Simplfy the expression: (x - 9)^2

1 answer:

6 0

The answer would be x^2-18x+81. This can be found be writing "(x-9)^2" twice, and distributing. Combine like terms, and you should get this answer.

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A pottery maker an make 24 vases in 8 days, if the pottery maker works 6 hours each day, how long does it take to make 1 vase???

kolbaska11 [484]

first of all you must find out how many vases he makes per day;

24 ÷ 8 = 3 vases per day

So if he makes 3 vases per day now to find how much time he takes per vase you must divide the number of hours he works per day by the number of vases he makes per day;

6 hours ÷ 3 vases =

6 ÷ 3 = 2

so your final answer would be: 2 hours per vase

4 0

3 years ago

Read 2 more answers

(15-16) Consider the Infinite Geometric Series:

vodka [1.7K]

15 Answer: S₁ = 1 S₂ = 4 S₃ = 13 S₄ = 40 Sum = NO

<u>Step-by-step explanation:</u>

1 + 3 + 9 + 27 + ... $\implies\sum^{\infty}_{n=1}3^{n-1}\implies\sum^{\infty}_{n=1}\dfrac{3^n}{3}\\\\\bullet S_1=1\\\bullet S_2=1+3=4\\\bullet S_3=1+3+9=13\\\bullet S=1+3+9+27=40\\\\\\ \lim_{n \to \infty} \dfrac{3^n}{3} \implies\dfrac{3^{\infty}}{3}\implies\infty\\\\\text{The series diverges so there is no sum.}$

16 Answer: $\bold{S_1=\dfrac{1}{2}\qquad S_2=\dfrac{2}{3}\qquad S_3=\dfrac{13}{18}\qquad S_4=\dfrac{39}{54}\qquad Sum=YES}$

<u>Step-by-step explanation:</u>

$\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}+\dfrac{1}{162}+...\implies \sum^{\infty}_{n=1}\dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\\\\\\\bullet S_1=\dfrac{1}{2}\\\\\bullet S_2=\dfrac{1}{2}+\dfrac{1}{6}=\dfrac{2}{3}\\\\\bullet S_3=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}=\dfrac{13}{18}\\\\\bullet S_4=\dfrac{1}{2}+\dfrac{1}{6}+\dfrac{1}{18}+\dfrac{1}{54}=\dfrac{39}{54}$

$\lim_{n \to \infty} \dfrac{1}{2}\bigg(\dfrac{1}{3}\bigg)^{n-1}\implies \dfrac{1}{2}\lim_{n \to \infty} \dfrac{1}{3^{\infty-1}}\implies \dfrac{1}{\infty}=0\\\\\\\text{The series converges so it does have a sum.}$