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Identify the means and the extremes in the proportion.

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

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Identify the means and the extremes in the proportion.

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

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

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

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

  5. Factor completely. (x + 15)(x – 15) x2 – 225

  6. Factor completely. 5(x2 – 25y4) 5(x + 5y2)(x – 5y2) 5x2 – 125y4

  7. Factor completely. 3x(4x12 – 25) 3x(2x6 + 5)(2x6 – 5) 12x13 – 75x

  8. Factor completely. (x + 4)(x + 8) x2 + 12x + 32

  9. Factor completely. (x – 4)(x – 8) x2 – 12x + 32

  10. Factor completely. (x + 4)(x – 8) x2 – 4x + 32

  11. Factor completely. (x + 9)(x + 5) x2 + 14x + 45

  12. Factor completely. (x + 12)(x + 3) x2 + 15x + 36

  13. 8 •-21 = -168 14 & -12 Factor completely. 8x2 + 14x – 12x – 21 2x(4x + 7) – 3(4x + 7) (4x + 7)(2x – 3) 8x2 + 2x – 21

  14. 12 •20 = 240 48 & 5 Factor completely. 12x2 + 48x + 5x + 20 12x(x + 4) + 5(x + 4) (x + 4)(12x + 5) 12x2 + 53x + 20

  15. 12 •-11 = -132 -22 & 6 Factor completely. 12x2– 22x + 6x – 11 2x(6x – 11) + 1(6x – 11) (2x + 1)(6x – 11) 12x2– 16x – 11

  16. 32 • 9 = 288 -24 & -12 Factor completely. 32x2– 24x – 12x + 9 8x(4x – 3) – 3(4x – 3) (8x – 3)(4x – 3) 32x2– 36x + 9

  17. Factor completely. (x – 12)(x – 3) x2– 15x + 36

  18. Factor completely. (x – 9)(x + 5) x2 + 4x – 45

  19. Factor completely. 2(x2 – 14x + 45) 2(x – 9)(x – 5) 2x2– 28x + 90

  20. Factor completely. 3(x2 – 9x – 36) 3(x – 12)(x + 3) 3x2– 27x – 108

  21. Find the missing side of the triangle. 122 + 162 = x2 144 + 256 = x2 400 = x2 20 = x x 16 12

  22. Find the missing side of the triangle. 22 + 32 = x2 4 + 9= x2 13 = x2 3.6 ≈ x x 3 2

  23. Find the missing side of the triangle. 102 + 182 = x2 100 + 324= x2 424 = x2 20.6 ≈ x x 10 18

  24. Find the missing side of the triangle. 122 + x2 = 192 144 + x2 = 361 x2 = 217 14.7 ≈ x 19 12 x

  25. Find the missing side of the triangle. 302 + x2 = 702 900 + x2 = 4900 x2 = 4000 63.2 ≈ x 70 x 30

  26. Find the missing side of the triangle. 72 + x2 = 252 49 + x2 = 625 x2 = 576 24 = x 25 x 7

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

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

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

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

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

  32. Do the following lengths form a right triangle? 22 + 72 ? 82 4 + 49 ? 64 53 ≠ 64 no! 2, 7, 8

  33. DBA DAC ∆ABC ~∆______ ~∆ _______ B D C A

  34. YBS BUS ∆YUB ~∆______ ~∆ _______ U S Y B

  35. PMQ QMR ∆PQR ~∆______ ~∆ _______ P M R Q

  36. GIH HIJ ∆GHJ ~∆______ ~∆ _______ G I J H

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

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

  39. ∆MNO ~∆PQR. Find the value of x. M P 6x + 1 46.5 5x – 6 28.5 Q N O R 34.5 232.5x – 279 = 171x + 28.5 61.5x = 307.5 x = 5 6x + 1 = 46.5 5x – 6 28.5

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