Answer:
a is 60 ft^3 and b is 45
Step-by-step explanation:
b is 45 because 60/4 is 15, which would mean that 4/4 is 60, and since it says 3/4, you subtract 15 from 60 to get 45.
a is 60 because volume equals length times width times height, the three measurements shown
(edit)
and when multiplied you get 60 altogether.
Answer:
36.54
Step-by-step explanation:
Find 45% of 81.2
'Vertex form', having just googled it, is another name for completing the square, which I have done extensively at school. This involved converting:
f(x) = ax^2 + bx + c --> f(x) = a(x-b)^2 + c
In the completed-square form, (b, c) are the co-ordinates of the vertex (which is the maximum/minimum point). So for part a:
- Here is the original
f(x) = x^2 + 12x + 11
- Halve the x-coefficient (the number before x) and use it as -b in the vertex form described above. You must then calculate the square of this number and minus it at the end because when you multiply it out, this is the surplus you will make along with x^2 + 12x:
f(x) = (x + 6)^2 - 36 + 11
- Tidy this up by collecting the constant (just number) terms together:
f(x) = (x + 6)^2 - 25
- Using the form a(x - b)^2 + c, we can work out that b = -6 (because -b = 6) and c = -25. This gives us the vertex (-6, -25) which is a minimum point because the graph is a positive quadratic, giving us the characteristing 'U' shape which has a bottom. If it were a negative quadratic (denoted by a negative x^2 coefficient), the vertex will be a maximum point because it has an 'n' shape instead.
- To solve the equation from here, make the function equal to zero:
(x + 6)^2 - 25 = 0
- Then take 25 to the other side:
(x + 6)^2 = 25
- Next, square-root both sides:
x + 6 = <span>±5
- Rearrange to finish:
x = -6 </span><span>± 5 = -1 or -11
- Therefore, the roots (solutions) to the equation x^2 + 12x + 11 = 0 are x = -1 or -11
This method will work the same for the other equations up there too, so I will leave them for you to do.
I hope this helps
</span>
<span>$8.22h ≥ $623
Let's look at the options and see what works and what doesn't.
$8.22h > $623
* This inequality mostly works and it's true. But there may be a better choice later. So let's hold off on this one.
$8.22h ≤ $623
* That less than or equal has issues. Let's buy the bike if I have less money than what's needed? Nope, not gonna work. Although that equal portion does have an element of truth to it. But this is a bad choice.
$8.22h ≥ $623
* And this third option is better than the first. It simply says that you have to have enough or more money to buy the bike. The 1st equation basically said you have to have more money than the cost of the bike. So this is the correct choice.
$8.22h < $623
* This is worse than the 2nd option. In a nutshell, is says buy the bike when you don't have enough money. So bad choice.</span>
Answer:
Step-by-step explanation:
A = (2)(3.14)(2)(4) + (2)(3.14)(2^2)
A = 75.36 in
