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Marysya12 [62]
3 years ago
11

Determine if x + 2 is a factor of p(x) = x 4 + 3x 3 + 4x 2 - 8 and explain why.

Mathematics
1 answer:
Andrej [43]3 years ago
3 0
The Factor Theorem says (x - a) is a factor of function p(x) if p(a)=0

so check for p(-2)

= -2^4 +3(-2)^3 + 4(-2)^2 - 8

= 16 - 24 +16 -8

= 0

so (x + 2) is a factor
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What is the prime factorization if 6400 using exponents
katovenus [111]

So prime factorization is as it seems, finding the prime factors for a number. With this number, break it down as such:

\underbrace{6400}_{\underbrace{64}_{\underbrace{8}_{\underbrace{4}_{\boxed{2*2}} \boxed{2}}*\underbrace{8}_{\underbrace{4}_{\boxed{2*2}}\boxed{2}}}*\underbrace{100}_{\underbrace{10}_{\boxed{5*2}}*\underbrace{10}_{\boxed{5*2}}}}

<u>Looking at our factors, the prime factorization of 6400 is 2^8*5^2</u>

5 0
3 years ago
(7i)(7i)<br>help! please show steps​
exis [7]

Answer:

-49

Step-by-step explanation:

multiply 7 with 7 then i with i and lastly multiply the result numbers

7i × 7i ➡ 7 × 7 = 49

i × i = i^2

49 × i^2 = 49i^2

i^2 = -1 ➡ 49 × (-1) = -49

7 0
3 years ago
After graduating from college, Jane has two job offers to consider. Job A is compensated at $100,000 a year but
vaieri [72.5K]

Answer: (a)  Job A , by approximately $69, 482

\\ (b)  Job A , by approximately $6,867

 \\(c) Job B , by approximately $ 767,362

  \\ (d) Job A

Step-by-step explanation:

JOB B

\\The starting Salary is $ 10,000

Since there is an increment of 25% at the beginning of each new year. The breakdown of the increment is as follow:

\\First year : 125% of $ 10,000 = $12,500

\\Second year : 125% of $ 12,500 = $15,625

\\Third year : 125% of $15,625= $19,531.25

\\Fourth year: 125% of $19,531.25 = $24,414.06

\\Fifth year : 125% of $24,414.06 = $30,517.58

\\Sixth year: 125% of $30,517.58 = $38,147.00

\\Seventh year: 125% of $38,147.00 = $47,683.75

\\Eight year: 125% of $47,683.75 = $59,604.69

\\Ninth year: 125% of $59,604.69 = $74,505.86

\\Tenth year: 125% of $74,505.86 = $93,132.32

\\Following the same procedure:

\\Eleventh year = $116,415.40

\\Twelfth year = $145,519.25

\\Thirteenth year = $181,899.06

\\Fourteenth year = $227,373.82

\\Fifteenth year = $ 284,217.29

\\Sixteenth year = $355,271.61

\\Seventeenth year = $444,089.51

\\Eighteenth year = $555,111.89

\\Nineteenth year = $693,889.86

\\Twentieth year = $867,362.32

\\(a) Following the analysis above, at the beginning of the fifth year Job A will have a greater annual salary

\\Difference: Salary of Job A at the beginning of fifth year remains $ 100,000 while that of Job B resulted into $ 30,517.58, the difference implies

$100,000 - $ 30,517.58 = $69,482

\\(b) At the beginning of tenth year, Job A is still $100,000, Job B resulted into $93,132.32. Job A is still greater by approximately $6,867

\\(c) At the beginning of the twentieth year, the annual salary of A is still $ 100,000 while the annual salary of B is $ 867,362.32. Job B annual salary is greater by approximately $ 767,362

\\(d) If I were in Jane’s shoe I will take Job A and work for few years to gain more experience the look for a job that pays better. Waiting for many years in case of Job B is risky , market situation is uncertainty.

8 0
3 years ago
A manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs
Hitman42 [59]

Answer:

Step-by-step explanation:

Let X be the solvent present

Then given that the manufacturer of industrial solvent guarantees its customers that each drum of solvent they ship out contains at least 100 lbs of solvent.

X is N(101.3, 3.68)

a) P(X>100) = P(Z>\frac{100-101.3}{3.68} =P(Z>-0.35)\\=0.6368

Probability = 0.6368

b) P(X>100)= 0.97 means Z score = 1.88

X=100+1.88(s) =101.3

s=1.3/1.88=0.6914

4 0
3 years ago
In a sample of people on the school board 2 out of 5 were in favor of a new high school being built if 3,500 people vote in the
ioda

Answer:

Just about 2100 people

Step-by-step explanation:

2 out of 5 is 60% and 7*5 is 35 so if you multiply 7 by 3 then you get 21 and if you multiply that by 100 then you get 2100

7 0
3 years ago
Read 2 more answers
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