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3 years ago

A) find an equation for the family of linear functions with slope 2 and sketch several members of the family

1 answer:

3 0

They are asking us to find another 'family' of linear functions. This time, they are asking that 'f(2) = 1' be true for any f(x) in the family. Because we are now provided with a point and no slope, it would be best to use a point-slope form definition. (If we use slope-intercept, we would end up with an unknown intercept and nothing to do about it!) So, our point would be (2,1). The slope will remain as a variable. f(x)−f(x1)=m(x−x1) f(x)−1=m(x−2) f(x)=m(x−2)+1 If you check, x=2, f(x) will always equal 1, so we have found the correct function family that satisfies the given information.They want you to define a 'family' of linear functions and they give you only a slope, so we are going to have a set of functions in the form f(x)=mx+b;m=2 f(x)=2x+b This function, "f(x) = 2x + b," can represent any linear function given some y-intercept 'b', so this will be sufficient for first part of our answer. Then, we are asked to graph a few functions of the family. So, we can choose any values for 'b' that we want and graph these on the xy-plane. I would recommend choosing b values close to 0 for ease of graphing. So, b=1, b=0, and b=-1 should be sufficient (they really are not clear about 'how many'). I assume you know how to graph them, but I would be glad to show you how if you are not certain.

 We know that to meet the requirements of BOTH parts, it has to be a function of slope 2 and value of f(2) = 1. Well, we already have a function that defines the f(2)=1 is true part, and if we substitute m=2 into that family, then we will have a function of slope 2. f(x)=(2)(x−2)+1=2x−4+1=2x−3

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What are two numbers that multiply for 54 and add to give you -3

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9 and -6 multiply to -54 and add to 3

Step-by-step explanation:

when listing the factors of 54, we can find a pair that add to 3

1, 2, 3, 6, 9, 18, 27 and 54

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3 years ago

Help please number 4, 5, 6, and 7

FinnZ [79.3K]

Step-by-step explanation:

4. So, total time traveled is calculated by adding travel times in both directions.

From Detroit to Chicago, Charlie flew 300 miles at 150 miles per hour speed. That means that he traveled:

t1 = s / v1

t1 = 300 miles / 150 miles per hour

t1 = 2 hours

Now, let's do the same for the opposite direction. Since it's the same distance, he again flew 300 miles, but the speed this time was 100 miles per hour:

t2 = s / v2

t2 = 300 miles / 100 miles per hour

t2 = 3 hours

So, total time he traveled was t1 + t2 = 2 hours + 3 hours = 5 hours.

For the trip distance we need to add distances in both directions. We already said that the distance is the same, so the total trip distance is 300 miles + 300 miles = 600 miles.

Displacement shows how far are the ending and the starting point. Since Charlie started from Detroit, flew to Chicago, and then came back to Detroit, his ending point is the same as the starting, so the displacement is 0.

We can calculate average speed by dividing total distance with the total travel time. We already found that the total trip distance was 600 miles, and the total travel time was 5 hours. That means that:

v(average) = s(total) / t (total)

v(average) = 600 miles / 5 hours

v (average) = 120 miles per hour

As for the average velocity, we calculate it by dividing displacement by total travel time. Since the displacement was 0, average velocity will also be 0.

5. From the left graph we see that the object went from 0 to 2 meters (it moved 2 meters) in 1 second. That means that its speed was:

v1 = s1 / t1

v1 = 2 meters / 1 second

v1 = 2m/s

From there, it went from 2 to 4 meters (it moved 2 meters) in the next 4 seconds. That means that its speed, during that interval, was:

v2 = s2 / t2

v2 = 2 meters / 4 seconds

v2 = 0.5 m/s

So, our graph will show, for the first second, velocity of 2m/s, and for the next four seconds, the velocity of 0.5 m/s.

6. Again, when calculating speed, we use the equation:

v = s / t

In this case, the distance (s) is 325 miles and the time (t) is 5 hours. So, the speed will be:

v = 325 miles / 5 hours

v = 65 mph

7. Now, we have the same distance (s) of 325 miles ant the speed (v) of 70 mph. We want know how long will the drive take:

t = s / v

t = 325 miles / 70 mph

t = 4.64 hours.

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3 years ago