The equation that describes the given polynomial is:
P(x) = x²*(x - 2)²*(x + 2)
<h3>
How to find the equation for the polynomial?</h3>
Remember that a polynomial with a leading coefficient A and roots:
x₁, x₂, x₃,...,xₙ
The equation that describes the polynomial is:
P(x) = a*(x - x₁)*(x - x₂)*...*(x - xₙ)
In this case, we know that the leading coefficient is 1, and the roots are:
2, 2, 0, 0, -2.
(the first two appear two times because have a multiplicity of two).
Then we can write the equation of the polynomial as:
P(x) = 1*(x - 2)*(x - 2)*(x - 0)*(x - 0)*(x + 2)
P(x) = x²*(x - 2)²*(x + 2)
Learn more about polynomials:
brainly.com/question/4142886
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You need to find "two-fifths of 30." Of here means multiplication:
![\begin{aligned}\dfrac{2}{5}\cdot 30 &= \dfrac{2}{5}\cdot\dfrac{30}{1}\\[0.5em] &= \dfrac{60}{5}\\[0.5em] &= 12\end{aligned}](https://tex.z-dn.net/?f=%5Cbegin%7Baligned%7D%5Cdfrac%7B2%7D%7B5%7D%5Ccdot%2030%20%26%3D%20%5Cdfrac%7B2%7D%7B5%7D%5Ccdot%5Cdfrac%7B30%7D%7B1%7D%5C%5C%5B0.5em%5D%20%26%3D%20%5Cdfrac%7B60%7D%7B5%7D%5C%5C%5B0.5em%5D%20%26%3D%2012%5Cend%7Baligned%7D)
There are 12 athletes in the club.
Answer: 3:4
First step: 33 hats are purchased
Second step: for total number of hats you would do 33+11=44
Third step: simplify the ratio 33:44 —> 3:4
Answer:
h = 6 cm
l = (32-2(6)) = 20 cm
w = (40-2(6)) = 28 cm
Step-by-step explanation:
Given in the question a piece of cardboard having dimensions 32 by 40
Suppose we cut square of length x
When you cut square corners from a piece of cardboard, two sides are 32-2x, and other two sides are 40-2x lengths
<h3>Step 1</h3>
Formula for the volume of box
v = height * length * width
v = x (32-2x) (40-2x)
v = 4x³ - 144x² + 1280x
<h3>Step 2</h3>
Find derivative and equal it to 0
dv/dx = 4(3)x² - (2)144x + 1280
0 = 12x² - 288x + 1280
x1 = 18.110
x2 =5.88
<h3>Step 3</h3>
Select x and plug value of x to find dimension
(32-2x) > 0
2x < 32
x < 16
so domain say that x should be less than 16 which means x = 5.88 ≈ 6 cm
h = 6 cm
l = (32-2(6)) = 20 cm
w = (40-2(6)) = 28 cm
