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3 years ago

M is the midpoint of , cm = 2x + 3, and md = 3x – 6. what is cd? answer

1 answer:

7 0

<span>If M is the midpoint of CD, CM = 2x+3 and MD = 3x-6, then:

MD = CM
3x - 6 = </span>2x + 3
3x - 2x = 3 + 6
x = 9

CM = 2x+3 = 2*9+3 18+3 = 21
MD = CM = 21
CD = CM + MD = 21 + 21 = 42

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3 years ago

Jailyn has ½ of a pizza left over. She wants to share the pizza with 3 of her friends. What fraction of the original pizza will

N76 [4]

Answer:

Jailyn and her 3 friends will each receive 1/8 of the original pizza.

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2 years ago

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3 years ago

Read 2 more answers

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

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

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3 years ago

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