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max2010maxim [7]

3 years ago

11

A small child has 6 more quarters than nickels. If the total amount of the coins is $3.00, find the number of nickels and quarte

rs the child has.

1 answer:

avanturin [10]3 years ago

4 0

Answer:

nickels- 5, quarters- 11

Step-by-step explanation:

nickel= 5 p, quarter= 25 p

5x+25(x+6)= 300

30x+150=300

30x=150

x=150/30

x=5 nickels

x+6= 11 quarters

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Using the Factor Theorem, which of the polynomial functions has the zeros 2, radical 3 , and negative radical 3 ? f (x) = x3 – 2

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To solve this question, we use the factor theorem, and using it, the polynomial function is:

$f(x) = x^3 - 2x^2 - 3x + 6$

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The factor theorem means that if k is a root of f(x), f(k) = 0.

Thus, applying the factor theorem for this question, we have to choose the function for which: $f(2) = 0, f(\sqrt{3}) = 0, f(-\sqrt{3}) = 0$

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Function 1:

$f(x) = x^3 - 2x^2 - 3x + 6$

Testing the values:

$f(2) = 2^3 - 2(2)^2 - 3(2) + 6 = 8 - 8 - 6 + 6 = 0$

$f(\sqrt{3}) = \sqrt{3^3} - 2(\sqrt{3})^2 - 3\sqrt{3} + 6 = \sqrt{3^2\times3} - 6 - 3\sqrt{3} + 6 = 3\sqrt{3} - 3\sqrt{3} = 0$

$f(-\sqrt{3}) = -\sqrt{3^3} - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 = -\sqrt{3^2\times3} - 6 + 3\sqrt{3} + 6 = -3\sqrt{3} + 3\sqrt{3} = 0$

Thus, since all three conditions are satisfied, $f(x) = x^3 - 2x^2 - 3x + 6$ is the polynomial function.

A similar question is given at brainly.com/question/11378552

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