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ra1l [238]
3 years ago
11

For f(x)=4x+1 and g(x)=x^2-5 find (g/f)(x)

Mathematics
2 answers:
Ipatiy [6.2K]3 years ago
6 0

f(x)=4x+1\\\\g(x)=x^2-5\\\\(g/f)(x)=\dfrac{g(x)}{f(x)}=\dfrac{x^2-5}{4x+1}

Rama09 [41]3 years ago
3 0

Answer:

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

Step-by-step explanation:

We have been given two function formulas f(x)=4x+1 and g(x)=x^2-5.

By the definition of composition (\frac{g}{f})(x)=\frac{g(x)}{f(x)}.

Upon substituting our given values we will get,

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

Since we can not simplify our expression further, therefore, (\frac{g}{f})(x)=\frac{x^2-5}{4x+1}.

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Solve for k<br><br> 10/3 = k/9<br><br> K =
Gnesinka [82]
10/3=k/9
(10/3)9=k
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5 0
3 years ago
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h(n)=-13nh(n)=−13nh, left parenthesis, n, right parenthesis, equals, minus, 13, n Complete the recursive formula of h(n)h(n)h, l
mr Goodwill [35]

Answer:

h(1)=-13

h(n)=h(n-1)-13, n\geq 2

Step-by-step explanation:

We are given that

h(n)=-13n

We have to find the recursive formula of h(n).

Substitute n=1

h(1)=-13

n=2

h(2)=-13-13=-26=h(1)-13

n=3

h(3)=-13(3)=-39=-26-13=h(2)-13

h(4)=-13(4)=-52=-39-13=h(3)-13

:

:

:

h(n)=h(n-1)-13

Therefore, the recursive formula is given by

h(1)=-13

h(n)=h(n-1)-13, n\geq 2

5 0
3 years ago
ASAPPP!!!! HELP I WILL GIVE 100POINTS AND BRAINLIST Question 9 (Essay Worth 10 points)
Luda [366]

Answer:

Part A)

The <em>x-</em>intercepts are (-1/4, 0) and (4, 0).

Part B)

The vertex is a maximum because the leading coefficient is negative.

The vertex is (1.875, 72.25).

Part C)

We can plot the zeros and the vertex, and connect them with a curve.

Step-by-step explanation:

The function given is:

f(x)=-16x^2+60x+16

Part A)

To find the <em>x-</em>intercepts of the function, set the function equal to 0 and solve for <em>x: </em>

<em />0=-16x^2+60x+16<em />

We can divide both sides by negative four:

0=4x^2-15x-4

Factor:

0=(4x+1)(x-4)

Zero Product Property:

x-4=0\text{ or } 4x+1=0

Solve for each case:

\displaystyle x=-\frac{1}{4}\text{ or }x=4

Hence, our zeros are:

\displaystyle \left(-\frac{1}{4}, 0\right)\text{ and } \left(4, 0\right)

Part B)

Note that the leading coefficient of our function is negative.

So, our function will be concave down.

Hence, our vertex will be the maximum.

The vertex is given by:

\displaystyle \left(-\frac{b}{2a}, f\left(-\frac{b}{2a}\right)\right)

In this case, <em>a </em>= -16, <em>b</em> = 60, and <em>c</em> = 16.

Find the <em>x-</em>coordinate of the vertex:

\displaystyle x=-\frac{(60)}{2(-16)}=\frac{15}{8}=1.875

Substitute this back into the function to find the <em>y-</em>coordinate:

f(1.875)=-16(1.875)^2+60(1.875)+16=72.25

Hence, our vertex is:

(1.875, 72.25)

Part C)

Since we already determined the zeros and the vertex, we can plot the two zeros and the vertex and draw a curve between the three points.

The graph is shown below. Again, to do this by hand, simply plot the three points and connect them with a parabola. If necessary, we can also find the <em>y-</em>intercept.

7 0
3 years ago
Explain how to find the surface area of a can of fruit with a height of 80 mm and a diameter of 60 mm.
raketka [301]

Answer:

Just multiply 60 by 80

Step-by-step explanation:

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Answer:1437

Step-by-step explanation:

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