Pre-Algebra

Which of the following statements demonstrates the associative property of addition?

None of the examples in the other responses demonstrates the associative property of addition.

Explanation

The associative property of addition states that to add three numbers, any two can be added first, followed by adding the sum to the third. Of the statements given, only

demonstrates this property, so it is the correct choice.

Explanation

When two negative values are multiplied, the answer becomes positive. Then, we multiply normally. We should get or .

$400\div -20\div 10$

Explanation

We have two positive numbers and one negative number. We work from left to right. When a positive number is divided by a negative number, the answer is a negative number. The same applied when divided by a positive number.

$\frac{400}{-20}=\frac{20\cdot 20}{-20}=-20$

Now the expression becomes,

$-20\div10$

$\frac{-20}{10}=\frac{-2\cdot 10}{10}=-2$ .

Answer is .

Sarah is building a fence for her dog's square play area. To reduce the cost, she is using her house as 1 side of the play area, meaning she only has to purchase fencing for the other sides. If she needs to fence in 225 meters2 for her dogs, and fencing costs $2.50 per meter of fencing, what will be the cost of fencing in this square play area?

$\small \small $ 112.50$

$\small $ 562.50$

$\small $ 140.63$

$\small $ 45$

$\small $75$

Explanation

The first step is to figure out the perimeter of the square play yard with an area of 225 meters, first using the fomula:

$\small (area) = (base)^2$

Find the square root of both sides to calculate the length of the base of the square

$\small \small \small \small \sqrt225 = (base) = 15$

All the sides are of equivilent length, so the total amount of fence required is:

$\small \small (15)*3 = 45$

One side is "fenced" by the house, so that fenching does not need to be paid for. Thus, only the remaining 3 sides need to be paid for.

Finally, multiply the length of fencing needs by the cost of fence per foot to find your answer:

$\small 45 * $2.50 = $112.50$

Solve for .

$\frac{x}{-0.9}=-3.1$

Explanation

$\frac{x}{-0.9}=-3.1$ Multiply both sides by . When multiplying decimals, first multiply normally and then count the number of decimal places in the problem. We have . So starting from the right, we shift two places to the left to get a decimal of . Since we are multiplying with negative numbers, we need to determine if the answer is negative. There are two negative numbers and that means the answer is positive.

Which expression simplifies to

Explanation

results in when simplifying with the foil method as follows:
First: $x\cdot x= x^2$

Inner: $x\cdot 3=3x$

Outer: $x\cdot -3=-3x$

Last: $3\cdot -3=-9$

$x^{2}+3x-3x-9=x^{2}-9$

Write the ordered pair of points a, b, and c.

Coordinate plane

$a =(1, 4),\ b= ( -5, 2),\ c =(0, -5)$

$a =(4, 1),\ b =(2, -5),\ c= (-5, 0)$

$a =(1, 4),\ b =(5, 2),\ c =(5, 0)$

$a= (0, 4),\ b =(0, -5),\ c =(0, -5)$

$a= ( 1, 5),\ b= ( 1, 7),\ c =( 1, 5)$

Explanation

An ordered is always written in the following format:

where x is the position on the x-axis, and y is the position on the y-axis.

Coordinate plane

If we look at point a, we find where it falls on the x-axis. We can see that it's position on the x-axis is 1. Then, we see where it falls on the y-axis. It's position on the y-axis is 4. So, we can write the ordered pair for point a as

We will do the same for b. The position of point b on the x-axis is -5. The position of point b on the y-axis is 2. So, we can write the ordered pair for point b as

And finally for c. The position of point c on the x-axis is zero. The position of point c on the y-axis is -5. So, we can write the ordered pair of point c as