ilorty

For anyone who can't seem to see the LaTeX, here is the picture:

(I plugged it into a latex site and screenshoted it)

But I'm not just here to give you a picture of something you probably already know. 

We need to simplify 3y= 12x-6 until the y is isolated. Thus, we divide by 3:

3y= 12x-6

y = 4x - 2

Therefore, the answer is F

We can graph both lines just to make sure:

And....it looks like they are the same!

:)

EDIT: Sorry for the large pictures  I adjusted the resolution but it did not come out correct...

Let the original price be x. With what we know, we can say:

0.85x = 34

We isolate the "x" by dividing by 0.85:

x = 34/0.85 = $40

We now need to check our work:

40 * 0.85 = 34.

And, we solved the problem in the matter of thirty seconds!

have a lovely discounted dress i got for you:

it's a russian one from the 1717...isn't history super sophisticated?

:)

@OP: I'm not sure why you posted this as off-topic

@guest that answered: I'm not sure if you can see the LaTeX, but \overline{} means "repeating decimal", not fraction. (the command for fraction is \frac{}{} or \dfrac{}{} depending on what size you want it to be)

The answer begins here:

Because my LaTeX is not working, I will do my best to write the fractions and repeating decimals.

We want to convert this to a fraction:

     ––

0.510, which is 0.51010101010101010101010.....

To begin, let's call this fraction "x". Based on what we know:

1000x = 510.10101010...

10x = 5.101010101010...

Subtract one from the other:

990x = 505

Divide by 990:

x = 505/990 = 101/198

:)

You will need to know what "slope intercept" form is to solve these probelems. Basically, they are the equation of a line in this form:

y = [slope]x + [y-intercept]

Therefore, for each line, we need to find the slope and the y-intercept.

Here are a few basic things you need to know before we continue:

What is a slope?

The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run" (change in y divided by change in x).

- Khan Academy

What is the y-intercept?

It is the y coordinate at the point where the line touches the y-axis.

How to tell if a slope is positive or negative?

Found these pictures on quora. The second one is a funny way to remeber:

1)

SLOPE:

To find this, let's find two points on the line: (2, 0) and (0, 3)

                             rise        -3

We see that the  -------- = ----      (AKA the difference of y over difference of x)

                             run         2

Y-INTERCEPT:
 

This is easy. It is on the graph. It basically is where the line touches the y-axis. This is at y = 3

THE EQUATION:

y = -3/2 x + 3

2)

SLOPE:

To find this, let's find two points on the line: (2, 2) and (0, 3)

                             rise        -1

We see that the  -------- = -----      

                             run         2

Y-INTERCEPT:
 

This is at y = 3

THE EQUATION:

y = -1/2 x + 3

3)

SLOPE:

To find this, let's find two points on the line: (3, 3) and (0, 1)

                             rise        3

We see that the  -------- = -----      

                             run         2

Y-INTERCEPT:
 

This is at y = 1

THE EQUATION:

y = 3/2 x + 1

:)

For lines like such to be parallel, the slope (the m) has to be parallel. We first need to arrange all of them into slope intercept form:

y = [slope]x + [y - intercept]

Line 1: y = -1/4 x + 4

already in the right form! Great 👍 

Line 2: x + 4y = 3

Move the "x" to the right side:

4y = 3 - x

4y = -x + 3

Divide by 4

y = -1/4 x + 3/4
 

Line 3: y = -1/2 x - 6

already in the right form! Great 👍

Line 4: y + 1 = -2(x - 5)

Distribute:

y + 1 = -2x + 10

Subtract 1:

y = -2x + 9

We see that the only two lines that have the same slope is line 1 and line 2.

Double check answer with graph:

Instead of circles and whatnot, we can instead call this a "heptagon"

AKA this shape:

Anyways, we can reword this question: How many diagonals / sides does a 7-sided heptagon have?

Sure, you can go draw all the lines. I'll wait for you. But there is a quicker, mathematical way to do it.

We see that there are 7 dots to choose from. From these 7 points, how many more points can we use to choose the second dot? There are 7 - 1 = 8 points (because you can't your original point)

Now, we multiply:

7 x 8 = 56

But, remember, the order does not matter! This means that we need to divide by 2! to cancel out the repeats.

56/2! = 56/2 = 28 diagonals / chords       <------ answer that guest got!

have you finished drawing the lines yet? if i were you, i would not draw 28 lines!

:)

Instead of using words to think about it, let's use variables and numbers!

What the problem is asking is: For what numbers 1 - 100 is n^2 - 1 prime?

First, we need to know what n^2 - 1 is. This is (n-1)(n+1). (Difference of squares?)

We see that for it to be a prime number, n - 1 has to be 1. The only number that this works is 2.

So the answer is 1/100

Guest. Do you understand now?

:)