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bonufazy [111]
3 years ago
12

Write the equation of a circle with center upper c left-parenthesis 4 comma negative 5 right-parenthesis that passes through upp

er p left-parenthesis 1 comma negative 2 right-parenthesis number .

Mathematics
1 answer:
Tcecarenko [31]3 years ago
4 0
The square of the distance between C(4, -5) and P(1, -2) is given by the Pythagorean theorem as
  (4-1)² +(-5-(-2))² = 18
This is the square of the radius of the circle, so we can use it for r² in the formula
  (x -h)² +(y -k)² = r² . . . . . . . circle of radius r and center (h, k)

Your circle has equation ...
  (x -4)² +(y +5)² = 18

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Answer:

y= 2x -3

Step-by-step explanation:

Let's rewrite the given equation into the form of y=mx+c, so that we can find the gradient of the line. In this form, m (coefficient of x) is the gradient.

4x -2y= 3

2y= 4x -3

<em>Divide</em><em> </em><em>by</em><em> </em><em>2</em><em> </em><em>throughout</em><em>:</em>

y = 2x - 1 \frac{1}{2}

Thus the gradient is 2.

Parallel lines have the same gradient thus the line would also have a gradient of 2.

Substitute m=2 into the equation:

y= 2x +c

To find the value of c, substitute a pair of coordinates.

When x=2, y=1,

1= 2(2) +c

1= 4 +c

c= 1 -4

c= -3

Thus, the equation of the line is y= 2x -3.

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Angie divides the polynomial function f(x)=x3+3x2−7x−21 by (x + 3). What can she conclude from the fact that the remainder is eq
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Answer:

See below

Step-by-step explanation:

<u>Given function</u>

  • f(x)=x³ + 3x²- 7x - 21

<u>We can find its factors:</u>

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We can conclude that the given polynomial function is fully divisible by (x + 3) and the quotient is (x² - 7)

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