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3 years ago

The first and last terms of a 10-term arithmetic series are listed in the table. What is the sum of the series?

1 answer:

4 0

The sum of an arithmetic series:
$S_n=\frac{n(a_1+a_n)}{2}$

$a_1=3 \\
a_{10}=75 \\ \\
S_{10}=\frac{10(a_1+a_{10})}{2}=\frac{10(3+75)}{2}=5(3+75)=5 \times 78=390$

The sum of the series is 390.

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3 years ago

What is the simplified form of 12x/900x²y4z6?

zalisa [80]

Answer:

$360xy^2|xz^3|$

Step-by-step explanation:

Given expression:

$12x \sqrt{900x^2y^4z^6}$

$\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:$

$\implies 12x \sqrt{900}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}$

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$\implies 12x \sqrt{30^2}\sqrt{x^2}\sqrt{y^4}\sqrt{z^6}$

$\textsf{Apply radical rule} \quad \sqrt{a^2}=a, \quad a \geq 0:$

$\implies 12x \cdot 30|x|\sqrt{y^4}\sqrt{z^6}$

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(We need to use the absolute value of √x² since the x term was originally to the power of 2, which means the value of x² is always positive since the exponent is even).

$\textsf{Apply exponent rule} \quad \sqrt{a^m}=a^{\frac{m}{2}}:$

$\implies 360x|x|\cdot y^{\frac{4}{2}}\cdot z^{\frac{6}{2}}$

Simplify:

$\implies 360xy^2|xz^3|$

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3 years ago

Can someone help me D: thanks in advance :D

max2010maxim [7]

Answer:

3) 27 cubed

4) 72 cubed

5) 125 cubed

8) 27 cubed. 3 is the length, 3 is the width, and 3 is the height.

9) 72 cubed. 6 is the length, 3 is the width, and 4 is the height.

10) 125 cubed. 5 is the length, 5 is the width, and 5 is the height.

Step-by-step explanation

Here's what to show if your teacher requires for you to show your work.

3) 3 x 3 x 3 = 27

4) 6 x 3 x 4 = 72

5) 5 x 5 x 5 = 125

8) 3 x 3 x 3 = 27

9) 6 x 3 x 4 = 72

10) 5 x 5 x 5 = 125

These are the ones I'd suggest putting the up and down form on.

10) and 5) Also put 5 x 5 = 25. 4) and 9) Also put 6 x 3 = 18.

2 3

25 18

x 5 x 4

125 72

Hoped this answered everything! Feel free to ask me if there's something I missed! :)

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2 years ago