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Elenna [48]
3 years ago
6

Use the remainder theorem to find the remainder of 2x^4 + x^2 - 10x -1 divided by x +2.

Mathematics
1 answer:
I am Lyosha [343]3 years ago
4 0

Answer:

The remainder is 55

Step-by-step explanation:

Let

p(x)= 2 {x}^{4}  +  {x}^{2}  - 10x - 1

According to the remainder theorem, if p(x) is divided by x+a, the remainder is p (-a).

The given divisor is x+2, therefore the remainder is given by:

p( - 2)

We substitute x=-2 to get:

p( - 2)= 2 {( - 2)}^{4}  +  {( - 2)}^{2}  - 10( - 2) - 1

We simplify to obtain:

p( - 2)= 2  \times 16 +  4  +  20- 1

We multiply to get:

p( - 2)=3 2  +  4  +  20- 1 = 55

Therefore the remainder is 55

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Help and explain thanks!
katen-ka-za [31]

Answer:

120 cm

Step-by-step explanation:

One way to tackle this is by getting another sheet of paper and drawing it out, then counting up the total of the sides. If you draw it, you can see that you're dealing with a rectangle; two sides of length 12 and two sides of length 8. If you don't like drawing or don't want to in this case, another way to get the answer is by knowing one vertex is at (0, 0), so the next vertex (0, 8), would create a side that's exactly 8 units long. Kind of the same, you know from (0, 0), you also have a point (12, 0), so drawing that would create a side that's 12 units long. All in all, to get the perimeter in units, you have 12 + 12 + 8 + 8 = 40.

The problem says it wants the amount of wood in centimeters needed for the perimeter. What we just found was the perimeter in generic units, so if the problem says every "grid square", or unit, is 3 centimeters long, then all you have to do is take our result 40 and multiply it by 3 to get the number of centimeters. Your perimeter in centimeters would be 120 cm.

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3 years ago
How to write slope intercept form of<br> y = -5/4 (x+4)
Mkey [24]

Answer: y=−5/4x−5

Step-by-step explanation:

5 0
3 years ago
What conclusion can be made when r, the correlation coefficient between two variables, is 0?
IgorLugansk [536]
The correlation coefficient between two variables, r, is always going to be between -1 and 1.

- If the correlation coefficient is 0, means that there is no strong correlation relationship in one direction or the other direction. 
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- If the correlation coefficient is 1, means that these two variables move in the same direction.
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3 years ago
The theoretical probability of landing on blue on a single spin of a spinner with 1 purple, 1 blue , 1 red , and 1 orange sectio
erik [133]

Hey there!

\large\boxed{25\%}

Assuming that all the sections are the same size, there are four sections of equal size.

Blue would be one out of those four sections, so the probability is 1/4. In decimal form this is .25, and as a percent this is 25%.

Hope this helps!

5 0
3 years ago
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A card is chosen at random from a pack of playing cards. what is the probability that it is either a heart or the queen spades​
vesna_86 [32]

Answer:

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total outcomes = 52

hope it helps

4 0
3 years ago
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