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frozen [14]
3 years ago
6

Simplify the expression

Mathematics
1 answer:
makvit [3.9K]3 years ago
7 0

Answer:

3x+18

Step-by-step explanation:

6+3(x+4)=6+3x+12

              =3x+18

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What is the surface area of the equilateral triangular prism? A) 51 cm2 B) 56 cm2 C) 62 cm2 D) 67 cm2
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You have to give some info about the prism
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The 21st, 37th and 56th term of an A.P. are consecutive terms of a G.P. Find the common ratio of the G.P.​
mash [69]

just use what you know about this stuff

(a+36d)/(a+20d) = (a+55d)/(a+36d)

(a+36d)^2 = (a+55d)(a+20d)

a^2+72ad+1296d^2 = a^2+75ad+1100d^2

3ad = 196d^2

3a = 196d

That is, for any value of n,

a=196n

d=3n

So, there is no unique solution.

If n=1, then a=196 and d=3. The terms are

196+20*3 = 256

196+36*3 = 304

196+55*3 = 361

304/256 = 361/304

You can easily verify that it works for any value of n.

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3 years ago
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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.

3 0
3 years ago
I am having trouble figuring out this question, repost again...
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12,740 - 200= 12,540 Ft above sea level
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3 years ago
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Find the equation of the line with slope = -8 and passing through (9,-73). Write your equation in the form
Morgarella [4.7K]

Answer:

1. Find the equation for the line that passes through (−2,9) that has slope 7/3 Give your answer in point-slope form. You do not need to simplify. 2. Find the equation of the line with slope = -4 and passing through (-6,29). Write your equation in the form y= 3. Find the equation for the line that passes through the points (7,−4) and (4,9). Give your answer in point-slope form. You do not need to simplify.

Step-by-step explanation:

7 0
2 years ago
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