Answer:
Height of the box = 11.5 in
Step-by-step explanation:
Let h be the height of the box.
Assuming the volume of the Box is
.
Given:
Length = Height - 4 = h - 4
Width = 3 in
We need to find the height of the box.
Solution:
We know that the volume of the box.

Substitute all given value in above formula.

Rewrite the equation as:



whole equation divided by 3.

Use quadratic formula with

Put these a, b and c value in above equation.




For positive sign
h = 11.5 in
For negative sign

h = -7.5
We take positive value of h.
Therefore, the height of the box h = 11.5 in
So I'm going to assume that this question is asking for <u>non extraneous solutions</u>, or solutions that are found in the equation <em>and</em> are valid solutions when plugged back into the equation. So firstly, subtract 2 on both sides of the equation:

Next, square both sides:

Next, subtract x and add 2 to both sides of the equation:

Now we are going to be factoring by grouping to find the solution(s). Firstly, what two terms have a product of 6x^2 and a sum of -5x? That would be -3x and -2x. Replace -5x with -2x - 3x:

Next, factor x^2 - 2x and -3x + 6 separately. Make sure that they have the same quantity on the inside of the parentheses:

Now you can rewrite the equation as 
Now, apply the Zero Product Property and solve for x as such:

Now, it may appear that the answer is C, however we need to plug the numbers back into the original equation to see if they are true as such:

Since both solutions hold true when x = 2 and x = 3, <u>your answer is C. x = 2 or x = 3.</u>
Answer:
A
Step-by-step explanation:
Answer:
T == R + NH
Step-by-step explanation:
The fixed rate R is added to the hourly charges to get the total T. The hourly charges are the product of the number of hours and the charge per hour, NH.
The sum is then ...
... T = R + NH
Distribute the negative:
6x-3-8x-11
Combine like terms:
-2x-14
Simplify by factoring:
-2(x+7)