Concepts - HSPT Math

First, we multiply –4 and 2. A negative and a positive number multiplied together give us a negative number, so (–4)(2) = –8. A negative times a negative is a positive so (–8)(–1) = 8. (8)(–3) = –24.

When multiplying negative numbers, we get a negative answer if there are an odd number of negative numbers being multiplied. We get a positive answer if there are an even number of negative numbers being multiplied.

a3 + b2 becomes (–2)3 + (–3)2 which equals –8 + 9 = 1

You simplify the expression to be 1 – 1 + 3 + 4 = 7

Multiplying a negative number and another negative number makes the product positive.

Divide .

Answer: Jasmine has completed 80% of the race.

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).

2(4x-3x)-6t+5x

First distribute the 2: 8x-6x-6t+5x

Combine the like terms: 7x-6t

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)