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3 years ago

The volume of a cube is 729 cubic inches. What is the area of each face of the cube

Mathematics

1 answer:

kogti [31]3 years ago

6 0

121.5 in. You divide 729 by 6 because their are 6 faces of the cube.

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A shirt that normally costs 30 dollers s on sale for 21.75 what percent of the regular price is the sale price

ivanzaharov [21]

72.5%

You can get this by dividing the new price by the original price and then multiplying by 100.

3 0

3 years ago

Given that cot θ = 1/√5, what is the value of (sec²θ - cosec²θ)/(sec²θ + cosec²θ) ?

Bogdan [553]

Step-by-step explanation:

$\mathsf{Given :\;\dfrac{{sec}^2\theta - co{sec}^2\theta}{{sec}^2\theta + co{sec}^2\theta}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{{sec}\theta = \dfrac{1}{cos\theta}}}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{co{sec}\theta = \dfrac{1}{sin\theta}}}}$

$\mathsf{\implies \dfrac{\dfrac{1}{cos^2\theta} - \dfrac{1}{sin^2\theta}}{\dfrac{1}{cos^2\theta} + \dfrac{1}{sin^2\theta}}}$

$\mathsf{\implies \dfrac{\dfrac{sin^2\theta - cos^2\theta}{sin^2\theta.cos^2\theta}}{\dfrac{sin^2\theta + cos^2\theta}{sin^2\theta.cos^2\theta}}}$

$\mathsf{\implies \dfrac{sin^2\theta - cos^2\theta}{sin^2\theta + cos^2\theta}}$

Taking sin²θ common in both numerator & denominator, We get :

$\mathsf{\implies \dfrac{sin^2\theta\left(1 - \dfrac{cos^2\theta}{sin^2\theta}\right)}{sin^2\theta\left(1 + \dfrac{cos^2\theta}{sin^2\theta}\right)}}$

$\bigstar\;\;\textsf{We know that : \large\boxed{\mathsf{cot\theta = \dfrac{cos\theta}{sin\theta}}}}$

$\mathsf{\implies \dfrac{1 -cot^2\theta}{1 + cot^2\theta}}$

$\mathsf{Given :\;cot\theta = \dfrac{1}{\sqrt{5}}}$

$\mathsf{\implies \dfrac{1 - \left(\dfrac{1}{\sqrt{5}}\right)^2}{1 + \left(\dfrac{1}{\sqrt{5}}\right)^2}}$

$\mathsf{\implies \dfrac{1 - \dfrac{1}{5}}{1 + \dfrac{1}{5}}}$

$\mathsf{\implies \dfrac{\dfrac{5 - 1}{5}}{\dfrac{5 + 1}{5}}}$

$\mathsf{\implies \dfrac{5 - 1}{5 + 1}}$

$\mathsf{\implies \dfrac{4}{6}}$

$\mathsf{\implies \dfrac{2}{3}}$

Hence, option (a) 2/3 is your correct answer.

3 0

2 years ago

Solve for x: 4(x+6) = 2-6 (x+3)

laiz [17]

Answer:

x = - 4

Step-by-step explanation:

6 0

3 years ago

On a field trip there are 18 chaperones supervising 81 children. If the children are broken into groups how many adults are need

Butoxors [25]

Answer:

Step-by-step explanation:

you first divide 81 by 18 and get 4.5, that is the number of children per adult.

next you'll divide 27 by 4.5 and 6.

that's the answer.

3 0

3 years ago

Please help me 3x - 12y = 60 x + 2y = 14 will mark brainliest

Setler79 [48]

Answer:

x = 8, y = 3

Step-by-step explanation:

3x - 12y = 60

x + 2y = 14

3x - 12y = 60

3x + 6y = 42 (multiply by 3 so the x is the same as the top equation)

6y = 18 (subtract the equations)

y = 18 / 6

= 3

To find x, substitute y into the 2nd equation since it is the simplest so:

x + 2(3) = 14

x + 6 = 14

x = 14 - 6

= 8

7 0

3 years ago