Algebra - HSPT Math

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.

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

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

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).

First distribute the 2:

Combine the like terms:

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.

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

.

In order to simplify this expression, distribute and multiply the outer term with the two inner terms.

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.

To simplify this expression, reduce the term inside the parenthesis.

Rewrite the negative exponent as a fraction.

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, 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

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

.

Make a simple algebra equation and test it against each combination:

Total Cost = $2.50 * (# Oranges) + $1.50 * (# Apples) + $0.50 * (# Bananas)

Cara finishes first. Ann and Bailey finish before Jill. If Jack finishes right before Bailey, then Jill finishes last.

Divide

Answer: The tank must be filled up at least 3 times.

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 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.