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Illusion [34]
3 years ago
12

Solve the quadratic equation by completing the square.

Mathematics
1 answer:
ivolga24 [154]3 years ago
6 0
X^2 - 10x + 15 = 0
x^2 - 10x = -15
x^2 - 10x + 25 = -15 + 25
(x - 5)^2 = 10 <====
x - 5 = (+-)sqrt 10
x = 5 (+-) sqrt 10

solutions are :
x = 5 + sqrt 10 and x = 5 - sqrt 10


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An 18% discount on a watch saved a shopper $72. Find the price of the watch before the discount
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Identify the perimeter and area of a square with diagonal length 11in. Give your answer in simplest radical form. HELP PLEASE!!
Nataliya [291]

Answer:

  • Perimeter = 22*sqrt(2)
  • Area = 60.5 inches
  • D

Step-by-step explanation:

Remark

You need 2 facts.

  1. A square has 4 equal sides.
  2. It contains (by definition) 1 right angle but since we are not including and statement about parallel sides, it needs 4 right angles.

That means you can use the Pythagorean Theorem.

If one side of a square is a then the 1 after it is a as well.

Formula

  • a^2 + a^2 = c^2
  • 2a^2 = c^2

Givens

  • c = 11

Solution

  • 2a^2 = 11^2
  • 2a^2 = 121                    Divide by 2
  • a^2 = 121/2                  Take the square root of both sides
  • sqrt(a^2) = sqr(121/2)    
  • a = 11/sqrt(2)                Rationalize the denominator
  • a = 11 * sqrt(2)/[sqrt(2) * sqrt(2)]
  • a = 11 * sqrt(2) / 2

<em><u>Perimeter</u></em>

P = 4s

  • P = 4*11*sqrt(2)/2
  • P = 44*sqrt(2)/2
  • P = 22*sqrt(2)

You don't need the area. The answer is D

<em><u>Area</u></em>

  • Area = s^2
  • Area = (11*sqrt(2)/2 ) ^2
  • Area = 121 * 2 / 4
  • Area = 60.5


8 0
3 years ago
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