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ohaa [14]
3 years ago
9

Give the quotient in simplest form:

Mathematics
1 answer:
pickupchik [31]3 years ago
6 0

Answer:

x

Step-by-step explanation:

x/y / 1/y =

x / 1 x y / y =

x / 1 x 1 =

x

<em>Hope that helps!</em>

<em>-Sabrina</em>

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<img src="https://tex.z-dn.net/?f=f%28x%29%20%3D%20%5Cfrac%7B%282x%2B1%29%28x-5%29%7D%7B%28x-5%29%28x%2B4%29%5E%7B2%7D%20%7D" id
dybincka [34]

i) The given function is

f(x)=\frac{(2x+1)(x-5)}{(x-5)(x+4)^2}

The domain is

(x-5)(x+4)^2\ne 0

(x-5)\ne0,(x+4)^2\ne 0

x\ne5,x\ne -4

ii) For vertical asymptotes, we simplify the function to get;

f(x)=\frac{(2x+1)}{(x+4)^2}

The vertical asymptote occurs at

(x+4)^2=0

x=-4

iii) The roots are the x-intercepts of the reduced fraction.

Equate the numerator of the reduced fraction to zero.

2x+1=0

2x=-1

x=-\frac{1}{2}

iv) To find the y-intercept, we substitute x=0 into the reduced fraction.

f(0)=\frac{(2(0)+1)}{(0+4)^2}

f(0)=\frac{(1)}{(4)^2}

f(0)=\frac{1}{16}

v) The horizontal asymptote is given by;

lim_{x\to \infty}\frac{(2x+1)}{(x+4)^2}=0

The horizontal asymptote is y=0.

vi) The function has a hole at x-5=0.

Thus at x=5.

This is the factor common to both the numerator and the denominator.

vii) The function is a proper rational function.

Proper rational functions do not have oblique asymptotes.

6 0
3 years ago
I’ll give brainliest
NemiM [27]

Answer:

6

Step-by-step explanation:

We need to find the slope

We have 2 points

(0,0) and (1,6)

m = (y2-y1)/(x2-x1)

   = (6-0)/(1-0)

   = 6/1

  = 6

y = 6x

The constant of proportionality is 6

6 0
3 years ago
Read 2 more answers
Helppp it's timed
fomenos

Answer:

D.

Step-by-step explanation:

h(x)=f(x)g(x) means multiply the expression for f to the expression for g.

That is the problem is just asking you to do (11x-5)(-2x-4).

Let's use foil.

First:  11x(-2x)=-22x^2

Outer: 11x(-4)=-44x

Inner: -5(-2x)=10x

Last: -5(-4)=20

------------------------Add together!

-22x^2-34x+20

D.

6 0
3 years ago
What is the equation of a line, in general form, with a slope of -2 and a y-intercept of 8?
Ksenya-84 [330]

Answer:

y = -2x + 8 is the answer to the question

8 0
4 years ago
Explain how you would use fraction bars to find the quotient of 10/12 ÷ 4/6. What is the quotient?
mylen [45]
(10/12) / (4/6)...when dividing with fractions, flip what u r dividing by, then multiply

10/12 * 6/4 = 10/8 which reduces to 5/4 or 1 1/4
4 0
3 years ago
Read 2 more answers
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