74 + 35 + 16 + 45 =
= 74 + 16 + 35 + 45
= 70 + 4 + 10 + 6 + 30 + 5 + 40 + 5
= 70 + 10 + 4 + 6 + 30 + 40 + 5 + 5
= 80 + 10 + 70 + 10
= 80 + 10 + 10 + 70
= 100 + 70
= 170
• The following formula can be used to find the slope of a line:
These points are on the line:
Given the following points:
Then, you can set up that:
Therefore, substituting values into the formula and evaluating, you get:
• As you can notice, the slope is negative. Therefore, you can determine that it is decreasing.
Therefore, the answers are:
• Slope of the line:
• It is decreasing.
18. The shape is only shifted to a different location and orientation but remains the same size so this is congruent.
19 and 20 are both scaled to a different size so they are both similar.
We would know if a system is consistent, inconsistent, or coincident depending on the number of solutions it has. If it has only one solution, the system is said to be consistent. If it has none, the system is inconsistent; and if the system has an infinite number of solutions, it is said to be consistent and coincident.
Let's solve the system to know how many solutions it has.
Notice that dividing the second equation by 2 would yield the exact same equation as 1. This would therefore allow us to conclude that AN INFINITE NUMBER of pairs of (x,y) coordinates would satisfy the system. Thus, the system is said to be
consistent and coincident.