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No, last time was a continuous fraction. unless the process of solving this integral is the same as the continuous fraction integral

I am sure this exact same one was looked at recently - is this a repeat post, I mean did you post it last time too?

Oh!! That's a good way of explaining it 

sin (S) = opposite / hypotenuse

sin (S) = QR / 68

To find the length of QR, we can use the Pythagorean theorem.

QR² + 60² = 68²

QR² = 68² - 60²

QR = \(\sqrt{68^2-60^2}=\sqrt{4624-3600}=\sqrt{1024}=32\)

So..

sin (S) = \(\frac{32}{68}=\frac{8}{17}\)     :)

I am assuming this is annual complex interest, in which, once a year, x% of the money already in the account is deposited in the account. $70*1.1³(10% increase as a decimal) = $93.17 after 3 years.

4 possibilities:

a) \(2x+3x-5+9x+\frac{1}{2}=?\)

Combine like terms --> \(14x-4.5=?\)

b)\(2(x+3x-5+9x+\frac{1}{2})=?\)

Distribute --> \(2x+6x-10+18x+1=?\)

Cobine like terms --> \(26x-9=?\)

c)\(\frac{2x+3x-5+9x+1}{2}=?\)

Combine like terms: ​\(\frac{14x-4}{2}=?\)

Simplify: \(7x-2=?\)

d)\(2(\frac{x+3x-5+9x+1}{2})=?\)

The 2 as the coefficient cancel out with the 2 in the denominator: \(x+3x-5+9x+1=?\)

Combine like terms:\(13x-4=?\)

Really hope one of those answered your question!

\(\frac{1}{7} + \frac{1}{3}+\frac{1}{4} =\frac{12}{84}+\frac{28}{84}+\frac{21}{84}= \frac{12+28+21}{84} = \frac{61}{84}\)

I used 84 as the denominator, as it was the Least Common Denominator of 7, 3, and 4.

Thanks Asad :)

Don't forget: it's negative. If one of the parts of a fraction is negative, the entire fraction is negative. It acts like an exclusive-or gate: If one or the other is true, then the output is true, but if the inputs are the same, the output is false.

Please make it more specific as to what the fraction is next time. The LaTeX way to write a fraction is \frac{numerator}{denominator}

So, your equation is: \(\frac{2}{5}x+ 4 = 10\)

Isolate x and its coefficient by subtracting 4: \(\frac{2}{5}x=6\)

Divide each side of the equation by  \(\frac{2}{5}\)(The coefficient of x) [or multiply by the reciprocal of the coefficient of x]:

\(x = \frac{6}{\frac{2}{5}} = \frac{6*5}{2} = \frac{30}{2} = 15\)

x = 15

If the focus  is   ( -2 , 4)   and the directrix  is y = 2, the vertex  is ( -2, 3)

So....p  = 1      and we have the form

4p(y - 3) =   ( x + 2)^2

4(y - 3)  =   (x + 2)^2

y - 3  =  (1/4)(x + 2)^2

y = (1/4) ( x + 2)^2 +  3

That is the quadratic formula, used in finding the x intercepts of a parabola. The two answers come from the +- in the equation being -b+-sqrt(...). 

.666... repeating. It's equal to -2/3, which is the fraction in simplest form.

sixty one million two hundred and fifty thousand

1)

Multiply 10 by f and bring it into the numerator. The expression is now \(\frac{6+10f}{f}=\frac{2(3+5f)}{f}\)

2)

Multiply 5a by b, add to numerator: \(\frac{5ab+2a}{b}\)

An alternate way of writing that: \(\frac{a(5b+2)}{b}\)

(Since both terms in the numerator have the letter a, you can divide each by a, and place them in parenthesis, then multiply the sum by a.)

@Melody: Was that a sufficient explanation?

The center  is  ( -1, 1 )    and the radius  is   3

So....the equation is

(x + 1)^2   + ( y - 1)^2  =  9

x^2 + 2x + 1  + y^2 - 2y + 1  = 9

x^2 + y^2 + 2x - 2y - 7  =  0

I assume that you like math and coding. += has no place in math, but since you are using the letter m, I can tell you are asking for a slope. So the slope / 3 += 13. I am assuming you might be in calculus and are attempting to take a derivative? This would mean that x is quadratic.

That's a big increase in slope. It appears to be 39. This would mean that the equation is \(y = 19.5 x^2 + bx + c\)

If, however, you are not, and the + just got in there randomly: simply multiply each side by 3.

The Pythagorean Theorem states that for any right triangle with side lengths a and b, the length of the hypotenuse, c, can be solved by using this equation:

a² + b² = c².

This is also represented as \(hypotenuse = \sqrt{leg1^2 + leg2^2}\)

If you are going to be making art with it, what they want you to do is draw a bunch of right triangles.

Good luck!

Simplified: \(w^2 - 4w+4\)

To simplify: first, multiply the first number in the parenthesis by itself.

Then, multiply the first number by the second number, then double it.

Finally, multiply the last number by itself.

Add them all together, that is your answer.

If I'm not being clear, I'm 110% sure Melody could explain this better than me.

y=−1/12x^2−2x−1      factor as

y =  (-1/12) [ x^2  + 24x  + 12 ]             complete the square on x

y = ( -1/12) [ x^2  +  24x  +  144  + 12  - 144]

y = (-1/12) [ ( x + 12)^2  -  132 ]

y =  (-1/12) (x + 12)^2  +  11

(y - 11)  = (-1/12) (x + 12)^2

The vertex is   ( -12, 11)   and this parabola opens downward

And  4p  = -1/12    →  p  =  - 1 / 48

So....the coordinates of the focus are  ( -12 - 1/48, 11)   =  ( - 577/48, 11 )

The square root of a number x is a number that, when multiplied by itself, or squared, is equal to x.

To put it another way: Assume you have a square with area x. The square root of the area is equal to any of the side lengths.

The mode of a data set has absolutely no relevance to a box plot. A box plot looks like this:

|(minimum value)---------|(lower quartile/Q1)=====|(median)=======|(upper quartile/Q3)----------------------|(maximum value)

Fast facts about a box plot:

IQR (inter-quartile range) = Q3 - Q1

Range = Maximum - Minimum

Lower half of the data is in between the minimum and the median

The upper half of the data is between the median and the maximum

The middle half of the data is in between Q1 and Q3.

a)

Since the October price was a 20% increase over the price in September, the price in October is 120% of that in September.

To get the multiplier to get to the September price from the October price, we need to divide the current price by the price difference. So, solve this: \({1.5}\div{1.2}\)

b was cut off. What was the rest of the question?

First, we take the minimum and maximum value of the data:

Maximum of the data set = 20.42

Minimum of the data set = 4.75

Then, divide by the number of units you have in that direction to use.

After that, round the result up to the nearest fairly composite number.

^ Only use this method if you can abbreviate the graph, by skipping intervals. ^

If you can't skip intervals, replace the minimum value with 0. Then, divide by the number of units you can use in that direction.

Take the result and round up to the nearest fairly composite number.

Of course, you don't want the intervals to be too out of scale, so using the scale of the other axis is a good place to start.

There are 2 possibilities I see here. I'll solve both.

a) \(2(2-\frac{x}{5})+1\)

First, distribute the parenthesis. That is, multiply the number before the parenthesis by each term inside it 2 and \(\frac{x}{5}\)

We get: \((4-\frac{2x}{5})+1\)

We can now discard the parenthesis and combine like terms: \(5 - \frac{2x}{5}\)

If we want to get a single fraction, we can multiply the 5 by the denominator, placing the value on top as we do so: \(\frac{25-x}{5}\)

b) \(2(\frac{2-x}{5})-1\)

Let's start, again, by distributing the coefficient of the parenthesis: \(\frac{4-2x}{5}-1\)

Now, we put the -1 into the numerator: \(\frac{4-2x-5}{5}\)

Combining like terms, we get: ​\(\frac{-1-2x}{5}\)

Does that help?