Rosa graphs the line y = 3x + 5.then she dilates the line by a factor of 1/5 with (0,7) as the center of dilation .

Answers

Answer 1

Answer:

The equation of the dilated line is y = (3/5)x + (33/5), and it passes through the point (0,7).

How to measure dilation?

To dilate the line y = 3x + 5 by a factor of 1/5 with (0,7) as the center of dilation, we can follow these steps:

Shift the line so that the center of dilation is at the origin. To do this, we subtract 7 from the y-intercept of the original line, giving us y = 3x - 2.

Apply the dilation factor to the line. To do this, we multiply the coordinates of each point on the line by 1/5. This gives us the new equation:

y = (3/5)x - (2/5)

Shift the line back to its original position. To do this, we add 7 to the y-intercept of the dilated line, giving us the final equation:

y = (3/5)x + (33/5)

Therefore, the equation of the dilated line is y = (3/5)x + (33/5), and it passes through the point (0,7).

To know more about dilation follow

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Answer 2

Answer:

Different slope of 3

Step-by-step explanation:

Just did it

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Determine whether the following sequence converges or diverges and describe whether it does do so monotonically or by oscillation. Give the limit when the sequence converges. {(-1.00000005)^n}

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. The sequence diverges by oscillation.
b. The sequence converges monotonically. It converges to:________
c. The sequence converges by oscillation. It converges to:________
d. The sequence diverges monotonic ally.

Answers

Answer:

Step-by-step explanation:

(-1.00000005)^n

as n becomes very large, the function increases in both positive and negative direction.

If n=1, -1.00000005

if n=2, 1.0000001

if n= 3, -1.00000015

if n=20, 1.000001

if n=21, -1.00000105

The half-life of radium-226 is 1620 yr. Given a sample of 1 g of radium-226, the quantity left Q(t) (in g) after t years is given by:Q(t)= 1/2^t/1620

Required:
a. Convert this to an exponential function using base e.
b. Verify that the original function and the result from part (a) yield the same result for Q(0), Q(1620), and Q(3240).

Answers

Answer:

(a) $e^(-0.000428 t)$

Step-by-step explanation:

We are given that

Half life of radium-226=1620 yr

The quantity left Q(t) after t years is given by

$Q(t)=((1)/(2))^{(t)/(1620)}$

a. We have to convert the given function into an exponential function using base e.

$Q(t)=((1)/(2))^{(t)/(1620)}$

= $(((1)/(2))^t)^{(1)/(1620)$

= $e^(ln(1/2) t/1620)$

$=e^({(ln(1/2))/(1620)t)$

= $e^(-0.000428 t)$

(b)

$Q(0)=e^(-0.000428 * 0)$

From original function

Q(0)=1

$Q(1620)=((1)/(2))^{(t)/(1620)}$

$Q(1620)=(1)/(2)=0.5$

From exponential function

$Q(1620)=e^(-0.000428 * 1620)$

$=0.499\approx 0.5$

$Q(3240)=((1)/(2))^{(3240)/(1620))=0.25$

$Q(3240)=e^(-0.000428 * 3240)$

Q(3240)=0.249= $\approx 0.25$

Hence, verified.

WILL GIVE BRAINLYIST.For this problem, use the tables and charts shown in this section. For total cost of an American tourist traveling on the European continent, Is the average price (1) higher, or (2) lower than the highest total figure shown for the Pacific area? higher lowes

Answers

Step-by-step explanation:

higher

A bicycle wheel has a circumference of 75 inches. What is the approximate radius of the wheel?

Answers

Answer:

23.87

Step-by-step explanation:

When graphed, which function has a horizontal asymptote at 4? A. f(x)= 2(3^x)+4
B. f(x)=2x-4
C. f(x)=-3x+4
D f(x)= 3(2^x)-4

Answers

Answer:

A. f(x)= 2(3^x)+4

Step-by-step explanation:

The linear equations of answer choices B and C will not have a horizontal asymptote. The exponential equation of choice D will have a horizontal asymptote at y=-4.

The appropriate choice is the exponential equation with 4 added:

f(x) = 2(3^x)+4

The price of a technology stock has risen to $9.82 today. Yesterday's price was $9.71. Find the percentage increase. Round your answer to the nearest tenth of a percent.