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victus00 [196]
2 years ago
13

Prove each of the following statements about integers by proving thecontrapositive of the statement.A. If 3nis even, thennis eve

n.B. Ifx y zis odd, then at least one ofx; yandzis odd.
Mathematics
1 answer:
frozen [14]2 years ago
6 0

Answer and Step-by-step explanation:

(A) Suppose 3n is even, this implies that the product of 3n is a multiple of two, let's say 2(3k) where k is a real number. Rearranging that, we have 3(2k), let 2k = n. Therefore, n is even.

(B) Suppose xyz is odd, then let x = 2k, y = 2p + 1 and z = 2q + 1. xyz = 2k(2p + 1)(2q + 1) and this is obviously even since it is a multiple of 2.

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What is the value of n?
givi [52]

Answer:

7 cm

Step-by-step explanation:

First you need to check if the equation line was 10, then use it!

3 0
2 years ago
Read 2 more answers
A pilot flew a 400 mile flight in 2.5 hours flying into the wind. Flying the same rate and with the same wind speed the return t
eduard

Answer: 20 mph

Explanation:

Speed is a physical quantity which is equal to the ratio between the distance covered (d) and the time taken (t):

v=\frac{d}{t}

In the first part of the problem, the plane flew a distance of d=400 mi in a time of t=2.5 h. The speed of the plane in this case was the difference between the proper speed of the plane, v, and the speed of the wind, w, since the plane flew opposite to the wind. So we can write:

v-w=\frac{400mi}{2.5h}=160 mph (1)

During the return trip, the plane flew with a speed (v+w), since the wind was on the tail, and it took 2 hours to cover the same distance:

v+w=\frac{400 mi}{2 h}=200 mph (2)

So we have two equations with two unknown variables. From (1), we get

v=160+w

Substituting into eq.(2)

(160+w)+w=200\\160+2w=200\\2w=40\\w=20 mph

So, the speed of the wind was 20 mph.

3 0
2 years ago
Read 2 more answers
Two cars travel at the same speed to different destinations. Car A reaches its destination in 17 minutes. Car B reaches its dest
Goryan [66]

Answer:

speed of car A =Speed of car B=0.8 miles/minutes.

Step-by-step explanation:

We are given that speed of car A is equal to speed of car B.

Also let car A travels x miles.

and car B travels y miles.

Car A  reaches its destination in 17 minutes.

this means that speed of car A is given by:  \dfrac{x}{17} miles/minutes  ( since speed is defined as the ratio of distance and time).

Car B reaches its destination in 32 minutes.

This means that the speed of car B is given by: \dfrac{y}{32} miles/minutes

as speed of both cars are equal this means:

\dfrac{x}{17}=\dfrac{y}{32}------(1)

Also we are given Car B travels 12 miles farther than Car A.

this means y-x=12

y=12+x------(2)

on using equation (1) and (2) we have:

\dfrac{x}{17}=\dfrac{12+x}{32}\\  \\32x=17(12+x)\\\\32x=17\times12+17x\\\\32x-17x=17\times12\\\\15x=122\times17\\\\x=13.6

Hence the speed of car A is 0.8 miles/minutes  ( since x/17 is the speed of car A)

Speed of car B=0.8 miles/minutes.



8 0
3 years ago
Order the weights of the donations from greatest to least. 4.3, 5.5 6 1/6, 15/4, 4 3/8
nata0808 [166]
6 1/6, 5.5, 4 3/8, 4.3, 15/4
4 0
3 years ago
Divide £72cm in the ratio 2:3:1 working out please
ale4655 [162]
2:3:1
2+3+1 = 7

£72 / 7 = £10.28

Answer:
£10.28 * 2 = £20.56
£10.28 * 3 = £30.84
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If you want to check if it's correct. add all three of them and see if you get the £72.

Please make this answer the brainiest!
4 0
2 years ago
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