Mathematics, 17.06.2021 03:40 aliay6857

A. -11/3

B. -7/3

C. 7/3

D. 11/3

A. -11/3
B. -7/3
C. 7/3
D. 11/3

Answers: 1

Show answers

Answers

Answer from: dorothybean

$\displaystyle a = \frac{-11}{3}$

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

$\displaystyle 9 = (\frac{1}{27})^{a + 3}$

Step 2: Solve for a

Rewrite: $\displaystyle 3^2 = (\frac{1}{27})^{a + 3}$ Rewrite: $\displaystyle 3^2 = (\frac{1}{3^3})^{a + 3}$ Rewrite [Exponential Rule - Rewrite]: $\displaystyle 3^2 = (3^{-3})^{a + 3}$ Exponential Rule [Powering]: $\displaystyle 3^2 = 3^{-3(a + 3)}$ Set up: $\displaystyle 2 = -3(a + 3)$ [Division Property of Equality] Divide -3 on both sides: $\displaystyle \frac{-2}{3} = a + 3$ [Subtraction Property of Equality] Subtract 3 on both sides: $\displaystyle \frac{-11}{3} = a$ Rewrite: $\displaystyle a = \frac{-11}{3}$

Answer from: Quest

x= -3 and $x=\frac{-3+/-3i\sqrt{3} }{2}$

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

$(x^3-a^3)=$ $(x-a)(x^2+ax+a^2)$

where a is the cube root of $a^3$ .

here this is 27 and the cube root of 27 is 3. so we write using the form:

$(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9)$ .

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

$x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}$

where a = 1, b=3, and c=9

$x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}$

this cubic has two complex roots.

Answer from: Quest

step-by-step explanation:

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You know the right answer?

A. -11/3

B. -7/3

C. 7/3

D. 11/3
...