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Vera_Pavlovna [14]
3 years ago
13

Use long division to find the quotient below. (2x3 + x2 + 25) /(2x+5)

Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
8 0

Answer:

x^2               -2x              +5

Step-by-step explanation:

x^2               -2x              +5

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

2x + 5  /    2x^3      +     x^2       +    0x         + 25

              -(2x^3      +   5x^2)

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

                                   -4x^2       +    0x        

                                 -( -4x^2      -    10x )

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

                                                          10x           + 25

                                                        -(10x            + 25)

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

                                                                                  0

The desired quotient is x^2               -2x              +5

             

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Prove each of the following statements below using one of the proof techniques and state the proof strategy you use.
pochemuha

Answer:

See below

Step-by-step explanation:

a) Direct proof: Let m be an odd integer and n be an even integer. Then, there exist integers k,j such that m=2k+1 and n=2j. Then mn=(2k+1)(2j)=2r, where r=j(2k+1) is an integer. Thus, mn is even.

b) Proof by counterpositive: Suppose that m is not even and n is not even. Then m is odd and n is odd, that is, m=2k+1 and n=2j+1 for some integers k,j. Thus, mn=4kj+2k+2j+1=2(kj+k+j)+1=2r+1, where r=kj+k+j is an integer. Hence mn is odd, i.e, mn is not even. We have proven the counterpositive.

c) Proof by contradiction: suppose that rp is NOT irrational, then rp=m/n for some integers m,n, n≠. Since r is a non zero rational number, r=a/b for some non-zero integers a,b. Then p=rp/r=rp(b/a)=(m/n)(b/a)=mb/na. Now n,a are non zero integers, thus na is a non zero integer. Additionally, mb is an integer. Therefore p is rational which is contradicts that p is irrational. Hence np is irrational.

d) Proof by cases: We can verify this directly with all the possible orderings for a,b,c. There are six cases:

a≥b≥c, a≥c≥b, b≥a≥c, b≥c≥a, c≥b≥a, c≥a≥b

Writing the details for each one is a bit long. I will give you an example for one case: suppose that c≥b≥a then max(a, max(b,c))=max(a,c)=c. On the other hand, max(max(a, b),c)=max(b,c)=c, hence the statement is true in this case.

e) Direct proof: write a=m/n and b=p/q, with m,q integers and n,q nonnegative integers. Then ab=mp/nq. mp is an integer, and nq is a non negative integer. Hence ab is rational.

f) Direct proof. By part c), √2/n is irrational for all natural numbers n. Furthermore, a is rational, then a+√2/n is irrational. Take n large enough in such a way that b-a>√2/n (b-a>0 so it is possible). Then a+√2/n is between a and b.

g) Direct proof: write m+n=2k and n+p=2j for some integers k,j. Add these equations to get m+2n+p=2k+2j. Then m+p=2k+2j-2n=2(k+j-n)=2s for some integer s=k+j-n. Thus m+p is even.

7 0
3 years ago
if I went to store with 90.00 and spent 36.81 and got 20% off what would I have left need answer fast thanks
vichka [17]
I'm guessing the 20 percent off is from the $36.81 so you take 36.81 times 0.80 making it $29.448. Take 90 dollars and minus that amount.

Answer: $60.552 
Rounded Answer: $60.55 or $60.60 or $61

Not sure if this helped, but yeah.....
3 0
3 years ago
This connects to the last one I did
vichka [17]
-4x+3 and -2y idk if that's completely right tho
4 0
3 years ago
Read 2 more answers
Which fraction is equivalent to 1/2 • 4/3 divided by 5/6 ?
Katen [24]

I believe the answer you are looking for is 4/5.

Solution:

1/2 • 4/3=2/3

2/3÷5/6=2/3 • 6/5

4/5

5 0
3 years ago
HELP ASAP! LOOK AT PIC PLS
ra1l [238]

Answer:

E

Step-by-step explanation:

well, yes we know what coins there are and that they’re in jars right? but to find which jar is worth the most, we need to know how many coins are in each. she could have 300 pennies, 2 quarters, 4 dimes, and 7 nickels. we need more information to answer this question so E is the only correct option!

6 0
3 years ago
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