You spin the spinner shown to the right once. The spinner has 4 equal sectors colored pink, purple, blue, and green. What is P(N
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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
The equation is 0.1x + 0.15(50-x)=1.20(50)
Step-by-step explanation:
Here you need 50ml of 12% alcohol solution.
You have 10% and 15% alcohol solutions.
Take volume of 10% alcohol solution to be x ml
Take volume of 15% alcohol solution to be y ml
Form equations;
x+y=50 ml--------------------------equation 1
0.1x +0.15 y= 12% of 50
0.1x+0.15y=6-----------------------equation 2
Now you have simultaneous equations, use a graph tool to solve for values of x and y as attached.
or use the mixture equation the get value of x
0.1x + 0.15(50-x)=1.20(50)
The values of x and y are ;
(x,y) (30,20) which means;
y is 20 ml of 15% alcohol
x is 30 ml of 10% alcohol
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Keywords : concentration, mixture
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