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sweet [91]
1 year ago
11

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

a sequence of transformations, find an equation for gWhat is the equation for g?

Mathematics
1 answer:
german1 year ago
3 0

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

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A vehicle is purchased for $18,000, with a down payment of $6,098. The balance in financed for three years at an annual rate of
mestny [16]
The Present value of an annuity is given by PV = P(1 - (1 + r/t)^-nt)/(r/t)
where: P is the monthly payment, r is the annual rate = 7% = 0.07, t is the number of periods in one year = 12 and n is the number of years = 3.

18,000 - 6,098 = P(1 - (1 + 0.07/12)^-(3 x 12)) / (0.07/12)
11,902 = P(1 - (1 + 0.07/12)^-36) / (0.07/12)
P = 0.07(11,902) / 12(1 - (1 + 0.07/12)^-36) = 367.50

Therefore, monthly payment = $367.50
7 0
3 years ago
Mr. Blue drove from Allston to Brockton, a distance of 105 miles. On his way back, he increased his speed by 10 mph. If the jour
andrew-mc [135]

Answer:

His original speed was 60 mph.

Step-by-step explanation:

The average speed formula is shown below:

speed = distance / time

For the first leg of the trip Mr. Blue drove at a speed of "x" mph, for a distance of 105 miles, therefore the time that took to complete the trip is:

time 1 = distance / speed

time 1 = 105 / x h

On the second leg of the trip Mr. Blue drove faster at a speed of "x + 10" mph, so the time it took him to complete the trip was 15 minutes less, therfore:

time 2 = time1 - (15/60) = (105/x) - 0.25 = (105 - 0.25*x)/x h

Applyint the time and speed from the second leg to the average speed formula we have:

x + 10 = {105/[(105 - 0.25*x)/x]}

x + 10 = 105*x/(105 - 0.25*x)

(x + 10)*(105 - 0.25*x) = 105*x

105*x + 1050 -0.25*x² - 2.5*x = 105*x

-0.25*x² -2.5*x + 1050 = 0 /(-0.25)

x² + 10*x - 4200 = 0

x1 = [-(10) + sqrt((10)² - 4*(1)*(-4200))]/2 = 60

x2 = [-(10) - sqrt((10)² - 4*(1)*(-4200))]/2 = -70

Since his speed couldn't be negative the only possible value was 60 mph.

5 0
3 years ago
Read 2 more answers
What number is 4/7 of 210
vitfil [10]

Answer:

4 / 7 of 210 is 120.

(4 / 7) * 210 = 120

8 0
3 years ago
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(c) Find the number of sets where all three cards are the same for exactly $0$ attributes. (d) Find the number of sets where all
Cloud [144]

C. For the first card, there are three ways to choose the number of card.

For the another, there two options, and likewise there's only 1 choice of card. So there are 3 × 2 × 1 = 6 ways that the calculation can be chosen.

Doing this for the other attributes, we get 6 × 6 × 24 × 6 ways. But the order of cards does not count in a set of card, so we divide by 3! 6 * 6 * 24 × 6 ÷ 3! = 864. It means there are 864 sets for part.

D. The cards may have the same number, color, shapess, orshading.

However, also there are 6 × 24 × 6 × 3! = 144 sets of cards, If all the colors are thesame. How ever, also there are 144 sets of cards.

If all the calculation are the same. We get the same number for shape and shadings, so there are 4 × 144 = 576 sets of cards.

what is Probability?

Probability is branches of mathematics concerning numerical descriptions of how to the likely an event is to occurs, or how to the likely it is that a proposition is true. The probability of an event is a numbers between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the events and 1 indicates certain of cards.

Learn more about Probability here

brainly.com/question/13604758

#SPJ10

5 0
2 years ago
What is the constant of proportionality, y/X
Daniel [21]

Answer:

Best answer would be 1/2. If that doesn't work then 0.5/1 would be the answer.

8 0
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