Mr Thompson, Please help!

firsts question is A

Step-by-step explanation:

Problem 1

Explanation:

Use the difference of squares rule here.

That rule says (a-b)(a+b) = a^2-b^2

In this case, a = x and b = 2.

Problem 2

Work Shown:

(2x+5)(x+1)

y(x+1) let y = 2x+5

xy+y

x(y) + 1(y)

x(2x+5) + 1(2x+5) ... plug in y = 2x+5

2x^2+5x+2x+5

2x^2+7x+5

Problem 3

Explanation:

The standard form of a quadratic is ax^2+bx+c, where a,b,c are real numbers. In the case of choice A, we have a = -1, b = -5, c = 7.

Problem 4

Explanation:

Along the top we have three green rectangles. If each of them are of length x, then we have x+x+x = 3x so far. Then adding on a yellow piece of 1 unit leads to 3x+1 as the total horizontal width across the top.

Similarly, along the left side we have 1 green portion and 2 yellow leading to x+2. So this shows why this diagram represents (3x+1)(x+2)

A rectangle must be formed with the smaller pieces glued together. We cannot have any gaps or overlaps. The reason we're aiming for a rectangle is because the area of a rectangle is length*width. Think of (3x+1) as the length and (x+2) as the width.

point a is the center of the circle that passes through points e, f, and g and the center of the circle that passes through points x, y, and z.

yes because there is exactly one y value for every x value

for function there can't be more than one value for every x value