7. In the diagram below, AB = CD. Find the length of AD. 2x+8
X-3
4x-6
A
B
C
D

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Ответ:

morganzahn16

09.04.2020

Mathematics

B. $\displaystyle \frac{-7}{2}$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Exponential Rule [Powering]: $\displaystyle (b^m)^n = b^{m \cdot n}$ Exponential Rule [Rewrite]: $\displaystyle b^{-m} = \frac{1}{b^m}$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle \bigg( \frac{1}{4} \bigg)^{x + 1} = 32$

Step 2: Solve for x

Rewrite: $\displaystyle \bigg( \frac{1}{2^2} \bigg)^{x + 1} = 2^5$ Exponential Rule [Rewrite]: $\displaystyle (2^{-2})^{x + 1} = 2^5$ Exponential Rule [Powering]: $\displaystyle 2^{-2(x + 1)} = 2^5$ Set: $\displaystyle -2(x + 1)} = 5$ [Division Property of Equality] Divide -2 on both sides: $\displaystyle x + 1 = \frac{-5}{2}$ [Subtraction Property of Equality] Subtract -1 on both sides: $\displaystyle x = \frac{-7}{2}$

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7. In the diagram below, AB = CD. Find the length of AD. 2x+8 X-3 4x-6 A B C D