Ratio and prooprtion
scale:actualdistance=5in:29mi
so
5:29=?:87
5/29=?/87
times both sides by 87
435/29=?
15=?
they would be 15in apart
So for each of the graphs, you basically just have to fill out slope form, which is y=my+b. And to make this equation, you need to find each variable.
First, find the slope. To calculate slope, count the rise (how many units up or down) the line goes from any point to the next immediate point, then the run (how many units left or right.) This should leave you with a fraction, rise/run. For example, on number 3, from labeled points (-5, -4) to (5,2) (double check cause it’s hard to see on my phone, but i think those are the points on 1??) it rises 6 units (-4 to 2) and runs 10 units (-5 to 5). This gives you your rise/run fraction, which is 6/10, simplified to 3/5.
So the slope fills out the m part of the equation. For 3, we found that slope is 3/5, and that fits into the m variable of the slope equation.
This makes it y=3/5x+b.
The last (and considerably less confusing) step is to find b. b is the y-intercept, which is just the point in the graph where the line crosses the y-axis and x=0. On 3, this would be (0,-1) or just -1.
So fill -1 into the b slot of the equation, and you get y=3/5x-1. And thats it!!
Let me know if you still need help on any of the other problems, but I hoped this helped to clear it up!! :)
Answer:
a. 140 in²
Step-by-step explanation:
Find the area of triangle
1/2×10×6 = 30
The area of rectangle
10×11 = 110
Total of area = 30 + 110
= 140 in²
Answer:
Let v(t) be the velocity of the car t hours after 2:00 PM. Then 
. By the Mean Value Theorem, there is a number c such that 
with 
. Since v'(t) is the acceleration at time t, the acceleration c hours after 2:00 PM is exactly 
.
Step-by-step explanation:
The Mean Value Theorem says,
Let be a function that satisfies the following hypotheses:
- f is continuous on the closed interval [a, b].
- f is differentiable on the open interval (a, b).
Then there is a number c in (a, b) such that
Note that the Mean Value Theorem doesn’t tell us what c is. It only tells us that there is at least one number c that will satisfy the conclusion of the theorem.
By assumption, the car’s speed is continuous and differentiable everywhere. This means we can apply the Mean Value Theorem.
Let v(t) be the velocity of the car t hours after 2:00 PM. Then 
and 
(note that 20 minutes is 
of an hour), so the average rate of change of v on the interval ![[0 \:h, \frac{1}{3} \:h]](https://tex.z-dn.net/?f=%5B0%20%5C%3Ah%2C%20%5Cfrac%7B1%7D%7B3%7D%20%5C%3Ah%5D)
is
We know that acceleration is the derivative of speed. So, by the Mean Value Theorem, there is a time c in 
at which .
c is a time time between 2:00 and 2:20 at which the acceleration is .
Answer:
$936
Step-by-step explanation:
10% is just divided by 10 so 9360 divided by 10 is 936
