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Kelly painting rate =   1 room / 4hours = 1/4

Richard painting rate = 1 room / 8hours = 1/8

Remember    job / rate = time       ( or distance / rate = time)

Now combine the rates

1 room / ( 1/4 + 1/8)  =   1 / (2/8 + 1/8) = 1/(3/8) =  8/3 hour       2   2/3 hour  for both of them working

Yep......11  is correct

So 11 is the answer

https://web2.0calc.com/questions/help_22327#r5

Let  M  be the  total members...so...

(3/5)M  = 33

M  = 33 (5/3)  =  55

Those  that  voted for pretzels  =  55  - 33  =  22       ( 11 fewer  )

1. \(x^2+4x+3 = (x+1)(x+3) \)

2. Cannot be simplified further

3. \(x^2 + x = x(x+1) \)

4. \(2x^2-3x+1 = \left(2x-1\right)\left(x-1\right)\)

5. \(\frac{4\left(x+6\right)}{x-2}\cdot \frac{x+10}{24\left(x+6\right)} = \frac{x+10}{6\left(x-2\right)}\)

Hope this helped!  

AnxiousLlama

Is that you 

Here's  an  easy  way  to  do this

1/4  +   1/8    =

2/8  + 1/8  =

3/8

Take the   reciprocal of this fraction  =   8/3   =   hrs  to paint the  room if they  work together  =  2 + 2/3 hrs = 

2hrs  40 min

oops im wrong its 25

So here's the problem figure 

From figure, 

\(tan 25 = {EF \over DE}\)

\(0.47={9 \over DE}\)

\(DE=19.15\)

∴ Length of DE is 19.15 cm.

Let  x  be  the amt  given to the Library Fund

Then  1.5x   was  given  to   Clean Air Fund  =  15

So

1.5x  =  15

x  = 15  /1.5  =  $10  to Library Fund

Total given  =   10  +  15   =   $ 25

The smallest possible value of gcd(b,c) is 42.

To find the answer you need to add 50% to 15 and to that is to simply add 5 to 15 which is 20.

and since it wants to know how much money it gave altogether add 20 + 15 which is 35.

So 35 is your answer

Y  is  a 90  degree angle......tan  90  is  undefined

Savings --> 7 units

Remaining amount of money --> 7 - 1 = 6

Bag(1/2 of remaining amount of money) --> 6 / 2 = 3

Left --> 7 - 1 - 3 = 3

3/7 of his savings was left.

Let a and b be real numbers, such that a is the real part of z, and b is the imaginary part. Therefore,

\(2(a+bi)-3i(a-bi)=7-2i\\ 2a+2bi-3ai-3b=7-2i\\ (2a-3b)+(2b-3a)i=7-2i\)

Notice the real part of the right-hand side is 2a-3b, and the real part of the left-hand side is 7, so \(2a-3b=7\). Similarly, the imaginary part of the right-hand side is 2b-3a, and the imaginary part of the left-hand side is -2, so that means that \(-3a+2b=-2\). Now it's just a system of 2 linear equations, and can be easily solved with elimination:

\(6a-9b=21\\-6a+4b=-4\\-5b=17\\b=-\frac{17}{5}\\-3a+2(-\frac{17}{5})=-2\\-3a-\frac{34}{5}=-2\\ -3a=\frac{24}{5}\\a=-\frac{8}{5}\)

Therefore, the complex number z is equal to \(\boxed{-\frac{8}{5}-\frac{17}{5}i}\)

There are 5*21*20 = 2100 ways.

Thanks Phill!! 

Lets assume there are \(x\) games in their collection. 

So, now we have 

Blake found = \({3x \over 4}\) video games 

Andy found = \({3x \over 4}-18\) video games 

Back to the question... total no. of video games are \(x\)

∴ \({3x \over 4}+{3x \over 4} -18=x\)

   \({6x \over 4}-x=18\)

   \(2x=72\)

    \(x=36\)

Hence, there are 36 video games in their collection. 

Very nice, amy!!!!

12  +  .50N   ≤  21

.50N ≤  21  - 12

.50N ≤   9

N ≤  9 / .50

N ≤ 18

You  can get up to 18 toppings

I looked up on google and it said that grant hat 2/3 and gave 1/6

And if thats the question the answer is 1/6

It is given that 

\(f(x)=x^2-2x+5\)

\(g(x)=x+8\)

∴ \(g(5) = 5 + 8 \)

            \(= 13\)

\(f(g(5)) = f(13) \)         

              \(= 169 - 2(13) + 5             \)

               \(=148\)

Now, 

\(f(5) = 25 - 10 +5\)

         \(=20\)

\(g(f(5))=g(20)\)

               \(= 20+8\)

               \(=28\)

∴ \(f(g(5)) - g(f(5)) = 148-28\)

                                    \(=120\)

3.7 ( x - 1)^2  - 2.5 (x + 2)  =  x - 3.9    simplify

3.7  ( x ^2  - 2x  + 1)  - 2.5 (x + 2)  =  x - 3.9

3.7x^2  - 7.4x + 3.7  - 2.5x  - 5  =  x - 3.9

3.7x^2 - 9.9x  - 1.3  =  x - 3.9

3.7x^2  - 10.9x + 2.6  =  0             multiply  through  by 10

37x^2  - 109x + 26  =  0

Use  the quad formula

x  =    109 ±√ (109^2  - 4 (26)(37)

         __________________________

                           2 * 37

This  evaluates to     

x   ≈  .261       or       x   ≈  2.684

P**p