What solid 3D object is produced by rotating the triangle about line m?

A cone with height 3 and radius 1

Step-by-step explanation:

Hi, searching I found the image for the question, attached down below.

By rotating the triangle about line m, a cone with height 3 and radius 1 is produced.

Solid 3d objects are produced by rotating a 2d figure around a straight line that lies in the same place.

in our case, if we rotate the triangle around the line, the vertices in touch with the line m remains stationary, while the  remaining vertex follows the path of a circle, creating a cone.

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.