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Vladimir79 [104]
3 years ago
6

Which of the following is the graph of the rational function? y=x^2+2x-8/x^2-9

Mathematics
1 answer:
rusak2 [61]3 years ago
7 0
Notice that we can simplify both numerator and denominator of our rational function. In the numerator we have a quadratic expression of the form ax^2+bx+c. To to simplify it, we are going to find tow numbers that add to 2 and multiply to -8; those numbers are 4 and -2.
x^2+2x-8=(x+4)(x-2)
In the denominator we have a difference of squares:
x^2-9=x^2-3^2=(x+3)(x-3)

Now we can rewrite our function:
y= \frac{x^2+2x-8}{x^2-9} = \frac{(x+4)(x-2)}{(x+3)(x-3)}

From the simplified form of our rational function we can infer that its graph has two vertical asymptotes at x=3 and x-3

We can conclude that the graphic of our rational function is: 

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A square is cut from a rectangle. The side length of the square is half of the unknown width w. The area of the shaded region is
Virty [35]

Answer:

  • See below

Step-by-step explanation:

<u>The side of the square is w/2, then its area is:</u>

  • A = (w/2)² = w²/4

<u>The shaded area is the difference of areas of the rectangle and the square:</u>

  • 14w - w²/4 = 84

<u>This can be simplified:</u>

  • 56w - w² = 336
  • w² - 56w + 336 = 0

8 0
2 years ago
1.5 Determine the degree of the following algebraic expressions:
tatuchka [14]

By identifying the largest exponent in each expression, we see that the answers are:

a) D = 3.

b) D = 5.

c) D = 0.

<h3></h3><h3>How to determine the degree of an expression?</h3>

The degree is just the largest exponent of the variable in an expression.

First, we have:

a) √3xyz - 5

The largest exponent is on the term √3*xyz is 3 (because we add the 3 exponents 1 of x, y, and z) so this expression has a degree of 3.

b)  y² - 3y⁵ -y + 2y³ - 4

Here the largest exponent is on the second term, so we can see that the degree is 5.

c) -10³

Here we don't have a variable, so this is a constant, which means that the degree is zero, because we could write:

-10³*x⁰

Where we use the fact that x⁰ = 1

If you want to learn more about degrees:

brainly.com/question/1600696

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6 0
2 years ago
A certain electronics manufacturer found that the average cost C to produce x DVD/Blu- ray players can be found using the equati
Marina CMI [18]

Answer:

Minimum average cost = 743.75

Number of dvds to achieve the cost = 62.5

Step-by-step explanation:

Given the cost equation

C = 0.04x² − 5x + 900

To Obtian the minimum average cost ;

Find dc/dx = 0

Diffentiate cost, c it ith respect to x

dc/dx = 2(0.04x) - 5

dc/dx = 0.08x - 5 = 0

0.08x = 5

x = 5 / 0.08

x = 62.5

Substitute the value of x into C to obtain the minimum average cost

C = 0.04(62.5)² - 5(62.5) + 900

C = 743.75

6 0
2 years ago
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