All Answers 358087 Answers

1.  (7 + 1/4) (4)   =   29

     (5  + 1/2) (4)  =   22

The first  train had 7 more  riders  than the 3rd

2.   3/4  of  a row  was empty.......(3/4) (4)  = 3  more riders needed  to completely fill the train

3.    8 - ( 5 + 1/2)  = 8 - ( 11/2)  =  (16/2)  - (11/2)   =  5/2  =  2 1/2  rows were empty

(5/2) (4)  =  20 / 2  = 10 more  rideres needed  to completely fill the train

Let's go through and check each one:

A)

$8*5+9*6=40+54+94$(works!)

B)

$9*5+8*6=45+48=93$(does not work)

C)

$5*6+6*5=30+30=60$(does not work)

D)

$7*5+6*6=35+36=71$(does not work)

Out of these only $\boxed{A}$ works

So in total she read $\frac{1}{4}*136+29=34+29=63$.

She has $136-63=\boxed{73}$ pages left to read

So after giving away 5 candies to each of her friends she has $45-5*3=30$, and $30-\frac{2(30)}{5}=30-2*6=30-12=\boxed{18}$ candies left

Impressive, EP!!!!!

Specifically, you are missing the second quadratic.

Yes you can....is that what you wanted.....or an explanation as to how?

Starts this way   make 3 piles  7   7    1

   balance the 7's    if they balance, then the '1' is the fake

                                if they DON't balance, the lighter 7 has the fake

      take the lighter 7   make 3 piles   3  3  1

          balance the 3's   if they balance then the '1' is the fake

                                       if they don't balance then the lighter 3 has the fake

               take the lighter 3     make 3 piles  1  1   1

                    balance two of the 1's

                                             if they balance , the third '1' is the fake

                                                       if they don't balance , the lighter one is the fake .....with only THREE balances done !

Given that a > 0, if f(g(a)) = 8, where f(x) = x^2 + 8 and g(x) = x^2 - 4, what is the value of a?

Substitute in g(x)

f(g(a)) = f(a^2 - 4)

f(a^2 - 4) = (a^2 - 4)^2 + 8

We bring that back into the original equation

(a^2 - 4)^2 + 8 = 8

(a^2 - 4)^2 = 0

a^2 - 4 = 0

a^2 = 4, a = 2

Answer: a = 2

Check:

f(0) = 0^2 + 8 = 8

:)

We're  missing something here.......

Taking $x=y-3$ and plugging it into $2x+y=12$ gives $2(y-3)+y=12$, so $2y-6+y=12$, $3y=18$, $\boxed{y=6}$.

Now, because $x=y-3$, $x=(6)-3$, $\boxed{x=3}$

No everything is fine thank for your help

Let  the first  term  =  6

Let  the  number  sold  on  the nth  day  be   8n

And  we  need  to  solve  this inequality

[  6 + 8n ]  *  ( n/ 2)   ≤  300

(3  +  4n)n  ≤  300

4n^2  + 3n  - 300 ≤  0

Let  n  = x  and see the  graph here  :  https://www.desmos.com/calculator/d24dtkqwy0

It shows  that he runs  out  after  about  8.3  days  

1. How much money does Kevin have?

We know that he has 18 dimes, 12 nickels, and 6 quarters

18 x 10 = 180 cents

12 x 5 = 60 cents

6 x 25 = 150 cents

180 + 60 + 150 = 390 cents

Kevin has 390 cents or $3.90

2. How many slices of pizza can Kevin buy?

Each slice of pizza is 75 cents, so to find the number of slices he can buy, we just divide 390 by 75

390/75 = 5.2

He can't buy 0.2 of a slice of pizza, so the max he can buy is 5 slices.

Kevin can buy 5 slices of pizza

Let me know if I made a careless error 

:)

Moving all the terms to the left side and arranging gives $5x^2+30x+18=0$

Using the quadratic formula, you get $x=\frac{-30+\sqrt{30^2-4(18)(5)}}{2(5)}$ and $x=\frac{-30-\sqrt{30^2-4(18)(5)}}{2(5)}$, which simplifies to

$x=-3+\frac{3\sqrt{15}}{5}$ and $x=-3-\frac{3\sqrt{15}}{5}$.

When rounded, these give $x=-3+2=-1$ and $x=-3-2=-5$.

When multiplied, these give $-1*-5=\boxed{5}$

Benny and Emmet have 135 altogether. Emmet has 53 more than Benny. How much does Benny have?

Benny = B, Emmet = E

We know that B + E = 135 and E = B + 53

This turns into a simple substitution

B + (B + 53) = 135

2B + 53 = 135

2B = 82

B = 41

Benny has 41

Check:

41 + (41 + 53) = 41 + 94 = 135 

:)

Thanks!

30 * .70  =  21  were  chocolate  chip,  9  were  chocolate

If the pct of chocolate milkshakes sold  dipped to 25%, then 75%  of the final totla must  be  chocolate chip

So

Let  x  be  the  nuber  of  additional  chocolate chip milkshakes  sold   and  we  have  that

[21  + x]   / [ 30 + x]  =  .75            cross-multiply

21 + x  =  .75  [ 30  + x]

21 + x  =  22.5 + .75x

x - .75x  =  22.5  -21

.25x  = 1.5

x  = 1.5  / .25  =     6 =   number of additional chocolate chip milkshakes sold

Proof :  30 +  6 =    36 in total were sold.....9  were chocolate....9 / 36  =  1/ 4  =  25%

Ummmm... that would be $\pi*1524155677489$, which assuming $\pi \approx 3.14$ gives about $\boxed{4785848827315.46}$

However, I feel that this was just a random question though.

*Not sure if this is right but here I go*

We know that 2 large boxes is half as many nails as 6 small ones, therefore 2 large boxes = 3 small boxes

If we have x equal the number of nails in 2 large boxes or 3 small boxes, then you can set up the equation like this:

x/2 = x/3 + 20

-x/3     -x/3

(x/2 - x/3) = 20

*multiply to change the denominators*

(3x/6 - 2x/6) = 20

x/6 = 20

6(x/6) = 6(20)

x = 120 (nails in 2 large boxes or 3 small boxes)

Now we just halve that to get the number in one large box.

1 large box = 60 nails

Hint: Find the numbers of original chocolate chip and chocolate milkshakes. Then find the percentages of the numbers.

Call the number of points  that  Hassan originally had, H

Call the number of points  that Vick  originally had = 2H

Assuming  the Vick scored  no more points, we  have  that

H + 36  =  2  (2H)     simplify

H + 36  =  4H

36  =  4H - H

36  = 3H

36 / 3   = H    = 12

Vick had  2(12)  =  24  points originally

No problem!

Ty you got it right