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3 years ago

PLEASE GIVE ME A VALID ANSWER IM GIVING ALOT OF POINTS!

Mathematics

1 answer:

seraphim [82]3 years ago

3 0

Answer:

Step-by-step explanation: It is 1/2 of 14 = 7 hours to the moot

And plug in 7 hours to the equation 4*7+14*7=126 divide that by 2 and the distance is 63

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Find the co-ordinates of the point where the line y = 3x - 8 crosses the y-axis.

lana66690 [7]

(0,-8)

Explanation: In y=mx + b, m represents the slope of the line and b represents the y intercept, since b is -8, it will cross the y-axis at (0,-8)

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2 years ago

Use induction to prove: For every integer n > 1, the number n5 - n is a multiple of 5.

nignag [31]

Answer:

we need to prove : for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

1) check divisibility for n=1, $f(1)=(1)^{5}-1=0$ (divisible)

2) Assume that $f(k)$ is divisible by 5, $f(k)=(k)^{5}-k$

3) Induction,

$f(k+1)=(k+1)^{5}-(k+1)$

$=(k^{5}+5k^{4}+10k^{3}+10k^{2}+5k+1)-k-1$

$=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k$

Now, $f(k+1)-f(k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-(k^{5}-k)$

$f(k+1)-f(k)=k^{5}+5k^{4}+10k^{3}+10k^{2}+4k-k^{5}+k$

$f(k+1)-f(k)=5k^{4}+10k^{3}+10k^{2}+5k$

Take out the common factor,

$f(k+1)-f(k)=5(k^{4}+2k^{3}+2k^{2}+k)$ (divisible by 5)

add both the sides by f(k)

$f(k+1)=f(k)+5(k^{4}+2k^{3}+2k^{2}+k)$

We have proved that difference between $f(k+1)$ and $f(k)$ is divisible by 5.

so, our assumption in step 2 is correct.

Since $f(k)$ is divisible by 5, then $f(k+1)$ must be divisible by 5 since we are taking the sum of 2 terms that are divisible by 5.

Therefore, for every integer n>1, the number $n^{5}-n$ is a multiple of 5.

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3 years ago

A high school athlete ran the 100 meter sprint in 13.245 seconds. what is the time rounded to the nearest tenth. Award is brainl

monitta

If you round 13.245 seconds to the nearest tenth, the answer is 13.2 seconds.
Hope this helped!

6 0

3 years ago

Read 2 more answers

snow_tiger [21]

Answer:

Range is 18.

Step-by-step explanation:

Range can be calculated by subtracting the smallest value of the data set from the largest value of the data set.

The values are:

13, 17, 18, 15, 12, 21, 10, 6, 8, 11, 3

Largest Value in this data set: 21

Smallest Value in this data set: 3

Range = Largest Value - Smallest Value

Range = 21 - 3

Range = 18

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3 years ago

Thomas bought 4 shirts from a store. The price of each shirt was the same. After he bought the shirts, his account balance showe

ludmilkaskok [199]

$89.08 divided by 4 is $22.27, aka the price of one shirt

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3 years ago

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