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neonofarm [45]
2 years ago
6

When x = a is a zero of a polynomial function f, the three statements below are true.

Mathematics
1 answer:
Lunna [17]2 years ago
4 0

Answer:

x = a is a zero of a polinomial f(x), this is the same than: f(x) has a root at x = a

Then: f(a) = 0.

a) x = a is a ____ of the polynomial equation f(x) = 0.

If we define f(x) = 0, then x = a is a solution of the equation.

Then the complete sentence is:

x = a is a solution of the polynomial equation f(x) = 0.

b) ____ is a factor of the polynomial f(x).

Remember that if a polynomial p(x) of degree n has the roots x₁, x₂, ..., xₙ

Then we can write p(x) in the factorized form as:

p(x) = A*(x - x₁)*(x - x₂)*...*(x - xₙ)

Where A is a real number.

Then if in this case we know that a is a root of f(x), then (x - a) is a factor of the polynomial f(x), then the complete sentence is:

(x - a) is a factor of the polynomial f(x).

c) (a, 0) is a ____ of the graph f(x)

We usually use the notation y = f(x).

Then the points of the form (x, f(x)) are the points that belong to the graph of f(x).

In this case, the point (a, f(a)) = (a, 0)

This point belongs to the graph of f(x), then the complete sentence can be written as:

(a, 0) is a point of the graph f(x).

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Answer:

PART 2:

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3 years ago
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JulijaS [17]
Answer: 32

Explanation:

The number of leaves in a tree diagram for probabilities is equal to the number of possible outcomes.

Tossing a coin 5 times leads to these results:

First,second, third and fourth tossing are the nodes; and fifth tossing has the leaves.

Root → 2 nodes → 2² nodes → 2³ nodes → 2⁴ → 2⁵ leaves = 32

Those 32 leaves is this sample space:

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head-head-tail-tail-head
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2 years ago
Manny is an online student who currently owns an older car that is fully paid for. He drives, on average, 110 miles per week to
Step2247 [10]

Answer:

The new car costs more

Old car = $5062.125

New car = $7161.357

Step-by-step explanation:

Manny drives an average of 110 miles per week with his old car. The old car gets 16 miles per gallon. The cost per gallon is $2.65 repair and Maintainance costs an average of $740 per year.

For the old car, to find the amount spent on the car we have

110/16 * 2.65 = $18.21875 / week

There are 52 weeks in a year. We have

10.21875*52 = $ 947.375

947.375 + 740

= $1687.375

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= $5062.125

The new car cost $6500 over a three year loan process.

The car gets 28 miles per gallon. It requires a maintenance f $10 per month. For the new car to find the amount, we have

110*28 * 2.65 *52 = $541.357

541.357 + 10(12) + 6500

= $7161.357

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