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3 years ago

Write an equation for a circle with a diameter that has endpointsat (-4, -7) and (-2 ,-5)

Mathematics

1 answer:

sergiy2304 [10]3 years ago

7 0

Answer:

(x + 3)^2 + (y + 6)^2 = (√2)^2 = 2

Step-by-step explanation:

The standard equation for a circle with center at (h, k) and radius r is

(x - h)^2 + (y - k)^2 = r^2. We need to find h, k and r for this particular circle.

The length of the radius is half the length of the diameter. Find the length of this diameter first, and than halve the result.

diameter^2 = 2^2 + 2^2, or diameter^2 = 8, or diameter = √8 = 2√2.

This is because x changes from -4 to -2 (+2) and y changes from -7 to -5 (+2).

Then the radius is r = 2√2.

The coordinates of the center are found using the midpoint formula:

-4-2

xcenter = -------- = -3

-7-5

ycenter = -------- = - 6

Inserting -3 for h, -6 for k and √2 for r, we get:

(x + 3)^2 + (y + 6)^2 = (√2)^2 = 2

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Ira Lisetskai [31]

Answer:

y = -⅓x - 5

Step-by-step explanation:

the slope of g(x) = 3

=> the slope of the line perpendicular

to g(x) = -1 /3

so,

the line is :

y +5 = -⅓(x-0)

y = -⅓x - 5

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3 years ago

You just paid $435,000 for a policy that will pay you and your heirs $17,300 per year forever with the first payment in one year

Marysya12 [62]

Answer:

3.98%

Step-by-step explanation:

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5 0

3 years ago

Find the sum. + 1.5 + 3.9 A) 4.14 B) 41.4 C) 5.4 D) 0.54

Natalija [7]

Answer:

5.4

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Solve for x. Round to the nearest hundredth.

zlopas [31]

Given that the length of the hypotenuse is 8 and the angle is 42°

The length of the one leg of the triangle is x.

We need to determine the value of x.

Value of x:

The value of x can be determined using the trigonometric ratio.

Thus, we have;

$sin \ \theta=\frac{opp}{hyp}$

Substituting the values, we get;

$sin \ 42^{\circ}=\frac{x}{8}$

Multiplying both sides of the equation by 8, we get;

$sin \ 42^{\circ}\times8=x$

Simplifying, we get;

$0.669 \times 8=x$

$5.352\approx x$

Therefore, the value of x is 5.35(app.)

Hence, Option A is the correct answer.

8 0

3 years ago

jeanine Baker makes floral arrangements. She has 13 different cut flowers and plans to use 7 of them. How many different selecti

Ksju [112]

A total of 1,716 selections of the 7 flowers are possible.

Step-by-step explanation:

Step 1:

There are 13 flowers from which Jeanine Baker plans to use 7 of them.

To determine the number of selections that are possible we use combinations.

The formula for combinations is; $^{n} C_{r}=\frac{n !}{(n-r) ! r !}$ .

Step 2:

In the given formula, n is the total number of options and r is the number of options to be selected.

For this question, $n = 13$ and $r=7$ .

So $^{13} C_{7}=\frac{13 !}{(13-7) ! 7 !} = \frac{13 !}{(6) ! 7 !} = 1,716.$

So a total of 1,716 selections are possible.

3 0

3 years ago