Question

2. Mrs. Long just got a new puppy! The puppy is learning how to run on hard wood floors. The puppy is running at a rate if 4 feet per second straight toward a wall that is 20 feet away. Select all that apply to this situation.

The slope is -4 ft per second since the puppy is running at a rate of 4 ft per second.

The y-intercept is 20 ft because the puppy is 20 feet away from the wall.

The slope is 4 ft per second since this is how fast the puppy is running.

The y-intercept is 4 ft since the puppy is running at a rate of 4 feet per second.

The puppy will run into the wall after 5 seconds


5. A system of linear equations is graphed.

Which ordered pair is the best estimate for the solution to the system?

(2, −6.5)

(−1.5, 0)

(0, −6.5)

(2.5, −6.5)

7. Asanji and Pranav each improved their yards by planting rose bushes and ivy. They bought their supplies from the store. Asanji spent $42 on 3 bushes and 3 pots of ivy. Pranav spent $48 on 3 rose bushes and 3 pots of ivy. What is the cost of one rose bush and the cost of one pot of ivy?

rose bush: $7 ; ivy: $4

rose bush: $5 ; ivy: $7

rose bush: $3 ; ivy: $5

rose bush: $6 ; ivy: $10

Answer 1

1.The puppy will run into the wall after 5 seconds

Answer 2

Part 1)

The slope is
`4` ft per second since this is how fast the puppy is running

The puppy will run into the wall after
`5` seconds

Part 2)
`(2,-6.5)`

Part 3)
`rose\ bush: \$6 ; ivy: \$10`

Explanation:

Part 1)

Let

x------> the time in seconds

y-----> the distance in feet

we know that

The linear equation that represent the distance that the puppy runs is equal to

`y=4x`

the slope is equal to
`m=4(ft)/(sec)`

For
`x=5\ sec`

`y=4(5)=20\ ft`

so

For
`x>5\ sec` -------> the puppy will run into the wall

therefore

The statements that are true are the following

The slope is
`4` ft per second since this is how fast the puppy is running

The puppy will run into the wall after
`5` seconds

Part 2)

we know that

The solution of the system of equations is the intersection point both graphs

In this problem

The x-coordinate of the intersection point is equal to
`x=2`

The y-coordinate of the intersection point belong to the interval---->
`(-6,-6.5)`

therefore

the best estimate for the solution to the system is the point
`(2,-6.5)`

Part 3)

Let

x-------> the cost of one rose bush

y------> the cost of one pot ivy

z------> the cost of one bush

we know that

`3z+3y=42` ------> equation A

`3x+3y=48` ------> equation B

There is not enough information to solve the system of equations

so

Verify the values of each case in the equation B

case A)
`rose\ bush: \$7 ; ivy: \$4`

`3(7)+3(4)=48`

`33=48` ------> is not true

case B)
`rose\ bush: \$5 ; ivy: \$7`

`3(5)+3(7)=48`

`36=48` ------> is not true

case C)
`rose\ bush: \$3 ; ivy: \$5`

`3(3)+3(5)=48`

`24=48` ------> is not true

case D)
`rose\ bush: \$6 ; ivy: \$10`

`3(6)+3(10)=48`

`48=48` ------> is true

therefore

The case D is the solution