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

Answer:

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) $rose\ bush: \ 6 ; ivy: \ 10$

Step-by-step 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 $m=4\frac{ft}{sec}$

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