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3 years ago

F(x) = 4x − 12 f−1(x) =_? x +__?

Mathematics

1 answer:

natali 33 [55]3 years ago

6 0

Answer:

$f^{-1}(x)=\frac{1}{4}x+3$

Step-by-step explanation:

We have been given the function $f(x)=4x-12$

Below are steps for finding the inverse of the function.

Step 1:

Replace f(x) with y

$y=4x-12$

Step 2:

Interchange x and y

$x=4y-12$

Step 3:

Solve for y

$x+12=4y\\\\y=\frac{1}{4}x+3$

Step 4:

Replace y with $f^{-1}(x)$

$f^{-1}(x)=\frac{1}{4}x+3$

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Find the area of the shape shown below.

Igoryamba

Answer:

Area = 16

Step-by-step explanation:

4 x 2 x 2 x 1 = 16

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3 years ago

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8_murik_8 [283]

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2 years ago

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3 years ago

Find the standard form of the equation of the ellipse with the given characteristics. Vertices: (4, 0), (4, 14); endpoints of th

saul85 [17]

Answer:

The standard form of the ellipse is $\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$ .

Step-by-step explanation:

The major axis of the ellipse is located in the y axis, whereas the minor axis is in the x axis. The center of the ellipse is the midpoint of the line segment between vertices, this is:

$(h, k) =\frac{1}{2}\cdot V_{1} (x,y) + \frac{1}{2}\cdot V_{2} (x,y)$ (1)

If we know that $V_{1} (x,y) = (4,0)$ and $V_{2}(x,y) = (4, 14)$ , then the coordinates of the center are, respectively:

$(h,k) = \frac{1}{2}\cdot (4, 0) + \frac{1}{2}\cdot (4,14)$

$(h,k) = (2,0) + (2, 7)$

$(h, k) = (4, 7)$

The length of each semiaxis is, respectively:

$a = \sqrt{(1 - 4)^{2}+(7-7)^{2}}$

$a = 3$

$b = \sqrt{(4-4)^{2}+(0-7)^{2}}$

$b = 7$

The standard equation of the ellipse is described by the following formula:

$\frac{(x-h)^{2}}{a^{2}}+ \frac{(y-k)^{2}}{b^{2}} = 1$

Where:

$h$ , $k$ - Coordinates of the center of the ellipse.

$a$ , $b$ - Length of the orthogonal semiaxes.

If we know that $h = 4$ , $k = 7$ , $a = 3$ and $b = 7$ , then the standard form of the ellipse is:

$\frac{(x-4)^{2}}{9} + \frac{(y-7)^{2}}{49} = 1$

4 0

3 years ago

The means and mean absolute deviations of the individual times of members on two 4 times 400 meter relay track teams are shown i

Yakvenalex [24]

The correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

Mean is defined as the ratio of the sum of the number of the data sets to the total number of the data.

The difference between the mean times is about 16 times the mean absolute deviation of the data set.

59.32 - 59.1 = 0.22

2.4 - 1.5 = 0.9

0.22 / 0.9 = 0.25

Therefore the correct answer is option C which is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B will be 0.25.

To know more about mean follow

brainly.com/question/968894

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2 years ago

F(x) = 4x − 12 f−1(x) =___? x +____?

F(x) = 4x − 12 f−1(x) =_? x +__?