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anygoal [31]
3 years ago
15

Kerri Payne is employed by Caterer’s Central. She has a family membership in the health insurance program. The annual premium is

$6,486. Kerri’s employer pays 80% of the total cost. Her contribution is deducted from her paycheck. What is Kerri’s annual contribution?
Mathematics
1 answer:
VladimirAG [237]3 years ago
7 0
This is the concept of commercial arithmetic, we are required to calculate the amount that Kerri contributes towards her health insurance if the total annual contribution is $6,486 and the employer pays 80% of this;
percentage insurance that Kerri pays is:
1000-80
=20%
Annual premium= $6,486
Amount paid by Kerri will be:
20/100*[total amount paid]
20/100*6,486
=$1,297.2
The answer is $ 1,297.2
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Verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial
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Answer:

i) Since P(2), P(-1) and P(½) gives 0, then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

ii) - the sum of the zeros and the corresponding coefficients are the same

-the Sum of the products of roots where 2 are taken at the same time is same as the corresponding coefficient.

-the product of the zeros of the polynomial is same as the corresponding coefficient

Step-by-step explanation:

We are given the cubic polynomial;

p(x) = 2x³ - 3x² - 3x + 2

For us to verify that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial, we will plug them into the equation and they must give a value of zero.

Thus;

P(2) = 2(2)³ - 3(2)² - 3(2) + 2 = 16 - 12 - 6 + 2 = 0

P(-1) = 2(-1)³ - 3(-1)² - 3(-1) + 2 = -2 - 3 + 3 + 2 = 0

P(½) = 2(½)³ - 3(½)² - 3(½) + 2 = ¼ - ¾ - 3/2 + 2 = -½ + ½ = 0

Since, P(2), P(-1) and P(½) gives 0,then it's true that 2,-1 and 1⁄2 are the zeroes of the cubic polynomial.

Now, let's verify the relationship between the zeros and the coefficients.

Let the zeros be as follows;

α = 2

β = -1

γ = ½

The coefficients are;

a = 2

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c = -3

d = 2

So, the relationships are;

α + β + γ = -b/a

αβ + βγ + γα = c/a

αβγ = -d/a

Thus,

First relationship α + β + γ = -b/a gives;

2 - 1 + ½ = -(-3/2)

1½ = 3/2

3/2 = 3/2

LHS = RHS; So, the sum of the zeros and the coefficients are the same

For the second relationship, αβ + βγ + γα = c/a it gives;

2(-1) + (-1)(½) + (½)(2) = -3/2

-2 - 1½ + 1 = -3/2

-1½ - 1½ = -3/2

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LHS = RHS, so the Sum of the products of roots where 2 are taken at the same time is same as the coefficient

For the third relationship, αβγ = -d/a gives;

2 * -1 * ½ = -2/2

-1 = - 1

LHS = RHS, so the product of the zeros(roots) is same as the corresponding coefficient

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3 years ago
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grin007 [14]

Answer:  x = 480

Steps: x/2.4 + 39 = 239

Subtract 39 from both sides: x/2.4 + 39 - 39 = 239 - 39

Simplify: x/2.4 = 200

Multiply both sides by 2.4: x/2.4  ×  2.4 = 200 ×  2.4

Simplify: x = 480

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Answer:

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Step-by-step explanation:

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