Problem: A bus company took a tour bus on the ferry when there were 30 people aboard. The ferry charged the bus company $180. The following week, the bus had 50 people on board and the ferry charged them $220. How much is the "base rate" for the empty bus? How much does each person cost? Show this using y = mx + b form.
Solution:
Let x = the number of people on the bus
Let y = the total cost for the bus with its passengers to use the ferry.
Then, when there are 30 people on the bus (x = 30), the cost was $180 (y = 180). This means the point (x, y) = (30, 180).
Also, when there were 50 people on the bus, the cost was $220. So that is the point (50, 220).
You see - we have two points and so we can write the equation of a line that goes through those points. The first thing we have to do is find the slope.
The slope of the line joining two points is the rise divided by the run. That means
m = (y2 - y1) / (x2 - x1)
So we put in the values of (30, 180) and (50, 220):
m = (220 - 180) / (50 - 30)
m = 40 / 20
m = 2.
The slope is 2. Now we can write it in the form y = mx + b, using 2 for m:
y = 2x + b.
This equation connects both points, so that means it goes through those points. We want to know "b" next, so we can now substitute in either point for the x and the y. I will substitute in x = 50 and y = 220:
220 = 2(50) + b
220 = 100 + b
b + 100 = 220
b = 120.
Now I know the b and the m, so I can finally write the full y=mx + b form of the equation:
y = 2x + 120.
For the other questions, I can look at the equation I got. The y-intercept (b value) is $120. That means that we are adding $120 on to the price all the time. That's the price for the empty bus. The 2x means to multiply the number of people by two and add this to the $120. So each person is $2.
Here's an example: if you had just 10 people on the bus, you'd pay $120 for the empty bus and $2 for each person. That's $20 for the people and $120 for the bus. That total is $140. Let's see if (10, 140) works in the equation we got:
y = 2x + 120
140 ?=? 2(10) + 120
140 ?=? 20 + 120
yes. 140 = 140. It does work.
Now you try it with your question.
Answer:
Total number of people in the concert
= 186
Step-by-step explanation:
There are 80 people in level 2
Then in level one
The dimensions of the room are 62 feet by 31 feet.
15 people fit in a 3 feet by 6 feet space.
Area of the room= 62*31= 1922 feet²
area of 15 people space= 3*6= 18 feet²
To know how many 15 people we get in the 2nd level
=Area of room/area of 15 people space
= 1922/18
= 106.77
= 106 (we round down because this is human being.)
Total number of people in the concert
= 106+80
= 186
Answer:
Domain {x : x > 1}
Range {y : y ∈ R}
Vertical asymptote x = 0
x-intercept (1, 0)
End behavior consistent
Graph attached down
Step-by-step explanation:
Let us study the equation:
∵ y = log(x)
→ It is a logarithmic function, so no negative values for x
∴ Its domain is {x : x > 1}
∴ Its range is {y : y ∈ R}, where R is the set of the real numbers
→ An asymptote is a line that a curve approaches, but never touches
∵ x can not be zero
∴ It has a vertical asymptote whose equation is x = 0
→ x-intercept means values of x at y = 0, y-intercept means
values of y at x = 0
∵ x can not be zero
∴ There is no y-intercept
∵ y can be zero
∴ The x-intercept is (1, 0)
→ The end behavior of the parent function is consistent.
As x approaches infinity, the y-values slowly get larger,
approaching infinity
∵ y = log(x) is a parent function
∴ The end behavior is consistent
→ The graph is attached down
Answer:
The lines are parallel, and their slope is 1/3.
Step-by-step explanation:
Slope = Rise/Run
Rise tells us the distance between the two points on the y-axis and the run tells us the distance between the two points on the x-axis.
For Line 1, the rise is one unit and the run is three units. Therefore, the slope is 1/3.
For Line 2, the rise is one unit and the run is three units. Therefore, the slope is also 1/3.
Hope this helps!
The answer is 78/7 which is 11 1/7
