A model of a volcano that is 22 cm tall with a volume of 586.7 cubic centimeters. What is the area of the base of the model? Round the answer to the nearest tenth.

  80.0 cm^2

Step-by-step explanation:

We need to assume that the shape of the model is a cone or pyramid, something that tapers linearly to a point. Then its volume is given by the formula ...

  V = 1/3Bh

where B is the area of the base, and h is the height. Filling in the given numbers, we have ...

  586.7 =  (1/3)B(22)

Dividing by the coefficient of B gives ...

  B = 3(586.7)/22 = 80.0 . . . cm^2

The area of the base of the model is about 80.0 cm^2.

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions