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Whitepunk [10]
3 years ago
10

Please help me please

Mathematics
1 answer:
Gnoma [55]3 years ago
7 0
Eq1
Y intercept -2,0


X intercept 0,2
Slope 1

Eq2
X intercept-2,0
Y intercept 0,2
Slope 1
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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.

3 0
3 years ago
-15= z/-2 answer please?​
faust18 [17]

Answer:

30

Step-by-step explanation:

-15=\frac{z}{-2}\\\\(-15)(-2)=z\\\\30=z

4 0
3 years ago
What is 20% tip on a bill of 59.61
Ugo [173]

Answer:

about $12

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11.922 rounded up is 12.

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Step-by-step explanation:

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It's a horizontal line (look at the picture).

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