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2 years ago

What is the equation for the translation of x2 + y2 = 16 seven units to the right and five units up?

Mathematics

1 answer:

asambeis [7]2 years ago

6 0

Answer:

(x − 7)2 + (y − 5)2 = 16

Step-by-step explanation:

The given circle has equation

$\sf \: x^2+y^2=16x$

The equation of a circle with center (h,k) and radius r units is

$\sf(x-h)^2+(y-k)^2=r^2(x−h)$

$\sf(x-7)^2+(y-5)^2=4^2(x−7)$

$\sf(x-7)^2+(y-5)^2=16(x−7)$

This is the equation that has its center at the origin with radius 4 units.

When this circle is translated seven units to the right and five units up, then the center of the circle will now be at (7,5).

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Cally wants to coat her driveway with a winter sealer. Her driveway is 18 feet long and shaped like a trapezoid. At the garage d

stellarik [79]

Answer:

Amount of Winter sealer for 2 coats[in square feet] = 576 square feet

Step-by-step explanation:

Given:

Length of drive way at garage door = 12 feet

Length of drive way at street = 20 feet

Length of total driveway = 18 feet

Find:

Amount of Winter sealer for 2 coats[in square feet]

Computation:

Amount of Winter sealer for 2 coats[in square feet] = 2[Area of trapezoid]

Amount of Winter sealer for 2 coats[in square feet] = 2[(1/2)(Sum of parallel side)(Height)]

Amount of Winter sealer for 2 coats[in square feet] = 2[(1/2)(12 + 20)(18)]

Amount of Winter sealer for 2 coats[in square feet] = 2[(1/2)(32)(18)]

Amount of Winter sealer for 2 coats[in square feet] = 32 x 18

Amount of Winter sealer for 2 coats[in square feet] = 576 square feet

5 0

2 years ago

Find 415 of 619 in simplest form,

Finger [1]

Answer:

415/619

Step-by-step explanation:

619 is a prime number, so the fraction is in simplest form already.

8 0

3 years ago

Which of the following is equivalent to y + 6 = -4(x+3)

Darya [45]

What are the options?

4 0

2 years ago

Your boss tells you that she knows the length of the widgets your company makes is normally distributed with a mean of 25 inches

sp2606 [1]

Answer:

Mean of sampling distribution = 25 inches

Standard deviation of sampling distribution = 4 inches

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 25 inches

Standard Deviation, σ = 12 inches

Sample size, n = 9

We are given that the distribution of length of the widgets is a bell shaped distribution that is a normal distribution.

a) Mean of the sampling distribution

The best approximator for the mean of the sampling distribution is the population mean itself.

Thus, we can write:

$\bar{x} = \mu = 25\text{ inches}$

b) Standard deviation of the sampling distribution

$s = \dfrac{\sigma}{\sqrt{n}} = \dfrac{12}{\sqrt{9}} = 4\text{ inches}$

8 0

3 years ago

I have the picture attached

Lisa [10]

Answer:

y = 2/3x + 4

Step-by-step explanation:

First, we look at where the equation intersects the y axis. It intersects at y = 4, which means that in the end of the equation there must be a "+4", so we can rule out the first two.

Second, we look at the slope of the line. Slope is defined as rise over run. As you can see in the graph, the line moves up 2 units while moving right 3 units. That means the coefficient of x (which is the slope) will be 2/3, which means the answer is y = 2/3x + 4.

4 0

2 years ago