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3 years ago

When writing linear equations, how do you determine which form of a line to use?

2 answers:

6 0

When given two points, use point-slope form
When given a point and the intercept, use slope-intercept form.
When given a point and the slope, use point slope form.

mojhsa [17]3 years ago

4 0

If it does not specifically specify, the slope intercept form is usually acceptable. (y = mx + b).

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a system of equations is shown below: y=3x-7 and y=2x+7. what is the solution to the system of equations?

castortr0y [4]

A system of equations means that both equations need to be true in the same time.
Since y is equal with 3x-7 and 2x+7 then those must be equal with eachother.
3x-7=2x+7
3x-2x=7+7
X=14
Now that we know x use any given equation of y and substitute x with 14
Y=3•14-7=35
Solution: x=14, y=35

7 0

3 years ago

Find the measure of CD in parallelogram ABCD.

Alchen [17]

Answer:

A =16

Step-by-step explanation:

Since its a Parallelogram and in a parallelogram the opposite side are always equal. AB and CD are opposite sides of a parallelogram. Hence CD =16

6 0

2 years ago

Ali is moving into her new apartment. Her bedroom on the floor plan is 3 inches. If the floor plan uses a scale of 1 inch = 4 fe

spayn [35]

Answer:

12 feet.

Step-by-step explanation:

1 inch = 4 feet.

Multiply 3 by 4.

3×4=12

I multiplied 3 by 4 because 1-inch equals 4 feet, which means if we multiply both terms by 3, you will get 3 inch = 12 feet.

Hope this helps!

3 0

2 years ago

Francine just created a music video and uploaded it to YouTube. She is keeping track of the number of hits (visits) to her video

dsp73

The base, 1.74, represents 100% of the original number of hits plus the percent increase, 0.74=74%, daily.

8 0

3 years ago

Read 2 more answers

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