48x3 +128x2 − 75x − 200 factor

Line e is a segment bisector of AB at point M. If AM = 4n-40 & MB = 7(-2n+2), find the value of n.

Mrac [35]

Answer:

the answer orange is n=3

7 0

2 years ago

Suppose you want to create a set of weights so that any object with an integer weight from 1 to 40 pounds can be balanced on a t

Archy [21]

Answer:

You need 4 weights, and the weights are 1; 3; 9 and 27.

Step-by-step explanation:

<em>Since the scale has two plates, we can place weights on either side and also the object so it can be balanced. </em>

This is a key part of the problem, it's not only on the other side of the scale, but on both sides.

Let's do the math now.

If i get two weights, 1 and 3. I can form this combinations.

Object of 1lb = 1

Object of 2lb + 1 weight = 3 weight.

Object of 3lb = 3 weight

Object of 4lb = 1 weight + 3 weight.

So what if i want to add the next weight and that weight to add me the maximum amount of objects. The weight would have to have a difference with the last object plus one. So if i grab 9. 9 minus 4 is 5. And that is a difference with the last object plus 1.

With a weight of 9, now i can add all the integers up to 13lb.

And the next step? Lets add one more. Keeping the last rule, the weight would have to have a difference with the last object plus one. So if i grab 27, 27 minus 13 is 14. And that is a difference witht the last object plus 1.

The sum of all the weights adds up to 40 pounds. And i can balance any integer in the middle.

The formula we are using is p – n = n + 1

Where p is the new weight. and n is the last object we weighted. And the sum of the weights goes up to the last object we can place on the scale, and in this case is 40.

4 0

3 years ago

A group will equally split 3/4 pounds of a rare spice. How much spice will each person get?

Lyrx [107]

That depends on how many people are in the group!

6 0

2 years ago

Find a compact form for generating functions of the sequence 1, 8,27,... , k^3

pantera1 [17]

This sequence has generating function

$F(x)=\displaystyle\sum_{k\ge0}k^3x^k$

(if we include $k=0$ for a moment)

Recall that for $|x|$ , we have

$\displaystyle\frac1{1-x}=\sum_{k\ge0}x^k$

Take the derivative to get

$\displaystyle\frac1{(1-x)^2}=\sum_{k\ge0}kx^{k-1}=\frac1x\sum_{k\ge0}kx^k$

$\implies\dfrac x{(1-x)^2}=\displaystyle\sum_{k\ge0}kx^k$

Take the derivative again:

$\displaystyle\frac{(1-x)^2+2x(1-x)}{(1-x)^4}=\sum_{k\ge0}k^2x^{k-1}=\frac1x\sum_{k\ge0}k^2x^k$

$\implies\displaystyle\frac{x+x^2}{(1-x)^3}=\sum_{k\ge0}k^2x^k$

Take the derivative one more time:

$\displaystyle\frac{(1+2x)(1-x)^3+3(x+x^2)(1-x)^2}{(1-x)^6}=\sum_{k\ge0}k^3x^{k-1}=\frac1x\sum_{k\ge0}k^3x^k$

$\implies\displaystyle\frac{x+4x^3+x^3}{(1-x)^4}=\sum_{k\ge0}k^3x^k$

so we have

$\boxed{F(x)=\dfrac{x+4x^3+x^3}{(1-x)^4}}$

5 0

3 years ago

Choose the correct simplification of the expression (8x − 5)(2x2 − 5x − 6). (1 point)

OleMash [197]

The easiest terms to check are the first (8x)(2x²) = 16x³ and the last (-5)(-6) = 30. This check eliminates the first choice. The remaining choices differ only in the sign and coefficient of the squared term, so that is the one we need to find.

The squared term will be the sum of the products of factors whose degrees total 2:
(8x)(-5x) + (-5)(2x²) = -40x² -10x² = -50x²

The appropriate choice is
16x³ -50x² -23x +30

6 0

2 years ago