Answer:
Width = 86 feet
Step-by-step explanation:
Create two equations with the info:
L = 27 + W
where L represents the length and W the width of the backyard.
The other one is about the area of the rectangular backyard:
Area = L x W
where you replace the area with 9718 and the length (L) with (27 + W):
![Area= L\,*\,W\\9718=(W+27)\,W\\9718=W^2+27\,W\\W^2+27\,W-9718=0](https://tex.z-dn.net/?f=Area%3D%20L%5C%2C%2A%5C%2CW%5C%5C9718%3D%28W%2B27%29%5C%2CW%5C%5C9718%3DW%5E2%2B27%5C%2CW%5C%5CW%5E2%2B27%5C%2CW-9718%3D0)
and solve for W using the quadratic equation:
![W=\frac{-27+/-\sqrt{27^2-4(1)(-9718)} }{2\,(1)} \\W=\frac{-27+/-\sqrt{39601}}{2} \\W=\frac{-27+/- 199}{2}](https://tex.z-dn.net/?f=W%3D%5Cfrac%7B-27%2B%2F-%5Csqrt%7B27%5E2-4%281%29%28-9718%29%7D%20%7D%7B2%5C%2C%281%29%7D%20%5C%5CW%3D%5Cfrac%7B-27%2B%2F-%5Csqrt%7B39601%7D%7D%7B2%7D%20%5C%5CW%3D%5Cfrac%7B-27%2B%2F-%20199%7D%7B2%7D)
This gives us two solutions:
W = - 113
and W = 86
We use the positive solution since this is a distance.
Therefore the width is: 86 feet
Answer:
QUESTION 1
The given system of equation,
We simplify to get.
The correct answer is option A.
1.
A.) (4, −2)
2.
x = -7
y = 2
3.
x = 5
y = 14
QUESTION 2
The given system of equations is
and
We make y the subject in equation (2) to get,
We put equation (3) into equation (1) to obtain,
We group like terms to get,
This implies that,
we divide through by to get,
Hence the x-coordinate is
QUESTION 3
The given system is
and
We make the subject in equation (2)
We put equation (3) into equation (1) to obtain,
We expand the bracket to get,
Group like terms to get,
We simplify to get;
This implies that,
Therefore the y-coordinate is 14.
Step-by-step explanation:
Answer:
I got this one
<n would equal 20, <m would equal 50
We know that the probability density function of a variable that is normally distributed is f(x) = 1/(σ√2π) * exp[1/2 (x – µ). Its inflection point is the point where f"(x) = 0.
Taking the first derivative, we get f'(x) = –(x–µ)/(σ³/√2π) exp[–(x–µ)²/(2σ²)] = –(x–µ) f(x)/σ².
The second derivative would be f"(x) = [ –(x–µ) f(x)/σ]' = –f(x)/σ² – (x–µ) f'(x)/σ² = –f(x)/σ² + (x-µ)² f(x)/σ⁴.
Setting this expression equal to zero, we get
–f(x)/σ² + (x-µ)² f(x)/σ⁴ = 0
Multiply both sides by σ⁴/f(x):
–σ² + (x-µ)² = 0
(x-µ)² = σ²
x-µ= + – σ
x = µ +– σ
So the answers are x = µ – σ and x = µ + σ.