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2 years ago

What is AE? Enter your answer in the box. units

Mathematics

1 answer:

svp [43]2 years ago

8 0

Answer:

AE = 18

Step-by-step explanation:

The triangles must be similar so we can use ratios

2x+4 12

-------- = ---------

x+8 10

Using cross products

(2x+4)10 = 12 (x+8)

20x +40 = 12x+96

Subtract 12x from each side

20x-12x +40 = 12x-12x +96

8x +40 = 96

Subtract 40 from each side

8x = 96-40

8x = 56

Divide by 8

x = 56/8

x = 7

AE = 2x+4 = 2(7) +4 = 14+4 = 18

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Answer:

x = 2, 1 + 3i, 1 − 3i

Step-by-step explanation:

Find the Roots (Zeros)

x^4 − 6x^3 + 22x^2 − 48x + 40

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Factor x^3 − 4x^2 + 14x − 20 using the rational roots test.

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Combine like factors.

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If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

(x − 2)^2 = 0

x^2 − 2x + 10 = 0

Set (x − 2)^2 equal to 0 and solve for x.

Set (x − 2)^2 equal to 0.

(x − 2)^2 = 0

Solve (x − 2)^2 = 0 for x.

x = 2

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Set x^2 − 2x + 10 equal to 0. x^2 − 2x + 10 = 0

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Use the quadratic formula to find the solutions.

−b ± (√b^2 − 4 (ac) )/2a

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Simplify.

Simplify the numerator.

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Multiply 2 by 1

x = 2 ± 6i/2⋅1

Simplify

2 ± 6i/2

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