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goblinko [34]
3 years ago
13

Very confusing i know

Mathematics
1 answer:
777dan777 [17]3 years ago
7 0

Answer:

  • (x + 10)² + (y + 4)² = 232

Step-by-step explanation:

<h3>Given </h3>
  • Center = (-10, -4)
  • Point on circle = (4, 2)
<h3>To find </h3>
  • The equation of circle
<h3>Solution</h3>

<u>Remember the standard equation of circle:</u>

  • (x - h)² + (y - k)² = r², where (h, k) is the center and r is radius

<u>We have</u>

  • h = -10, k = -4

Use distance formula (Pythagorean theorem) to work out the length of the radius. We know that radius is the distance from the center to any point on the circle.

<u>Here we are finding the distance between points (-10, -4) and (4, 2)</u>

  • r² = (-10 - 4)² + (-4 - 2)²
  • r² = 14² + 6²
  • r² = 232

<u>So the equation is:</u>

  • (x + 10)² + (y + 4)² = 232
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tatyana61 [14]

Answer:

The ordered pair (6,25) is a solution to both

y=-\frac{5}{2}x+40  and  y=\frac{5}{3}x+15

Step-by-step explanation:

Part 7)

<em>step 1</em>

Find the equation of the line with positive slope

take the points (0,15) and (9,30)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the given values

m=\frac{30-15}{9-0}

m=\frac{15}{9}

simplify

m=\frac{5}{3}

Find the equation of the line in slope intercept form

y=mx+b

we have

m=\frac{5}{3}

b=15

substitute

y=\frac{5}{3}x+15

<em>step 2</em>

Find the equation of the line with negative slope

take the points (0,40) and (8,20)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the given values

m=\frac{20-40}{8-0}

m=-\frac{20}{8}

simplify

m=-\frac{5}{2}

Find the equation of the line in slope intercept form

y=mx+b

we have

m=-\frac{5}{2}

b=40

substitute

y=-\frac{5}{2}x+40

step 3

Find the solution of the system

we know that

The solution of the system of equations is the intersection point both graphs

The intersection point is (6,25) ----> see the graph

therefore

The ordered pair (6,25) is a solution to both y=-\frac{5}{2}x+40  and  

y=\frac{5}{3}x+15

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