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3 years ago

The graph of y = x^3 is transformed as shown in the graph below. Which equation represents the transformed function?

Mathematics

1 answer:

Kay [80]3 years ago

8 0

Answer:

y = -6 * x^3

Step-by-step explanation:

We can model the new function as:

f(x) = ax^3

the function y = x^3 have positive values of y for positive values of x, and negative values of y for negative values of x.

As the negative values of x have positive values of y and vice-versa, the first change is to put a negative sign in front of x^3, so we know that 'a' is negative.

Then, for x=1 we have y = -6, so:

-6 = a*1^3

a = -6

So the equation of the transformed function is:

y = -6 * x^3

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After five weeks they will have the same amount of money.

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3 years ago

A) If the 5th term of an A.P. is double the 7th term, show that the sum of the 17 terms zero.

gayaneshka [121]

Answer:

see explanation

Step-by-step explanation:

The nth term of an AP is

$a_{n}$ = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₅ is double a₇ , then

a₁ + 4d = 2(a₁ + 6d) , that is

a₁ + 4d = 2a₁ + 12d ( subtract a₁ from both sides )

4d = a₁ + 12d ( subtract 12d from both sides )

- 8d = a₁

The sum of n terms of an AP is

$S_{n}$ = $\frac{n}{2}$ [ 2a₁ + (n - 1)d ] , substitute values

$S_{17}$ = $\frac{17}{2}$ ( 2(- 8d) + 16d)

= 8.5(- 16d + 16d)

= 8.5 × 0

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3 years ago

What number goes in the box in the followng sequence 5 11 23 ? 95 191

Alina [70]

Answer:

Step-by-step explanation:

The number that should go after 23 is 47.

The pattern seems to be (n * 2) + 1, where n is the value of the previous number.

We start with the number 5:

(5 * 2) + 1 = 11

(11 * 2) + 1 = 23

(23 * 2) + 1 = 47

... and so on

The pattern should continue as follows.

Hope this helps!

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3 years ago

Triangle FGH has the following side lengths: FG = 5 ft, GH = 10 ft, HF = 12 ft Triangle PQR is similar to triangle FGH. The long

7nadin3 [17]

The first thing we must do for this case is find the scale factor.
We have then that for the larger side of both triangle, the scale factor is:
$k = \frac{RP}{HF}$
$k = \frac{7.2}{12}$
$k = 0.6$
To find the other two sides, we must apply the scale factor on each side of the triangle FGH.
We have then:

For PQ
$PQ = k * FG

PQ = 0.6 * 5

PQ = 3$

For QR
$QR = k * GH

QR = 0.6 * 10

QR = 6$

Answer:
You have that the lengths for the other two sides of triangle PQR are:
$PQ = 3

QR = 6$

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4 years ago