True or False. The mapping diagram shows a function.

Mathematics

1 answer:

Anna [14]3 years ago

6 0

Answer:

False.

Step-by-step explanation:

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What is the sum of the infinite geometric series 9−6+4−83+...9-6+4-83+...??

vivado [14]

Successive terms have a common factor of $-\dfrac23$ , which means the $n$ th partial sum of the series can be written as

$S_n=9-6+4-\dfrac83+\cdots+9\left(-\dfrac23\right)^{n-1}$
$S_n=9\left(1+\left(-\dfrac23\right)^1+\left(-\dfrac23\right)^2+\left(-\dfrac23\right)^3+\cdots+\left(-\dfrac23\right)^{n-1}$

$\implies-\dfrac23S_n=9\left(\left(-\dfrac23\right)^1+\left(-\dfrac23\right)^2+\left(-\dfrac23\right)^3+\left(-\dfrac23\right)^4+\cdots+\left(-\dfrac23\right)^n\right)$

$\implies S_n-\left(-\dfrac23\right)S_n=9\left(1-\left(-\dfrac23\right)^n\right)$
$\dfrac53S_n=9\left(1-\left(-\dfrac23\right)^n\right)$
$S_n=\dfrac{27}5\left(1-\left(-\dfrac23\right)^n\right)$

As $n\to\infty$ , the geometric term vanishes, leaving you with

$S=\displaystyle\lim_{n\to\infty}S_n=\dfrac{27}5$

7 0

3 years ago

Solve the system of linear equations by substitution

ziro4ka [17]

$y - x = 0 ...equation 1$
$2x - 5y = 9 \: ...equation \: 2$
working with equation 1
$y = x \: ...equation \: 3$
next subsitue equation 3 in equation 1
$2x - 5(x) = 9$
$2x - 5x = 9$
$- 3x = 9$
divide by -3
$x = - 3$
substitute x= -3 in equation 1
$y - ( - 3) = 0$
$-(-3) = + 3$
$y = - 3$

6 0

3 years ago

PLEASE HELP ME I NEED HELP PLEASE HELP

lyudmila [28]

Answer:

1st question is 1:2

2nd question is 5

Step-by-step explanation:

15 times two is 30, so if you divide both 15 and 30 by 15, you get 1:2

Divide 300 and 60 and you get 5.

6 0

3 years ago