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levacccp [35]
3 years ago
12

Apply the square root principle to solve (x – 2)2 + 20 = 0.

Mathematics
1 answer:
Temka [501]3 years ago
7 0

(x-2)^2+20=0

(x-2)^2=-20

If you root both sides you will yield complex numbers (i, imaginary unit is such that i^2=-1),

x-2=20i

x=2+20i

and whenever x is a solution a complex conjugate x* is also a solution,

x*=2-20i

So the answer is A.

Hope this helps :)

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6 0
3 years ago
Read 2 more answers
Triangle V U W is shown. The length of side W V is 6 centimeters, the length of side W U is 3 StartRoot 3 EndRoot centimeters, a
Nat2105 [25]

Answer:

The angle measures of Δ VUW are m∠V = 60°, m∠U = 90°, m∠W = 30° ⇒ last answer

Step-by-step explanation:

In any triangle if the sum of the squares of the shortest two sides is equal to the square of the longest side, then the triangle is a right triangle and the angle opposite to the longest side is the right angle

In Δ VUW

∵ WV = 6 cm

∵ WU = 3\sqrt{3} cm

∵ UV = 3 cm

- Use the rule above tho check if it is a right Δ or not

∴ The longest side is WV

∴ The shortest two sides are WU and UV

∵ (WV)² = (6)² = 36

∵ (WU)² + (UV)² = (3\sqrt{3} )² + (3)² = 27 + 9 = 36

∴ (WV)² =  (WU)² + (UV)²

- That means ∠U which opposite to WV is a right angle

∴ Δ VUW is a right triangle at ∠U

∴ m∠U = 90°

Let us use the trigonometry ratios to find m∠W and m∠V

→ sin Ф = \frac{opposite}{hypotenuse}

∵ UV is the opposite side of ∠W

∵ WV is the hypotenuse

∵ sin(∠W) = \frac{UV}{WV}

∵ sin(∠W) = \frac{3}{6}=\frac{1}{2}

- Use sin^{-1} to find ∠W

∴ ∠W = sin^{-1}(\frac{1}{2})

∴ m∠W = 30°

∵ WU is the opposite side of ∠V

∵ WV is the hypotenuse

∵ sin(∠V) = \frac{WU}{WV}

∵ sin(∠V) = \frac{3\sqrt{3}}{6}=\frac{\sqrt{3}}{2}

- Use sin^{-1} to find ∠V

∴ ∠V = sin^{-1}(\frac{\sqrt{3}}{2})

∴ m∠V = 60°

The angle measures of Δ VUW are m∠V = 60°, m∠U = 90°, m∠W = 30°

6 0
3 years ago
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