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3 years ago

M is the midpoint of CF (line over it) for the points C(3,4) and F(9,8). Find MF

1 answer:

3 0

$(\frac{x_{1} + x_{2}}{2}, \frac{y_{1} + y_{2}}{2}) \\(\frac{3 + 9}{2}, \frac{4 + 8}{2}) \\(\frac{12}{2}, \frac{12}{2}) \\(6, 6)$

Midpoint of CF: (6, 6)

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Ill give brainlist please <br> 17. 1- (sec²y- tan²x)

siniylev [52]

Answer:

Step-by-step explanation:

6 0

2 years ago

Prove that 2n^3 + 3n^2 + n is divisible by 6 for every integer n > 1 by mathematical induction. (7 marks)

notka56 [123]

Answer:

The answer is True

Step-by-step explanation:

A <em>mathematical induction</em> consists in only 2 steps:

<u>First step</u>: Show the proposition is true for the first one valid integer number.

<u>Second step</u>: Show that if any one is true then the next one is true

Finally, if first step and second step are true, then the complete proposition is true.

So, given $2*n^3+3*n^2+n$

First step: using and replacing n=2 (the first valid integer number >1)

$2*(2)^3 +3*(2)^2+2=30$

$\frac{30}{6} =5$

As the result is an integer number, so the first step is true.

Second step: using any next number, $n+1$ , let it replace

$2*(n+1)^3+3*(n+1)^2+(n+1)\\2*(n^3+3*n^2+3*n+1)+3*(n^2+2*n+1)^2+(n+1)\\2*n^3+6*n^2+6*n+2+3*n^2+6*n+3+n+1\\(2*n^3+3*n^2+n)+(6*n^2+12*n+6)$

As the First step is true, we know that

$2*n^3+3*n^2+n$ $=6*k$ ,

So let it replace in the previous expression

$6*k+6*(n^2+2*n+1)\\6*[k+(n^2+2*n+1)]$

Finally

$\frac{6*[k+(n^2+2*n+1)]}{6} =k+(n^2+2*n+1)$

where the last expression is an integer number

So the second step is true, and the complete proposition is True

5 0

3 years ago

floodwaters are used to prevent damage from floods. A town built a floodwall 4 4/8 feet tall. Another town built a floodwall 7 1

Sveta_85 [38]

It's basic subtraction. you subtract 7 1/8 with 4 4/8 by turning one of the one from the seven to 8/8 and add that to 1/8 so you get 9/8. Then 6 9/8 - 4 4/8 = 2 5/8.

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3 years ago

I will give 30 points if u help now

Amiraneli [1.4K]

Answer:

3. x=16

4. x=51

Step-by-step explanation:

3. 3x-8=x+24

2x=32

x=16

4. 2/3(x+27)= 180-(3x-25)

2/3x+18=180-3x+25

11/3x=187

11x=561

x=51

5 0

3 years ago

Read 2 more answers

For how many integers $n$ is it true that $\sqrt{n} \le \sqrt{4n - 6} < \sqrt{2n + 5}$?

ale4655 [162]

$\bf \sqrt{n}\leqslant \sqrt{4n-6}$

$\bf \sqrt{n}< \sqrt{2n+5}\implies \stackrel{\textit{squaring both sides}}{n< 2n+5}\implies 0\leqslant 2n - n + 5 \\\\\\ 0 < n+5\implies \boxed{-5 < n} \\\\\\ \stackrel{-5\leqslant n < 2}{\boxed{-5}\rule[0.35em]{10em}{0.25pt}0\rule[0.35em]{3em}{0.25pt}2}$

namely, -5, -4, -3, -2, -1, 0, 1. Excluding "2" because n < 2.

6 0

3 years ago