Mathematics, 26.06.2021 05:20 jetblackcap

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What is the solution to this equation? (1/4)^x+1 =32

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Answer from: anthony3913

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: $\displaystyle x = \frac{-7}{2}$

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$

from $a_2 = 3$ , to get to $a_3 = 6$ , we add $3 (=2+1)$

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

$a_1 = 1$ , and $a_{n+1} = a_n +(n + 1)$ for $n \ge 1$

Answer from: Quest

Ya i could just need to know what type of math

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