Answer:
1&2)
GH = 28
FH = 56
XY = 7
XZ = 14
3-6) Acute, Obtuse, Acute, Right
7) Perimeter: 40 in. Area: 84 in^2
8) Perimeter: 42 m. Area: 84 m^2
9) Perimeter: 15.2 yd. Area: 14.44 yd^2
10) 1, 8, 27, 64, 125 These are the cubes of 1, 2, 3, 4, 5 so it's just the cube of the next number that was cubed before.
11) 128, 32, 8, 2, 1/2 Divide the previous number by 4.
12) 2, -6, 18, -54, 162 Multiply the previous number by -3
13-15) I'm sorry we didn't do those so I don't really know how that works sorry.
16) 3x - 14 = 34
3x = 48 Add 14 to each side (to isolate 3x)
x = 16 Divide by 3 both sides (to get x)
17) -4(x+3) = -28
x+3 = 7 divide by -4 on both sides (to get a step closer to solving for x and isolating x+3)
x = 4 subtract 3 from both sides (to get x (isolating x))
18) 43 - 9(x-7) = -x - 6
43 - 9x + 63 = -x - 6 distribute 9 to x and 7 (to expand)
106 - 9x = -x - 6 combine like terms (easier to deal with)
106 - 8x = -6 add x to both sides (so there's only x on one side)
112 - 8x = 0 add 6 to both sides (only one number left)
112 = 8x move -8x to the right side
x = 14 divide by 8 (to isolate x)
19) x = 29 degrees
20) x = 13 degrees
21) x = 9 degrees, y = 31 degrees
Explanation:
4x = 5x-7
x = 7
GH = 5(7) - 7 = 35 - 7 = 28
FH = 4x + 5x - 7 = 4(7) + 28 = 28*2 = 56
3x - 5 = x + 3
x = 4
XY = 3(4) - 5 = 12 - 5 = 7
XZ = 7*2 = 14
Acute is < 90
Obtuse is > 90
Right is = 90
Straight is = 180
7) 2(6+14) = 2(20) = 40 in
6*14 = 84 in^2
8) 13+14+15 = 42 m
(12*14)/2 = 6*14 = 84 m^2
9) 3.8*4 = 15.2 yd
3.8^2 = 14.44 yd^2
19) 34 + 4x + 30 = 180
64 + 4x = 180
4x = 116
x = 29
20) 4x + 7x + 37 = 180
11x = 143
x = 13
21) 3y + 42 = 9x + 54
y + 14 = 3x + 18
y = 3x + 4
3y + 42 + 5x + 9x + 54 + 5x = 360
3y + 19x = 264
substitute y with 3x + 4
3(3x + 4) + 19x = 264
9x + 12 + 19x = 264
28x = 252
x = 9
so y = 3(9) + 4 = 27 + 4 = 31