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Yanka [14]
2 years ago
5

The ratio of North American butterflies to South American butterflies at a butterfly park is 3 :5

Mathematics
1 answer:
patriot [66]2 years ago
6 0

Answer:A) 18

B) 12

Step-by-step explanation:

The ratio of North America butterflies to South America butterflies at a butterfly park is 5:3. The total ratio is 5 + 3 = 8

Let x represent the total number of south America and north America butterflies. If there are 30 North American butterflies at the butterfly park then,

5/8 × x = 30

5x = 30 × 8 = 240

x = 240/5 = 48

Therefore, the number of south America butterflies are

48 - 30 = 18

The ratio of South America butterflies to European butterflies is 3:2. Total ratio = 3 + 2 = 5

Let y represent the sum of South America and European butterflies. Therefore,

3/5 × y = 18

3y = 5 × 18 = 90

y = 90/3 = 30

Therefore, the number of European butterflies are 30 - 18 = 12

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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:

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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