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Vera_Pavlovna [14]
3 years ago
10

Given f(x) =7x-4, find the average rate of change over from x=2 to x=4.

Mathematics
1 answer:
yuradex [85]3 years ago
6 0

Answer:

m = (f(4) - f(2)) / (4 - 2)

m = (24 - 10) / (4 - 2)

m = 14 / 2

m = 7

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Can some please help and explain your steps thanks
boyakko [2]
For A you would have to convert from that equation to the slope-intercept form of the equation. To do that, first add 2x to both sides, because you want to have x on the right side of the equation. And that's it! That gives you 4y = 2x + 8. And from that equation you can identify the slope (2) and the y-int (8)

For B, the same thing. Converting to slope-intercept form, just with an extra step. First, you would subtract 1y from both sides to move it to the left of the equal sign, since that's where it needs to be for slope-intercept form. That gives you -1y + 7 = -x. Don't worry about the negatives for now. Next, subtract 7 from both sides to get y by itself on the left (because that's how it is in slope-intercept form) which gives you -1y = -x - 7. Then, because you can't have negative variables, divide both sides by negative 1 (a negative divided by a negative equals a positive), to equal y = x + 7. (I've attached a picture showing my steps if the words are too confusing)

For C, you need to find the slope first, then use the slope to find the y-intercept. So subtract. (I've shown in the picture) that equals -8 over 4 which simplifies to -2. So -2 is the slope! Now to find the y-intercept, plug in an ordered pair from the problem (doesn't matter which one) and the slope to find the y-intercept (b). I'm just going to use (-2, 5). So plug in the y from the pair (5) and the slope (-2) and the x from the pair (-2) into the slope-intercept equation to equal 5 = -2(-2) + b. Since you don't know b (the y-intercept) leave it blank and solve like a one step equation! (steps in the picture). And there you have it, the slope is -2 and the y-int is 1!

For D, it's like C, but you dont have the chart. Use subtraction to find the slope. Change in y over change in x (which means subtract the y values and divide them by the difference in x values). So. You'd do 0 - 3 over -6 - 3 which equals -3 over -9, which simplifies to 1/3. And that's your slope! So to find the y-int just do the same thing you did in the last problem, plug in an ordered pair and the slope into the slope-intercept equation and solve as a one step equation (steps in picture). And there you have it, the slope which is 1/3, and the y-int which is 2.

6 0
3 years ago
(4.0), (1,3)<br> Write in slope intercept form with steps
maxonik [38]
Slope:0
y-intercept: (0,5.2)

7 0
3 years ago
Two classes have a total of 60 students. The students need to make teams of 8t
Step2247 [10]

Answer:

We have 7 complete teams

Step-by-step explanation:

Here, we have students preparing to make a team of 8 students per team. We now want to know how many complete teams they can make if they are a total of 60;

To get this, we need the multiples of 8;

we have;

8, 16 , 24 , 32, 40 , 48 , 56

So breaking it in 8s, we have;

8 8 8 8 8 8 8

We have 7 8s;

So there would be four left overs

3 0
3 years ago
The probability that a household owns a pet is 0. 55. Suppose there are 5 houses on a block. Assuming each household is independ
Alexandra [31]

If the probability that a household owns a pet is 0.55 then the probability that all households will have pets is equal to 0.0503.

Given that the probability that a household owns a pet is 0.55 and there are 5 houses on a block.

We are required to calculate the probability that all the five households will have pets.

Probability is basicallly the chance of happening an event among all the events possible. It cannot be negative.

Binomial probability distribution is basically the probability calculations but in different combinations.

In this we have to calculate the probability that all the houses will have the pets then the probability that all five households will have pets is equal to 5C_{5}(0.55)^{5} (1-0.55)^{0}

=1(0.0503)(0.45)^{0}

=1*0.0503*1

=0.0503

Hence the probability that all the five households will have pets is equal to 0.0503.

Learn more about probability at brainly.com/question/24756209

#SPJ4

6 0
1 year ago
After the fraction x plus 1 all over 2 minus the fraction x plus 2 all over 3 x have been combined using the least common denomi
RoseWind [281]

If I've read this correctly, it looks like this.

\dfrac{(x + 1)}{2 - \dfrac{(x + 2)}{3x}}

If that is correct, then the first step is to put the top part of the denominator over 3x

\dfrac{(x + 1)}{\dfrac{6x - (x + 2)}{3x}} = \dfrac{(x + 1)}{\dfrac{5x -2}{3x}}

The next part is to flip a three tier fraction. I'm afraid I have to show what happens. My latex is not that strong.

What you get is

\dfrac{3x*(x + 1)}{(5x - 2)}

This is just about your final answer. You could write it as

\dfrac{3x^2 + 3x}{(5x - 2)}

6 0
3 years ago
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