Heidi solved the equation 3(x + 4) + 2 = 2 + 5(x – 4). Her steps are below: 3x + 12 + 2 = 2 + 5x – 20 3x + 14 = 5x – 18 14 = 2x

Y = 12x - 40

the x variable denotes the total number of hours Sam spends working at the airport
the y value signifies how much money Sam has after compensating Daniel
the 12 represents the amount Sam earns per hour in dollars
the 40 indicates the dollar amount Sam owes to Daniel

In this problem, we need to find the measures of all three angles in a triangle.

Let the angles be represented as p, q, and r.

Given that the measure of angle q is one-third of angle p, we have:

The measure of angle r represents the difference between angles p and q, which gives us:

(Equation 1)

Applying the triangle angle sum property, it is known that the cumulative angle measure in a triangle is

p+q+r=

Substituting the value for r from Equation 1, we find:

p+q+p-q=

2p=

Thus, p=

Since

Since angle r is equal to p-q, we can conclude:

r =

Answer:

                          π

V-foam = 4r³( 2 - ----- )

                             3

Step-by-step explanation:

Let r denote the radius of the sphere. The volume of the sphere is expressed as

V = (4/3)(π)(r³).

Next, understand that the cube's side length is 2r, hence the cube's volume is

V = (2r)³, which equals 8r³.

The volume of the foam is derived from the cube's volume subtracting that of the sphere:

V-foam = 8r³ - (4/3)(π)(r³). This can be simplified to

                          π

V-foam = 4r³( 2 - ----- )

                             3