Answer:
12
Step-by-step explanation:
A profit, or money you have, or money you deposit in a bank account is usually positive.
A debt, or money you withdraw from a bank account, or money you give away is usually negative.
Answer: 12
Part I
We have the size of the sheet of cardboard and we'll use the variable "x" to represent the length of the cuts. For any given cut, the available distance is reduced by twice the length of the cut. So we can create the following equations for length, width, and height.
width: w = 12 - 2x
length: l = 18 - 2x
height: h = x
Part II
v = l * w * h
v = (18 - 2x)(12 - 2x)x
v = (216 - 36x - 24x + 4x^2)x
v = (216 - 60x + 4x^2)x
v = 216x - 60x^2 + 4x^3
v = 4x^3 - 60x^2 + 216x
Part III
The length of the cut has to be greater than 0 and less than half the length of the smallest dimension of the cardboard (after all, there has to be something left over after cutting out the corners). So 0 < x < 6
Let's try to figure out an x that gives a volume of 224 in^3. Since this is high school math, it's unlikely that you've been taught how to handle cubic equations, so let's instead look at integer values of x. If we use a value of 1, we get a volume of:
v = 4x^3 - 60x^2 + 216x
v = 4*1^3 - 60*1^2 + 216*1
v = 4*1 - 60*1 + 216
v = 4 - 60 + 216
v = 160
Too small, so let's try 2.
v = 4x^3 - 60x^2 + 216x
v = 4*2^3 - 60*2^2 + 216*2
v = 4*8 - 60*4 + 216*2
v = 32 - 240 + 432
v = 224
And that's the desired volume.
So let's choose a value of x=2.
Reason?
It meets the inequality of 0 < x < 6 and it also gives the desired volume of 224 cubic inches.
2x2−5x=3
I think the first step would be to
Subtract 3 from both sides
2x2−5x−3=3−3
2x2−5x−3=0
Then
For this equation: a=2, b=-5, c=-3
2x2+−5x+−3=0
Lastly you would
Use quadratic formula with a=2, b=-5, c=-3
I think your answer would then have to be...
x = 3 or x = −1
/2
Answer:
B and A
Step-by-step explanation:
What I did for these problems is plug in the numbers listed for the x-value. For example, in your calculator you’d put; (1/2)^3 and that’d get you 1/8. Then, try it for 8^(2 - 3) which is also 1/8. So, (1/2)^3 = 8^(2 - 3).
The same process for the second problem. 16^(2(7/3) -3) = 4^((7/3) + 1). This should give you 101.59…
I hope this helps :)!
Answer:
y - 1 = 
(x - 3)
Step-by-step explanation:
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
Calculate m using the slope formula
m = 
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (3, 1) ← 2 points on the line
m = 
=
and using (a, b) = (3, 1 ) , then
y - 1 = (x - 3)
