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3 years ago

What is the inverse of the function f(x) = 2x – 10?

Mathematics

2 answers:

Lana71 [14]3 years ago

7 0

Answer:

$h(x)=\dfrac{x}{2}+5$

Step-by-step explanation:

You are given the function $f(x)=2x-10$ . To find the inverse function $f^{-1}(x)$ do such steps:

1. Rewrite the function f(x) as

$y=2x-10$

2. Express x in terms of y:

$y+10=2x\\ \\x=\dfrac{y}{2}+5$

3. Change x into y and y into x:

$y=\dfrac{x}{2}+5$

Now, the inverse function is

$f^{-1}(x)=\dfrac{x}{2}+5$

Trava [24]3 years ago

6 0

Answer:

Option D.

Step-by-step explanation:

The given function is

$f(x)=2x-10$

We need to find the inverse of the function f(x).

Step 1 : Substitute f(x)=y.

$y=2x-10$

Step 2: Interchange x and y.

$x=2y-10$

Step 3: Isolate variable y.

$x+10=2y$

$\frac{x+10}{2}=y$

$\frac{x}{2}+\frac{10}{2}=y$

$\frac{x}{2}+5=y$

$y=\frac{x}{2}+5$

Step 4: Substitute y=h(x).

$h(x)=\frac{1}{2}x+5$

The inverse of the function f(x) is $h(x)=\frac{1}{2}x+5$ .

Therefore, the correct option is D.

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HELPPPP PLEASE HELP ME WITH BASIC MATH I REALLY APPRECIATE IT ((WILL MARK AS BRAINLIEST))

Yakvenalex [24]

Answer:

3) 522

4) 468

Step-by-step explanation:

hello!

3) in the question, it says the cross section is a square, and the area of PQRS is 81.

for the square, we know that the length and height have to be the same, so if the area is 81, then we know the sides are both 9 because 9*9 is 81 and they're the same numbers multiplied. (same height and length)

with the information that all 4 sides of the square is 9 and the other side is labeled 10, we can figure out the rest.

both squares : 81+81=162

both 10 by 9 sides: 90+90=180

both 10 by 9 sides (top and bottom): 90+90=180

total surface area=162+180+180=522

4) for this problem, we can see that the triangle is a right triangle.

to solve the area of the triangle, we can do (9*12)/2=108/2=54.

there are two sides with triangles, so we double 54 (54*2=108)

9 by 10 side: 90

10 by 12 side: 120

now for the last slide, theres no information on the length. the formula for the diagonal is

a^2+b^2=c^2

which is

9^2+12^2=81+144=255=15^2

with this, the area of the rectangular side gives us 10*15 which is 150.

adding it together, we get

108+90+120+150=468.

hope this helps!

7 0

3 years ago

Of 136 randomly selected adults, 33 were found to have high blood pressure. Construct a 95% confidence interval for the true of

navik [9.2K]

Answer:

The 95% confidence interval of the proportion of all adults that have high blood pressure is 0.17059 < $\hat{p}$ < 0.314695

Step-by-step explanation:

The confidence interval for a proportion is given by the following formula;

$CI=\hat{p}\pm z\times \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$

Where:

x = 33

n = 136

$\hat{p}$ = x/n = 33/136 = 0.243

z value for 95% confidence is 1.96

Plugging in the values, we have;

$CI=0.243\pm 1.96\times \sqrt{\frac{0.243(1-0.243)}{136}}$

Which gives;

0.17059 < $\hat{p}$ < 0.314695

Hence the 95% confidence interval of the proportion of all adults that have high blood pressure = 0.17059 < $\hat{p}$ < 0.314695

From the above we have;

23.2 < x < 42.798

Since we are dealing with people, we round down as follows;

23 < x < 42.

4 0

3 years ago

Matt is saving to buy a new motorcycle. If he deposits $70 at the end of each month in an account that pays an annual interest r

gladu [14]

P = $70, p = 2.5% = 0.025
q = 1 + 0.025 / 12 = 1.002
Future value of a periodic deposit:
A = P · q · ( q^30 - 1 ) / ( q - 1 )
A = 70 · 1.002 · ( 1.002^30 - 1 ) / ( 1.002 - 1 )
A = $2,166
Answer:
He will have $2.166 in 30 months.

6 0

3 years ago

Read 2 more answers

Which of these numbers is irrational? -3.5 3.5 ОО 35 √5 help

Molodets [167]

Answer:

√5 is irrational

Step-by-step explanation:

A rational number is one that can be written exactly as an integer or ratio of integers. Written as a decimal number, it will have a finite number of digits, or a repeating decimal fraction.

<h3>Application</h3>

Usually, a number that can only be expressed exactly using a symbol will be irrational. For square roots, any root of an integer other than a perfect square will be irrational.

The integer 5 is not a perfect square. It is between the squares 2²=4 and 3²=9. The square root of 5 is irrational.

Additional comment

A reduced fraction whose denominator has factors other than 2 or 5 will translate to a repeating decimal. The number of repeating digits may be as many as 1 less than the denominator. For example, 1/19 has an 18-digit repeating decimal equivalent.

5 0

1 year ago

Aunt bess uses 3 cups of oatmeal to bake 6 dozen cookies how many cups of oatmeal will she need to bake 18 dozen cookies

Andrei [34K]

There are several important information's already given in the question. Based on those information's the answer to the question can be easily deduced.
Number of cups of Oatmeal
required by Aunt Bess for making 6 dozen cookies = 3
Then
Number of cups of oatmeal
required by Aunt Bess for making 1 dozen cookies = (3/6)
= 1/2
So
Number of cups of oatmeal
required by Aunt Bess for making 18 dozen cookies = (1/2) * 18
= 9 cups
So Aunt Bess will require 9 cups of oatmeal for baking 18 dozen cookies. I hope the procedure is clear enough for you to undestand.

4 0

3 years ago