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lara31 [8.8K]
2 years ago
9

What is the inverse of the function f(x) = one-quarterx – 12? h(x) = 48x – 4 h(x) = 48x + 4 h(x) = 4x – 48 h(x) = 4x + 48

Mathematics
2 answers:
DaniilM [7]2 years ago
8 0

Answer:

h(x) = 4x+48

Step-by-step explanation:

Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.

Then we will make x the subject of the formula as shown:

y = 1/4x - 12

adding 12 to  both sides we have;

y + 12= 1/4x - 12 + 12

y + 12 = 1/4x

Multiplying both sides by 4 we have;

4(y+12) = x

x = 4y + 48

Substituting y for x

y = 4x+48

f^-1(x) = 4x+48

h(x) = 4x+48

Thee final expression will give the inverse of the function

Basile [38]2 years ago
4 0

Answer:

<h2>h(x) = 4x+48</h2>

Step-by-step explanation:

Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.

Then we will make x the subject of the formula as shown:

y = 1/4x - 12

adding 12 to  both sides we have;

y + 12= 1/4x - 12 + 12

y + 12 = 1/4x

Multiplying both sides by 4 we have;

4(y+12) = x

x = 4y + 48

Substituting y for x

y = 4x+48

f^-1(x) = 4x+48

h(x) = 4x+48

Thee final expression will give the inverse of the function

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Answer:

No

Step-by-step explanation:

the ratio between AD and DE is 3:1.

The geometric centroid (center of mass) of the polygon vertices of a triangle is the point D which is also the intersection of three triangle's medians.

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viva [34]

Answer:

119.45 m

Step-by-step explanation:

Given:

When angle of elevation of the sun changes from 58° to 36° the length of shadow of a pole increases by 90 m.

To find:

Length of pole = ?

Solution:

Kindly refer to the attached image.

\triangle ABC represents the 1st angle of elevation of sun i.e.  58°

\triangle ABD represents the 2nd angle of elevation of sun i.e.  36°

Change in shadow is represented by CD = 90 m

Let height of pole, AB = h m

Let side BC = x m

Now, let us apply tangent rules in \triangle ABC, \triangle ABD one by one:

tan\theta = \dfrac{Perpendicular}{Base}\\\Rightarrow tan58^\circ=\dfrac{AB}{BC}\\\Rightarrow tan58^\circ=\dfrac{h}{x}\\\Rightarrow x = 0.624h ..... (1)

tan36^\circ = \dfrac{h}{x+90}

Putting value of x using equation (1):

tan36^\circ = \dfrac{h}{0.624h+90}\\\Rightarrow 0.726\times 0.624h+0.726\times 90 = h\\\Rightarrow h-0.453h =65.34\\\Rightarrow \bold{h = 119.45\ m}

119.45 m is the height of pole.

7 0
2 years ago
A pipe of diameter 64mm discharges water at a rate of 2.05mm/s into an empty cylindrical tank of diameter 7.6cm and height 2.3m.
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Answer:

Diameter of pipe = D = 64mm

cross sectional Area of pipe= A = pi * (D/2)^2 = pi * (32)^2 = 1024pi  mm^2

Discharge Rate of water = v = 2.05 mm/s

Volume of Cylinder = V = pi * (D/2)^2 * h = pi * (38)^2 * 2300 = 3321200pi  mm^3

(Area of pipe)*(Rate) = (Volume) / (Time)

Time = T = (Volume) / [(Area of pipe)*(Rate)]

              = (3321200pi)/(1024pi * 2.05)

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The substitution property of equality allows you to say that if 7j + 14k = 28 And j = 2 then
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