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3 years ago

6

can someone please help me with these they're due tomorrow and its the only page i have left and i absolutelly have no clue how

to do them... please help

1 answer:

Readme [11.4K]3 years ago

5 0

Answer:

Step-by-step explanation:

thats easy though:/

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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

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William ran a total of 14 miles in seven days each day he ran the same number of miles how many miles did William run each day

worty [1.4K]

Two. He ran 14 miles in 7 days, where he ran the same amount each day, so we can set up a ratio between them to find that he ran 2 miles every 1 day.

4 0

3 years ago

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762÷4 for division

Sonbull [250]

Answer:

190.5

Step-by-step explanation:

it is just 762÷4 use a calculator

4 0

3 years ago

Can someone help me out

Likurg_2 [28]

False i think, i did it in my head so it might be wrong, but im pretty sure its false. hope it helped

8 0

3 years ago

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Records on a fleet of trucks reveal that the average life of a set of spark plugs is normally distributed with a mean of 22,100

seraphim [82]

Answer:

69030.05

Step-by-step explanation:

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3 years ago