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nadezda [96]
2 years ago
12

Given f of x is equal to the quantity x minus 4 end quantity divided by the quantity x squared plus 13x plus 36 end quantity, wh

ich of the following is true?
f(x) is decreasing for all x > –9
f(x) is increasing for all x < –9
f(x) is increasing for all x > –4
f(x) is decreasing for all x > –4
Mathematics
1 answer:
gavmur [86]2 years ago
8 0

The simplified expression of the function f(x) =\dfrac{x-4}{x^2+13x+36} is

f(x) = \dfrac{x-4}{(x+9)(x+4)}. f(x) is increasing for all x > –4.The correct answer is option C.

<h3>What is a function?</h3>

A function is defined as a relation between the set of inputs having exactly one output each.

The function expression is given as:

f(x) =\dfrac{x-4}{x^2+13x+36}

Expand the denominator

f(x) =\dfrac{x-4}{x^2+4x +9x+36}

Factorize the denominator

f(x) =\dfrac{x-4}{x(x+4)+9(x+4)}

Factor out x + 9

f(x) = \dfrac{x-4}{(x+9)(x+4)}

The simplified expression of the function f(x) =\dfrac{x-4}{x^2+13x+36} is

f(x) = \dfrac{x-4}{(x+9)(x+4)}. f(x) is increasing for all x > –4

Read more about functions at:

brainly.com/question/1851758

#SPJ1

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Find the slope of the line through each pair of points. (2,5) and (6, 8)
Ymorist [56]
(2,5) (6,8)

Y2-Y1 divided by X2-X1

8-5=3
———-
6-2=4

so your slope is 3/4
5 0
3 years ago
Two perpendicular lines have opposite y-intercepts. The equation of one of these lines is y = mx + b. Express the x-coordinate o
Fofino [41]

Answer:

x = -2bm/(m²+1)

Step-by-step explanation:

One line has equation

... y = mx + b

The slope of the perpendicular line is the negative reciprocal of the slope of the original line. The perpendicular line with the opposite y-intercept has equation

... y = (-1/m)x - b

The point of intersection is where the x- and y-values are equal, so ...

... mx + b = (-1/m)x - b

... (m +1/m)x = -2b . . . . . . . add 1/m - b to both sides

... (m²+1)x = -2bm . . . . . . . multiply by m

... x = -2bm/(m²+1) . . . . . . divide by the coefficient of x

6 0
3 years ago
The measures of the angles of a triangle are shown in the figure below. Find the measure of the smallest angle.
nataly862011 [7]

Answer:

(2x+18) degrees

Step-by-step explanation:

A triangle is a total of 180 degrees, so you would do:

(2x+18)+55+(4x+11)=180

(2x+4x)+(18+55+11)=180           <- take out parentheses and add like terms

6x+84=180                         <- subtract 84 from both sides of the equation

6x=96                                    <- divide 6 from each side

x=16

Now that you know what x is you would plug it into each of the angles

Angle 1: 2x+18 --> 2(16)+18= 32+18= 50

Angle 2: 55

Angle 3: 4x+11 --> 4(16)+18= 64+18= 82

Then out of these three angles of the triangle, angle 1 (2x+18) would be the smallest.

4 0
3 years ago
Read 2 more answers
<img src="https://tex.z-dn.net/?f=4x%5E%7B2%7D%20%2B%2011x%20-%2020%20%3D%200" id="TexFormula1" title="4x^{2} + 11x - 20 = 0" al
STALIN [3.7K]
Answer using quadratic formulae=5/4 and -4

6 0
3 years ago
Find the indicated length
Setler79 [48]

Answer:

x=6

AC = 28

Step-by-step explanation:

4x+4= AC

4x +4 = 14 + 3x -4

4x-3x= 14-4-4

x = 6

AC = 4(6) +4 = 24+4 = 28

3 0
3 years ago
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