Question

1. Henry's current age is 10 times Justin's current age. In 6 years, Henry's age will be 4 times Justin's age. Which system of equations can be used to calculate H, Henry's current age and J, Justin's current age?
A: J=10H
J+6=4 [H+6]
B: J+6=H
J+4=H+10
C: H=10J
H+6=4 [J+6]
D: H=10J
H+4=6 [J+4]

2. Kevin plotted a linear equation on a graph with 18 as the y-intercept. Which of the following could be the equation plotted by Kevin?
A: 3x=6-1/3y
B: 7x+2y=38
C: 4y+18y=21
D: 1/2y=9x+5

3. Janie was given [-2,3] as the end point of a line segment and [1,0] as it's midpoint. Which ordered pair should Janie choose as the other endpoint?
A: [ -1/2, 3/2}
B: [ 1/2, 1/2]
C: [ - 5, 6 ] So this one and the following are not negatives, the line is at the top of the 5 not above it but next to it, higher than the actual 5.
D: [ 4, -3 ] This is the same situation, the line isn't a negative and isn't directly above the 3 but it is higher than the 3 and is to the left of it.

4. Mrs. Matthews drew a hexagon with a perimeter of 60 centimeters on a sheet of paper. She used the photocopier in her office to make copies of the drawing. The length of each side of the hexagons on the photocopies is 1 1/2 times the length of each side of the hexagon on the drawing. What is the perimeter in centimeters of each hexagon on the photocopies?
A: 40
B: 90
C: 69
D: 150

5. Jim used 3 logs to mark the perimeter of his triangular flower bed. One side of the flower bed is 6 feet long and another side is 9 feet long. Which could be the length in feet of the third side?
A: 2
B: 3
C: 13
D: 15

6. What is the distance between [ 45, 76 ] and [ 76, 76 ] along the x-axis on a coordinate grid?
A: 76
B: 31
C: 121
D: 0

7. Which set of data should be graphed using a scatter plot instead of a line graph?
A: The height of a child from birth to age 12.
B: The cans of drinks sold each day in the snack bar.
C: The depth of the water in a lake over 2 months.
D: The temperature of a cup of coffee over an hour.

8. If the point [ 5, k ] lies on the line represented by the equation 2x+y=9, the value of k is:
A: 1
B: -1
C: 2
D: -2

Answer 1

1. C
2. A
3. D
4. B
5. C
6. B
7. B
8. B

Answer 2

Answer:

Part 1. Option C

Part 2. Option A

Part 3. Option D

Part 4. Option B

Part 5. Option C

Part 6. Option B

Part 7. Option B

Part 8. Option B

Step-by-step explanation:

Part 1)

Let

H------> Henry's current age

J------> Justin's current age

we know that

$H=10J$ ------> equation A

$H+6=4(J+6)$ ------> equation B

the answer is the option C

Part 2)

we know that

The y-intercept is the value of y when the value of x is equal to zero

In the equation

$3x=6-\frac{1}{3}y$

evaluate for $x=0$

$3(0)=6-\frac{1}{3}y$

$6=\frac{1}{3}y$

$y=18$

therefore

the equation $3x=6-\frac{1}{3}y$ is the solution

Part 3) we know that

The formula to calculate the midpoint is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

Find the x-coordinate of the ordered pair

$1=(-2+x2)/2\\2=-2+x2\\x2=4$

Find the y-coordinate of the ordered pair

$0=(3+y2)/2\\0=3+y2\\y2=-3$

the endpoint is $(4,-3)$

Part 4)  we know that

In this problem the scale factor is equal to $1\frac{1}{2}=1.5$

The perimeter on the photocopies is equal to the perimeter on a sheet of paper multiplied by the scale factor

so

$60*1.5=90\ cm$

Part 5)   we know that

The Triangle Inequality Theorem.states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

Let

c------> the length of the third side

$6+9>c$ ------> $15>c$ ------> $c<15$

$6+c>9$ -----> $c>3$

the answer is the option C $13$

Part 6) we know that

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

$A(45,76)\\B(76,76)$  

substitute the values

$d=\sqrt{(76-76)^{2}+(76-45)^{2}}$

$d=\sqrt{0^{2}+(31)^{2}}$

$d=31\ units$

Part 7)  we know that

Line graphs provide an excellent way to map independent and dependent variables that are both quantitative.

Scatter plots are similar to line graphs in that they start with mapping quantitative data points. The difference is that with a scatter plot, the decision is made that the individual points should not be connected directly together with a line but, instead express a trend.

The cans of drinks sold each day in the snack bar should be graphed using a scatter plot instead of a line graph

Part 8) we know that

If a ordered pair lies on the line

then

the ordered pair must be satisfy the equation of the line

Substitute the values of the ordered pair in the equation

$2x+y=9$ ------> $2(5)+k=9$ -----> $k=9-10=-1$