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find the lateral area of the regular prism with height h, if the base of the prism is:
a) equilateral triangle with the side 4 cm and h=2.5 cm
b) square with the side 2 cm and h=125 mm
c) regular pentagon with the side 6 cm and h=15 cm

A) 30 cm^2.

B) 100 cm^2.

C) 450 cm^2.

Step-by-step explanation:

A)  As all the sides of an equilateral triangle are equal the lateral area consists of 3 rectangles of size 4*2.5 cms.

Lateral area of the prism = 3 * 4 * 2.5 = 30 cm^2.

B)  There are 4 rectangles making up the lateral area because the base is square. The height = 125 mm = 12.5 cm.

Lateral area = 4 * 2 * 12.5 = 100cm^2.

C) Since a regular pentagon has 5 equal sides the lateral area consists of 5 rectangles. each of  area  6*15 = 90 cm^2.

Lateral area = 5 * 90 = 450 cm^2.

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

2/3x + 7 = 29

step-by-step explanation:

two thirds = 2/3

plus a number = x

at least 29 = 29

there for you should get 2/3x + 7 = 29