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3 years ago

what is the center of a circle whose equation is x2 + y2 – 12x – 2y + 12 = 0? o (-12,-2) o (-6, -1) o (6, 1) (12, 2)

Mathematics

1 answer:

Leno4ka [110]3 years ago

7 0

Answer:

(6,1)

Step-by-step explanation:

1.) group the x and y terms (and move the constant to the other side)

x²-12x+y²-2y= -12

divide the coeficcents for the terms with just 1 or 1 x variable by 2 and then square it (and add that to both sides)

x²-12x+36+y²-2y+1= -12+36+1

factor

(x-6)²+(y-1)²= 25

the center is therefore (6,1)

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Find the average value of the function f(t)=cos13(5t)sin(5t) f(t)=cos13⁡(5t)sin⁡(5t) on the interval [4,10].

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3 years ago

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Step-by-step explanation:

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3 years ago

Read 2 more answers

Given the equation 5x − 4 = –2(3x + 2), solve for the variable. Explain each step and justify your process.

blagie [28]

A.
$5x-4=-2(3x+2) \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
5x-4=-2 \times 3x-2 \times 2 \\
5x-4=-6x-4 \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 6x to both sides} \\
11x-4=-4 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 4 to both sides} \\
11x=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{divide both sides by 11} \\
x=0$

B.
$3(2x-4)=5x-1 \\
6x-12=5x-1 \\
\boxed{11x-12=-1} \Leftarrow \hbox{the first mistake} \\
11x=11 \\
\boxed{x=11} \Leftarrow \hbox{the second mistake}$

Megan's solution isn't correct.
The first mistake: she subtracted 5x from the right-hand side of the equation, but added 5x to the left-hand side.
The second mistake: she divided the right-hand side of the equation by 11, but didn't divide the left-hand side.

The correct solution:
$3(2x-4)=5x-1 \ \ \ \ \ \ \ \ \ \ \ |\hbox{expand the bracket} \\
3 \times 2x+3 \times (-4)=5x-1 \\ 6x-12=5x-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{subtract 5x from both sides} \\
x-12=-1 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ |\hbox{add 12 to both sides} \\
x=11$

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3 years ago

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pishuonlain [190]

Answer:

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Step-by-step explanation:

We have, 76% × x = 190

Multiplying both sides by 100 and dividing both sides by 76,

we have x = 190 × 100/76

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If you are using a calculator, simply enter 190×100÷76, which will give you the answer.

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