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Vlada [557]
3 years ago
11

Determine, if possible, if (x – 8) is a factor of (x3 – 3x2 – 31x – 72). A. Only if x = 2 B. Yes C. No D. Not enough information

to determine
Mathematics
2 answers:
vovikov84 [41]3 years ago
8 0
The polynomial remainder theorem says when we divide polynomial f(x) by x-a we'll get remainder f(a).

f(x)=x^3 - 3x^2 - 31x - 72

f(8)=8^3 - 3(8^2) - 31(8) - 72

f(8)=512 - 3(64) - 31(8) - 72 = 512-192-248-72 = 0

Since <em>f(8)=0</em> that means <em>x-8</em> has a remainder zero when divided by <em>f(x).</em> In other words, it's a factor of <em>f(x)</em>.

Answer B
 
Annette [7]3 years ago
3 0
I believe the answer is C
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If x^2-x-6 and x^2+3x-18 hacpve a common factor (x-a) then find the value of a.​
DedPeter [7]

Answer:

a = 3

Step-by-step explanation:

Factor both expressions

x² - x - 6

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (- 1)

The factors are - 3 and + 2 , since

- 3 × 2 = - 6 and - 3 + 2 = - 1 , thus

x² - x - 6 = (x - 3)(x + 2)

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

x² + 3x - 18

consider factors of constant term (- 18) which sum to give the coefficient of the x- term (+ 3)

The factors are + 6 and - 3 , since

6 × - 3 = - 18 and 6 - 3 = + 3 , thus

x² + 3x - 18 = (x + 6)(x - 3)

Both expressions have a common factor of (x - 3)

Compare with (x - a ), then a = 3

3 0
2 years ago
Read 2 more answers
A rare form of malignant tumor occurs in 11 children in a​ million, so its probability is 0.000011. Four cases of this tumor occ
Shkiper50 [21]

Answer:

a) The mean number of cases is 0.14608 cases.

b) The probability that the number of cases is exactly 0 or 1 is 0.990.

c) The probability of more than one case is 0.010

d) No, because the probability of more than one case is very small

Step-by-step explanation:

We can model this problem with a Poisson distribution, with parameter:

\lambda=r*t=0.000011*13,280=0.14608

a) The mean amount of cases is equal to the parameter λ=0.14608.

b) The probability of having 0 or 1 cases is:

P(k=0)=\frac{\lambda^0 e^{-\lambda}}{0!}=\frac{1*0.864}{1} =0.864\\\\ P(k=1)=\frac{\lambda^1 e^{-\lambda}}{0!}=\frac{0.14608*0.864}{1} =0.126\\\\P(k\leq1)=0.864+0.126=0.990

c) The probability of more than one case is:

P(k>1)=1-P(k\leq 1)=1-0.990=0.010

d) The cluster of 4 cases can not be due to pure chance, as it is a very high proportion of cases according to the average rate. Just having more than one case has a probability of 1%.

7 0
3 years ago
Temp of 20* C will drop by 4*c
svp [43]

Answer:

16* C

Step-by-step explanation:

This is simply 20 - 4

---> 20 - 4 = 16

=> Celcius (C)

Thus, 16° C

4 0
3 years ago
A triangle can have at most___ right angle<br> О<br> 2<br> 4<br> 1
ICE Princess25 [194]

a right angle can have at least 2

6 0
3 years ago
The length and width of a rectangle are shown below.
natulia [17]

Answer:

-2x² + 90x + 500

Step-by-step explanation:

Use FOIL method

Area of rectangle = length * width

                             = (50 - x)(2x + 10)

                             = 50*(2x) + 50*10 + (-x)*2x + (-x)*10

                             = 100x + 500 - 2x² - 10x

                             = -2x² + 10<u>0x - 10x </u>+ 500  {Combine like terms}

                            = -2x² + 90x + 500

7 0
3 years ago
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