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ValentinkaMS [17]
2 years ago
5

Use synthetic division to divide x^3+5x^2−9x−7 by x−2 1 5 -9 -7 The quotient is: _____ The remainder is: ______

Mathematics
1 answer:
RoseWind [281]2 years ago
5 0

Answer:

 The quotient is x² + 6x +3

       Remainder  = -1      

 Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given Polynomial equation

   f(x) = x³+5x²−9x−7

By using synthetic division

 

 <em> x = 2  </em>         1       5       -9      -7

   <u>                   0       1       12     6</u>

  <u>                 1      6         3     </u><em><u> -1   </u></em><u>         </u>

 The quotient is x² + 6x +3

       Remainder  = -1      

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2 years ago
Write an equation of the circle that has a diameter with endpoints (12, 3) and<br> (-18,3).
Mademuasel [1]

The equation of the circle that has a diameter with endpoints (12, 3) and(-18,3) is x² + y² + 6x - 6y - 207 = 0

<h3>Coordinates of center of circle</h3>

Since the endpoints of the diameter are (x₁, y₁) = (12,3) and (x₂, y₂) = (-18,3), the coordinates of the center of the circle are the midpoints of the diameter. So, the midpoints are

  • x = (x₁ + x₂)/2 = (12 + (-18))/2 = (12 - 18)/2 = -6/2 = -3 and
  • y = (y₁ + y₂)/2 = (3 + 3)/2 = 6/2 = 3.

So, the coordinates of the center of the circle are (-3, 3)

<h3>The radius of the circle</h3>

The radius of the circle r = √[(x₁ - h)² + (y₁ - k)²] where

  • (x₁, y₁) = coordinates of end of diameter = (12, 3) and
  • (h, k) = coordinates of center of circle = (-3, 3)

So, substituting the values of the variables into r, we have

r = √[(x₁ - h)² + (y₁ - k)²]

r = √[(12 - (-3))² + (3 - 3)²]

r = √[(12 + 3)² + 0²]

r = √[15² + 0²]

r = √15²

r = 15

<h3>The equation of the circle</h3>

The equation of a circle with center (h,k) is given by

(x - h)² + (y - k)² = r² where r = radius of circle.

Substituting the values of the variables into the equation, we have

(x - h)² + (y - k)² = r²

(x - (-3))² + (y - 3)² = 15²

(x + 3)² + (y - 3)² = 15²

x² + 6x + 9 + y² - 6y + 9 = 225

x² + 6x + y² - 6y + 9 + 9 - 225 = 0

x² + y² + 6x - 6y - 207 = 0

The equation of the circle that has a diameter with endpoints (12, 3) and(-18,3) is x² + y² + 6x - 6y - 207 = 0

Learn more about equation of a circle here:

brainly.com/question/18435467

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2 years ago
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sleet_krkn [62]

Answer:

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Step-by-step explanation:

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Chocolate chip and peanut butter cookies are randomly chosen from a cookie jar and placed onto a plate. The first plate had four
soldier1979 [14.2K]

Answer:

3 peanut cookies

Step-by-step explanation:

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Probability of drawing chocolate chip from plate 1 and then plate 2 = 8/ 25

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8(10 + 5p) = 8 * 25

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Answer:

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Step-by-step explanation:

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