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4 years ago

Ordered pair 12, 24 in the context of the problem

Mathematics

1 answer:

Schach [20]4 years ago

7 0

It would be 36 because ypu are adding 12.

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21. The equation x² + y² - 6x + 8y = 74<br> represents circle C.<br> What is the radius of circle C?

marin [14]

Answer:

The radius is $3\sqrt{11}$ .

Step-by-step explanation:

The standard equation for a circle is $(x-h)^2+(y-k)^2=r^2$ .

I like to call this form center-radius form because it tells you the center (h,k) and the radius r.

So we put it in this form to determine r, the radius, which is the desired value here.

We will need to complete the square.

Thankfully there is a formula to take more thinking out of the process:

$x^2+dx+(\frac{d}{2})^2=(x+\frac{d}{2})^2$ .

Let's begin:

$x^2+y^2-6x+8y=74$

Reorganize the equation so the x's are together and the y's are together.

$x^2-6x+y^2+8y=74$

Now time to being completing the square. Keep in mind whatever you add to one side you need to add the other side to keep the equation equivalent to what it once was.

$x^2-6x+(\frac{-6}{2})^2+y^2+8y+(\frac{8}{2})^2=74+(\frac{-6}{2})^2+(\frac{8}{2})^2$

Use the other side of the formula I mentioned for completing the square:

$(x+\frac{-6}{2})^2+(y+\frac{8}{2})^2=74+(-3)^2+(4)^2$

$(x-3)^2+(y+4)^2=74+9+16$

$(x-3)^2+(y+4)^2=74+25$

$(x-3)^2+(y+4)^2=99$

So the center is (3,-4).

The radius is $\sqrt{99}$ .

You can actually simplify the radius since 99 contains a factor that is a perfect square.

$\sqrt{99}=\sqrt{9}\sqrt{11}=3\sqrt{11}$

7 0

4 years ago

Read 2 more answers

The function f (x) has an average rate of change on the interval -2 < x < 3 of 3.4. If f (-2) = 9 then which of the follow

ad-work [718]

Answer:

The value of f(3)=12.4

Step-by-step explanation:

Average rate of change = 3.4

Interval: -2 < x < 3

f(-2) = 9

We need to find f(3)

The formula used to calculate Average rate of change is: $Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}$

here we have a=-2 and b=3

Now finding f(3)

$Average \ rate \ of \ change=\frac{f(b)-f(a)}{b-a}\\3.4=\frac{f(3)-f(-2)}{3-2} \\3.4=\frac{f(3)-9}{1}\\3.4=f(3)-9\\f(3)=3.4+9\\f(3)=12.4$

So, The value of f(3)=12.4

3 0

3 years ago

HELPPPPPPP FASTTTTTT PLSSSSSS

bulgar [2K]

Answer:

that questons are from imagen math omg the answer is question 2

8 0

3 years ago

In the equation y = kx, if x is doubled, what happens to y? doubles triples quadruples unknown

s344n2d4d5 [400]

Correct answer is
<u>doubles</u>

7 0

3 years ago

Read 2 more answers

In triangle abc, the measure of angle b is 20 more than three times the measure of angle

sleet_krkn [62]

Let x be the degree of angle a.

Angle b: 20+3x
Angle c: 55+x

We know that all angles add up to 180 degrees.

180=x+(20+3x)+(55+x)
180= 5x+75
180-75=5x
105/5=x
21=x

Angle a: 21 degrees
Angle b: 20+3(21) => 83 degrees
Angle c: 21+55 => 76 degrees

Hope I helped :)

5 0

4 years ago