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4 years ago

The volume of a cube is 27n^27 cubic units. What is the length of one side of the cube?

Mathematics

2 answers:

elena-14-01-66 [18.8K]4 years ago

8 0

The volume of a cube (V) is given in terms of its side length (s) as

... V = s³

You have

... 27n²⁷ = s³

You may recognize that 27 = 3³, so this can be written as

$3^3\cdot n^{3\cdot 9} = \left(3n^{9}\right)^{3}=s^{3}\\\\3n^{9}=s\qquad\mbox{taking cube roots}$

This result matches your second selection

... 3n⁹ units

lawyer [7]4 years ago

4 0

B) 3n^9 units

I just took the quiz on edge

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5. Write two expressions for the area of the big rectangle.

4vir4ik [10]

Answer:

Two expressions for the area are;

i) x/3 + 2·y + 6

ii) (1/3) × (x + 6·y + 18)

Step-by-step explanation:

The given dimension of the rectangle are;

The height of the rectangle, h = 1/3

The width of the smallest rectangle, w₁ = x

The width of the med sized rectangle, w₂ = 6·y

The width the large rectangle, w₃ = 18

The area, 'A', of the entire rectangular figure, the big rectangle, can be expressed as follows;

A = A₁ + A₂ + A₃

Where;

A₁ = The area of the smallest rectangle

A₂ = The area of the mid sized rectangle

A₃ = The area of the large rectangle

∴ A = (1/3) × x + (1/3) × 6·y + (1/3) × 18 = x/3 + 2·y + 6

The area of the big rectangle. 'A', can also be found as follows;

A = (1/3) × (x + 6·y + 18)

Therefore, two expressions for the area of the big rectangle are;

x/3 + 2·y + 6 and (1/3) × (x + 6·y + 18).

3 0

3 years ago

The function f(x)=x^2 -6x+3 is transformed such that g(x)=f(x-2). Find the vertex of g(x).

Lisa [10]

Answer:

$g(x) = (x-2)^2 -6(x-2) +3$

$g(x) = x^2 -4x +4 -6x +12 +3$

$g(x) = x^2 -10 x +19$

$g(x) = x^2 -10 x + 25 +19 -25$

$g(x) = (x-5)^2 -6$

$y= (x-h)^2 -kk$

Where h,k represent the vertex and we got:

$(h,k)= (5,6)$

(5,6)

Step-by-step explanation:

We have this original function given :

$f(x) = x^2 -6x +3$

And we want to find the vertex for this new function $g(x) = f(x-2)$ and we have:

$g(x) = (x-2)^2 -6(x-2) +3$

And solving the square we got:

$g(x) = x^2 -4x +4 -6x +12 +3$

And adding similar terms we got:

$g(x) = x^2 -10 x +19$

Now we can complete the square like this:

$g(x) = x^2 -10 x + 25 +19 -25$

$g(x) = (x-5)^2 -6$

The general equation is given by:

$y= (x-h)^2 -kk$

Where h,k represent the vertex and we got:

$(h,k)= (5,6)$

(5,6)

5 0

4 years ago

Ronald draws a blueprint of his house. He uses a scale 1/2 centimeter equals 3/4 foot on the actual house. How many centimeters

sattari [20]

For this question you have:
1/2 centimeter = 3/4 foot
so you can say:
1/2*2 centimeter = 3/4 *2 foot
so you will have:
1 centimeter = 3/2 foot or 1.5 foot :))))
i hope this is helpful
have a nice day

8 0

3 years ago

-8+ 8b = 16 8b+8=16 -8=-8 8b=8

e-lub [12.9K]

$b = 3 \\ b = 1 \\ 0 \\ b = 1$

7 0

4 years ago

A mountain bike is priced at $425. If the sales tax is 8.5 percent, what is the cost to purchase the mountain bike? Round to the

MrMuchimi

Answer:

Step-by-step explanation:

bike = $425

tax = 8.5%

cost to purchase = $425 ( 1.085)

= $461.1

6 0

3 years ago