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AlexFokin [52]
3 years ago
6

The sum of Joy's age and her brother's age is 24. Joy's brother's age is 3 years older than twice joy's age. What is the differe

nce between their ages?
Mathematics
1 answer:
enyata [817]3 years ago
3 0
Let Joy be x years old

<span>Joy's brother's age is 3 years older than twice joy's age.
</span>Joy's Brother = 2x + 3

<span>The sum of Joy's age and her brother's age is 24.
x + 2x + 3 = 24
3x + 3 = 24
3x = 24 - 3
3x = 21
x = 21 </span>÷ 3 
x = 7

Joy:
x = 7

Brother:
2x + 3 = 2(7) + 3 = 17

Difference in their age = 17 - 7 = 10 years

They are 10 years apart.
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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
Basile [38]

Answer:

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

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According to the Factor Theorem, if (<em>x</em> - <em>k</em>) is a factor of a polynomial P(x), then P(k) must equal zero.

We are given that a polynomial function has the zeros 2, √3, and -√3. So, we can let <em>k</em> = 2, √3, -√3.

So, according to the Factor Theorem, P(2), P(√3) and P(-√3) must equal 0.

Testing each choice, we can see that only A is true:

\displaystyle f(x) = x^3 - 2x^2 - 3x + 6

Testing all three values yields that:

\displaystyle \begin{aligned} f(2) &= (2)^3 - 2(2)^2 -3(2) + 6 \\ &= (8) - (8) -(6) + (6) \\ &= 0\stackrel{\checkmark}{=}0 \\ \displaystyle  f(\sqrt{3}) &= (\sqrt{3})^3 - 2(\sqrt{3})^2 - 3(\sqrt{3}) + 6 \\ &=(3\sqrt{3}) -(6)-(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0 \\ f(-\sqrt{3}) &= (-\sqrt{3})^3 - 2(-\sqrt{3})^2 - 3(-\sqrt{3}) + 6 \\ &=(-3\sqrt{3}) -(6)+(3\sqrt{3}) + 6 \\ &= 0\stackrel{\checkmark}{=}0   \end{aligned}

Hence, our answer is A.

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2 years ago
The height of a trapezoid is 6 in. and its area is 36 in2. One base of the trapezoid is 6 inches longer than the other base. Wha
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Step-by-step explanation:

Area of a trapezoid is given by

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Substituting in what we know

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Simplifying

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8 0
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