12 and 15, which equals 3.
You now have x3 - 4x2 + 3 and are finished. Just a reminder that x3 and 4x2 are not like terms as the x’s have different exponents.
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Which of the following does not simplify to 
?
Which of the following does not simplify to
5x – (6x – 2x) = 5x – (4x) = x
(x – 1)(x + 2) - x2 + 2 = x2 + x – 2 – x2 + 2 = x
x(4x)/(4x) = x
(3 – 3)x = 0x = 0
5x – (6x – 2x) = 5x – (4x) = x
(x – 1)(x + 2) - x2 + 2 = x2 + x – 2 – x2 + 2 = x
x(4x)/(4x) = x
(3 – 3)x = 0x = 0
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Simplify the following expression:
2x(x2 + 4ax – 3a2) – 4a2(4x + 3a)
Simplify the following expression:
2x(x2 + 4ax – 3a2) – 4a2(4x + 3a)
Begin by distributing each part:
2x(x2 + 4ax – 3a2) = 2x * x2 + 2x * 4ax – 2x * 3a2 = 2x3 + 8ax2 – 6a2x
The second:
–4a2(4x + 3a) = –16a2x – 12a3
Now, combine these:
2x3 + 8ax2 – 6a2x – 16a2x – 12a3
The only common terms are those with a2x; therefore, this reduces to
2x3 + 8ax2 – 22a2x – 12a3
This is the same as the given answer:
–12a3 – 22a2x + 8ax2 + 2x3
Begin by distributing each part:
2x(x2 + 4ax – 3a2) = 2x * x2 + 2x * 4ax – 2x * 3a2 = 2x3 + 8ax2 – 6a2x
The second:
–4a2(4x + 3a) = –16a2x – 12a3
Now, combine these:
2x3 + 8ax2 – 6a2x – 16a2x – 12a3
The only common terms are those with a2x; therefore, this reduces to
2x3 + 8ax2 – 22a2x – 12a3
This is the same as the given answer:
–12a3 – 22a2x + 8ax2 + 2x3
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Simplify the expression:
Simplify the expression:
Factor out a (2_x_) from the denominator, which cancels with (2_x_) from the numerator. Then factor the numerator, which becomes (x + 1)(x + 1), of which one of them cancels and you're left with (x + 1).
Factor out a (2_x_) from the denominator, which cancels with (2_x_) from the numerator. Then factor the numerator, which becomes (x + 1)(x + 1), of which one of them cancels and you're left with (x + 1).
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Simplify the following expression:
Simplify the following expression:
First distribute the 2: 
Combine the like terms: 
First distribute the 2:
Combine the like terms:
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You are given that 
are whole numbers.
Which of the following is true of 
if 
and 
are both odd?
You are given that
Which of the following is true of
If 
is odd, then 
is odd, since the product of two odd whole numbers must be odd. When the odd number 
is added, the result, 
, is even, since the sum of two odd numbers must be even.
If 
is even, then 
is even, since the product of an odd number and an even number must be even. When the odd number 
is added, the result, 
, is odd, since the sum of an odd number and an even number must be odd.
If
If
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Simplify the expression:
Simplify the expression:
Combine all the like terms.
The 
terms can be combined together, which gives you 
.
When you combine the 
terms together, you get 
.
There is only one 
term so it doesn't get combined with anything. Put them all together and you get
.
Combine all the like terms.
The
When you combine the
There is only one
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Simplify: 
Simplify:
In order to simplify this expression, distribute and multiply the outer term with the two inner terms.
In order to simplify this expression, distribute and multiply the outer term with the two inner terms.
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Simplify: 
Simplify:
When the same bases are multiplied, their exponents can be added. Similarly, when the bases are divided, their exponents can be subtracted. Apply this rule for the given problem.
When the same bases are multiplied, their exponents can be added. Similarly, when the bases are divided, their exponents can be subtracted. Apply this rule for the given problem.
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Simplify: 
Simplify:
To simplify this expression, reduce the term inside the parenthesis.
Rewrite the negative exponent as a fraction.
To simplify this expression, reduce the term inside the parenthesis.
Rewrite the negative exponent as a fraction.
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Simplify the expression 
Simplify the expression
To simplify this expression, combine like terms. In this expression, 
and
are like terms. They are like terms because each term consists of a single variable,
, and a numeric coefficient. Add the coefficients of these terms. Addition is the operation that you would use denoted by a plus sign next to the x.
and 
are also like terms. They are like terms because each term consists of a single variable, 
, and a numeric coefficient. These two like terms are separated by a subtraction sign, therefore subtraction is the operation you would use
Therefore, the correct answer is
To simplify this expression, combine like terms. In this expression,
Therefore, the correct answer is
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Simplify the expression 
Simplify the expression
To simplify this expression, combine like terms. In this expression, 
and 
are like terms. They are like terms because each term consists of a 
, and a numeric coefficient. Add the coefficients of these terms. Addition is the operation that you would use denoted by a plus sign.
and 
are also like terms. They are like terms because each term consists of 
and a numeric coefficient. These two like terms are separated by a addition sign, therefore addition is the operation you would use.
Therefore, the correct answer is
To simplify this expression, combine like terms. In this expression,
Therefore, the correct answer is
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Simplify the expression:
Simplify the expression:
Combine all the like terms.
The terms can be combined together, which gives you .
When you combine the terms together, you get .
There is only one term so it doesn't get combined with anything. Put them all together and you get
.
Combine all the like terms.
The
When you combine the
There is only one
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Suzanne is at the grocery store. She has $5.00 to spend on produce. Oranges are $2.50 per pound, apples cost $1.50 per pound and bananas are $0.50 per pound. Which combination of fruit will fit her budget?
Suzanne is at the grocery store. She has $5.00 to spend on produce. Oranges are $2.50 per pound, apples cost $1.50 per pound and bananas are $0.50 per pound. Which combination of fruit will fit her budget?
Make a simple algebra equation and test it against each combination:
Total Cost = $2.50 * (# Oranges) + $1.50 * (# Apples) + $0.50 * (# Bananas)
Make a simple algebra equation and test it against each combination:
Total Cost = $2.50 * (# Oranges) + $1.50 * (# Apples) + $0.50 * (# Bananas)
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Solve for 
: 
Solve for
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Ann, Bailey, Cara, Jack, and Jill are running a marathon. Cara finishes 4 minutes before Ann. Jill finishes after Bailey, who finishes after Ann. Jack finishes right before Bailey. Who else does Jack finish the race before?
Ann, Bailey, Cara, Jack, and Jill are running a marathon. Cara finishes 4 minutes before Ann. Jill finishes after Bailey, who finishes after Ann. Jack finishes right before Bailey. Who else does Jack finish the race before?
Cara finishes first. Ann and Bailey finish before Jill. If Jack finishes right before Bailey, then Jill finishes last.
Cara finishes first. Ann and Bailey finish before Jill. If Jack finishes right before Bailey, then Jill finishes last.
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Jasmine is participating in a swimming race. If the race is 3000 yards, what percentage of the race has she completed at the 2400 yardline?
Jasmine is participating in a swimming race. If the race is 3000 yards, what percentage of the race has she completed at the 2400 yardline?
Divide 
.
Answer: Jasmine has completed 80% of the race.
Divide
Answer: Jasmine has completed 80% of the race.
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A full helium tank can blow up 50 balloons. At least how many times does the tank have to be re-filled in order to blow up 140 balloons?
A full helium tank can blow up 50 balloons. At least how many times does the tank have to be re-filled in order to blow up 140 balloons?
Divide 
Answer: The tank must be filled up at least 3 times.
Divide
Answer: The tank must be filled up at least 3 times.
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Alegra is taking a cooking class with friends. It is 40 dollars for every two people who participate because people are supposed to work in pairs. But if someone does not have a partner, that person can still participate but must pay $30 for him or herself. Alegra's four best friends participate in the class with her, and they divide the cost evenly. What is the total cost per person?
Alegra is taking a cooking class with friends. It is 40 dollars for every two people who participate because people are supposed to work in pairs. But if someone does not have a partner, that person can still participate but must pay $30 for him or herself. Alegra's four best friends participate in the class with her, and they divide the cost evenly. What is the total cost per person?
Since Alegra is taking the class with 4 friends, that means there are a total of 5 people. This means that there are 2 pairs of friends, and one alone friend.
Below are the prices that will be charged based on this make up:
2 pairs of people at 40 dollars per pair = 80 dollars
1 solo person at 30 dollars per person = 30 dollars
80 dollars plus 30 dollars is 110 dollars, the grand total.
When 110 dollars is divided by 5, the answer is 22. Therefore, 22 dollars is the correct answer.
Since Alegra is taking the class with 4 friends, that means there are a total of 5 people. This means that there are 2 pairs of friends, and one alone friend.
Below are the prices that will be charged based on this make up:
2 pairs of people at 40 dollars per pair = 80 dollars
1 solo person at 30 dollars per person = 30 dollars
80 dollars plus 30 dollars is 110 dollars, the grand total.
When 110 dollars is divided by 5, the answer is 22. Therefore, 22 dollars is the correct answer.
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In a math contest, the team from Lincoln High comprised five students - Melanie, Ned, Olivia, Phyllis, and Quinn. Melanie outscored Ned by 12 points; Ned outscored Quinn by 19 points; Phyllis outscored Ned by 45 points and Olivia by 20 points. Who came in third among the five?
In a math contest, the team from Lincoln High comprised five students - Melanie, Ned, Olivia, Phyllis, and Quinn. Melanie outscored Ned by 12 points; Ned outscored Quinn by 19 points; Phyllis outscored Ned by 45 points and Olivia by 20 points. Who came in third among the five?
Since this reasoning is valid regardless of the actual scores, suppose Quinn scored 100. Then Ned scored 19 more than Quinn, or 119, and Melanie scored 12 more than Ned, or 131. Phyllis scored 45 more than Ned, or 164, and Olivia scored 20 points fewer than Phyllis, or 144. This makes the order, from greatest to least:
Phyllis, Olivia, Melanie, Ned, Quinn
Melanie scored third among the five.
Since this reasoning is valid regardless of the actual scores, suppose Quinn scored 100. Then Ned scored 19 more than Quinn, or 119, and Melanie scored 12 more than Ned, or 131. Phyllis scored 45 more than Ned, or 164, and Olivia scored 20 points fewer than Phyllis, or 144. This makes the order, from greatest to least:
Phyllis, Olivia, Melanie, Ned, Quinn
Melanie scored third among the five.
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