Question

5-46. what values of x will make the following equations true? homework help(please show work):a. $x^3=64$b. $(x + 1)^3-64=0$5-47.determine the measures of x, y and z at right. justify each conclusion using geometric relationships.homework help

Explanation:

For 5-46:

Step1: Solve $x^3=64$

Take cube root of both sides:
$$x = \sqrt[3]{64}$$

Step2: Calculate cube root

$$x = 4$$
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Step1: Isolate the cubic term

Rearrange $(x+1)^3 -64=0$:
$$(x+1)^3 = 64$$

Step2: Take cube root of both sides

$$x+1 = \sqrt[3]{64}$$

Step3: Solve for x

$$x+1 = 4 \implies x = 4-1 = 3$$

Step1: Find $x$ (isosceles triangle rule)

The triangle has two equal sides, so base angles are equal:
$$x = 28^\circ$$

Step2: Find $z$ (triangle angle sum)

Sum of angles in a triangle is $180^\circ$:
$$z = 180^\circ - 28^\circ - 28^\circ = 124^\circ$$

Step3: Find $y$ (corresponding angles, parallel lines)

The arrows show parallel lines, so corresponding angles are equal:
$$y = x = 28^\circ$$

Answer:

a. $x=4$
b. $x=3$

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For 5-47: