AnswersMO-Algebra II ASolving Linear Systems by Substitution

Modeling with Systems Answers

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1
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What is the slope of the line that represents the turtle's path?

Answer:

0.8

2
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Which system models the height of the tennis ball and the height of the dog's mouth over time?

A
h = 4.5t + 18 and h = -16t2 + 1.5t + 21
B
h = 18t + 4.5 and h =-16t2 + 21t + 1.5
C
h = -16t2 + 4.5t + 18 and h = -16t2 + 1.5t + 14
D
h = -16t2 + 18t + 4.5 and h = -16t2 + 21t + 1.5
3

+

Answer:

8

4

Which system of equations could you use to determine where the paths intersect?

A
y = 0 and y = -0.12(x - 20)2
B
y = 0.8x and y = -0.12x2 + 20
C
y = 0.8x and y = -0.12(x - 20)2
D
y = 0.8x + 8 and y = -0.12x2 + 20
5

What does the t-coordinate of the solution to this system represent?

A
the time at which the ball and the dog hit the ground
B
the time at which the ball and the dog begin moving
C
the time at which the ball and the dog's mouth are at the same height
6

Which system models this situation?

A
y = 26x and y = 8,400(x-500)2+15,900
B
y = 26x and y = -0.030(x-500)2+15,900
C
y = x/26 and y = -0.030(x-500)2+15,900
D
y = x/26 and y =8,400(x-500)2+15,900
7

How many helmets must the company make and sell to break even? helmets

Answer:

600

8

How much will it cost the company to make 600 helmets?$

Answer:

15,600

9

Which system models this situation?

A
h = 3t+10 and h = -16t2+15t+6
B
10t+3 and h = -16t2+6t+15
C
-16t2+3t + 10 and h =-16t2+15t+6
D
-16t2+10t + 3 and h = -16t2+6t+15
10

How many real solutions does the system of equations have?noneonetwo✔ infinitely many

A
none
B
one
C
two
D
✔ infinitely many
11

What can you conclude about the paths of the skaters?

A
There is no chance that the skaters will hit each other.
B
The skaters' paths cross each other at two different points on the rink.
C
The skaters are traveling on the same path, but possibly in different directions.
12

A quarterback throws a football toward a receiver from a height of 6 ft. The initial vertical velocity of the ball is 14 ft/s. At the same time that the ball is thrown, the receiver raises his hands to a height of 8 ft and jumps up with an initial vertical velocity of 10 ft/s. Projectile motion formula: h = -16t2 + vt + h0 t = time, in seconds, since the ball was thrown h = height, in feet, above the ground

Answers:
Blank 1:6
h = -16t² +:10
+:8
13

After seconds, the receiver's hands and the ball will be at the same height.

Answer:

0.5

14

The receiver's hands and the ball are at the same height at ⇒ 9 ft above the ground.

Answer:

7

15

Which facts did your response include?

A
The cost to produce 400 caps is the same as the income made from selling 400 caps.
B
The company will break even when it sells 400 caps; it will not make a profit.
16

The system has no real solutions. What does this indicate about the worker's arms and the measuring tape?

A
They will never be at the same height at the same time.
B
They will be at the same height exactly once.
C
They will be at the same height at two different times.
17

Which system of equations models the paths of the two skaters?

A
y = 0.08x2-1.6x+13 and y = 0.08(x-10)2+5
B
y = 0.08x2-1.6x+13 and y = 1.6(x-10)2+5
C
y = 0.08x2-1.6x+13 and y = 0.8(x-10)2+5
D
y = 0.08x2-1.6x+13 and y = 5(x-10)2+5
18

h = -16t² +

Answer:

10

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