Describe and correct the error a student made when starting to solve the equation 8 ^ (x + 3) = 2 ^ (2x - 5) 8 ^ (x + 3) = 2 ^ (2x - 5) (2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5) 2 ^ (3x + 3) = 2 ^ (2x - 5) Choose the correct answer below A. The student should have divided both sides by 2 ^ 2 to simplify the expression B. The student did not convert 8 to the correct power of 2 C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3 D. The student should have expressed the initial rational exponent as the sum of two rational exponents ..

C. is the correct option

C. The student did not distribute 3 in * (2 ^ 3) ^ (x + 3) x + 3

and x = - 14

Step-by-step explanation:

8 ^ (x + 3) = 2 ^ (2x - 5)

Here is how the student solved the equation

8 ^ (x + 3) = 2 ^ (2x - 5)

8 ^ (x + 3) = 2 ^ (2x - 5)

(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)

2 ^ (3x + 3) = 2 ^ (2x - 5) -----  This is where the student made the error.

The student did not distribute 3 in * (2 ^ 3) ^ (x + 3).

This is how to solve the equation

8 ^ (x + 3) = 2 ^ (2x - 5)

8 ^ (x + 3) = 2 ^ (2x - 5)

(2 ^ 3) ^ (x + 3) = 2 ^ (2x - 5)

Then, we will 3 distribute in  (2 ^ 3) ^ (x + 3), so that we get

2 ^ (3x +9) = 2 ^ (2x -5)

Since the bases on both sides of the equation are equal, we can equate the powers so that we get

(3x +9) = (2x -5)

Then we will collect like terms

3x - 2x = -5 -9

∴ x = -14

This solution could be better written in this format

b. an equilateral triangle inscribed in a circle

step-by-step explanation:

we are given the figure of two circles having a triangle inside.

now, we know that,

"when a figure is lying inside an another figure, then the outside figure is known as circumscribed figure and the figure lying inside is referred to as the inscribed figure".

as we see that, the circles are containing the triangle completely.

thus, the circles are the circumscribed figures and the triangle is the inscribed figure.

hence, we get, 'an equilateral triangle is inscribed in a circle'.

i think 5 miles per hour

step-by-step explanation: