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kondaur [170]
3 years ago
12

Find the value of c so that (x+2) is a factor of the polynomial p(x). p(x)=4x^3+cx^2+x+2

Mathematics
1 answer:
Wittaler [7]3 years ago
6 0

Answer:

c = 8

Step-by-step explanation:

Use synthetic division here; it's the fastest approach.

Given that (x + 2) is a factor, take -2 and use this as the divisor in synthetic division:

-2     4         c                1           2

                  -8    (-2c+ 16)      (4c-34)

       ---------------------------------------------

         4    (c - 8)   (-2c + 17)     4c - 32

The remainder, 4c - 32, must equal zero if (x + 2) is a factor.

Then 4c - 32 = 0, and c = 8

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Pretty much you’re going to need to subtract the -9x to get it on the other side, so that you get y= 9x+6

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3 years ago
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ZanzabumX [31]

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Step-by-step explanation:


3 0
3 years ago
Bottles of mango juice are assumed to contain 275 milliliters of juice. There is some variation from bottle to bottle because th
pentagon [3]

Answer:

Step-by-step explanation:

The mean of the set of data given is

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Standard deviation = √(summation(x - mean)^2/n

n = 7

Summation(x - mean)^2 = (275.4 - 275.56)^2 + (276.8 - 275.56)^2 + (273.9 - 275.56)^2 + (275.0 - 275.56)^2 + (275.8 - 275.56)^2 + (275.9 - 275.56)^2 + (276.1 - 275.56)^2 = 5.0972

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We would set up the hypothesis test.

For the null hypothesis,

µ = 275

For the alternative hypothesis,

µ ≠ 275

This is a 2 tailed test.

Since the number of samples is small and no population standard deviation is given, the distribution is a student's t.

Since n = 7

Degrees of freedom, df = n - 1 = 7 - 1 = 6

t = (x - µ)/(s/√n)

Where

x = sample mean = 275.56

µ = population mean = 275

s = samples standard deviation = 0.85

t = (275.56 - 275)/(0.85/√7) = 1.74

We would determine the p value using the t test calculator. It becomes

p = 0.132

Because the p-value of 0.132 is greater than the significance level of 0.05, we would fail to reject the null hypothesis. We conclude the data does not provide convincing evidence that the mean amount of juice in all the bottles filled that day differs from the target value of 275 milliliters.

8 0
3 years ago
The mean vitamin C level for 20 dogs was 7.6 milligrams per liter, with a standard deviation of 2.1 milligrams per liter.
SpyIntel [72]

Answer:  The mean increases.

Step-by-step explanation:

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2 years ago
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