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1)
\(\text{Find amounts of each reactant in moles}\\ 2.50g\;H_2*\frac{1mol\;H_2}{2.016g\;H_2}=1.24\;mol\;H_2\\ 30.0L\;CO_2*\frac{1mol\;CO}{22.4L\;CO}=1.34\;mol\;CO\\ \text{Find amount of H}_2\text{ that fully reacts with CO or vice versa}\\ 1.34mol\;CO*\frac{2mol\;H_2}{1mol\;CO}*\frac{2.016g\;H_2}{1mol\;H_2}=5.36\;g\;H_2\\ \text{5.36g of hydrogen is needed to fully react with 30.0L of CO, making hydrogen the limiting reagent} \)

2)
\(2.50g\;H_2*\frac{1mol\;H_2}{2.016g\;H_2}*\frac{1mol\;CH_3OH}{2mol\;H_2}*\frac{32.042g\;CH_3OH}{1mol\;CH_3OH}=19.9g\;CH_3OH\)

3)
\(2.50g\;H_2*\frac{1mol\;H_2}{2.016g\;H_2}*\frac{1mol\;CO}{2mol\;H_2}=0.620\;mol\;CO\\ 1.34mol\;CO-0.620mol\;CO=0.72mol\;CO\)

20n  must be the amount of money that he has

Thus    12, 14  and 15    must divide 20 n    evenly

Find the LCM of  (12, 14, 15)  

12 = 2^2 * 3

14= 2 * 7

15   = 5 * 3

So....the LCM is   2^2 * 7 * 3 * 5 =  420

So....

420 = 20n

420 /20  = n

21 = n

Looks like you are correct CU ....!!!!

b.) (2x^3 - 5x^2 + 3x - 1)/(x - 3)

Since we don't have any missing powers in the dividend polynomial......I'm going to use synthetic division to find the residual polynomial and remainder

The divisor is     x - 3 = 0  ⇒   x = 3

So we have

3 [    2        - 5         3          -1 ]

                    6         3         18

       _____________________

       2           1        6         17

The remaining polynomial (quotient)  is    2x^2   + x   + 6

The remainder is  17

Checking  x = 3    with the Remainder Theorem...we get

2(3)^3  - 5(3)^2   + 3(3)  - 1   =

54  - 45 + 9 - 1   =

63   -  46  =

17......just as we hoped for   !!!!

Please anyone help??????

a.) (x^4 + 10x + 5)/(x + 2)

Gotta' be careful to account for missing powers, GM.....so we have

              x^3                   - 2x^2    +   4x    + 2

x + 2   [  x^4    + 0 x^3   +  0x^2  +  10x   + 5 ]

              x^4    + 2x^3

           ________________________________

                         -2x^3  + 0 x ^2

                        -2x^3  -  4x^2

                      ___________________________

                                    4x^2   + 10x

                                    4x^2 +    8x

                                   _____________________

                                                2x     +    5

                                                2x     +   4

                                               _____________

                                                              1

Checking the Remainder Theorem  (remember that x + 2 is the divisor....so we are checking  x + 2 = 0 ⇒ x = -2  )

(-2)^4 + 10 (-2) + 5

16 - 20 + 5

21 - 20  =

1

Yep......works right out    !!!

Note that angle ABC  =  124°   because it is an alternate interior angle to the other 124°  angle

And since AB = BC  ...then angle ACB = angle CAB    =  [ 180 - 124] / 2  =  56 / 2  =  28°

And x is an alternate interior angle to angle ACB....so it also measures 28°

THANK YOU

45.5% =45.5 / 100 = 0.455 x 1000/1000 =455/1000 = 91 / 200

I get this many  :

sqrt (n) =  a*sqrt(b) with   a ≥ 10

sqrt (100) =  10sqrt (1)

sqrt (200) = 10sqrt(2)

sqrt (300) = 10sqrt (3)

sqrt (400) = 10sqrt (4)  or   20sqrt(1)

sqrt (500) = 10sqrt(5)

sqrt (121) = 11sqrt(1)

sqrt (242) = 11sqrt(2)

sqrt(363) = 11sqrt(3)

sqrt (484) = 11sqrt(4)   or    22sqrt(1)

sqrt ( 144) = 12sqrt (1)

sqrt (288) = 12sqrt(2)

sqrt (432) = 12 sqrt (3)

sqrt (169) =  13 sqrt (1)

sqrt (338) = 13sqrt(2)

sqrt (196) = 14sqrt(1)

sqrt (392) = 14sqrt (2)

sqrt(225) = 15sqrt (1)

sqrt (450) = 15sqrt(2)

sqrt  (256) = 16sqrt(1)

sqrt (289) = 17sqrt (1)

sqrt ( 324) = 18sqrt(1)

sqrt(361) = 19sqrt(1)

sqrt (441) = 21sqrt(1)

ok 89/200

i need it in simplist form

445/1000

Very nice, CU.....!!!!

A "Best Answer "

Sorry, misread it.

1. We can plug in \((1,2)\) for both equations

\(x=\frac{1}{4}y+a\rightarrow 1=\frac{2}{4}+a\rightarrow\boxed{a=\frac{1}{2}}\)

\(y=\frac{1}{4}x+b\rightarrow2=\frac{1}{4}+b\rightarrow\boxed{b=\frac{7}{4}}\)

2. Then add:

\(\frac{1}{2}+\frac{7}{4}=\boxed{\frac{9}{4}}\)

That is the answer

Volume of a cylinder =Pi x r^2 x h
Volume =Pi x r^2 x h
                  =Pi x (6/2)^2 x 8
                  =226.195  cm^3
Volume of a Cube =S^3
                V =3^3 =27 cm^3
226.195 / 27 =8.378 =~8 - Wax cubes that Brenda will need.

Here's the second one

Angle AEB= Angle DEC

Angle ABE = Angle DCE 

So.....triangle AEB is similar to Triangle DEC

So 

DC / AB = 12/18 = 2/3

So

DE /  AE =  2 / 3   ⇒    AE = (3/2)DE

Which implies that

DE / AE  =  EC / EB

2 / 3  =   EC / EB

EC = (2/3)EB

EB + DE = 19

EC + AE = 21

EB + DE =  19

(2/3)EB  + (3/2)DE = 21

EB + DE  = 19

-EB - (9/4)DE = -63/2

-(5/4)DE = -25/2

DE = (25/2) (4/5) = 10

So

AE = (3/2)DE =  15

And

EB + DE = 19

EB + 10 = 19

EB = 9

So

EC = (2/3)EB

EC = (2/3)(9) = 6

And

[ BEC] = (1/2)(EB) (EC) sin BEC  =  (1/2) (9)(6) sin BEC

[ AED ] = (1/2)(DE) (AE) sinAED = (1/2) (10)( 15) sin AED

And sin BEC = sin AED

So

[BEC ] / [ AED] =   (9)(6) / [ 10 * 15]  =   54 / 150  =   9 /  25

\(f(2) = f^{-1}(2) = 4\\ \text{Take }f(\cdot) \text{ of both sides}\\ f(f(2)) = f(f^{-1}(2)) = 2\)

oh.. yeah.. intervals get \cup too... intervals are like sets

That is understandable.    

(-3) + 8 =    5

(0) + 8   =    8

(5) + 8 =   13

how closely I stick to those rules is inversely proportional to how many beers I've had... :D

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