Use the net to find the lateral area of the cylinder Give your answer in terms in pi

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

zalisa [80]

Answer:

$360xy^2|xz^3|$

Step-by-step explanation:

Given expression:

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

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

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

Replace 900 with 30² :

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

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

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

$\implies 360x|x|\sqrt{y^4}\sqrt{z^6}$

(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:

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

(We need to use the absolute value of z³ since the z term was original to the power of 6, which means the value of z⁶ is always positive since the exponent is even).

7 0

1 year ago

Find the widest range of scores that you can get on a final exam in order to receive a grade of B for the class. Using interval

Drupady [299]

Answer:

Correct choice is B

Step-by-step explanation:

Let x% be your final test score, then the average of all test scores is

$\dfrac{96+77+74+x}{4}.$

Since you must have an average between 80% and 89%, then

$80\le \dfrac{96+77+74+x}{4}\le 89,\\ \\320\le 247+x\le 356,\\ \\73\le x\le 109.$

X is measured in percent, then the greatest value of x can be 100%. You get that

$73\%\le x\le 100%.$

4 0

3 years ago

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A wedding planner purchased both small and large lanterns for a wedding reception. The planner purchased a total of 40 lanterns

Olegator [25]

Answer:

The wedding planner must have purchased 28 small lanterns and 12 large lanterns.

Step-by-step explanation:

8 0

2 years ago

a rhombus as an area of 72 ft and the product of the diagonals is 144. What is the length of each diagonal?

SashulF [63]

A = (1/2)(x)(y)

Let x = diagonal 1

Let y = diagonal 2

The product of xy = 144.

This means that x = 12 and y = 12.

So, 12 • 12 = 144

Each diagonal is 12 feet.

Prove:

72 feet = (1/2)(12)(12) feet

72 feet = (1/2)(144) feet

72 feet = 72 feet

6 0

3 years ago

I need help with these

IrinaVladis [17]

Let x be the number.
"twelve decreased by twice a number" ---> 12 - 2x
"8 times the sum of number and 4" ---> 8(x + 4)
12 - 2x = 8(x + 4)
12 - 2x = 8x + 32 (distributive property)
12 = 10x + 32 (add 2x to both sides)
-20 = 10x (subtract 32 from both sides)
x = -2 (divide both sides by 10)

6 0

2 years ago

Read 2 more answers