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2 years ago

6

What are the three ratios equivalent to 8:12

1 answer:

aivan3 [116]2 years ago

6 0

2/3- divide both numerator and denominator by its common factors which in this case is 4 (following this would get you 2/3)
4/6- divide both numerator and denominator by its common factor which in this case is 2 (following this would get you 4/6)
16/24- multiply both the numerator and denominator by 2

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Order the subjects from least to greatest 4/25 or 13% or 0.28 or 7% or 21/100 0.15

motikmotik

Answer:

The answer is: 7% ; 13% ; 0.15 ; 4/25 ; 21/100 ; 0.28

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3 years ago

Jamie is trying to work out the surface area of the cuboid below. Spot any mistakes and write the correct answer.

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3 years ago

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Show that 1n^ 3 + 2n + 3n ^2 is divisible by 2 and 3 for all positive integers n.

Dmitry_Shevchenko [17]

Prove:

Using mathemetical induction:

P(n) = $n^{3}+2n+3n^{2}$

for n=1

P(n) = $1^{3}+2(1)+3(1)^{2}$ = 6

It is divisible by 2 and 3

Now, for n=k, $n > 0$

P(k) = $k^{3}+2k+3k^{2}$

Assuming P(k) is divisible by 2 and 3:

Now, for n=k+1:

P(k+1) = $(k+1)^{3}+2(k+1)+3(k+1)^{2}$

P(k+1) = $k^{3}+3k^{2}+3k+1+2k+2+3k^{2}+6k+3$

P(k+1) = $P(k)+3(k^{2}+3k+2)$

Since, we assumed that P(k) is divisible by 2 and 3, therefore, P(k+1) is also

divisible by 2 and 3.

Hence, by mathematical induction, P(n) = $n^{3}+2n+3n^{2}$ is divisible by 2 and 3 for all positive integer n.

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3 years ago