In the diagram, AB:BC is 3:4 and AC:42 Find BC
1 answer:
From the diagram:
AB + BC = AC
we know that AC = 42, therefore:
AB + BC = 42 ..............> equation I
We know that the ratio AB:BC is 3:4. This means that:
AB/BC = 3/4
4AB = 3BC
AB = (3/4) BC ...............> equation II
Substitute by equation II in equation I to get BC as follows:
(3/4) BC + BC = 42
1.75 BC = 42
BC = 24
Substitute with the value of BC in equation II to get AB as follows:
AB = (3/4) * 24 = 18
AB + BC = AC
we know that AC = 42, therefore:
AB + BC = 42 ..............> equation I
We know that the ratio AB:BC is 3:4. This means that:
AB/BC = 3/4
4AB = 3BC
AB = (3/4) BC ...............> equation II
Substitute by equation II in equation I to get BC as follows:
(3/4) BC + BC = 42
1.75 BC = 42
BC = 24
Substitute with the value of BC in equation II to get AB as follows:
AB = (3/4) * 24 = 18
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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 = - = -
= 8
product of zeros = αβ = = 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