Answer:
288 minutes
Step-by-step explanation:
first off, let's recall that a cube is just 6 squares stacked up to each other, like in the picture below. Since we know its volume, we can find how long each side is.
part A)
![\bf \textit{volume of a cube}\\\\V=x^3~~\begin{cases}x=side\\[-0.5em]\hrulefill\\V=64\end{cases}\implies 64=x^3\implies \sqrt[3]{64}=x\implies 4=x](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ctextit%7Bvolume%20of%20a%20cube%7D%5C%5C%5C%5CV%3Dx%5E3~~%5Cbegin%7Bcases%7Dx%3Dside%5C%5C%5B-0.5em%5D%5Chrulefill%5C%5CV%3D64%5Cend%7Bcases%7D%5Cimplies%2064%3Dx%5E3%5Cimplies%20%5Csqrt%5B3%5D%7B64%7D%3Dx%5Cimplies%204%3Dx%20)
part B)
they have a painting with an area of 12 ft², will the painting fit flat against a side? Well, it can only fit flat if the sides of the painting are the same length or smaller than the sides of the crate, we know the crate is a 4x4x4, so are the painting's sides 4 or less?
![\bf \textit{area of a square}\\\\A=s^2~~\begin{cases}s=side\\[-0.5em]\hrulefill\\A=12\end{cases}\implies 12=s^2\implies \sqrt{12}=s\implies \stackrel{yes}{3.464\approx s}](https://tex.z-dn.net/?f=%20%5Cbf%20%5Ctextit%7Barea%20of%20a%20square%7D%5C%5C%5C%5CA%3Ds%5E2~~%5Cbegin%7Bcases%7Ds%3Dside%5C%5C%5B-0.5em%5D%5Chrulefill%5C%5CA%3D12%5Cend%7Bcases%7D%5Cimplies%2012%3Ds%5E2%5Cimplies%20%5Csqrt%7B12%7D%3Ds%5Cimplies%20%5Cstackrel%7Byes%7D%7B3.464%5Capprox%20s%7D%20)
The following are the answers to
the questions presented:
Part 1:
Vertex: <span>(<span><span>−3</span>/ 2</span>,<span> 11/2</span>)</span>
Axis of
symmetry = x = -3/2
Domain = all
real numbers
Range = <span>y </span><span>≤ </span>11/2
Part 2:
A quadratic equation is symmetrical around its vertex. The
equation for the axis of symmetry is x = -3/2 since the equation is in terms of
x. Since no value of x is undefined, then the domain of the equation is clearly
all real numbers. Since the value of “a” is negative, then that means the y
coordinate of the vertex is the maximum value so the range will never get above
11/2. I am hoping that these answers have satisfied your queries and it
will be able to help you in your endeavors, and if you would like, feel free to
ask another question.
Answer:
I am not sure which one it is due to what you put in. I think it would be A.
x = 0
y = 2/3
Step-by-step explanation:
Step: Solve x + 6y= 4 for x:
x + 6y + −6y = 4 + −6y
x= −6y + 4
Step: Substitute −6y + 4 for x in 2x + 3y = 2:
2x + 3y = 2
2 (−6y + 4) + 3y = 2
−9y + 8 = 2
−9y + 8 + −8 = 2 + −8
−9y = −6
-9y/-9 = -6/-9
y = 2/3
Step: Substitute 2/3 for y in x = −6y + 4:
x = −6y + 4
x = -6 (2/3) + 4
x = 0
Sorry if it is long and confusing. But I hope this helps!
Answer:
150(10s + h)
Step-by-step explanation:
We need to write an expression for the total items they shipped.
Let each skateboard be s.
Let each helmets be h.
The factory ships 100 boxes with 15 skateboards in each box. That is:
100 * (15 * s) = 1500s
The factory ships 10 boxes with 15 helmets in each box. That is:
10 * (15 * h) = 150h
The total number of items shipped is therefore:
1500s + 150h = 150(10s + h)
This expression represents the total number of items shipped.
