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Paha777 [63]
2 years ago
7

These two lines are parallel. Write an equation for each. Either upload a picture or type in the answer box.

Mathematics
2 answers:
yaroslaw [1]2 years ago
7 0

Answer:

(top line) y=4/5x + 0, (bottom line) y=4/5-0.32

Step-by-step explanation:

so take the equation y=mx+b

b is the y intercept, which is where the line crosses (0,b)

the m is the slope, which is rise/run.

If the lines are parallel, the slopes are the same, just different y intercept

scoray [572]2 years ago
7 0

Step-by-step explanation:

the usual equation for a line is

y = ax + b

a is the slope. it is always the factor of x and is expressed as ratio y/x. this indicates how many units y changes, when x changes a certain amount of units when moving from one point to another.

(0, -3.2) is one point. and (4, 0) is another.

x changes by +4 (from 0 to 4).

y changes by +3.2 (from -3.2 to 0)

the slope is therefore

3.2/4 = 32/10 / 4 = 32/40 = 4/5

b is the y-intercept. that is the point, where the line crosses the y-axis (the y value when x = 0).

the given point specifies this already.

so, the line equation of the lower line is

y = (4/5)x - 3.2 or (4/5)x - 32/10 or (4/5)x - 16/5

the upper line is parallel, so the slope is the same.

and what is b, the y-intercept ? we see that the line goes directly through the origin (0, 0). so, b = 0.

the line equation of the upper line is

y = (4/5)x

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Henry's baseball practice starts at 2:00, will last an hour and forty-five minutes, and will end at 3:45.

Step-by-step explanation:

2 + 1 = 3

3  + 45 minutes = 3 : 45

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3 years ago
Ms. Willer wanted to donate 27 cans of food to each of 8 food banks each of food to each of 8 food banks each of the 23 students
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3 years ago
Does anyone know how to simplify this expression? I know it has to do with properties of summation and special summation rules b
dusya [7]
<h3>Answer:     -n/(n+1)</h3>

============================================================

Explanation:

Let's expand this out up to say n = 6 terms

I'll write the summation in such a way that each (1/(k+1) - 1/k) grouping will get its own row. Each row has the same value of k.

If we plug in k = 1 through k = 6, but not evaluate just yet, we will have this:

1/(1+1) - 1/1

1/(2+1) - 1/2

1/(3+1) - 1/3

1/(4+1) - 1/4

1/(5+1) - 1/5

1/(6+1) - 1/6

All I've done so far is replace k with 1 through 6. Again, each row represents a different k value. Each row has the general format 1/(k+1)-1/k.

Let's simplify everything in the first column.

So the (1+1) turns into 2, the (2+1) turns into 3, and so on.

Doing that leads to...

1/2 - 1/1

1/3 - 1/2

1/4 - 1/3

1/5 - 1/4

1/6 - 1/5

1/7 - 1/6

Then note how we have the cancellations shown in the diagram below. The color coding shows how the terms pair up to cancel out. By "cancel out", I mean specifically that the fractions add up to 0. Eg: 1/2 + (-1/2) = 0.

Nearly everything cancels out. The only things left after the dust settles is the -1/1 in the first row and the 1/7 in the bottom row. This evaluates to 1/7-1/1 = 1/7 - 7/7 = (1-7)/1 = -6/7

If you were to try this with n = 7, then you should find that again nearly everything cancels but the fractions -1/1 and 1/8. Then 1/8 - 1/1 = -7/8.

For n = 8, you should end up with 1/9 - 1/1 = -8/9.

You can probably see the pattern.

A conjecture is that the answer is -n/(n+1). The general proof of this isn't too tricky. Simply follow the same ideas as mentioned above. Expand out a few terms and see how things cancel out. You'll find that everything cancels except for the -1/1 in the first row and the 1/(n+1) just one term before the very end. Then we can say:

1/(n+1) - 1/1

1/(n+1) - (n+1)/(n+1)

(1-(n+1))/(n+1)

(1-n-1)/(n+1)

-n/(n+1)

If we tried n = 6, then we find,

-n/(n+1) = -6/(6+1) = -6/7

which was the result we found earlier when we added the first n = 6 terms of this series. Trying out n = 7 should lead to -n/(n+1) = -7/8, and so on.

3 0
3 years ago
Given the parallelogram
Mashutka [201]

Answer: 55.

Step-by-step explanation:R = 55. You put all the angles equal to 180 and then get the variable by itself.

4 0
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