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3 years ago

100 POINTS!!!!!!! PLZ HELP!!!

Mathematics

1 answer:

Marysya12 [62]3 years ago

5 0

Answer:

A) I agree

B)SSS because all three sides would be congruent to the sides from the other triangle

Step-by-step explanation:

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Use induction to show that 12 + 22 + 32 + ... + n2 = n(n+1)(2n+1)/6, for all n > 1.

dlinn [17]

Answer with Step-by-step explanation:

Let $P(n)=1^2+2^2+3^2+.....+n^2=\frac{n(n+1)(2n+1)}{6}$

Substitute n=2

Then $P(2)=1+2^2=5$

$P(2)=\frac{2(2+1)(4+1)}{6}=5$

Hence, P(n) is true for n=2

Suppose that P(n) is true for n=k >1

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

Now, we shall prove that p(n) is true for n=k+1

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

LHS

$P(k+1)=1^2+2^2+3^2+.....+k^2+(k+1)^2$

Substitute the value of P(k)

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

$P(k+1)=(k+1)(\frac{k(2k+1}{6})+k+1)$

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

$P(k+1)=(k+1)(\frac{2k^2+7k+6}{6})$

$P(k+1)=(k+1)(\frac{2k^2+4k+3k+6}{6})$

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

LHS=RHS

Hence, P(n) is true for all n >1.

Hence, proved

4 0

3 years ago

I need help haven’t done math since quarantine and I get an assignment with these it’s not -t exponent 5

MA_775_DIABLO [31]

Answer:

$-t^5$

Step-by-step explanation:

Since you are multiplying the same thing by itself, it'll have an exponential value, so count the t's and that is your exponent. Don't forget the "-" sign.

7 0

4 years ago

Assume that the probability of a driver getting into an accident is 8.6%, the

allsm [11]

- The answer is option B. The insurance company must request a premium of $ 1095.16

3 0

3 years ago

The sales tax rate is 8% how much money is 8% of $14

Leona [35]

Answer: $1.12

Explanation:

6 0

3 years ago

Which equation, when graphed, has x-intercepts at (-1,0) and (-5,0) and a y-intercept at (0, -30)?

Vladimir [108]

If a function has roots -1 and -5, it must be in the form

$f(x)=a(x+1)(x+5)$

We can fix the coefficient a by imposing the passing through (0,-30):

$f(0)=-30=a(1)(5)\iff a=-6$

So, the function is

$f(x)=-6(x+1)(x+5)$

7 0

3 years ago