Answer:
The value of k is 6
Step-by-step explanation:
we know that
If two segments are parallel, then their slopes are the same
we know that
The formula to calculate the slope between two points is equal to
step 1
Find the slope MN
we have
M(0, −3), N(−2, −4)
substitute

step 2
Find the slope AB
A(2, 5), B(4, k)
substitute in the formula
Remember that the slopes MN and AB must be equal

Solve for k


therefore
The value of k is 6
If the length of one side of the cube 4 units then the area of one its face is 4 × 4 = 16 square units. From the net, we can see that there are six equal faces and so we get the total surface area is 6 × 16 = 96 square units.
Simple interest: $495 (i=p•r•t)
Volume of the prism: V= Ab*h
Area of the base of the prism: Ab=Area of the equilateral triangle
Height of the prism: h=6
Ab=A triangle= sqrt(3)/4*s^2
Ab=sqrt(3)/4*3^2
Ab=sqrt(3)/4*9
Ab=9 sqrt(3)/4
V=Ab*h
V=[9 sqrt(3)/4](6)
V=54 sqrt(3) /4
V=27 sqrt(3) / 2
V=27/2 sqrt(3)