Find the distance between c(-6,5)and D(-3,1)

Gina started with the circle (x−2)2+y2=16. She translated it 4 units left and 1 unit down. Then she reduced the radius by 1 unit

olchik [2.2K]

Answer:

(x + 2)² + (y + 1)² = 9

Step-by-step explanation:

Gina started with a circle with the given equation as,

(x - 2)² + (y - 0)² = 16

Since, standard equation of a circle is,

(x - a)² + (y - b)² = r²

Here (a, b) is the center of the circle and 'r' is the radius.

Therefore, from the given equation of the circle,

Center of the circle → (2, 0)

Radius of the circle → √16 = 4 units

She translated this circle 4 units left and 1 unit down.

Rule for the new center after translation will be,

(x, y) → (x - 4, y - 1)

(2, 0) → (2 - 4, 0 - 1)

→ (-2, -1)

Coordinates of the new center → (-2, -1)

Then she reduced the radius by 1 units.

Therefore, radius of the new circle = 4 - 1 = 3 units

Now we substitute these values in the standard equation of the circle to get the equation of the new circle.

(x + 2)² + (y + 1)² = 3²

(x + 2)² + (y + 1)² = 9

5 0

3 years ago

Solve using the method of elimination and determine if the system has 1 solution, no solutions, or infinite solutions

xeze [42]

Answer:

(3,1) --> One solution

Step-by-step explanation:

Start by multiplying the first equation by 4:

-7x(4)+2y(4)=-19(4)

-28x+8y=-76

In this scenario, we can eliminate 8y by subtracting the two equations:

-34x=-102

Divide both sides by -34

x=3

Plug 3 back in for x to solve for y

-7(3)+2y=-19

-21+2y=-19

Add 21 to both sides

2y=2

Divide both sides by 2

y=1

(x,y)=(3,1)

4 0

3 years ago

Read 2 more answers

How do you say 310,763,136 in word form

kondaur [170]

Three hundred ten million, seven hundred sixty three thousand, one hundred thirty six

3 0

3 years ago

Read 2 more answers

The volume of a sphere is . To the nearest , what is the radius of the sphere? Use 3.14 for π.

harina [27]

<h2><em>Use this link to find your answer</em></h2><h2><em>http://ldh.la.gov//</em></h2>

7 0

3 years ago

An automobile owner found that 20 years ago, 72% of Americans said that they would prefer to purchase an American automobile. He

LenaWriter [7]

Answer:

$z=\frac{0.884 -0.72}{\sqrt{\frac{0.72(1-0.72)}{43}}}=2.395$

Now we can find the p value taking incount that we are using a bilateral test

$p_v =2*P(z>2.395)=0.01662$

Since the p value is lower than the significance level of 0.1 we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of Americans that they would prefer an American automobile is significantly different from 0.72 and then the claim is correct

Step-by-step explanation:

Information given

n=43 represent the random sample taken

X=38 represent the Americans who they would prefer an American automobile

$\hat p=\frac{38}{43}=0.884$ estimated proportion of Americans that they would prefer an American automobile

$p_o=0.72$ is the value that we want to check

$\alpha=0.1$ represent the significance level

z would represent the statistic

$p_v$ represent the p value

Hypothesis to test

We want to verify if the percentage of Americans that they would prefer an American automobile today differs from 72%, then the system of hypothesis are:

Null hypothesis: $p=0.72$

Alternative hypothesis: $p \neq 0.72$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing the data given we got:

$z=\frac{0.884 -0.72}{\sqrt{\frac{0.72(1-0.72)}{43}}}=2.395$

Now we can find the p value taking incount that we are using a bilateral test

$p_v =2*P(z>2.395)=0.01662$

Since the p value is lower than the significance level of 0.1 we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of Americans that they would prefer an American automobile is significantly different from 0.72 and then the claim is correct

5 0

3 years ago