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san4es73 [151]
2 years ago
10

Can someone help me with this please?

Mathematics
1 answer:
AVprozaik [17]2 years ago
8 0

Answer:

y=70°

z= 60°

w= 70°

Step-by-step explanation:

Since the two triangles are similar, we know that all of the corresponding angles must be the same.  On the triangle on the left, we can see that the angle formed between sides AB and AC is 60°.  This means that the same angle is formed at Z, which is in the same location on the triangle to the right.  From there, we can find the missing angle, W, from the difference of 180°.

180°-50°-60°=70°.

The same way we found Z, we can also find Y, since it has to be the same as W.

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If alpha and beta are the zeroes of the polynomial f(x)= xsquare -8x +gamma such that alpha - beta = 2 find the value of gamma.
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Answer:

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Step-by-step explanation:

Given

f(x) = x² - 8x + Γ

with a = 1, b = - 8 and c = Γ , then

sum of zeros α + β = - \frac{b}{a} = - \frac{-8}{1} = 8

product of zeros = αβ = \frac{c}{a} = Γ

Given α - β = 2 , then

(α - β)² = 2²

α² - 2αβ + β² = 4 → (1)

and

(α + β)² = 8²

α² + 2αβ + β² = 64 → (2)

Add (1) and (2) term by term

2α² + 2β² = 68 ( divide through by 2 )

α² +β² = 34

Substitute α² + β² = 34 into (1)

34 - 2αβ = 4 ( subtract 34 from both sides )

- 2αβ = - 30 ( divide both sides by - 2 )

αβ = 15

Now

αβ = Γ = 15

Thus

f(x) = x² - 8x + 15

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