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2 years ago

What is the inverse of the function f(x) = one-quarterx – 12? h(x) = 48x – 4 h(x) = 48x + 4 h(x) = 4x – 48 h(x) = 4x + 48

Mathematics

2 answers:

DaniilM [7]2 years ago

8 0

Answer:

h(x) = 4x+48

Step-by-step explanation:

Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.

Then we will make x the subject of the formula as shown:

y = 1/4x - 12

adding 12 to both sides we have;

y + 12= 1/4x - 12 + 12

y + 12 = 1/4x

Multiplying both sides by 4 we have;

4(y+12) = x

x = 4y + 48

Substituting y for x

y = 4x+48

f^-1(x) = 4x+48

h(x) = 4x+48

Thee final expression will give the inverse of the function

Basile [38]2 years ago

4 0

Answer:

Step-by-step explanation:

Given the function f(x) = 1/4x -12. To get the inverse of the function, first we will let y = f(x) to have y = 1/4x - 12.

Then we will make x the subject of the formula as shown:

y = 1/4x - 12

adding 12 to both sides we have;

y + 12= 1/4x - 12 + 12

y + 12 = 1/4x

Multiplying both sides by 4 we have;

4(y+12) = x

x = 4y + 48

Substituting y for x

y = 4x+48

f^-1(x) = 4x+48

h(x) = 4x+48

Thee final expression will give the inverse of the function

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What is the equation of a line in slope intercept form that contains the points (-4,3) and (2,-6)

Nataly_w [17]

Answer:

y = (-3/2)x - 3

Step-by-step explanation:

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Given two points, we can calculate the slope by dividing the change in y (or the difference in the y-coordinates) by the change in x (or the difference in the x-coordinates). Our two points are (-4, 3) and (2, -6):

m = (3 - (-6)) / (-4 - 2) = 9 / (-6) = -3/2

So, we can update our equation:

y = (-3/2)x + b

The y-intercept is where the graph crosses the y-axis, or the y-value where x = 0. Let's plug in 3 for y and -4 for x:

3 = (-3/2) * (-4) + b

3 = 6 + b

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So, our y-intercept is -3.

Our slope-intercept form is thus:

y = (-3/2)x - 3

<em>~ an aesthetics lover</em>

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2 years ago

The 99 percent confidence interval for the average weight of a product is from 71.36 lbs. to 78.64 lbs. Can we conclude that μ i

Ilya [14]

Answer:

Step-by-step explanation:

Hello!

To decide over a hypothesis test using a confidence interval the following conditions are to be met:

1. The hypotheses should be two-tailed.

2. The hypotheses and the confidence interval should be made for the same parameter.

3. The confidence level and the significance level should be complementary, so if the CI is 1-α: 0.99 the level of significance should be α: 0.01

If all conditions are met, the decision rule is the following:

If the value stated in the null hypothesis is contained by the CI, the decision is to not reject the null hypothesis.

If the value stated in the null hypothesis is not contained by the CI, the decision is to reject the null hypothesis.

Let's say in this example the hypotheses are:

H₀: μ = 71

H₁: μ ≠ 71

α: 0.01

99% Confidence level is (71.36;78.64).

As you can see, 71 is not contained in the CI so the decision to take is to reject the null hypothesis, in other words, the population mean is not 71.

I hope it helps!

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2 years ago

The price that a company charged for a basketball hoop is given by the equation 50 - 5x^2 where x is the number of hoops that ar

DiKsa [7]

Answer: The correct option is first, the number of basketball hoops did the company previously produce to make the same profit is 1.3 million hoops.

Explanation:

Let the number of basketball hoops did the company previously produce to make the same profit be x.

Total Revenue = Price * Quantity

The total revenue in million dollars is,

$\text{Total Revenue}=(50-5x^2)x$

$\text{Total Revenue}=50x-5x^3$

The total cost in million dollars is,

Total Cost = One unit cost * Quantity

$\text{Total Cost}=30x$

Profit = Total Revenue - Total Cost

$\text{Profit}=50x-5x^3-30x$

The profit is 15 million.

$15=20x-5x^3$

$5x^3-20x+15=0\\x^2-4x+3=0\\(x-1)(x^2+x-3)=0$

The value of x is 1 and $\frac{-1\pm \sqrt{13}}{2}$ .

The production is always positive therefore the value of x either 1 or 1.3. Since 1 million is not available in the options therefore the the correct optin is 1.3 million hoops.

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2 years ago

Read 2 more answers

Which expression is equivalent to (4 + 7i)(3 + 4i)? –16 + 37i 12 – 28i 16 – 37i 37 + 16i

ASHA 777 [7]

Answer:

The equivalent expression is $\Rightarrow -16+37i$