Simplify each expression. 15. $$(7k^2 - 36k + 5) / (3k^2 - 12k - 15) · (42k + 6) / (1 - 49k^2)$$

$$(7k^2 - 36k + 5)/(3(k^2 - 4k - 5))$$ · $$6(7k+1)$$ / $$(-(49k^2-1))$$ = $$(7k^2 - 36k + 5)/(3(k-5)(k+1))$$ · $$6(7k+1)$$ / $$(-(7k-1)(7k+1))$$ = $$(7k^2 - 36k + 5)·6/3(k-5)(k+1)(-1)(7k-1)$$

$$\frac{7k^2 - 36k + 5}{3k^2 - 12k - 15}$$ · $$\frac{42k + 6}{1 - 49k^2}$$ = $$\frac{7k^2 - 36k + 5}{3(k-5)(k+1)}$$ · $$\frac{42k + 6}{(1-7k)(1+7k)}$$

$$\frac{7k^2 - 36k + 5}{3k^2 - 12k - 15}$$ · $$\frac{42k + 6}{1 - 49k^2}$$ = $$\frac{7k^2 - 36k + 5}{3(k-5)(k+1)}$$ · $$\frac{42k + 6}{(7k-1)(7k+1)}$$

$$\frac{7k^2 - 36k + 5}{3k^2 - 12k - 15}$$ · $$\frac{42k + 6}{1 - 49k^2}$$ = $$\frac{7k^2 - 36k + 5}{3(k-5)(k+1)}$$ · $$\frac{42k + 6}{(k-7)(k+7)}$$

Simplify each expression. 37. (-7 - 4i) / (-8 + i)

-60 - 45i / 65 = -12/13 - 9/13i

-60 + 45i / 65 = -12/13 + 9/13i

How many seconds will it take the ball to reach the ground?

t = 2.25 seconds (rounded to two decimal places)

t = 1.50 seconds (rounded to two decimal places)

t = 3.00 seconds (rounded to two decimal places)

t = 4.10 seconds (rounded to two decimal places)

Solve each equation. Be sure to check for extraneous solutions. 57. (k + 6)/(4 - k) = 2/(k - 4)

k = 2 (after checking for extraneous solutions)

Solve each equation. Be sure to check for extraneous solutions. 58. $$\frac{1}{2k^2} - \frac{3}{k} = \frac{1}{k^2}$$

k = -1, k = 2 (after checking for extraneous solutions)

Solve each equation. Be sure to check for extraneous solutions.

u = 2 (after checking for extraneous solutions)

u = -2 (after checking for extraneous solutions)

u = 0 (after checking for extraneous solutions)

u = 4 (after checking for extraneous solutions)

Solve each equation. Be sure to check for extraneous solutions.

y = 6 (after checking for extraneous solutions)

y = -6 (after checking for extraneous solutions)

y = 0 (after checking for extraneous solutions)

y = 12 (after checking for extraneous solutions)

Solve, graph, and write each solution in interval notation. 61. -6(4d + 3) + 8

d > -5 (interval notation: (-5, ∞))

d > 5 (interval notation: (5, ∞))

Solve, graph, and write each solution in interval notation. 62. |2x + 7| ≤ 3

-5 ≤ x ≤ -2 (interval notation: [-5, -2])

x ≤ -5 or x ≥ -2 (interval notation: (-∞, -5] ∪ [-2, ∞))

-2 ≤ x ≤ 5 (interval notation: [-2, 5])

x ≥ 5 or x ≤ -2 (interval notation: (-∞, -2] ∪ [5, ∞))

Solve, graph, and write each solution in interval notation. 63. -3|−10x − 2|

x 0 (interval notation: (-∞, -2) ∪ (0, ∞))

x 0 (interval notation: (-∞, 2) ∪ (0, ∞))

Solve, graph, and write each solution in interval notation. 64. 2 − 3|−3r + 6| ≥ −61

r ≤ -2 or r ≥ 4 (interval notation: (-∞, -2] ∪ [4, ∞))

r ≥ -2 or r ≤ 4 (interval notation: [-2, ∞) ∪ (-∞, 4])

r ≤ 2 or r ≥ -4 (interval notation: (-∞, 2] ∪ [-4, ∞))

r ≥ 2 or r ≤ -4 (interval notation: [2, ∞) ∪ (-∞, -4])

M4 Unit 1 (Fundamental Skills) Study Guide

Authored by Tammy Brackett

Mathematics

11th Grade

CCSS covered

Used 1+ times

M4 Unit 1 (Fundamental Skills) Study Guide

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