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lawyer [7]
3 years ago
15

Write a possible equation for a polynomial whose graph has the following horizonal intercepts. Show your work.

Mathematics
1 answer:
posledela3 years ago
6 0

Answer:

A) x - 4

B) x² - 4x

C) x³ - 2x² - 8x

D) 2x³ + 3x² - 32x + 15

Step-by-step explanation:

A)

x-intercepts: x = 4

Factors:

(x - 4)

B)

x-intercepts: x = 4, 0

Factor:

(x - 0)(x - 4)

x² - 4x

C)

x-intercepts: x = 4, 0, -2

Factor:

(x - 0)(x - 4)(x + 2)

(x² - 4x)(x + 2)

x³ - 4x² + 2x² - 8x

x³ - 2x² - 8x

D)

x-intercepts: x = 3, ½, -5

Factor:

(x - 3)(2x - 1)(x + 5)

(2x² - 6x - x + 3)(x + 5)

(2x² - 7x + 3)(x + 5)

2x³ - 7x² + 3x + 10x² - 35x + 15

2x³ + 3x² - 32x + 15

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find the formula for a rational function that satisfies all of the following. its x-intercept is (-3,0). it has a vertical asymp
Norma-Jean [14]

Let that be

\\ \rm\Rightarrow y=\dfrac{a(f(x))}{g(x)}

Two vertical asymptotes at -1 and 0

\\ \rm\Rightarrow y=\dfrac{a(f(x)}{x(x+1)}

If we simply

\\ \rm\Rightarrow y=\dfrac{a(f(x)}{x^2+1}

  • Denominator has degree 2
  • Numerator should have degree as 2 and coefficient as 3 inorder to get horizontal asymptote y=3 means the quadratic equation should contain 3x²
  • But there should be a x intercept at -3 so one zeros should be -3

Find a equation

  • 3x²+9x

Find zeros

  • 3x²+9x=0
  • 3x(x+3)=0
  • x=0,-3

Horizontal asymptote

  • 3x²/x²
  • 3

So our equation is

\\ \rm\Rightarrow y=\dfrac{3x^2+9x}{x(x+1)}

Graph attached

4 0
1 year ago
A rancher plans to make 4 identical and adjacent rectangular pens against a barn (see figure below), each with an area of 100 m^
Tasya [4]

Answer:

10 by 10 meters

Step-by-step explanation:

In calculus terms, you can use the formula for the perimeter which is 2l + 2w, and the area l × w.

Then since the area is 100

l × w = 100. So w = 100/l

Then substitute this into the perimeter formula.

w = 100/l → 2l + 2(w) = 2l + 2(100/l) = 2l + 200/l.

Then take the derivative d/dx [take the derivative of a quantity with respect to x], by using a simpler method known as the power rule:

d/dx[x^n] = nx^n-1

so p = 2l + 200/l becomes p' = 2 - 200/l^2

Since the derivative of a constant is 0, to solve for l, set p' to 0

0 = 2 - 200/l^2 → -200/l^2 = -2 → 200/l^2 = 2 → 2l^2 = 200 → l^2 = 100 → l = √100, l = 10.

Now that we know the length is 10, We can substitute the length in the original equation to find the width.

l = 10 → w = 100/l → w = 100/10, w = 10.

Therefore the perimeter of each rectangular pen is 40, with a length of 10 and width of 10.

If you want to do this algebraicly, there are more steps involved

7 0
2 years ago
Which of the following units for mass is an SI unit?
s2008m [1.1K]
Kilogram is an SI unit for mass.
Ounce and pound refer to American system for measuring things, and decakilogram is not the "basic" unit, but kilogram is.
5 0
2 years ago
Read 2 more answers
A male elephant weighs 6,728 pounds. A female
murzikaleks [220]
First, u need to add 6,728 and 5,843 together which is 12,571 then u  need to find the nearest hundred which is the 5 hope that helped!
6 0
3 years ago
Read 2 more answers
investments historically have doubled every 9 years. If you start will a $2,000 investment, how much money would you have after
azamat

Answer:

$64,000

Step-by-step explanation:

Friday, 45 / 9 = 5

So the investment will double 5 times

First time

2,000 (starting investment) × 2 = 4000

Second time

4000 × 2 = 8000

Third time

8000 × 2 = 16000

Fourth time

16000 × 2 = 32000

Fifth and final time

32000 × 2 = 64000

$64,000

7 0
2 years ago
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