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3 years ago

Find the Area of the shaded region of the trapezoid below. (show your work or explain how you got your answer in words) *

Mathematics

1 answer:

Rudiy273 years ago

5 0

This is the full answer to the question

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Find the inverse of the following function. Then prove they are inverses of one another.

solmaris [256]

Answer: $\dfrac{x^2+1}{2}$

Step-by-step explanation:

Given

$f(x)=\sqrt{2x-1}$

We can write it as

$\Rightarrow y=\sqrt{2x-1}$

Express x in terms of y

$\Rightarrow y^2=2x-1\\\\\Rightarrow x=\dfrac{y^2+1}{2}$

Replace y be x to get the inverse

$\Rightarrow f^{-1}(x)=\dfrac{x^2+1}{2}$

To prove, it is inverse of f(x). $f(f^{-1}(x))=x$

$\Rightarrow f(f^{-1}(x))=\sqrt{2\times \dfrac{x^2+1}{2}-1}\\\\\Rightarrow f(f^{-1}(x))=\sqrt{x^2+1-1}\\\\\Rightarrow f(f^{-1}(x))=x$

So, they are inverse of each other.

8 0

3 years ago

In a recent year, 31.6% of all registered doctors were female. If there were 53,000 female registered doctors that year, what wa

Naily [24]

Answer:

The total number of registered doctors was 167,722.

Step-by-step explanation:

Total number of doctors:

The total number of doctors is given by x.

31.6% of all registered doctors were female. 53,000 female doctors.

This means that:

$0.316x = 53000$

What was the total number of registered doctors?

We have to solve the above equation for x. So

$x = \frac{53000}{0.316}$

$x = 167722$

The total number of registered doctors was 167,722.

6 0

3 years ago

What is the place value of the 5 in the number 1.458?

mixas84 [53]

Answer:

Step-by-step explanation:

1.458

The 5 is in the hundredths place

6 0

3 years ago

The velocity of a body is increases from 10 m/s ti 15 m/s in 5seconds calculate its acceleration

larisa [96]

Answer:

$accelaration = \frac{change \: in \: veloity}{time} \\ = \frac{15 - 10}{5} \\ = \frac{5}{5} \\ = 1 \frac{m}{ {s}^{ - 2} }$

3 0

3 years ago

Read 2 more answers

Mary estimated that it would take 3 hours to write a book report, but it actually took her 5 hours. What is the percent error fo

Eduardwww [97]

Answer:

The percent error is 40%.

Step-by-step explanation:

5 (actual time) - 3 (estimated time) = 2

2 divided by 5 (actual time) = 0.4

0.4 x 100 = 40%

6 0

3 years ago