1. [5 pts] a rectangular swimming pool measures 14 feet by 30 feet. the pool is surrounded on all four sides by a path that is 3 feet wide. if the cost to resurface the path is $2 per square foot, what is the total cost of resurfacing the path? 2. the great pyramid outside cairo, egypt, has a square base measuring 756 feet on a side and a height of 480 feet. a. [3 pts] what is the volume of the great pyramid, in cubic yards? b. [2 pts] the stones used to build the great pyramid were limestone blocks with an average volume of 1.5 cubic yards. assuming a solid pyramid, how many of these blocks were needed to construct the great pyramid?

1) $600

2) a) 3386880 cubic yards

b) 2257920 limestone

Step-by-step explanation:

1)

Given;

Dimensions of the swimming pool = 14 feet × 30 feet

Dimensions of the pool with 3 feet wide path = ( 14 + 2 × 3 ) feet × ( 30 + 2 × 3 ) feet  

= 20 feet × 36 feet

[ 2 × width of path is added because the width is to be added both the sides  i.e 3 + 3 = 2 × 3 ]

Now,

The area without the path = 14 feet × 30 feet = 420 ft²

The area with the path = 20 feet × 36 feet = 720 ft²

Therefore,

the area of the path = 720 ft² - 420 ft² = 300 ft²

also,

cost to resurface = $2 per square feet

therefore,

The total cost to resurface = $2 × 300  = $600

2) Sides of the base of the pyramid = 756 feet

height of the pyramid = 480 feet

also,

1 feet = yards

thus,

Sides of the base of the pyramid = yards = 252 yards

height of the pyramid = yards = 160 yards

therefore,

the volume of the pyramid =

=  

= 3386880 cubic yards

b) average volume of limestone 1.5 cubic yards

Therefore,

The number of stones required =

=

= 2257920 limestone

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3

both graphs increase on their domain

neither graph has a y-intercept

step-by-step explanation:

the following points can be visualized easily from the graph