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stellarik [79]
2 years ago
14

austin is riding his bicycle. He rides for 27.5 kilometers at a speed of 11 kilometers per hours for how many hours did he ride?

​
Mathematics
1 answer:
Ludmilka [50]2 years ago
4 0
Divide 27.5/11, and you get 2.5.
Austin rode for 2.5 hours (2 and a half hours).
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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
2 years ago
I bought 2 1/2 gallons of paint but i only used 1/2 gallon of the paint. how much paint do i have left?
hjlf
I hope this helps you



2 1/2=2.2+1/2=5/2



5/2-1/2


4/2


2 used paint


2 1/2=5/2


5/2-2


2,5-2


0,5


1/2 left
3 0
2 years ago
Divide<br><br> -5/9 by 5/7 :<br><br> a)-7/9<br> b)-9/7<br> c)7/9<br> d)9/7
Reil [10]

Answer:

a

Step-by-step explanation:

-5/9 ÷ 5/7

= -5/9 × 7/5

= -7/9

The answer should be a

4 0
2 years ago
An exponent shows how many times the base number is multiplied by itself.
Stells [14]
The answer is a. true.
7 0
2 years ago
-2(x – 3) - 2<br> simplify the expression
Inessa [10]

Answer:

-2x+4

Step-by-step explanation:

-2(x-3)-2

-2x+6-2

-2x+4

4 0
2 years ago
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