We have that
<span>x - y = 4-------> multiply by -1-----> -x+y=-4-----> equation 1
x+ 2y = 4------> equation 2
add equation 1 and equation 2
-x+y=-4
x+2y=4
-----------------
0+3y=0-----> y=0
x+2y=4------> x+0=4------>x=4
the solution is the point (4,0)</span>
This is a line portrayed in point-slope form.
First, put a point at (0, -1). This is your y-intercept.
Next, go down 4 units and to the right one unit. Place a point at (1, -4). Then go down another 4 units and right once more. Place a point at (2, -8).
Now, go back to your y-intercept and go up 4 units and to the left one unit. Place a point at (-1, 3).
Finally, draw a line connecting all your points.
To find the volume we use an equation:
volume = length x width x height
Since this shape is a cube, you only need to know one side to find the volume since all of the sides are equal.
So all you need to find the volume is to multiply 4(1/2) which I am going to simplify to 4.5, is plug it into the equation.
volume = 4.5 x 4.5 x 4.5
Which will get you an answer of 91.125 inches cubed
Hope this helps :)
Volume is cubed. If the dimensions are doubled, cube the scale factor:
2^3 = 8
The volume will increase by a scale of 8.
The new volume would be 97 x 8 = 776 ft^3
The inequality is y<2x-1.
To draw the solutions, we first start our solution by drawing the line y=2x-1.
To draw a line, it is enough to determine 2 solutions (x, y), plot them in the coordinate axes, and finally join them by a line.
Let x=0, then y=2*0-1=0-1=-1, so we have the point (0, -1).
Now, if y=0, x=1/2, so we have the point (1/2, 0).
We can see that these 2 points are points of the lines on the 2 pictures on the left. Now we want to determine which region to color, the region below the line, or the one above it.
Consider any point which is not on the line, for example (1, 2). We plug x=1 and y=2 in the inequality. If the inequality holds, it means that we are in the solutions region. If it does not hold, then we are on the not solutions regions.
We check: for x=1, y=2 the inequality y<2x-1 is 2<1, which is not true. So the point (1, 2) can't be in the colored region.
Thus the answer is bottom left.
Answer: Bottom left picture.
