2x + 5y = -3 ⇒ 2x + 5y = -3
1x + 8y = 4 ⇒ <u>2x + 16y = 8
</u> -<u>11y</u> = <u>-11 </u>
-11 -11
y = 1
2x + 5(1) = -3
2x + 5 = -3
<u> -5 -5</u>
<u>2x</u> = <u>-8</u>
2 2
x = -4
(x, y) = (-4, 1)
2x + 1y = 7 ⇒ 2x + 1y = 7
1x - 2y = -14 ⇒ <u>2x - 4y = -28</u>
<u>5y</u> = <u>35</u>
5 5
y = 7
2x + 7 = 7
<u> -7 -7</u>
<u>2x</u> = <u>0</u>
2 2
x = 0
(x, y) = (0, 7)
It would be 45 cups because each number is multiplied by 5
2 x 5 = 10
3 x 5 = 15
4 x 5 = 20
9 x 5 = 45
Which transformations can be used to map a triangle with vertices A(2, 2), B(4, 1), C(4, 5) to A’(–2, –2), B’(–1, –4), C’(–5, –4
Romashka [77]
The triangles ABC and A'B'C' are shown in the diagram below. The transformation is a reflection in the line

. This is proved by the fact that the distance between each corner ABC to the mirror line equals to the distance between the mirror line to A'B'C'.
Find the vertex.
x=b/-2a
12/-2(1)
x=-6
then plug into equation
-6^2+12(-6)+6
36-72+6=-30
(-6,-30)
32 students choose a favorite topping for their slices.
Let x be the total number of students.
1/2 of the total students, or 1/2x, choose pepperoni.
1/4 of the total students, or 1/4x, choose extra cheese.
1/8 of the total students, or 1/8x, choose sausage.
4 students choose mushrooms.
We know that together, these equal the total number of students, x:
1/2x+1/4x+1/8x+4=x
We will use 8 as the common denominator:
4/8x+2/8x+1/8x+4=x
Combining like terms:
7/8x+4=x
Subtract 7/8x from both sides:
7/8x+4-7/8x=x-7/8x
4=1x-7/8x
4=1/8x
Divide both sides by 1/8:
4÷(1/8) = 1/8x÷(1/8)
4/1÷(1/8) = x
4/1×8/1 = x
32/1 = x
32 = x