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2 years ago

Simplly the square root of 75z^18

Mathematics

1 answer:

notsponge [240]2 years ago

8 0

Answer:5√(3)z^9

Step-by-step explanation:

Square root of 75z^18

√(75z^18)

√(75) x √(z^18)

√(25x3) x (z^18)^(1/2)

√(25) x √(3) x z^(18x1/2)

5 x √(3) x z^9

5√(3)z^9

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A giraffe measures 17 feet tall . A gorilla mesures 63 inches tall. How many feet taller is the giraffe than the gorilla

9966 [12]

Answer:

11.75 feet

Step-by-step explanation:

17 times 12 = 204 inches

204 - 63 = 141 inches

141/12 = 11.75 feet

4 0

1 year ago

Which statements are true regarding triangle LMN? Check all that apply.

dimaraw [331]

Answer:

$NM = x$

$LM = x\sqrt{2}$

$tan (45) = 1$

Step-by-step explanation:

Step 1: Pythagoras Theorem

Pythagoras theorem relates the three sides of the triangle in such a way that the sum of the square of base and perpendicular is equal to hypotenuse, such as:

$LM^{2} =LN^{2} +NM^{2}$

Step 2: Trigonometric Functions

Only for a right angle triangle following three trigonometric relations are valid

$sin (\theta) = \frac{opposite}{hypotenuse}$

$cos (\theta) = \frac{adjacent}{hypotenuse}$

$tan (\theta)=\frac{sin (\theta)}{cos (\theta)} = \frac{opposite}{adjacent}$

Step 3: Verifying all the possible answers

A: Since, LN = x and using $tan (45) =1$

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{NM}{x} =1$

therefore, NM = x (true)

B: As NM = x therefore it can not be equal to $x\sqrt{2\\}$ .

C: Using Pythagoras Theorem

$LM^{2} =LN^{2} +NM^{2}$

$LM^{2} =x^{2} +x^{2}$

$LM^{2} =2x^{2}$

$LM = \sqrt{2x^{2}} = x\sqrt{2}$

It can also be proved using trigonometric relation

$cos (45) = \frac{x}{LM}$

$LM = \frac{x}{cos (45)}$

As, $\frac{1}{cos (45)}= \sqrt{2}$

Therefore

$LM = x\sqrt{2}$

D and E:

Using same approach similar to part A

Since, LN = x and NM = x

we can calculate

$tan (\theta)= \frac{opposite}{adjacent}$

$tan (45)= \frac{x}{x} =1$

Therefore, $tan (45) = 1$ and not equal to $\frac{\sqrt{2} }{2}$

3 0

2 years ago

Read 2 more answers

A farmer sells 6.5 kilograms of pears and apples at the farmer's market. 3/4 of this weight is pears, and the rest is apples. Ho

Jet001 [13]

Answer:

1.625 kilograms

Step-by-step explanation:

Since total weight of pears and apples is 6.5 kilograms and 3/4 of this weight is pears, the weight of the pears is

→ 6.5 x 3/4 = 4.875 kilograms

Since the weight of the pears is 4.875, we can subtract it from the total weight to find the weight of the apples

→ 6.5 - 4.875 = 1.625 kilograms

8 0

1 year ago

Read 2 more answers

michael wittry has been investing inhis roth IRA retirement account for 20 years. Two years ago his account was worth $215,658.

Over [174]

Let's say

a = 215,658

ok... so.. he first lost 1/3 of that

$\bf \textit{\underline{lost} }\frac{1}{3}a\qquad \qquad a-\cfrac{1}{3}a\implies a-\cfrac{a}{3}\implies \cfrac{3a-a}{3}\implies \cfrac{2a}{3}
\\\\\\
\textit{then he \underline{gained} }\frac{1}{2}\textit{ of }\frac{2a}{3}\qquad \qquad \cfrac{2a}{3}+\cfrac{\frac{2a}{3}}{2}\implies \cfrac{\frac{2a}{3}}{\frac{2}{1}}
\\\\\\
\cfrac{2a}{3}+\cfrac{2a}{3}\cdot \cfrac{1}{2}\implies \cfrac{2a}{3}+\cfrac{2a}{6}\implies \cfrac{4a+2a}{6}
\\\\\\
\cfrac{6a}{6}\implies \boxed{a}\implies 215,658$

so, his nickname might just be even steven, because, he ended up with the same original amount after the 1/2 bump.

4 0

2 years ago

An average adult can hear sounds with frequencies between 20 waves per second and 16,000 waves per second. What is the wavelengt

frez [133]

Answer:

The wavelength, of a sound wave with a frequency of 20 waves per second is 15,000,000 m.

Step-by-step explanation:

In this question, we have to calculate the wavelength of a sound wave of frequency 20 waves per second.

We know that the speed of light in air/ vacuum is $3\times 10^{8}$ .