CPhill

Each card costs $3........

So

21 / 3   = 7 cards

5(-2x+4)-3x=2(2x+20)+14    simplify both sides

-10x + 20 - 3x = 4x + 40 + 14

-13x + 20  = 4x + 54      add 13x to both sides, subtract 54 from both sides

- 34  =  17x         divide both sides by 17

-2  = x

[ 7 + 1/2] / 3

[15/2]  /  [3]   =

[15/2 ] / [ 3/1 ] =

[15/2] * [1/3]  =

15/6  =  5/2  = 2 + 1/2  =  2.5  inches wide

w = 3t  + 11   subtract 11 from both sides

w - 11  = 3t    divide both sides by 3

[ w - 11 ]  / 3   = t

v

Yes....in general, "A"  is a diffferent variable than "a."  This creates confusion if the cases are mixed......

It's already in standard form.......

In scientific notation, we would have

9.3 x 10⁷       

(2cos2x)/sin2x=cotx-tanx

[ 2(cos^2x - sin^2x)] /  [2sinxcosx]  =

cos^2x / [ sinx cosx ]  -  sin^2x / [ sinx cosx]  =

cosx / sinx   -  sinx / cosx  =

cotx - tanx

Very nice, Will85237.....!!!!!

5 points from me.....!!!!

We can solve this with a proportion  by equating ounces and volumes of cylinders :

32 / [pi* (2)^2 * 5]  = x / [pi * (1.5)^2 * 8]    where x is the unknown no. of ounces

32 / 20  = x / 18     cross-multiply

18 * 32  = 20 * x

x = 32 * 18 / 20  = 28.8 ounces

Here is the graph of (2) .....the intercepts should be pretty clear.....

https://www.desmos.com/calculator/dg5hplo4jf

For (2),  the vertical intercept occurs at (0, -10).....this means that it must have cost $10 to make the brownies, so, if she doesn't sell any, she loses $10.......the horizontal intercept at (20,0) means that she will have to sell 20 brownies at .50 each to cover her expenses [ the $10 ]

For (3), you have the intercepts correct......(0, 11000) means that, if the costumes were free, they would "sell" all 11000 in stock.....[not realistic]

(55, 0)   means that if they price each costume at $55, they won't sell any......!!!!!