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2 years ago

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Mathematics

1 answer:

ExtremeBDS [4]2 years ago

6 0

Answer:

the question is about the table you have to make a table it is very easy

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The functions f and g are graphed in the same rectangular coordinate system, shown to the right. If g is obtained from f through

german

The first thing we notice is that the function is reflected. So we can start by reflecting it with respect to the x-axis.

We do this by adding a negative sign in the function:

$\begin{gathered} f_0(x)=x^2 \\ f_1(x)=-f_0(x)=-x^2 \end{gathered}$

Now, we have the function reflected, but in the wrong position. We can track its position by the vertex. It was originally at (0,0) and remains at (0,0) after the reflection.

But the final function have its vertex at (-5,0), so we have to translate the function 5 units to the left. we do this by adding 5 to the x in the function:

$f_2(x)=f_1(x+5)=-(x+5)^2$

Now, to check if there isn't any dilatation, we can check on other point in the graph to see if it checks out.

In the blue graph, we see the point (-3,-4), so let's input x = -3 and see if it checks out:

$f_2(-3)=-(-3+5)^2=-(2)^2=-4$

We got y = -4, so it checks out.

Thus, the answer is:

$g(x)=-(x+5)^2$

3 0

1 year ago

What is the unit rate for $4.75

Softa [21]

Answer:

2.436

Step-by-step explanation:

It’s Right Trust me

4 0

2 years ago

A sample of 25 undergraduates reported the following dollar amounts of entertainment expenses last year:

marin [14]

Answer:

$Range = 85$

$\sigma = 28.71$

$Interval = [666.78, 781.62]$

Step-by-step explanation:

Given

The data for 25 undergraduates

Solving (a): Range and Standard deviation

The range is:

$Range = Highest - Least$

From the dataset:

$Highest = 772$

$Least = 687$

So:

$Range = Highest - Least$

$Range = 772-687$

$Range = 85$

The standard deviation is:

$\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}$

First, calculate the mean

$\bar x = \frac{769 +691 +............+715}{25}$

$\bar x = \frac{18105}{25}$

$\bar x = 724.2$

So, the standard deviation is:

$\sigma = \sqrt{\frac{(769-724.2)^2 +(691-724.2)^2 +(699-724.2)^2 +(730-724.2)^2 +............+(715-724.2)^2}{25}}$

$\sigma = \sqrt{\frac{20604}{25}}$

$\sigma = \sqrt{824.16}$

$\sigma = 28.71$

Solving (b): The interval of the 95% of the observation.

Using the emperical rule, we have:

$Interval = [\bar x - 2*\sigma, \bar x+ 2*\sigma]$

$Interval = [724.2 - 2*28.71, 724.2 + 2*28.71]$

$Interval = [666.78, 781.62]$

4 0

2 years ago

If f(x)=5x, what is f^-1(x)?

dimulka [17.4K]

Answer:

The inverse function f^-1 (x) = (1/5) x

Step-by-step explanation:

* Lets explain what is the meaning of f^-1(x)

- f^-1 (x) the inverse function of f(x)

* How to find the inverse function

- In the function f(x) = ax + b, where a and b are constant

- Lets switch x and y

∵ y = ax + b

∴ x = ay + b

* Now lets solve to find y in terms of x

∵ x = ay + b ⇒ subtract b from the both sides

∴ x - b = ay ⇒ divide the two sides by a

∴ (x - b)/a = y

∴ The inverse function f^-1 (x) = (x - b)/a

* Lets do that with our problem

∵ f(x) = 5x ⇒ y = 5x

∴ x = 5y

- Find y in terms of x

∵ x = 5y ⇒ divide the both sides by 5

∴ x/5 = y

∴ f^-1 (x) = (1/5) x

* The inverse function f^-1 (x) = (1/5) x

7 0

3 years ago

Read 2 more answers

Raina is saving money to buy a game. The game costs $20, and so far she has saved four-fifths of this cost. How much money has R

Tanzania [10]

Answer:

$16

Step-by-step explanation:

8 0

3 years ago

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