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Phantasy [73]
3 years ago
6

What is: 2 x^4-x^2+3x+1 ÷ x^2+2x+2

Mathematics
1 answer:
Inessa [10]3 years ago
6 0
Your answer is: 2x^6-x^4+5x^3+2x^2+1\x^2
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Plzz anyone solve all answers plzzzzzzzz​
algol13

You posted a lot of problems here. In the future please only post one problem at a time. Thank you.

I'll do the first two problems to get you started. Hopefully it will help you finish off the rest of the questions.

==========================================

Problem 1

{18, a, b, -3} is an arithmetic sequence or arithmetic progression (AP).

This means we have some number d added on to each term to get the next term.

first term = 18

second term = first term + d = 18+d = a

third term = second term + d = (18+d)+d = 18+2d = b

fourth term = third term + d = (18+2d)+d = 18+3d = -3

----

Let's solve that last equation for d

18+3d = -3

18+3d-18 = -3-18

3d = -21

3d/3 = -21/3

d = -7

----

The value d = -7 tells us to add -7 to each term to get the next term. In other words, we subtract 7 from each term to get the next term

first term = 18

second term = first term + d = 18+d = 18+(-7) = 18-7 = 11

third term = second term + d = 11+d = 11+(-7) = 11-7 = 4

fourth term = third term + d = 4+d = 4+(-7) = 4-7 = -3

----

We see that a = 11 and b = 4 are the second and third terms respectively.

Therefore, a+b = 11+4 = 15

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

<h3>Answer: 15</h3>

==========================================

Problem 2

A multiple of 4 is in the form 4*n for some integer n, ie n is a whole number.

We want to know which values of 4*n are between 10 and 250.

----

Divide both 10 and 250 by 4 to get the following

10/4 = 2.5

250/4 = 62.5

If n = 2, then 4*n = 4*2 = 8 is not between 10 and 250; however n = 3 will make 4*n = 4*3 = 12 to be between 10 and 250. We see that n = 3 is the smallest possible allowed value.

If n = 62, then 4*n = 4*62 = 248 is between 10 and 250; while n = 63 will make 4*n too big because 4*63 = 252. The largest n can get is n = 62

----

The question posed in question 2 is equivalent to asking the following: "How many values are in the set {3, 4, 5, ..., 60, 61, 62}?"

You could count all of the values in the set, but that exercise is very tedious busywork. There's a much faster way. First lets consider the set below

{a, a+1, a+2, ..., b-2, b-1, b}

where a,b are integers. Basically this set starts at 'a', counts up until we get to 'b'. The handy formula

c = b-a+1

will provide the exact count of values in the set {a, a+1, a+2, ..., b-2, b-1, b}

----

In this case, a = 3 and b = 62, making

c = b-a+1

c = 62-3+1

c = 60

There are 60 values in the set {3, 4, 5, ..., 60, 61, 62}

There are 60 multiples of four that are between 10 and 250.

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

<h3>Answer: 60</h3>
4 0
3 years ago
please help im having such a hard time :( does this equation have no solution one solution or infinite solutions
WINSTONCH [101]

One solution!

Step-by-step explanation:

If we make a graph of the given equations, the lines will intersect at a point. We know that whenever lines intersect, it means the equations have one solution or a unique solution.

8 0
3 years ago
Read 2 more answers
The radius of a circle is 10. Using π, which equation expresses the ratio of the circumference of the circle to the circle's dia
aleksley [76]

The ratio of circumference to diameter is independent of the radius.



Defining C=circumference, r=radius, D=diameter =  2r



Circumference = C = 2 &pi; r = &pi; D  


=> 


ratio of circumference / diameter


= C/D = &pi;

7 0
3 years ago
Read 2 more answers
You have been assigned a nine-digit identification number.
garik1379 [7]

Answer:

Step-by-step explanation:

A tree diagram? I don't think so. Probably it would take a year's supply of paper to record all the possibilities. The question really is do you allow duplications and is 0 allowed to be the first digit.

I would think that both are fine.

So the total number for this number would be 10^9. There probably some sort of algorithm to reduce the number and to check if it is a legitimate choice  for this number.

3 0
2 years ago
Given: cos∅ =-4/5 , sinФ = -12/13 , ∅ is in the third quadrant, and Ф is in the fourth quadrant. Evaluate Sin(∅+Ф)
galina1969 [7]

Answer:

63/65

Step-by-step explanation:

the angles are in fourth and third quadrants so all the sin and cos values are minus

4 0
3 years ago
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