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x^2  -  x   - 12    =   0    factor

(x  - 4) ( x + 3)     =    0

Set both factors to 0  and solve for  x

x  - 4 =   0                 x  + 3     =0 

x  = 4                        x  = -3

You have been asked to create a tent for an upcoming trip. The length will be 6ft, the width 4 ft and the height 4 ft. Approximately what is the size of tarp needed to complete your tent? (you will include the floor and door.

We heed to  find the slant height of the sides.....this  =   

sqrt  ( 1/2width^2 + height^2)   =  

sqrt  (  2^2  +  4^2)    =

sqrt (20)  =  sqrt  (4 * 5)    = sqrt (4) * sqrt (5)  =   2sqrt (5)

The area  of the  sides   = 2 (2sqrt(5))  *length =  4[sqrt (5)] (6)  = 24sqrt (5)

We also need to  find the  area of both ends [ the door and the other end ] .....thes are triangles  with bases of  4 and heights of 4

The sum of these areas = 2 (1/2) ( 4)(4)  = 16

The  floor =  width of tent * length   = 4 * 6   = 24

So....the total  surface  area  =    24sqrt (5)  +  16  +  24  ≈   94 ft^2

Area_trapezoid   =    (1/2) height *  (sum of base lengths)

So we have

72  =(1/2) (6)  ( 9  +  B)         where B is the  unknown base lenght....simplify

72   =  3 ( 9  +  B)             divide both sides  by  3

24  =  9 +  B               subtract  9  from  both sides

15 =  B  = the length of the other base

Let  the original amount in both containers  = A

After  120 ml   is poured into B  we have that

4 ( A  - 120)   = A  +  120       simplify

4A  - 480  =  A  +  120      add 480 to  both sides,  subtract  A  from both sides

3A  =  600    divide  both sides  by  3

A =  200

The amount left in A =  A  - 120    =  200   - 120   =    80 ml

The pyramid will have the same number of faces as the the number of sides  of the  base  

So.....the  number of faces =   n 

Let the cost of one shirt =  S

Let the cost of a pair of pants   =  P

So....we have this system

5S  + 3P  =  105     (1)

4S  + 2P =   80       divide this equation through  by  2 →   2S  + P   = 40  rearrange as  P =  40  - 2S  (2)

Sub (2) into (1)   for  P

5S  +  3 (40  - 2S)  =   105            simplify

5S  +  120  -  6S  =  105

-1S  + 120 =  105              subtract 120 from  both sides

-1S =  -15     divide both sides  by  -1

S  = 15      [ 1 shirt costs $15   ] 

And using (2)   P   =  40  - 2(15)  =  40  - 30    = 10    [ the pants  cost $10 ] 

-5  + 4  - 16/5  + 64/25  - 256/125

The common ratio , r,  is    [ 4/ -5] =  -4/5

So tthe  sum is

First term                    -5                           -5                         -5                    

_______    =            _______    =           _______   =         _____  =      -5  (5/9)   =  -25  / 9

1  -   r                       1 - (-4/5)                  1 + 4/5                  9/5

well 1 top and 1 pair of pants is £25 together and so using the trial and improvement method, adding the fact that 5t and 3p is £105 but including 4t and 2p is £80. Sooner or later u will get it

OMG I messed up and I can't edit.  Turtle doesn't run at 0.4 mph; Turtle runs at 1 mph. 

I didn't copy the question like I usually do, and I wasn't glancing up at it as I worked through.

Evverywhere I referred to Turtle's speed as 0.4 mph above, change that to 1 mph. 

So the calculation should be                  D  =  S • T 

                                                              0.4 mile  =  (12 miles/hour) • T 

                                                              (0.4 mile) / (12 miles/hour)  =  T 

                                                              T  =  0.0333333 hour                  (i.e., 1/30 of an hour = 2 minutes ) 

Check the answer: 
Achilles -  (1/30 of an hour) • (13 miles/hour)  =  0.4333 mile 

Turtle    -  (1/30 of an hour) • (1 mile/hour)      =  0.0333 mile 

So, we confirm that at the end of 1/30 of an hour, Achilles is 0.4 mile ahead of Turtle. 

And I'm sorry for the error in my original answer; 

_.

The parabola is the set of all points (x,y) that are equidistant from the focus and directrix.

So, using the distance formula, we have:

√[(x+5)2 + (y-5)2] = √[(x-x)2 + (y+1)2]

x2 + 10x + 25 + y2 - 10y + 25 = y2 + 2y + 1

x2 + 10x + 25 = 12y - 24

(x + 5)2 = 12(y - 2)

y - 2 = (1/12)(x + 5)2

y = (1/12)(x + 5)2 + 2

I don't agree with the answers given.

For (1) we can treat each candy individually and multiply the results.

Using stars and bars we can distribute 8 candies among 4 children as

\(N_L = \dbinom{8+4-1}{4-1} = \dbinom{11}{3} = 165\\ N_W=\dbinom{7+4-1}{4-1}=\dbinom{10}{3} = 120\\ N = N_L \cdot N_W = 19800\)

For (2) we have to find the sum of the cases for the amount the twins get

\(N_0 = \dbinom{6+3-1}{3-1} = \dbinom{8}{2} = 28\\ N_1 = \dbinom{4+3-1}{3-1} = \dbinom{6}{2} = 15\\ N_2 = \dbinom{2+3-1}{3-1} = \dbinom{4}{2} = 6\\ N_3 = 1\\ 1 + 6 + 15 + 28 = 50\)

Thx for the help its 80ml

A=B

4(A-120) = A+120

Solve for A (THE original AMOUNT)  then subtract the 120 ml that was transferred.

its one i think

pi r^2 h    is the lateral surface area....be careful...you are given DIAMETER and should  use the RADIUS !

You have been asked to create a tent for an upcoming trip. The length will be 6ft, the width 4 ft and the height 4 ft. Approximately what is the size of tarp needed to complete your tent? (you will include the floor and door.

60 sq ft

96 sq ft

88 sq ft

44 sq ft

1 / 3  + 1 / 2 = 1 / T

T = 1.2 hours - or 1 hour and 12 minutes.

Yes. It works on some higher order polynomials as well.

That's cool !  I didn't know about this capability ....  

Come to think of it, the word "solve" is unnecessary:

a)  Probability  =  (30/40) x (29/39) x (28/38)

b)  Probability  =  (10/40) x (9/39) x (30/38)

c)  If you know nothing about any of the other washers, the probability that the third washer is thicker is  30/40.

Go to the calculator on the HOME page and type in solve followed by your quadratic equation, then hit enter.  See following example:

If BC is a ray in the interior of angle(ABD), then:

angle(ABC) + angle(CBD)  =  76^o

angle(ABC)  =  76^o - angle(CBD)

angle(CBD)  =  76^o - angle(ABC).

Let the number of green fish =G
The number of yellow fish      =G - 6

0.4[G + G - 6] = G - 6, solve for G
G = 18 number of green fish

Check:
18 - 6 = 12 yellow fish.
18 + 12 = 30 fish in total
40% x 30 =12 number of yellow fish.

Let her normal walking speed =W
Her walking speed WITH the walkway=W + 3.5
Her walking speed AGAINST the walkway =W - 3.5
Let the time it took her to walk with the walkway=T
The time it took her to walk against the walkway =40 - T

T * [W + 3.5] + [40 - T] * [W - 3.5] =70................(1)
[70/2] / [W+3.5]  +  [70/2] / [W-3.5]=40...............(2), solve for T, W.
T  =4.3846 seconds
W =4.4827 =~4.5 feet/sec - her normal walking speed.