A linear function that represents the number of animals adopted from the shelter is compared to a different linear function that represents the hours volunteers work at the shelter each week. Describe the key features of the functions that are needed to determine if these lines intersect.

1) These linear functions must not describe a pair of parallel lines.

2) Any intersection of two lines determines a point.

Step-by-step explanation:

Hi there!

Well, since no further details were given. Let's call the linear function that represents the number of animals adopted from the shelter . And

the hours the volunteers work at the shelter each week

1) These linear functions must not describe a pair of parallel lines.

If these lines intersect, then their slope must be different.

Equal slopes, parallel lines. Parallel lines, no intersection.

Different slopes, then there is an intersection at some point.

2) Any intersection of two lines determines a point. Let's find it.

So to find one common point equalize the two functions, then find the value for the x-coordinate. Plug it in one of the functions, e.g.

At the common point, both functions after inserted the same value in the Domain (x) return the same result for their respective  Range set.

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Cost of 7 gallons=$24.50

Cost of 1 gallon=24.50/7=3.5

Cost of 15 gallons=15*3.5=52.5

Cost of 15 gallons will be $52.5

The solution is in the following image

The answer is in the image 

The answer is in the image 

Salesperson will make 6% of 1800

=(6/100)*1800

=108

Salesperson will make $108 in $1800 sales

Here,

tip=18%of $32

tip=(18/100)*32

=0.18*32

=$5.76

Total payment=32+5.76=$37.76

The wood before starting =12 feet

Left wood=6 feet

Wood used till now=12-6=6 feet

Picture frame built till now= 6/(3/4)

=8 pieces

Therefore, till now 8 pieces have been made.