How To Solve Systems of Inequalities Graphically
1) Write the inequality in slope-intercept form or in the form
y
=
m
x
+
b
y=mx+b
.
For example, if asked to solve
x
+
y
≤
10
x+y≤10
, we first re-write as
y
≤
−
x
+
10
y≤−x+10
.
2) Temporarily exchange the given inequality symbol (in this case
≤
≤
) for just equal symbol. In doing so, you can treat the inequality like an equation. BUT DO NOT forget to replace the equal symbol with the original inequality symbol at the END of the problem!
So,
y
≤
−
x
+
10
y≤−x+10
becomes
y
=
−
x
+
10
y=−x+10
for the moment.
3) Graph the line found in step 2. This will form the "boundary" of the inequality -- on one side of the line the condition will be true, on the other side it will not. Review how to graph a line here.
4) Revisit the inequality we found before as
y
≤
−
x
+
10
y≤−x+10
. Notice that it is true when y is less than or equal to. In step 3 we plotted the line (the equal-to case), so now we need to account for the less-than case. Since y is less than a particular value on the low-side of the axis, we will shade the region below the line to indicate that the inequality is true for all points below the line:
5) Verify. Plug in a point not on the line, like (0,0). Verify that the inequality holds. In this case, that means
0
≤
−
0
+
10
0≤−0+10
, which is clearly true. We have shaded the correct side of the line.
If each of them cost $29.95 and you but four of them the formula you use is
29.95 x 4 = 119.80
Answer:
B
Step-by-step explanation:
To find the answer, translate each point and then use the process of elimination.
For the first point, the coordinates are (-4, -2). The -4 is x and the -2 is y. Translations up and down relate to the y value, while translations left and right relate to x. To translate up 4 units, add 4 to the y value of the coordinate. -2 + 4 is 2, so the y coordinate of the first point will be 2. That eliminated A and D.
For the second point, translate up 4 units (-5 + 4) and you get -1. So the y value of the second point will be -1. In option C, it is positive 1. So that leaves only B.
<span>In order to find the expected value, we must calculate the average returns on each ticket. So After doing this, we can say that each ticket will cost $6.50. I hope this is what you were looking for </span>
