All categories

3 years ago

Consider the diagram. The length of segment QS__ is units.

Mathematics

2 answers:

Paraphin [41]3 years ago

8 0

The Length of Segment QS is 17 units.

lianna [129]3 years ago

3 0

we know that

RT=TQ -----> given problem

Applying the Pythagoras Theorem

In the right triangle RTS

$RS^{2}=RT^{2}+TS^{2}$

In the right triangle TQS

$QS^{2}=TQ^{2}+TS^{2}$

remember that

RT=TQ

therefore

RS=QS

substitute the values

$(3x+2)=(5x-8)$

solve for x

$5x-3x=2+8$

$2x=10$

$x=5\ units$

Find the value of segment QS

$QS=5x-8=5*5-8=17\ units$

<u>The answer is</u>

The length of segment QS is $17\ units$

You might be interested in

A backpack costs $18 and has a 7 percent tax. How much will Sheila have to pay for the backpack after tax? $1.26 $12.60 $19.26 $

elixir [45]

If you add 18 to 7% your number comes out as 19.26

7 0

3 years ago

Read 2 more answers

For the following telescoping series, find a formula for the nth term of the sequence of partial sums

gtnhenbr [62]

I'm guessing the sum is supposed to be

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}$

Split the summand into partial fractions:

$\dfrac1{(5k-1)(5k+4)}=\dfrac a{5k-1}+\dfrac b{5k+4}$

$1=a(5k+4)+b(5k-1)$

If $k=-\frac45$ , then

$1=b(-4-1)\implies b=-\frac15$

If $k=\frac15$ , then

$1=a(1+4)\implies a=\frac15$

This means

$\dfrac{10}{(5k-1)(5k+4)}=\dfrac2{5k-1}-\dfrac2{5k+4}$

Consider the $n$ th partial sum of the series:

$S_n=2\left(\dfrac14-\dfrac19\right)+2\left(\dfrac19-\dfrac1{14}\right)+2\left(\dfrac1{14}-\dfrac1{19}\right)+\cdots+2\left(\dfrac1{5n-1}-\dfrac1{5n+4}\right)$

The sum telescopes so that

$S_n=\dfrac2{14}-\dfrac2{5n+4}$

and as $n\to\infty$ , the second term vanishes and leaves us with

$\displaystyle\sum_{k=1}^\infty\frac{10}{(5k-1)(5k+4)}=\lim_{n\to\infty}S_n=\frac17$

7 0

3 years ago

WILL GIVE BRAINLEST ! <br> hAVE A GOOD DAy :)!

NeX [460]

√84= √4•√21= final answer is
±2√21

7 0

3 years ago

A company that produces computers recently tested the battery in its latest laptop in six separate trials. The battery lasted 8.

Anna35 [415]

confidence interval for the mean battery life in the new model is [7.9489, 8.3045].

What is confidence interval ?

A confidence interval, in statistics, refers to the chance that a population parameter can fall between a collection of values for an exact proportion of times.

Main body:

Formula for confidence interval is =

CI = x- bar ± z*s/√n where,

CI = confidence interval

x- bar = sample mean

z = confidence level value

{s} = sample standard deviation

{n} = sample size

given ;

n = 6

mean = (8.23+7.89+8.14+8.25+8.30+ 7.95)/6

= 8.127

value of z for 95% C.I. = 1.96

C.I. = 8.127 ± 1.96 * 0.22/√6

C.I. = 8.127 ± 0.1781

C.I. =[7.9490, 8.3044]

Hence correct option is A.

To know more about confidence interval , visit:;

brainly.com/question/15712887

#SPJ4

8 0

10 months ago

Al Bank is worried about financing of his new home. The house sells for $490,000. If he puts down 20 percent, what will Al's mon

Anastaziya [24]

The answer is A,
how much interest:3675

4 0

3 years ago