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lisov135 [29]
2 years ago
11

Write the equation of the circle with center (-4, 8) and passes through the point (-2, -1)

Mathematics
1 answer:
anzhelika [568]2 years ago
8 0

Answer:

(x+4)^2+(y-8)^2=85

Step-by-step explanation:

The standard equation for a circle is given by:

(x-h)^2+(y-k)^2=r^2

Where (h, k) is the center and r is the radius.

We know that the center is (-4, 8). So, substitute -4 for h and 8 for k:

(x-(-4))^2+(y-8)^2=r^2\\

Simplify:

(x+4)^2+(y-8)^2=r^2

Now, we will need to find r.

We know that it passes through the point (-2, -1). So, we can substitute -2 for x and -1 for y and solve for r. So:

(-2+4)^2+(-1-8)^2=r^2

Evaluate:

(2)^2+(-9)^2=r^2

Square:

4+81=r^2

Add:

r^2=85

So, r squared is 85.

We don’t actually have to solve for r itself, since we will have to square it anyways.

So, we have:

(x+4)^2+(y-8)^2=r^2

Substituting 85 for r squared, we get:

(x+4)^2+(y-8)^2=85

And we have our equation.

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Answer:

Max is 9 ft above Brett

Step-by-step explanation:

Brett is 34 feet below the surface  = -34

Max is 25 feet below the surface = -25

Subtract the heights

-25 - -34

-25 +34

9

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Use rhombus ABCD and the given information to find each value.​
Semmy [17]

Answer: (c) 31    (d) 30     (e) 41     (f) 10

<u>Step-by-step explanation:</u>

NOTES about angles of a rhombus:

  1. diagonals are angle bisectors (cut the angle into 2 equal parts)
  2. diagonals are perpendicular to each other (90°)
  3. two adjacent triangles of a rhombus form an isosceles triangle

(c) Given: ∠CBD = 59°

    Per rule 2  →  ∠BEC = 90°

    Triangle Sum Theorem: sum of the angles of a triangle = 180°

∠CBD + ∠BEC  + ∠BCE = 180°

  59°  +    90°   + ∠BCE = 180°

       149°          + ∠BCE = 180°

                           ∠BCE =  31°

(d) Given:  ∠BCD = 120°

   Per rule 3  →   ∠CBD = ∠CDB

   Triangle Sum Theorem: sum of the angles of a triangle = 180°

∠CBD + ∠CDB  + ∠BCD = 180°

           2∠CBD  +   120°  = 180°

           2∠CBD                =  60°

             ∠CBD                =  30°

(e) Given: ∠AED = 2x+8

    Per rule 2  →  ∠AED = 90°

                            2x+8  = 90

                            2x      = 82

                              x      = 41

(f) Given: ∠BCE = 3x + 3  and   ∠ECD = 5x - 17

   Per rule 1   →    ∠BCE = ∠ECD

                           3x + 3 = 5x- 17

                                   3 = 2x - 17

                                 20 = 2x

                                  10 = x

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3/3=1

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