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3 years ago

Write the standard equation of the circle in the graph. Picture included.

Mathematics

1 answer:

Komok [63]3 years ago

5 0

Answer:

Option 1:

$(x-3)^2+(y+2)^2=9$

Step-by-step explanation:

We can observe the given graph to find the center and radius

By observing the graph we can conclude that the center of the circle is at

x = 3 and y = -2 which means the center is:

(h,k) = (3,-2)

Similarly the radius is 3 because the distance between the center and boundary of circle is 3 units.

So, r = 3

The standard form of equation of a circle is:

$(x-h)^2+(y-k)^2 = r^2$

Putting the values of h,k and r

$(x-3)^2+(y-(-2))^2=(3)^2\\(x-3)^2+(y+2)^2=9$

Hence, the correct answer is option 1 ..

You might be interested in

Rectangle RSTU and the image R’S’T’U’ are graphed on the coordinate grid below.

Ksju [112]

The rectangle R’S’T’U’ is a 90° counterclockwise rotation of RSTU so options (A) and (C) will be correct.

<h3>What is a rectangle?</h3>

The rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Given the rectangle RSTU if we plot it then it becomes a major horizontal rectangle.

If we transpose into R’S’T’U’ then it rotates 90 degrees counterclockwise and becomes a major vertical ractangle.

Hence the rectangle RSTU will rotate 90° counterclockwise to form R’S’T’U’.

For more about rectangles,

brainly.com/question/15019502

#SPJ1

5 0

2 years ago

At your gym, the bar you lift weighs 45 pounds. You add weights to the bar that are 10 pounds each. If you add 8 weights to the

lana66690 [7]

45 plus 80 which is 125 pounds

4 0

3 years ago

Read 2 more answers

According to a Washington Post-ABC News poll, 331 of 502 randomly selected U.S. adults interviewed said they would not be bother

k0ka [10]

Answer:

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124$

$p_v =P(z>7.124)=5.24x10^{-13}$

So the p value obtained was a very low value and using the significance level given $\alpha=0.05$ we have $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of interest is significantly higher than 0.5.

Step-by-step explanation:

Data given and notation

n=502 represent the random sample taken

X=331 represent the adults that said they would not be bothered if the NAtional security agency

$\hat p=\frac{331}{502}=0.659$ estimated proportion of people who would not be bothered if the NAtional security agency

$p_o=0.5$ is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is higher than the majority of 0.5:

Null hypothesis: $p\leq 0.5$

Alternative hypothesis: $p > 0.5$

When we conduct a proportion test we need to use the z statistic, and the is given by:

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

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.659 -0.5}{\sqrt{\frac{0.5(1-0.5)}{502}}}=7.124$

Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.01$ . The next step would be calculate the p value for this test.

Since is a right tailed test the p value would be:

$p_v =P(z>7.124)=5.24x10^{-13}$

4 0

3 years ago

In triangle ABC, angle A is a right angle, and measure of angle B = 45 degrees.

Ghella [55]

Answer:

13√2

Step-by-step explanation:

this is cuz of the 45 45 90 formula

6 0

3 years ago

Read 2 more answers

Lorene plans to make several open-topped boxes in which to carry plants. She makes the boxes from rectangular sheets of cardboar

Katen [24]

Answer:

29 feet in length, 5 feet in width and 12 feet in height

Step-by-step explanation:

We have that for the volume of a quadrangular prism is:

V = l * w * h

Ie length times width times height

In this case, the height is determined by the squares that you put in each corner, taking into account that a square has all the same sides, the height is 12 inches. h = 12

they tell us that the length is 24 inches more than the width, that is, l = 24 + w

replacing we have:

1740 = (24 + w) * w * 12

1740 = 12 * w ^ 2 + 288 * w

12 * w ^ 2 + 288 * w - 1740 = 0

if we calculate the root, we have w = 5 or w = -29

only works when w = 5

Thus:

l = 24 + 5

l = 29

which means that the dimensions are:

29 feet in length, 5 feet in width and 12 feet in height

5 0

3 years ago