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Your Welcome CPhill and Aziz!im glad you both liked it all!

B rackets

O rder

D ivide

M ultiplication

A ddition

S ubtraction

Brackets Order Division Multiplication Addition Subtraction

"Order" means operations like raising to a power.  Because powers are often called exponents, I prefer the mnemonic PEMDAS:

Parentheses Exponents Multiplication Division Addition Subtraction

These indicate the hierarchy of mathematical operations:

Brackets/Parentheses first

Order/Exponents next

Division & Multiplication next (doesn't matter which of these two is done first)

Addition & Subtraction last  (also doesn't matter which of these two is done first)

To turn a fraction into a percentage multiply by 100.

(1/8)*100 = 12.5%

Use the cosine rule in the form cos(A) = (b² + c² - a²)/(2bc)  where a is the side opposite angle A.

That's ok.  Just carry on and enter sqrt(x,y) to get the y'th root of x.

Let's call the number of pounds of caramel needed 'x"..so the final mixture will be (2 + x) lbs.   ...so we have.....

(2lbs) popcorn*(.80 lb) + (x lbs.) caramel*(2.30 lb.) = (2 + x)lbs of mixture * (1.80lb)

1.60 + 2.30x = (2 +x)(1.80)

1.60 + 2.30x = 3.60 + 1.80x  subtract 1.80x and 1.60 from both sides

.50x = 2.00   divide each side by .50

x = 4 lbs of caramel

This is a graph of a function that has some form such as y = x + Asin(Bx - C). The "x" part makes the graph an ever-increasing one........the period here is pi....this can be seen easily...note that a "relative minimum" of the function occurs just to the "left" of the y axis  at (-pi/4) and the next "relative minimum" occurs at (3pi)/4. So (3pi/4) - (-pi/4) = (4pi/4) = pi.

(I believe this is correct.......would any other forum members like to add anything - or make corrections??.....)

(4! + 4/4) * 4 =

(24 + 1) * 4  =

(25) * 4  =

100   !!!

And another thing!

AzizHusain, our "Albert Einstein" came back yesterday!

This is a 30° in the first quadrant ....and since both x and y are positive, it's also a 30° angle in the 3rd quadrant (i.e., 210°)......of course all co-terminal angles (±n2pi) to these will have the value......

Hi, Rosala! Thanks! Glad to see you and everyone else again, too! 

As always, lots of comical images! The education one stood out to me...reminds me of the education system here...it really does need modification...

The last image reminds me of women and STEM (science, tech, engineering, math). That is a powerful quote!!!

Thanks again!!

The slope-intercept form of a line is:  y = mx + b, where m represents the slope and b represents the y-intercept.

For the line   y = 2/3x - 4,  the slope is  2/3.

Any line perpendicular to that line has a slope that is the negative reciprocal of that slope.

The negative reciprocal of  2/3  is  -3/2.

To find the new equation, start with  y = mx + b.

Its slope is  -3/2  and because it passes through the point  (-5, 6) one of its x-values is  -5  and one of its y-values is  6.  Place these values into  y = mx + b:

                                                      6  =  (-3/2)(-5) + b  

Now, solve for b:                             6  =  15/2  +  b  --->   6  =  7.5 + b  -->  b  = -1.5

Place  m = -3/2  and  b = -1.5  into the slope-intercept form to get:  y  =  -3/2x + -1.5

Simplifying:  y  =  -1.5x - 1.5

This requires stoichiometry.

Find the molar mass (g/mol) of Magnesium and Magnesium Oxide by using the periodic table.

Then, simply use dimensional analysis to solve for mass of MgO.

Start with the given information and convert from there. Also, note the mole ratio is 2:2 or 1:1.

0.52g * (mol / # g Mg) * (2 mol MgO / 2 mol O) * ( # g MgO / mol) = ?

To find the period......look at the distance from one of the highest "peaks" to the next one......note that one highest "peak" occurs just before 0 and the next one occurs just before "pi."  So the period appears to be "pi.'  [Note that "peak" isn't strictly a "math" term, but it seems to work OK, here !!!]

It's Graph "C."   The function can be written as ....tan 1/2(x).... where the "1/2" makes the normal period of the tangent graph twice as long......!!!!

This is a graph of the normal sine function "flipped over" with an amplitude of 2 and shifted to the right by pi/2 units. So, since the normal sine graph has x intercepts at 0 ± n2pi and pi ± n2pi, this graph will have x intercepts at pi/2 ± n2pi and [(3 pi)/ 2] ± n2pi ....where n is just an integer

Thx fellas (:

Yes, 70.52° is correct.....!!!

Is the answer 70.52? I just used my calculator and haven't rounded yet.

It doesn't have a horizontal phase shift because a cos graph starts at a maximum at 0 and goes downward to the right.

You have a right triangle and you want to find the size of the angle that is formed by the 7' length and the 21' length. The 7' length is adjacent to the angle while the 21' length is the hypotenuse of the triangle.

Since you have the adjacent side and the hypotenuse, use the cosine because  cos = adj/hyp

cos X  =  7/21    --->   X = invCos (7/21)

Do you want to solve it, as an equation?  2p - 26  = 0

Or, do you want to factor it?