Answer:
3rd graph down
Step-by-step explanation:
greens are x and carrots are y in my equations
2x - y >= 3
x + 2y < 4
The first equation is solid and will highlight everything to the right of it because it is a >
the second is dashed and will highlight everything to the left of it because it is a <
the only 2 graphs that show this are 1 and 3
looking at the points you can see that the points for the solid line are both the same so ignore those and go to the dashed lined ones.
on the first graph the points are (0,4)
plugging those into our equation gives us 0 + 2*4 <4
or 8<4 which doesnt make sense making 3 the correct graph
(sorry my answer wasnt posting so i had to start over and make it less detailed, but comment if you need any explanation)
Answer:
D
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Here (h, k ) = (2, 3 ) and r = 6, thus
(x - 2)² + (y - 3)² = 6², that is
(x - 2)² + (y - 3)² = 36 → D
Answer:
It is given that the volume of a cone =
cubic units
Volume of cone with radius 'r' and height 'h' = 
Equating the given volumes, we get
=


It is given that the height is 'x' units.
Therefore, 

Therefore, r = 3x
So, the expression '3x' represents the radius of the cone's base in units.
Answer:

Step-by-step explanation:
Using right estimation point simply means to form a bunch of rectangles between the two limits, x =2 and x = 5. and add the areas of all those rectangles.
There must be 6 subdivisions between 2 and 5. so, to do that:

the length of each subdivision is 0.5 units. That also means that the 6 rectangles in between the limits will each have the base length of 0.5 units.
So the endpoints of each subdivision from 3 to 5 will be:

By <em>right </em>endpoint approx<em>, </em>we mean that the height of the rectangles will be determined by the right endpoint of each subdivision, that is, it must be equal to the function value of the first limit.

Note that we have used the right-end-point of the subdivision to determine the height the rectangles.
All that's left to do now is to simply calculate the areas of the each of the rectangles. And add them up.
the base of each of the rectangle is 
and the height is determined in the table above.



Answer:
5in by 5in by 5in
Step-by-step explanation:
We are not told wat to find but we can as well find the dimension of the prism that will minimize its surface area.
Given
Volume = 125in³
Formula
V = w²h ..... 1
S = 2w²+4wh ..... 2
w is the side length of the square base
h is the height of the prism
125 = w²h
h = 125/w² ..... 3
Substitute eqn 3 into 2 as shown
S = 2w²+4wh
S = 2w²+4w(125/w²)
S = 2w²+500/w
To minimize the surface area, dS/dw = 0
dS/dw =4w-500/w²
0= 4w-500/w²
Multiply through by w²
0 = 4w³-500
-4w³ = -500
w³ = 500/4
w³ =125
w = cuberoot(125)
w = 5in
Get the height
125 =w²h
125 = 25h
h = 125/25
h = 5in
Hence the dimension of the prism is 5in by 5in by 5in