Answer:
Here's what we know:
A = Lw (Area is length times width)
L = 2w + 6 (length is twice the width plus 6)
A = 140 (Area is 140 m2)
Plug in the variable values:
140 = w(2w + 6)
Distribute:
140 = 2w2 + 6w
Subtract 140:
2w2 + 6w - 140 = 0
Factor out a 2:
2(w2 + 3w - 70) = 0
Divide both sides by 2:
w2 + 3w - 70 = 0
(w + m)(w - n)
When we factor out the quadratic, we know it's going to be a +/- situation because the c value in the quadratic is negative, and the two numbers are going to be three away, the plus next to the 3 meaning that the larger number is going to be positive:
(w + 10)(w - 7) = 0
w = -10, 7
We can't have a negative length, so we can toss out the -10, leaving us with w = 7 meters.
L = 2 * 7 + 6
L = 14 + 6
L = 20
Check:
140 = 20 * 7
140 = 140
<span>The method of solving "by substitution" works by solving one of the equations (you choose which one) for one of the variables (you choose which one), and then plugging this back into the other equation, "substituting" for the chosen variable and solving for the other. Then you back-solve for the first variable.</span>
If you would like to evaluate 6 * [5 * (3 - 9) - 1] + 2 / 7 * (8 - 2) + 4, you can calculate this using the following steps:
6 * [5 * (3 - 9) - 1] + 2 / 7 * (8 - 2) + 4 = 6 * [5 * (-6) - 1] + 2/7 * 6 + 4 = 6 * [- 30 - 1] + 12/7 + 4 = 6 * [- 31] + 12/7 + 4 = - 186 + 12/7 + 4 = - 182 + 12/7 = - 1274/7 + 12/7 = - 1262/7
The correct result would be - 1262/7.
Answer:
e^2 -7 = x
Step-by-step explanation:
2=ln(x+7)
Raise each side to the base of e
e^2 = e^ln (x+7)
The e^ln cancel
e^2 = x+7
Subtract 7 from each side
e^2 -7 = x +7-7
e^2 -7 = x
