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2 years ago

A B 21 48° 6x-24 D [?] << <[ ] 11 C

Mathematics

1 answer:

r-ruslan [8.4K]2 years ago

3 0

The shape in the figure is a composite shape with two triangles, and the inequality is 4 < x < 12

<h3>How to determine the range of value of x?</h3>

In the given figure, the side lengths AB and AD are equivalent.

This means that, we have the following angle relationship:

CAD < CAB

Substitute known values

6x - 24 < 48

Add 24 to both sides

6x < 72

Divide both sides by 6

x < 12

Also, we have the following angle relationship:

CAD > 0

Substitute known values

6x - 24 > 0

Add 24 to both sides

6x < 24

Divide both sides by 6

x < 4

This means that:

x < 4 and x < 12

Combine both inequalities

4 < x < 12

Hence, the inequality is 4 < x < 12

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Read 2 more answers

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.

Komok [63]

Answer:

Γ = 15

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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3 years ago