<u>Explanation</u>
Slope= 2/3
Y intercept= -2
x y
0 3
----------------
-2 0
Linear equations are those equations between variables that give a straight line when plotted on the graph.The standard form for linear equations in two variables is Ax+By=C.
linear equation refers implicitly to the case of just one variable. Here the linear equation 200x-300y=600 gives straight line when plotted on the graph.
The graph linear equation means the linear equation has to be plotted on the graph. After plotting it on the graph we get straight line passing x and y axis. The graph has been attached to the answer.
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.
Answer: Edit: -0.0625
Step-by-step explanation:
Answer:
Step-by-step explanation:
The last one is also the answer
Using the rational exponet rule,
![\sqrt[n]{ {x}^{m} } = x {}^{ \frac{m}{n} }](https://tex.z-dn.net/?f=%20%5Csqrt%5Bn%5D%7B%20%7Bx%7D%5E%7Bm%7D%20%7D%20%20%3D%20x%20%7B%7D%5E%7B%20%5Cfrac%7Bm%7D%7Bn%7D%20%7D%20)
Using this number,
40 is the base so it will stay same. Remember this is a square root sign so our nth root is 2 so our denominator if the rational exponet is 2.
so our numerator is 1 so
