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max2010maxim [7]
3 years ago
12

Which of the following sets represents a function?

Mathematics
2 answers:
Ira Lisetskai [31]3 years ago
8 0
The answer would be B because to have a function none of the x's can be the same, and we know that it's (x,y) so all of the first numbers are x's
In the first answer choice the x's would be 0,1,3,5,&5 but the 5 is repeated so we toss that answer choice
In answer choice B, the x's are 3,4,&5, so that's a maybe
In C, the x's are 1,5,1,&5 so we know that's not correct because the 5's and the 1's are both repeated
Last but not least, in D, the x's are 5,7,&5, the 5's are repeated so that leaves us with our answer of B. {(0,1), (1,2), (3,4), (5,6), (5,7)}

gogolik [260]3 years ago
5 0
It would be D 
Your welcome ;)
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Step-by-step explanation:

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3 years ago
Find a polynomial of degree 3 with real coefficients and zeros of -3,-1, and 4, for which f(-2)=-24
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We want to find a polynomial

<em>f(x)</em> = <em>a</em> <em>x</em>³ + <em>b</em> <em>x</em>² + <em>c</em> <em>x</em> + <em>d</em>

such that the roots of <em>f</em> are <em>x</em> = -3, <em>x</em> = -1, and <em>x</em> = 4, and <em>f(x)</em> takes on a value of -24 when <em>x</em> = -2.

The factor theorem for polynomials tells us that we can factorize <em>f(x)</em> as

<em>a</em> <em>x</em>³ + <em>b</em> <em>x</em>² + <em>c</em> <em>x</em> + <em>d</em> = <em>a</em> (<em>x</em> + 3) (<em>x</em> + 1) (<em>x</em> - 4)

Expand the right side:

(<em>x</em> + 3) (<em>x</em> + 1) (<em>x</em> - 4) = <em>x</em>³ - 13<em>x</em> - 12

So we have

<em>a</em> <em>x</em>³ + <em>b</em> <em>x</em>² + <em>c</em> <em>x</em> + <em>d</em> = <em>a x</em>³ - 13<em>a</em> <em>x</em> - 12<em>a</em>

<em />

In order for both sides to be equal, the coefficients of both polynomials on terms of the same degree must be equal. This means

<em>a</em> = <em>a</em> (of course)

<em>b</em> = 0 (there is no <em>x</em>² term on the right)

<em>c</em> = -13<em>a</em>

<em>d</em> = -12<em>a</em>

<em />

We also have that <em>f</em> (-2) = -24, which means

<em>f</em> (-2) = <em>a</em> (-2 + 3) (-2 + 1) (-2 - 4)

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<em>a</em> = -4

which in turn tells us that <em>c</em> = 52 and <em>d</em> = 48.

So we found

<em>f(x)</em> = -4<em>x</em>³ + 52<em>x</em> + 48

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3 years ago
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Answer:

The probability of rolling a factor of 9 is 1/2, or 50%.

Step-by-step explanation:

The number 9's factors are 1, 3, and 9. Three of the six sides of the cube have a factor of 9. Therefore 3/6 of the sides are factors of nine.

Simplify 3/6 to 1/2 to get a probability of 50%.

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