kitty<3

"Standard form" really depends on what you are referring to. The standard form for conics is very different from that for quadratic equations. For polynomial equations, you would generally write one side of the equation as 0 and the other side as the terms listed in descending order of degree, such as 4x⁴ -3x³ -9x² + 6x + 7 = 0.

Assuming that you refer to linear equations, Standard Form is Ax + By = C, where A and B are integer coefficients, C is an integer constant, and the x and y variables are on the same side of the equation. An example would be: 3x + 4y = 7

To convert slope-intercept form to standard form, you would first multiply both sides of the equation by the least common denominator if there are any fractions. For example, if you start with y = -3/4x + 7/4 you would then multiply both sides by 4:

4y = -3x + 7

Then you would move the x variable so the y and x variables are on the same side of the equation and the constant is isolated:

4y + 3x = 7

Rearranged as:

3x + 4y = 7

*As a note, more specific questions usually receive clearer answers:)

Simplest answer: Use parentheses.

Ex: one-third minus two-fifths would be (1/3) - (2/5) = (-1/15),

And one-third times two-fifths would be (1/3) * (2/5) = (2/15).

You could also change the input on the site calculator to "Fractions" by clicking on the gray word "Scientific" (in the answer box) and selecting "Fractions" from the drop-down menu.

Nice design, Andre! :) My username's coming up a bit funny though...

Assuming you refer to the change of base formula for logarithms:

Most calculators only determine logs with a base of 10. Ex: log₁₀10000  = 4

To determine a log value with a different base, such as log₂8, you would use the change of base formula, which states that:

log_ax = log_bx / log_ba

b in this case could be 10 (or e) to let you find the value on a calculator.

So log₂8

= log₁₀8 / log₁₀2

= 3

*On the website calculator, you could write in log₂8 as log(8,2) and get the same answer:)

Late to the party, as usual~

Thanks, Melody! As I recall, we do like to brighten things up around here . . . you know, with all these people like zegroes around:)

And hey CPhill, maybe you can convince zegroes to lose the "g" from his name. I'm sure he won't mind at all. Then, voilà! Enough zeroes to last you another M years!

You would use arccosine to solve this problem, since you have the cosine and need the angle:

cos(x) = -1/2

x = acos(-1/2)

x = $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\mathtt{\,-\,}}{\frac{{\mathtt{1}}}{{\mathtt{2}}}}\right)} = {\mathtt{120^{\circ}}}$$

* Which is also equal to 2pi/3 radians.

The formula for finding the sum of a polygon's interior angles is 180(n-2), where n is the number of sides/angles.

Thus, for an octagon:

Sum of interior angles = 180(8-2)

= 180(6)

= 1080

Since the 8 angles are congruent, simply divide 1080 by 8 for the measure of each angle:

1080/8 = 135 degrees

Yes, there is:) It is in the top left corner of the site calculator, next to "2nd."

I think Anonymous and Melody were both onto something . . . so I just took the liberty to expand on their reasoning a bit, if they don't mind:)

They both mentioned negative and positive, as "never" has a negative connotation and "always" has a positive connotation.

So,

"Never forget" would mean that something was such a horrible experience that you could not erase it from your mind (negative), while "always remember" would mean that something was such a good experience that you believe your memory has engraved it in your mind until the end of time.

So while both essentially mean that your brain has stored the memory, they would correspond to different emotions.

^That's my two cents' worth, anyways:)

Aw, thanks Rosala:)

"What's in a name," anyways? :P

Hello Melody! And hello TJM, nice to meet you this way:)

It is always great to drop by and see the forum is busier than ever

The way I interpreted it, the man wants to make a 20% profit on the bag after the 15 discount.

In this case, you would first find what 20% profit on $30 is, and then find what the total would be before the 15% discount:

So:

20% * $30 + $30

= 1.2 * 30

= 36

So the man would need to sell the bag for a final price of $36, after the discount.

Therefore, we now need to find the price of the bag before the 15% discount, which we can call x:

x - 0.15x = 36

0.85 x = 36

x =42.35

So he needs to sell it for $42.35 before the discount, or $36 after the discount.

Always welcome! :D

While the cosine of a given angle is used to find the ratio of its opposite side / hypotenuse, the arccosine does the opposite: it finds the measure of an angle from the given ratio of its opposite side / hypotenuse.

For example,  $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}{\left({\mathtt{45}}^\circ\right)} = {\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}$$

So $$\underset{\,\,\,\,^{\textcolor[rgb]{0.66,0.66,0.66}{360^\circ}}}{{cos}}^{\!\!\mathtt{-1}}{\left({\frac{{\sqrt{{\mathtt{2}}}}}{{\mathtt{2}}}}\right)} = {\mathtt{45}}$$

So if you had the lengths of the opposite side and the hypotenuse for a right triangle, you would use arccosine to find the measure of the angle.