Which expression correctly represents three less than the product of a number and two increased by five?

Mathematics

1 answer:

daser333 [38]3 years ago

5 0

Answer:

The answer is 3-n2-5

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What is the sum of the geometric series

lbvjy [14]

If $S$ denotes the sum of the first $n$ terms of a geometric series with first term $a$ and common ratio $r$ , then

$S=a+ar+ar^2+\cdots+ar^{n-3}+ar^{n-2}+ar^{n-1}$
$rS=ar+ar^2+ar^3+\cdots+ar^{n-2}+ar^{n-1}+ar^n$
$\implies S-rS=a+(ar-ar)+(ar^2-ar^2)+\cdots+(ar^{n-1}-ar^{n-1})-ar^n$
$\implies (1-r)S=a(1-r^n)$
$\implies S=a=\dfrac{1-r^n}{1-r}$

Using summation notation, you have

$S=\displaystyle\sum_{x=1}^nar^{x-1}=\sum_{x=0}^{n-1}ar^x=a\dfrac{1-r^n}{1-r}$

In this case, you have $a=2$ , $r=\dfrac12$ , and $n=16$ . So the value of the sum is

$\displaystyle\sum_{x=0}^{15}2\left(\frac14\right)^x=2\dfrac{1-\left(\frac14\right)^{16}}{1-\frac14}\approx2.67$

Rounded to the nearest whole number, the answer would be 3.

4 0

3 years ago

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The figure below is a rectangular prism.

castortr0y [4]

D. AH

Segment AH is parallel to BD and if the lines were drawn out infinitely, the two lines would never meet.

6 0

3 years ago

Hurry Quick, help me do this problem. I don't understand how to do this so please help! (Problem in photo)

matrenka [14]

Answer:

1) The system of equations is $5x+4y=75$ and $x+y=18$