Find the center and radius of the circle with the equation x^2 + y^2+8x-4y=-11

2 answers:

8 0

$x^2 + y^2+8x-4y=-11 \\ \\ x^2+8x + y^2 -4y =-11\\ \\ (x^2+8x) + ( y^2 -4y) =-11\\ \\(x^2+8x+16) + ( y^2 -4y+4)-16-4 =-11 \\ \\(x+4)^2+(y-2)^2-20=-11$

$(x+4)^2+(y-2)^2 =-11+20\\ \\(x+4)^2+(y-2)^2 =9 \\ \\x+4=0 \ \ and \ \ y-2 =0 \\ \\ x=-4 \ \ and \ \ y=2 \\ \\ So \ the \ center \ of \ the \ circle \ is (-4, 2)$

$The \ radius \ of \ the \ circle \ is \ the \ square \ root \ of \ the \ right \\ \\ side \ of \ the \ equation \ for \ this \ circle. \\ \\ So\ the \ radius \ of \ this \ circle \ is \ \sqrt{9} \ so \ the \ radius \ of \ the \ circle \ is \ 3$

hoa [83]2 years ago

5 0

X^2+8x+16+y^2-4y+4=-11+16+4
[x+4]^2+[y-2]^2=9
radius is 3 and center is [-4,2]

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Find the indicated sum of each sequence S8 of -2,-13,-24,-35

valentina_108 [34]

Answer:

The sum of the arithmetic sequence is $S_{8}=-324$ .

Step-by-step explanation:

A sequence is a set of numbers that are in order.

In an arithmetic sequence the difference between one term and the next is a constant. In other words, we just add the same value each time infinitely.

If the first term of an arithmetic sequence is $a_1$ and the common difference is d, then the nth term of the sequence is given by:

$a_{n}=a_{1}+(n-1)d$

For the sequence

$-2,-13,-24,-35,...$

The pattern is continued by adding -11 to the last number each time.

An arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, $a_1$ and last term, $a_n$ , divide by 2 in order to get the mean of the two values and then multiply by the number of values, n

$S_{n}=\frac{n}{2}(a_{1}+a_{n})$

The sum of the arithmetic sequence is

$a_{8}=-2+(8-1)(-11)=-2-77=-79$

$S_{8}=\frac{8}{2}(-2-79})=4\left(-2-79\right)=4\left(-81\right)=-324$

3 0

3 years ago

(08.02)

alukav5142 [94]

Answer:

the median is 80.5

Step-by-step explanation:

first we put them in order

75,76,77,79,80,81,85,86,90,91

the median is the middle number...however, in cases where there are an even number of numbers, ur gonna have 2 middle numbers....so u take the average of those 2 numbers...basically, u add them and divide by 2.

So we have 2 numbers in the middle.....we add them and divide by 2 to get the median.

(80 + 81) / 2 = 161/2 = 80.5 <== the median

8 0

2 years ago

What is the solution of the equation 4[x + 2(3x – 7)] = 22x – 65?

Lelu [443]

X = -3/2
I hope my work .... helped you out a little.