Answer: The value of k for which one root of the quadratic equation kx2 - 14x + 8 = 0 is six times the other is k = 3.
Let's look into the solution step by step.
Explanation:
Given: A quadratic equation, kx2 - 14x + 8 = 0
Let the two zeros of the equation be α and β.
According to the given question, if one of the roots is α the other root will be 6α.
Thus, β = 6α
Hence, the two zeros are α and 6α.
We know that for a given quadratic equation ax2 + bx + c = 0
The sum of the zeros is expressed as,
α + β = - b / a
The product of the zeros is expressed as,
αβ = c / a
For the given quadratic equation kx2 - 14x + 8 = 0,
a = k, b = -14, c = 8
The sum of the zeros is:
α + 6α = 14 / k [Since the two zeros are α and 6α]
⇒ 7α = 14 / k
⇒ α = 2 / k --------------- (1)
The product of the zeros is:
⇒ α × 6α = 8 / k [Since the two zeros are α and 6α]
⇒ 6α 2 = 8 / k
⇒ 6 (2 / k)2 = 8 / k [From (1)]
⇒ 6 × (4 / k) = 8
⇒ k = 24 / 8
⇒ k = 3
You already have figured the main idea. In this case, the population is growing 1.9% a year. This word can be translated into: multiplied by 101.9% (100+1.9%). That means the P0 is 6 bill, the base is 101.9%(or 1.019) and the time is 50 years. The calculation would be:
<span>P(t)=P₀a^t
</span>P(t)=6 billion * 101.9%^50= 6 billion * <span>2.56276= 15.38 billion</span><span>
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Bob's car rental company makes you pay 10 dollars per day you rent the car and a 30 dollar insurance fee
joe's car rental company makes you pay 30 dollars per day you rent the car and a 10 dollar insurance fee
how many days do you need to rent a car for the cost for renting both are the same
bob=10x+30
joe=30x+10
set each to each other
10x+30=30x+10
subtract 10x
30=20x+10
subtract 10
20=20x
divide both sides by 20
1=x
you need to rent 1 day for them to be equal
The true statement is the correlation is most likely due to a lurking variable.
<h3>What is negative correlation?</h3>
Correlation is a statistical measure used to measure the relationship that exists between two variables. Negative correlation is when there is an inverse relationship between the two variables. If one variable increases, the other variable decreases.
Assume that the store is located near a school where the students live on an allowance. So, students do not have time to buy both computers and microwaves. When students buy computers they do not have enough money to buy microwaves. This explains the negative correlation.
To learn more about negative correlation, please check: brainly.com/question/27246345
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