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evablogger [386]
3 years ago
7

Someone help me out really quick

Mathematics
1 answer:
monitta3 years ago
3 0

Answer:

Roots: 3.746 and -13.746

Vertex: (-5, 153)

Step-by-step explanation:

  • The roots of the quadratic equation y = ax² + bx + c, are the values of x at y = 0
  • Its vertex is (h, k), where, h = \frac{-b}{2a} , and k is the value of y at x = h

Let us use these facts to solve the question

∵ y = -2x² - 20x + 103

→ Compare it by the form of the equation above

∴ a = -2, b = -20, and c = 103

→ To find its roots equate y by 0

∵ 0 = -2x² - 20x + 103

→ Use your calculator to find the values of x

∴ x = 3.746427842 and x = -13.74642784

→ Round them to 3 decimal places

∴ x = 3.746 and x = -13.746

∴ Roots: 3.746 and -13.746

→ To find its vertex use the rule of h above

∵ a = -2 and b = -20

∵ h = \frac{--20}{-2(2)} = \frac{20}{-4}

∴ h = -5

→ To find k substitute y by k and x by -10 in the equation

∵ k = -2(-5)² - 20(-5) + 103

∴ k = -2(25) + 100 + 103

∴ k = -50 + 100 + 103

∴ k = 153

∴ The vertex of the quadratic is (-5, 153)

∴ Vertex: (-5, 153)

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Answer:

Part 1) The perimeter is  P=6\sqrt{6}\ cm

Part 2) The diagonal is d=\sqrt{30}\ cm

Step-by-step explanation:

<u><em>The question in English is</em></u>

You have a rectangle whose base is twice the height and its area is 12

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step 1

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we know that

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The base is twice the height

so

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substitute equation B in equation A

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The perimeter is given by

P=2(b+h)

substitute

P=2(2\sqrt{6}+\sqrt{6})\\P=6\sqrt{6}\ cm

step 3

Find the diagonal of rectangle

Applying the Pythagorean Theorem

d^2=b^2+h^2

substitute

d^2=(2\sqrt{6})^2+(\sqrt{6})^2

d^2=30

d=\sqrt{30}\ cm

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