# Identify the means and the extremes in the

• Slides: 40

Identify the means and the extremes in the proportion. w x = y z Means: y & x Extremes: w & z

Identify the means and the extremes in the proportion. 9 6+y = 12 w 5 Means: 6 + y & 12 w Extremes: 9 & 5

Identify the means and the extremes in the proportion. q+3 5 m = 2 q Means: 5 m & 2 Extremes: q + 3 & q

Identify the means and the extremes in the proportion. m a = T h Means: a & T Extremes: m & h

Factor completely. x 2 – 225 (x + 15)(x – 15)

Factor completely. 5 x 2 – 125 y 4 5(x 2 – 25 y 4) 5(x + 5 y 2)(x – 5 y 2)

Factor completely. 12 x 13 – 75 x 3 x(4 x 12 – 25) 3 x(2 x 6 + 5)(2 x 6 – 5)

Factor completely. x 2 + 12 x + 32 (x + 4)(x + 8)

Factor completely. x 2 – 12 x + 32 (x – 4)(x – 8)

Factor completely. x 2 – 4 x + 32 (x + 4)(x – 8)

Factor completely. x 2 + 14 x + 45 (x + 9)(x + 5)

Factor completely. x 2 + 15 x + 36 (x + 12)(x + 3)

Factor completely. 8 x 2 + 2 x – 21 8 x 2 + 14 x – 12 x – 21 2 x(4 x + 7) – 3(4 x + 7)(2 x – 3) 8 • -21 = -168 14 & -12

Factor completely. 12 x 2 + 53 x + 20 12 x 2 + 48 x + 5 x + 20 12 x(x + 4) + 5(x + 4)(12 x + 5) 12 • 20 = 240 48 & 5

Factor completely. 12 • -11 = -132 -22 & 6 12 x 2 – 16 x – 11 12 x 2 – 22 x + 6 x – 11 2 x(6 x – 11) + 1(6 x – 11) (2 x + 1)(6 x – 11)

Factor completely. 32 x 2 – 36 x + 9 32 x 2 – 24 x – 12 x + 9 8 x(4 x – 3) – 3(4 x – 3) (8 x – 3)(4 x – 3) 32 • 9 = 288 -24 & -12

Factor completely. x 2 – 15 x + 36 (x – 12)(x – 3)

Factor completely. x 2 + 4 x – 45 (x – 9)(x + 5)

Factor completely. 2 x 2 – 28 x + 90 2(x 2 – 14 x + 45) 2(x – 9)(x – 5)

Factor completely. 3 x 2 – 27 x – 108 3(x 2 – 9 x – 36) 3(x – 12)(x + 3)

Find the missing side of the triangle. x 16 12 122 + 162 = x 2 144 + 256 = x 2 400 = x 2 20 = x

Find the missing side of the triangle. x 3 2 2 2 + 3 2 = x 2 4 + 9= x 2 13 = x 2 3. 6 ≈ x

Find the missing side of the triangle. x 10 18 102 + 182 = x 2 100 + 324= x 2 424 = x 2 20. 6 ≈ x

Find the missing side of the triangle. 19 12 x 122 + x 2 = 192 144 + x 2 = 361 x 2 = 217 14. 7 ≈ x

Find the missing side of the triangle. 70 x 30 302 + x 2 = 702 900 + x 2 = 4900 x 2 = 4000 63. 2 ≈ x

Find the missing side of the triangle. 25 x 7 72 + x 2 = 252 49 + x 2 = 625 x 2 = 576 24 = x

Do the following lengths form a right triangle? 7, 24, 25 72 + 242 ? 252 49 + 576 ? 625 = 625 yes!

Do the following lengths form a right triangle? 5, 13, 12 52 + 122 ? 132 25 + 144 ? 169 = 169 yes!

Do the following lengths form a right triangle? 9, 12, 15 92 + 122 ? 152 81 + 144 ? 225 = 225 yes!

Do the following lengths form a right triangle? 12, 20, 18 122 + 182 ? 202 144 + 324 ? 400 468 ≠ 400 no!

Do the following lengths form a right triangle? 19, 17, 18 172 + 182 ? 192 289 + 324 ? 361 613 ≠ 361 no!

Do the following lengths form a right triangle? 2, 7, 8 22 + 72 ? 8 2 4 + 49 ? 64 53 ≠ 64 no!

∆ABC ~ ∆DEF. Find the value of x. F C +3 4 x 4 x = 3 x + 3 A 30 27 D 21 27 3 x B 30 E 90 x + 90 = 108 x 90 = 18 x x=5

∆GHI ~ ∆JKL. Find the value of x. H J 0 – 2 2 x + 5 = 3 x – 20 K G 9 8 3 x L 10 I 9 16 x + 40 = 27 x – 180 220 = 11 x 8 x = 20

∆MNO ~ ∆PQR. Find the value of x. P. 5 46 . 5 6 x + 28 6 N – 5 x 1 M Q O 6 x + 1 = 46. 5 5 x – 6 28. 5 34. 5 R 232. 5 x – 279 = 171 x + 28. 5 61. 5 x = 307. 5 x=5