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borishaifa [10]
2 years ago
8

I WILL GIVE BRAINLIEST IF YOU CAN ANSWER THESE TWO QUESTIONS!!!!

Mathematics
1 answer:
marissa [1.9K]2 years ago
5 0

Answer:

2. Eunju is right

3. x^2+5x+6 is a factor of x^4+5x^3+2x^2-20x-24.

Step-by-step explanation:

<u>Polynomial Remainder Theorem</u>

The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by (x-a) is equal to f(a).

As a consequence, if a polynomial is divisible by x-a, f(a)=0.

Part 1:

Let's make:

f(x)=(x+b)^3+(x+c)^2-(b-c)

To find out if x+b is a factor of f(x), we find f(-b):

f(-b)=(-b+b)^3+(-b+c)^2-(b-c)

Operating:

f(-b)=(-b+c)^2-(b-c)

The value of f(-b) is not zero. This means Eunju is right, x+b is not a factor of f(x).

Part 2:

We must find out if x^2+5x+6 is a factor of x^4+5x^3+2x^2-20x-24 without using long division or synthetic division.

We can use the polynomial remainder theorem again, but since the factor is not in the form (x-a), we can factor it as follows:

x^2+5x+6 =(x+2)(x+3)

Now we just apply the theorem twice. If both remainders are zero, then the assumption is true.

Let's make:

f(x)=x^4+5x^3+2x^2-20x-24

Find f(-2):

f(-2)=(-2)^4+5(-2)^3+2(-2)^2-20(-2)-24

f(-2)=16-5*8+2*4+40-24 =16-40+8+40-24=0

Find f(-3):

f(-3)=(-3)^4+5(-3)^3+2(-3)^2-20(-3)-24

f(-3)=81-5*27+2*9+60-24

f(-3)=81-135+18+60-24 =0

Since both f(-2) and f(-3) are zero, x^2+5x+6 is a factor of x^4+5x^3+2x^2-20x-24.

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Round 5.852 to the nearest whole number.
bonufazy [111]

Answer:

6

Step-by-step explanation:

3 0
2 years ago
Greta bought 3 lb and 4 oz of peanuts and shared 1 lb 12 oz with the class. what is the weight of the remaining peanuts ?
makkiz [27]

Answer:

1lb 8 oz

Step-by-step explanation:

Take 3 lbs and separate it into 48oz + 4 oz = 52 oz.

Same with the 1 lb 12 oz. 16 oz + 12 oz = 28.

Subtract 28 from 52 = 24 oz = 1 lb  8 oz.

Hope this helps.

5 0
3 years ago
A recent survey estimated that 19 percent of all people living in a certain region regularly use sunscreen when going outdoors.
serg [7]

The correct option is: (E) It is plausible that the percent of all people living in the region who regularly use sunscreen is 18.5%.

<u>Step-by-step explanation:</u>

The margin of error is a statistic expressing the amount of random sampling error that occurred due to miscalculation and survey results. The margin error is usually a small amount of error.

Generally 5% of margin of error is common and acceptable. When the percentage of the margin of error increases, the confidence in the report result will be reduced.

The recent survey reveals that 19% of the people living in a certain region regularly use sunscreen when going outdoors. The permissible margin of error in this survey is 1%.

Probably the percentage of people using sunscreen in the particular region will be <u>18.5%. </u>

5 0
3 years ago
Solve the inequality for u<br>-5u+27 [less than or equal to] 2​
baherus [9]

Answer:

5≤u

Step-by-step explanation:

Put the words and numbers into an equation:

-5u+27≤2

Put all like terms on one side:

27-2≤5u ---> Do you see what I did there? Now you don't have to work with negatives. :)

Simplify:

25≤5u

Solve:

5≤u

:)

6 0
3 years ago
Please answer. I’ll give Brainliest!
Gnoma [55]

Answer:

answer is c

Step-by-step explanation:

0=theta symbol

SOH CAH TOA

SOH= Sin0=Oppisite/hypotnuse

CAH= Cos0=Adjecent/Hypotnuse

TOA= Tan0=Oppisite/Adjecent

5 0
3 years ago
Read 2 more answers
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