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4 years ago

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Jon performs 3 transformations on a pentagon. First, he reflects it over the x-axis. Then, he translates it 3 units to the left

and 4 units up. Finally, he reflects the image over the line x = 1. Are the original and transformed images congruent? Justify your answer.

1 answer:

Morgarella [4.7K]4 years ago

8 0

yes; Reflections and translations are rigid motions. Rigid motions preserve the size of the original image.

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A function f has the following verbal description: multiply by 3, add 5, and

STALIN [3.7K]

Regarding the functions in this problem, it is found that:

a) The verbal description of the inverse is: Take the third root, subtract by 5 and divide by 3.

b) The formulas are:

f(x) = (3x + 5)³.

$f^{-1}(x) = \frac{\sqrt[3]{x} - 5}{3}$

c) The compositions result in x, hence they are inverses.

<h3>How to obtain the inverse function?</h3>

The original function is described as follows:

Multiply by 3: 3x.

Add 5: 3x + 5.

Take the third power: (3x + 5)³.

Hence the function is:

y = (3x + 5)³.

To obtain the inverse functions, we exchange x and y and then isolate y, hence:

x = (3y + 5)³

$\sqrt[3]{x} = \sqrt[3]{(3y+5)^3}$

$3y + 5 = \sqrt[3]{x}$

$3y = \sqrt[3]{x} - 5$

$y = \frac{\sqrt[3]{x} - 5}{3}$

$f^{-1}(x) = \frac{\sqrt[3]{x} - 5}{3}$

The verbal description of the inverse is:

Take the third root. sqrt[3](x).

Subtract by 5: sqrt[3](x) - 5.

Divide by 3.

The compositions are given as follows:

$f(f^{-1}(x)) = f\left(\frac{\sqrt[3]{x} - 5}{3}\right) = \left(3\left(\frac{\sqrt[3]{x} - 5}{3}\right + 5)\right)^3 = (\sqrt[3]{x})^3 = x$

$f^{-1}(f(x)) = f^{-1}((3x + 5)^3) = \frac{\sqrt[3]{(3x + 5)^3} - 5}{3} = \frac{3x + 5 - 5}{3} = x$

More can be learned about inverse functions at brainly.com/question/11735394

#SPJ1

4 0

1 year ago

1 /x^−1 in simplest rational form

Allushta [10]

Here is a link to help you find the answer:
https://www.khanacademy.org/math/algebra2/rational-expressions-equations-and-functions/simplify-rati...

Hope this helps!

3 0

3 years ago

morpeh [17]

<h2>Answer:</h2>

Number of apples is the prediction of the total weight an extrapolation is:

18

<h2>Step-by-step explanation:</h2>

<u>Extrapolation--</u>

The extrapolation of a data point is an estimation of the value of the point based on the data that is provided to us.

In short it is a process of the estimation of the data which are beyond the original observation of the data that is provided to us.

Hence, here the extrapolated data is:

18

( Since 18 is beyond the range as the curve goes out of the area )

3 0

3 years ago

Read 2 more answers

A bag of marbles contains 10 blue marbles, 62 yellow marbles, 34 green marbles, 71 orange marbles, and 23 red marbles. What perc

melomori [17]

Answer:

your answer is C. 31%

percentage of yellow marbles =

$\frac{62}{10 + 62 + 34 + 71 + 23}$ × 100

$\frac{62}{200}$ × 100

$31\%$

4 0

3 years ago

Smith is a weld inspector at a shipyard. He knows from keeping track of good and substandard welds that for the afternoon shift

lord [1]

Answer:z = 3.87

Step-by-step explanation:

learning abt this in school rn

8 0

3 years ago