Answer:
x = 2, and 6
x = 2 , 6
Step-by-step explanation:
The quadratic function to analyze is: 
In order to find where the corresponding parabola intercepts the x axis, we set it equal to zero (y = 0):

This equation is easy to solve by factoring. We look for a air of integer numbers whose product equals the constant term "12", and whose combinig renders the coefficient of the middle term of the trinomial "-8".
The two such numbers are "-2" and "-6". We use them to split the middle term, and then solve by factoring by grouping:

For the product of two factors to render zero, we need either one to be a zero.This means that (x-2)=0 (that is x = 2), or (x-6)=0 (that is x = 6).
So, there are two x-intercepts: x= 2, and 6
Answer:
( -2.5, -2 )
Step-by-step explanation:
use the formula:
M= (x1 + x2/2,y1 + y2/2)
=(<u>-</u><u>3</u><u>+</u><u>-</u><u>2</u>, <u>4</u><u>+</u><u>-</u><u>8</u><u>)</u>
2. 2
=(<u>-</u><u>5</u> ,<u> </u><u>-</u><u>4</u>)
2. 2
=(-2.5 , -2)
Answer:
10=y/11-13
We move all terms to the left:
-10-(y/11-13)=0
-y/11+13-10=0
We multiply all the terms by the denominator
-y+13*11-10*11=0
We add all the numbers together, and all the variables
-1y+33=0
We move all terms containing y to the left, all other terms to the right
-y=-33
y=-33/-1
y=+33
The perimeter is 500 cm, meaning the width + width + length + length is 500 cm in this rectangle.
clearly, since their sum is 500 total, the length of any of the sides cannot be larger than 500, it has to be less to allow room for the other 3 sides. L < 500.
and the length cannot be 0 either, because if it's, then there's no rectangle :). L > 0
L < 500 and L > 0 0 < L < 500.
Answer:
$31,341.81
Step-by-step explanation:
The compound amount equation is A = P(1 + r/n)^(nt), where P is the unknown principal, r is the annual interest rate, n is the number of compounding periods per year and t is the number of years. We want to solve this for P:
A
------------------- = P
(1 + r/n)^(nt)
Substituting the given numerical values;
$45,000
--------------------------- = P
(1+0.073/4)^(4*5)
Using a calculator, we evaluate this expression, obtaining: $31,341.81