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What is the inverse of the function f(x)=2x+1?​
what is the inverse of the function f(x)=2x+1?​ - 1

Answers

Answer 1
Answer:

Answer:

  see the attachment

Step-by-step explanation:

You can find the inverse by swapping the variables and solving for y.

  y = f(x) . . . . . original function

  x = f(y) . . . . . variables swapped

  x = 2y +1

  x -1 = 2y . . . subtract 1

  (x-1)/2 = y . . . divide by 2

  y = (1/2)x -1/2 . . . expand

If the inverse function is named h(x), then it is ...

  h(x) = x/2 -1/2
Answer 2
Answer:

Answer:

Option 1.

Step-by-step explanation:

y=2x+1

x=2y+1

x-1=2y

(x-1)/(2) = (2y)/(2)

(x-1)/(2) = y

(1)/(2)x -(1)/(2) = y

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tanya makes 5/8 of the foul shots she attempts during a basketball practice, if she took 48 shots, how many did she make?

Answers

18

calculate (5)/(8) × 48 = 5 × 6 = 30

she had 30 foul shots hence 48 - 30 = 18

She made 18 shots
Made 5 shots every 8 attempts so if there were 48 attempts lets brake them in groups of 8.

48/8= 6 groups
5 made shots in each of the 6 groups is
5•6= 30 made shots.

30 shots were made out of 48 attempts

I'm not sure which region contains the solution. Where both the half planes over lap

Answers

Answer:

Um i have no idea sorry i couldnt help

Step-by-step explanation:

4 in.7 in18 in.4 in.The surface area of the rectangular prism issquare inches.The volume of the rectangular prism isy cubic inches.

Answers

We have been given a rectangular prism and we are required to find its surface area and volume.

We shall solve this question by first stating the formula of the parameter we want to find, then, we apply the respective formulas to find the values of these parameters.

Surface area:

The surface area is the sum total of all the areas of all the faces of the prism.

To solve this question, we need to note that there are 6 faces whose area we must calculate but out of the 6, there are two faces

each that are equal in area.

From the above figure, we have that:

FACE 1 = FACE 2

FACE 3 = FACE 4

FACE 5 = FACE 6.

Thus, once we find the area of FACE 1, we already have the area of FACE 2 and so on.

Also, since each face is a rectangle, the area of a rectangle is given by:

\begin{gathered} A=l* b \n l=\text{length} \n b=\text{breadth or width} \end{gathered}

Now, let us calculate the area of FACE 1, 3 and 5.

\begin{gathered} \text{FACE 1:} \n A_1=18*4=72in^2 \n \text{FACE 3:} \n A_3=4*7=28in^2 \n \text{FACE 5:} \n A_5=18*7=126in^2 \end{gathered}

Now we just sum up all the areas and multiply them by two to account for FACES 2, 4 and 6

\begin{gathered} A_S=2*(72+28+126) \n \therefore A_S=452in^2\text{ } \end{gathered}

Therefore, the Surface area of the rectangular prism is:

452 square inches

Volume:

The formula for the volume of a rectangular prism is given as:

\begin{gathered} V=l* w* h \n l=\text{length} \n w=\text{width or breadth} \n h=\text{height or depth} \end{gathered}

The length, width, and height are shown in the figure below:

Thus, we can easily calculate our volume as shown below:

\begin{gathered} V=7*18*4in^3 \n \therefore V=504in^3 \end{gathered}

Therefore, the Volume of the rectangular prism is:

V = 504 cubic inches

To recap, the final answers are:

Surface Area = 452 square inches

Volume = 504 cubic inches

Find the measures of the supplementary angles that satisfy each case.The measure of the first angle is 45° more than the measure of the second.
(I will make you braniliest if it is correct)

Answers

Answer:

67.5°, 107.5°

Step-by-step explanation:

For supplementary angles, their sum equals 180°.

Let x be the first angle and y be the second angle, then

x + y = 180°.

It is given that x = y + 45°.

So x + y = 180°

substituting x into the equation, we have

y + 45° + y = 180°

simplifying, we have

2y + 45° = 180°

collecting like terms, we have

2y = 180° - 45°

2y = 135°

dividing through by 2, we have

y = 135°/2

y = 67.5°

Since y = 67.5°

then x = y + 45°

x = 67.5° + 45°

x = 107.5°

Final answer:

The measures of the supplementary angles that satisfy the given conditions are 67.5° and 112.5°.

Explanation:

Let's say the measure of the second angle is x. Since the measure of the first angle is 45° more than the measure of the second, we can express the first angle as the measure of x + 45°.

By the definition of supplementary angles, we know that the sum of the measures of two supplementary angles is 180°. Therefore, we can create the following equation: x + (x + 45) = 180.

Solving this equation gives us:

  1. Add the expressions on the left side of the equation to get: 2x + 45 = 180.
  2. Subtract 45 from both sides of the equation to isolate the term containing x: 2x = 135.
  3. Divide both sides of the equation by 2 to solve for x: x = 67.5°.

So, "the second angle measures 67.5°, and the first angle, being x + 45°, measures 112.5°".

Learn more about Supplementary Angles here:

brainly.com/question/18164299

#SPJ12

A researcher examines 27 sedimentary samples for bromide concentration. The mean bromide concentration for the sample data is 0.383 cc/cubic meter with a standard deviation of 0.0209. Determine the 90% confidence interval for the population mean bromide concentration. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answers

Answer:

Critical value: z = 1.645

The 90% confidence interval for the population mean bromide concentration is (0.376, 0.39).

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = (1-0.9)/(2) = 0.05

Now, we have to find z in the Ztable as such z has a pvalue of 1-\alpha.

So it is z with a pvalue of 1-0.05 = 0.95, so z = 1.645. This value of z is the critical value

Now, find M as such

M = z*(\sigma)/(√(n))

In which \sigma is the standard deviation of the population and n is the size of the sample.

M = 1.645*(0.0209)/(√(27)) = 0.0066

The lower end of the interval is the mean subtracted by M. So it is 0.383 - 0.0066 = 0.376 cc/cubic meter

The upper end of the interval is the mean added to M. So it is 0.383 + 0.0066 = 0.39 cc/cubic meter

The 90% confidence interval for the population mean bromide concentration is (0.376, 0.39).

5 years ago, Cheryl was d years old, Brandon is 2 years older than Cheryl.a. how old is Cheryl

b. how old is Brandon

c. what was the difference in their ages 5 years ago?

d. what is the sum of their ages now?

e. what will the sum of their ages be two years from now?

f. what will the difference of their ages be two years from now

will mark the brainliest.

Answers

Answer: See explanation

Step-by-step explanation:

a. how old is Cheryl?

Cheryl's age = d + 5

b. how old is Brandon?

d + 5 + 2

= d + 7

c. what was the difference in their ages 5 years ago?

Cheryl age five years ago = d

Brandon's age five years ago = d + 2

Difference = d + 2 - d = 2 years

d. what is the sum of their ages now?

Cheryl's age = d + 5

Brandon age = d + 7

Sum = d + 5 + d + 7

= 2d + 12

e. what will the sum of their ages be two years from now?

Two years from now,

Cheryl's age = d + 5 + 2 = d + 7

Brandon age = d + 7 + 2 = d + 9

Sum = d + 7 + d + 9

= 2d + 16

f. what will the difference of their ages be two years from now

Two years from now,

Cheryl's age = d + 5 + 2 = d + 7

Brandon age = d + 7 + 2 = d + 9

Difference = Brandon age - Cheryl age

= (d + 9) - (d + 7)

= 2 years.
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