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PSYCHO15rus [73]
3 years ago
12

Using the Factor Theorem, which of the polynomial functions has the zeros 4,

Formula1" title="\sqrt7" alt="\sqrt7" align="absmiddle" class="latex-formula">, and -\sqrt{7\\}?
f (x) = x3 – 4x2 + 7x + 28
f (x) = x3 – 4x2 – 7x + 28
f (x) = x3 + 4x2 – 7x + 28
f (x) = x3 + 4x2 – 7x – 28
Mathematics
1 answer:
Serjik [45]3 years ago
8 0

Answer:

B

Step-by-step explanation:

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

Our zeros are 4, √7, and - √7. Hence, when evaluating P(4), P(√7), and P(-√7), all must evaluate to zero.

Testing each choice, we can see that only choice B is true. That is:

\displaystyle \displaystyle \begin{aligned} f(4)&= (4)^3 - 4(4)^2 - 7(4) + 28 \\ &= (64) - (64) - (28) + 28 \\ &= 0 \stackrel{\checkmark}{=}0 \\f(\sqrt{7}) &= (\sqrt{7})^3 - 4(\sqrt{7})^2 - 7(\sqrt{7}) + 28 \\ &= (7\sqrt{7}) - (28) - (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0\\ f(-\sqrt{7}) &= (-\sqrt{7})^3 - 4(-\sqrt{7})^2 - 7(-\sqrt{7}) + 28 \\ &= (-7\sqrt{7}) - (28) + (7\sqrt{7}) + 28 \\ &= 0 \stackrel{\checkmark}{=} 0  \end{aligned}

In conclusion, our answer is B.

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Mamont248 [21]

Answer:

D) because the sum of two sides must be greater than the third side

Step-by-step explanation:

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6 0
3 years ago
What is the probability of obtaining threethree tailstails in a row when flipping a​ coin? Interpret this probability.
Korolek [52]

Answer:

P=0.125

If it is repeated 10,000, it is expected "3 tails in a row" about 1,250 times.

Step-by-step explanation:

When flipping a coin a number of times, we can modeled this as a random variable with a binomial distribution.

In this case, we have to calculate the probability of 3 consecutive tails. If we define p as the probability of getting a tail (which has a value of p=0.5 if it is an unbiased coin), the probability of getting 3 tails in a row is:

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because we expect 0.125 events of this type for every try, so we can multiply this probability (or expected frequency) by the number of trials and we get the expected number of events described.

4 0
3 years ago
What is 45/18 as a mixed number?
mr_godi [17]
45 / 18 as a mixed fraction...
To change the improper fraction to the mixed fraction you have to:-
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3 0
2 years ago
Read 2 more answers
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tekilochka [14]

Answer:

30

Step-by-step explanation:

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C(n) = 5n, 0 ≤ n ≤10  ←   You can just ignore the 0≤ n ≤10 part.

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C(6) = 30

The answer is that 6 shirts costs 30 dollars.

6 0
2 years ago
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