Answer:
We can write:
x + y = -2
xy = -80
We can rewrite the first equation as x = -y - 2 and then plug that into the second equation to get (-y-2) * y = -80 → -y² - 2y = -80 → y² + 2y - 80 = 0 → (y - 8)(y + 10) = 0 → y = 8, -10. Substituting these values into the first equation we get x = -10, 8 so the answer is (x₁, y₁) = (-10, 8) or (x₂, y₂) = (8, -10).
Answer:
![f(x)=\sqrt[3]{x} +5\\\\\implies y = \sqrt{3}{x}+5](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D%20%2B5%5C%5C%5C%5C%5Cimplies%20y%20%3D%20%5Csqrt%7B3%7D%7Bx%7D%2B5)
a) Since the function is given to be one - one so the inverse of the function exist. Now f(x) maps x to y so the inverse of f(x) maps y to x
To find inverse, first interchange the roles of x and y :
![\implies x = \sqrt[3]{y}+5](https://tex.z-dn.net/?f=%5Cimplies%20x%20%3D%20%5Csqrt%5B3%5D%7By%7D%2B5)
Now, solve for y :
![x = \sqrt[3]{y}+5\\\\\implies \sqrt[3]{y}=x-5\\\\\text{Now, cubing both the sides. We get,}\\\\\implies y=(x-5)^3\\\\\implies y=x^3-15\cdot x^2+75\cdot x-125\\\\\implies\bf f^{-1}(x)=x^3-15\cdot x^2+75\cdot x-125](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7By%7D%2B5%5C%5C%5C%5C%5Cimplies%20%5Csqrt%5B3%5D%7By%7D%3Dx-5%5C%5C%5C%5C%5Ctext%7BNow%2C%20cubing%20both%20the%20sides.%20We%20get%2C%7D%5C%5C%5C%5C%5Cimplies%20y%3D%28x-5%29%5E3%5C%5C%5C%5C%5Cimplies%20y%3Dx%5E3-15%5Ccdot%20x%5E2%2B75%5Ccdot%20x-125%5C%5C%5C%5C%5Cimplies%5Cbf%20f%5E%7B-1%7D%28x%29%3Dx%5E3-15%5Ccdot%20x%5E2%2B75%5Ccdot%20x-125)
b) To find coordinates of f(x) :
![f(x)=\sqrt[3]{x} +5](https://tex.z-dn.net/?f=f%28x%29%3D%5Csqrt%5B3%5D%7Bx%7D%20%2B5)
First take y = 0 then take x = 0
⇒ x-coordinates : (-125,0) and y-coordinates : (0,5)
To find coordinates of inverse function of x :

First take y = 0 then take x = 0
⇒ x - coordinates : (5,0) and y - coordinates : (0,-125)
c) f(x) is defined for every real number.
⇒ Domain : -∞ < x < ∞
and Range : -∞ < f(x) < ∞
And inverse function of x is also defined for every real number :
⇒ Domain : -∞ < x < ∞

Answer: The length of the base is 10.
Step-by-step explanation:
You can draw an isosceles triangle like the one shown attached.
An isosceles triangle has two equal sides. Then, you can divide it into two right triangles, where the base of each one of them will be:

The hypotenuse of each right triangle shown is 13 and the other legs are (x+7) and x, therefore you can apply the Pythagorean Theorem:

Simplify the expression:

Use the quadratic formula, where:


Then:


Choose the positive value, because lengths are not negative.
Substitute the value of x into the base 2x. Therefore, the answer is:

It is expected the height of the melted wax in this shape is 9.57 inches, this height would make the volume remain constant.
<h3>What is the volume of the spherical ball?</h3>
The volume of a sphere can be calculated using the formula V = 4/3 πr³. Let's use this formula to calculate the volume of the spherical ball of wax:
- V = 4/3 π8³
- V = 4/3 π 512
- V= 4/3 x 3.1416 x 512
- V =2144.66 cubic inches
<h3>What is the height of the new shape?</h3>
Considering the volume should be the same (2144.66 cubic inches) and the volume of this shape can be calculated by multiplying the sides, this would be the equation:
- 2144.66 = 14 x 16 x y ( unknown value)
- y= 2144.66 / 14 x 16
- y = 9.57
This means the height would be 9.57 inches.
Learn more about volume in: brainly.com/question/1578538
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Answer:
In this scenario you should use chefs if you have less than 55 people and you should use cece's if you have more than 55 people.
Step-by-step explanation:
To find out which one will be cheaper you need to know where they intersect, to do this you need to set up a system of equations.
y=28x+590 (chefs)
y=31x+425 (cece's)
to know where they intersect you need to make the y=0
28x+590=31x+425
Then solve
subtract the x from each side
590=3x+425
Subtract 425 from each side
3x=165
divide each side by three
x=55
now evaluate
Place a number above 55 (60 for example) into the place of x
28(60)+590=2,270
31(60)+425=2,285
In this scenario you should use chefs if you have less than 55 people and you should use cece's if you have more than 55 people.