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3 years ago

Use the table below. Do x and y have a proportional relationship? Explain.

Mathematics

1 answer:

nydimaria [60]3 years ago

8 0

Answer:

Step-by-step explanation:

For x and y to have a proportional relationship, then

the ratio of k = $\frac{y}{x}$ must be equal for all points

(2, 5) → k = $\frac{5}{2}$ = 2.5

(3, 7.5) → k = $\frac{7.5}{3}$ = 2.5

(5, 12.5) → k = $\frac{12.5}{5}$ = 2.5

(18, 8) → k = $\frac{18}{8}$ = 2.25 ≠ 2.5

k is not equal for all values , hence no proportional relationship exists

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2 years ago

In Problems 23–30, use the given zero to find the remaining zeros of each function

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Answer:

x = 2i, x = -2i and x = 4 are the roots of given polynomial.

Step-by-step explanation:

We are given the following expression in the question:

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One of the zeroes of the above polynomial is 2i, that is :

$f(x) = x^3 - 4x^2+ 4x - 16\\f(2i) = (2i)^3 - 4(2i)^2+ 4(2i) - 16\\= -8i+ 16+8i-16 = 0$

Thus, we can write

$(x-2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

Now, we check if -2i is a root of the given polynomial:

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Thus, we can write

$(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

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$(x-2i)(x+2i)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16\\(x^2 + 4)\text{ is a factor of polynomial }x^3 - 4x^2 + 4x - 16$

Dividing the given polynomial:

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Thus, 2i, -2i and 4 are the roots of given polynomial.

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