9th Grade Math Ch. 7 & 8

Consider the system of equations

3x + 4y = 0

-3x +-4y = 2

Adding the two equations side-by-side and simplifying yields 0 = 2.

Which of the following can be concluded about the system of equations?

• It has a unique solution (2, 0).

• It has exactly two solutions (2, 0) and (0, 2).

• It has infinitely many solutions.

• It has no solution.

Answer explanation

Since both sides of the equation do not equal each other, this is how you can tell that a problem has no solution.

Tags

CCSS.8.EE.C.8B

Q is between P and M. Given that segment PQ= 3x + 2 and segment QM= 3x+4 and PM= 42. What is the value of x?

• 3

• 1

• 6

• 2

Answer explanation

point P and M create the full line segment since Q is between them. We would add the segments PQ and QM together to get PM. Thus,

3x +2 + 3x + 4 = 42

6x + 6 = 42

6x=42-6

6x=36

x=36/6

x=6

Tags

CCSS.HSG.SRT.B.4

On a number line, the coordinates of A and B are -3 and b, respectively. If the coordinate of the midpoint M of AB is 5, what is the value of b?

• 12

• 15

• 13

• 4

Answer explanation

If you subtract a point from the midpoint you are able to determine the length of that segment. Midpoint(M) - point of segment (A) = AM

Then use the property of midpoints:

AM=1/2(AxB)

[M is the midpoint of AB]

5-(-3) = 1/2(b-(-3)) [Substitution]

8= 1/2 (b+3)

8= 1/2b + 3/2

multiply both sides of the equation by 2

8x2=2(1/2b) + 2(3/2)

16=b + 3

16-3 = b

13 = b

Tags

CCSS.7.NS.A.1C

Refer to the graph above. The shaded region is the solution set of:

• $y\le2x+2$

• $y\ge2x+2$

• $y<2x+2$

• $y>2x+2$

Answer explanation

Locate 2 points on the graph of the line. For example: (-1, 0) & (0,2).

Use these points to figure out the slope of the line. $\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{0-\left(-1\right)}=\frac{2}{1}$
Then, find the point that is your y-intercept, [meaning where the line intersects the y-axis] (0,2) Now we know the equation is y=2x+2.
Since the line is a solid line and not dotted, we know that it is either $\le or\ge$ .
Finally, we try one of the ordered pairs we picked with both types of inequalities.

The only one that works and matches with the shaded region is $y\le2x+2$

Tags

CCSS.HSA.REI.D.12

Points N, M, and P are

• complementary

• collinear

• vertical

• non-collinear

Answer explanation

Points that belong to the same line are collinear.

Tags

CCSS.HSG.CO.A.1

Points K, L, and P are

• Complementary

• collinear

• vertical

• non-collinear

Tags

CCSS.4.G.A.1

Lines KN and PM intersect at what point?

• M

• P

• N

• K

Answer explanation

They try to throw you off here with labeling line PM instead of PN. It is still the entire line as long as it is not referred to as a segment.

Tags

CCSS.4.G.A.1

The lines KL and PM intersect at what point?

• N

• M

• P

• L

Tags

CCSS.HSG.CO.A.1

Another name for   $\angle A$  is

•  $\angle BAO$  

•  $\angle OAB$  
  

•  $\angle LOK$  

•  $\angle AON$  

Tags

CCSS.HSG.CO.C.9

Point O is the vertex of what angle?

• $\angle3$

• $\angle1$

• $\angle2$

• $\angle L$

Tags

CCSS.HSG.CO.A.1

CCSS.HSG.CO.C.9