To graph a line, first put the equation into slope-intercept form:
. So what can we do with our equation,
, to get it into slope-intercept form? If we divide both sides of the equation by
, we get
. This gives us several pieces of information. Remember that the
constant term, the one without a variable, tells us the y-coordinate of the y-intercept. The y-intercept is where the graph crosses the x-axis. So here, the constant term is 2; so the y-intercept is
(0,2). That is one of the points. Now what does the slope represent? It is rise/run. Here it is -1/3. So from our y-intercept, (0,2), we can go down one unit and to the right 3 units. This new point is
(3,1). From that point we can apply that again: go down 1 and right 3 units to get another point,
(6,0).
Answer:
Step-by-step explanation:
This is a translation up and right.
<u>Compare the coordinates of corresponding points:</u>
<u>The difference of coordinates:</u>
- -2 - (-5) = 3
- 3 - (-3) = 6
<u>The rule:</u>
The triangle height = 5√3 cm
So....the area =
(1/2) base x height = (1/2) (5) (5√3) = (25/2)√3
≈ 21.7 cm
Answer:
0.55
Step-by-step explanation:
The right-hand column of the table gives us the probabilities of the probability function. We know from elementary probability theory that the "probability" of any event(s) happening would be from 0 to 1 inclusive.
The total probability of all events would add up to 1. So, we look at the probabilities given for each even, x, and add them:
0.29 + 0.09 + 0.03 + 0.04 = 0.45
All of these probabilities and the probability at x = 2 (the unknown) would add up to 1, so we can say:
0.45 + probability (x = 2) = 1
Probability at x = 2 = 1 - 0.45 = 0.55
Answer:
6 hours
Step-by-step explanation:
she played game 25% of the time.
25% of 30 hours is 7.5 hours
she researched 5% of the time.
5% of 30 hours is 1.5 hours
so she played game 7.5-1.5=6 more hours than she researched
