Answer:
Volume of the box = x^3 - 4x^2
Step-by-step explanation:
V = L × W × H
Where,
V = volume of the rectangular prism
L= Length
W = Width
H = Height
volume of the rectangular prism = length × width × height
Length = x
Width= length = x
Height = x - 4
V = L × W × H
= x * x * (x - 4)
= x^2 (x - 4)
= x^3 - 4x^2
V = x^3 - 4x^2
Volume of the box = x^3 - 4x^2
2x^2 - 8x - 24
First, we can factor a 2 out of this expression to simplify it.
2(x^2 - 4x - 12)
Now, we can try factoring this two ways: by using the quadratic formula, or by using the AC method.
We're gonna try using the AC method first.
List factors of -12.
1 * -12
-1 * 12
2 * -6
-2 * 6 (these digits satisfy the criteria.)
Split the middle term.
2(x^2 - 2x + 6x - 12)
Factor by grouping.
2(x(x - 2) + 6(x - 2)
Rearrange terms.
<h3><u>(2)(x + 6)(x - 2) is the fully factored form of the given polynomial.</u></h3>
The discount was 85% off.
968.58=200.78+76.78w
-200.78
767.8=76.78w
/76.78
=10w
Riley must save for 10 weeks
Answer:
Step-by-step explanation:
The table shows a set of x and y values, thus showing a set of points we can use to find the equation.
1) First, find the slope by using two points and substituting their x and y values into the slope formula,
. I chose (-3, 13) and (0,17), but any two points from the table will work. Use them for the formula like so:

Thus, the slope is
.
2) Next, identify the y-intercept. The y-intercept is where the line hits the y-axis. All points on the y-axis have a x value of 0. Thus, (0,17) must be the y-intercept of the line.
3) Finally, write an equation in slope-intercept form, or
format. Substitute the
and
for real values.
The
represents the slope of the equation, so substitute it for
. The
represents the y-value of the y-intercept, so substitute it for 17. This will give the following answer and equation:
