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When it hits the ground, y  = 0....so....

-16t^2  + 28t  + 144  = 0        divide through by  -4

4t^2 - 7t  - 36  =  0       factor

(4t  + 9) ( t - 4)  = 0

Only the second factor  will produce a positive value for t

So

t  - 4  =   0

t  = 4 sec

Should it not be 21.84 or am I missing something here? 

Cheers

If the line cuts the x axis  at  x  = -1......then the point (-1,0)  is on the line

So we have

y  =  9 ( x- -1) + 0

y = 9 ( x + 1)

y = 9x  + 9

x  / 10.25  =  52  /13

x / 10.25  =   4         multiply both sides by 10.25

x =    41  gallons

The solution is -5 < x < 2.

First you find out how many gallons they consume per week, to do so you divide the consumed amount by the passed time (10.25/13) and you'll find they consume 0.788 gallons a week. Next you simply multiply the weekly consumption by the 52 weeks and get 0.788*52=41.

You can also write this as a single equation as (10.25/13)*52.

Cheers

(edit: Correction)

I find it easiest to  simplify  numerator / denominator separately

  1              2                   y  + 2x^2

____  +  _____   =        _________

x^2            y                       x^2y

5          6               5y^2  - 6x

__   -  ___  =      __________

x         y^2              xy^2

So  we have

   y  + 2x^2        

  ________

    x^2y                            y + 2x^2            xy^2            ( y + 2x^2) y

____________  =         ________   *     _______  =  _____________  =

  5y^2 - 6x                        x^2 y              5y^2 - 6x        ( 5y^2 - 6x)  x

  _________

       xy^2

(y^2 + 2x^2y)

____________

(5y^2x - 6x^2)

That is incorrect.

We have  this system of equations

a(-4)^2  + b(-4)  + c  = -22

a(-1)^2  + b(-1) + c = 2

a(2)^2 + b(2) + c  =  -1      simplify these

16a -4b + c  = -22

   a  - b   +  c =  2

4a  + 2b  + c  = -1

Subtract the  second and third equations  from the  first and we get that

15a - 3b  = -24     ⇒   5a -b  = -8     ⇒   -10a + 2b = 16  

12a  -6b  = -21   ⇒    4a - 2b  = -7   ⇒      4a  - 2b  = -7

Add the last two equations  and we have that

-6a = 9      divide both sides by -6

a  =9/-6 = -3/2

And

5(-3/2) - b  = -8

-15/2 - b = -16/2

-b = -16/2 + 15/2

-b = -1/2

b = 1/2

And

a - b + c  = 2

(-3/2) - (1/2) + c  = 2

-2 + c  = 2

c   = 4

So

f (x)   = ax^2 + bx + c  =  (-3/2)x^2 + (1/2)x  + 4

can u tho?

i like to know things

I WILL be glad to show you how I got f(x)....but....adding those co-efficients.....forget it  !!!!

I worked through this

f(x)  =  (-3/2)x^2  + (1/2)x + 4

g (x) = (f(x))^16

Here is the expansion of this

(43046721 x^32)/65536 - (14348907 x^31)/4096 - (157837977 x^30)/8192 + (518154975 x^29)/4096 + (4068180855 x^28)/16384 - (8827766451 x^27)/4096 - (14523632991 x^26)/8192 + (94257891351 x^25)/4096 + (220712269635 x^24)/32768 - (706381131105 x^23)/4096 - (23495103567 x^22)/8192 + (3940745861637 x^21)/4096 - (1959573354921 x^20)/16384 - (16925275164105 x^19)/4096 + (6150417128055 x^18)/8192 + (57033142395909 x^17)/4096 - (166621058538623 x^16)/65536 - (19011047465303 x^15)/512 + (683379680895 x^14)/128 + (626862043115 x^13)/8 - (24192263641 x^12)/4 - 129736489272 x^11 - 1031335136 x^10 + 165371348480 x^9 + 17223697920 x^8 - 156919300096 x^7 - 32238338048 x^6 + 104507375616 x^5 + 32107397120 x^4 - 43620761600 x^3 - 17716740096 x^2 + 8589934592 x + 4294967296

Adding the  coefficients on the even powered terms  would be very tedious....as you can imagine  !!!

L = W + 5

Perimeter  =  2 (L + W)

26  =  2 ( W + 5  + W)

26  = 2  ( 2W + 5)     divide both sides by 2

13 = 2W + 5      subtract  5 from both sides

8  = 2W   divide both sides by 2

4 = W

And L  = W + 5  =  9

And

Area =  W * L  =  4 * 9  = 36 units^2

pls im confused

I assume you mean the interior  angles of  a regular  38-gon

One interior angle  measures

(36/38) (180)  ≈ 170.53°

So...the sum of these angles = 38 * (170.53)  ≈   6480.14°

10 / 8   =  x / 5    cross-multiply

5 * 10  =  8 * x

50  =  8 * x               divide both sides by  8

50/8  = x =  25/4  =   $6.25

The side of the large square   = 5

The side of the small square  =  √7

Let the smaller dimension of a ectangle  = x

Let the larger dimension of a rectangle  = y

And we have this  system

2x + √7  = 5    ⇒    x  =  ( 5 - √7) / 2       (1)

x + y  = 5    (2)

Sub (1)  into (2)

(5 - √7) / 2  +  y  = 5

y  =  5 - (5 - √7)/2  = 5/2 + √7/2  =  ( 5 + √2)/ 2

The  square of the diagonal  length  =

x^2  + y^2  =

(5 - √7)^2 / 4  +  ( 5 + √7)^2/4  =

[ 25 - 10√7 + 7  + 25 + 10√7 + 7 ]  / 4  =

[ 50  + 14 ]  / 4  =

64/ 4  =

16

So....the length of the diagonal of a rectangle =  √16   =   4

We can solve this with a proportion

width on blueprint  /  length on blueprint   =  x / actual length

4/9  = x / 15.3     cross-multiply

15.3 *4  =  9x     simplify

61.2  = 9x       divide both sides by  9

6.8 in = the width

divide both sides by 8

Three siblings are comparing there ages. Jenna is the youngest. Her brother Carl is 6 years older than her. Her sister Eve is twice her age. The sum of there ages is 42. Find all three of their ages.

J+C+E = 42

C=J+6       E=2J

sub in

J+J+6+2J=42

You can take it from there.

No one else finish this please. 

(2x^2-1)/sqrt(x^2+1)

\(\displaystyle\int\frac{2x^2-1}{\sqrt{x^2+1}}\;dx\\\)

Taken from Wolfram Alpha

Call  the nuber of nickles  x

So....the number of dimes  = 15 - x

So

Number of Nickels * Value Each +  Number of Dimes * Value Each  =  Total Value

 x * 5   +  (15 - x) * 10  = 115      simplify

5x + 150 - 10x  = 115         subtract 150 from both sides

-5x  =  -35                divide both sides  by -5

x = 7 =  number of nickels

15  - 7  = 8  = number of dimes

first lawn  =   1. 5 hours

second lawn  =  (2) (1.5)  = 3 hrs

lunch break  =  .5 hours

last lawn  = 1. 4 hrs

So

(1.5 + 3 + .5 + 1.4)   = 

6.4 hours before  3 PM  =

.4 hrs =  (4/10)(60)  = 240/10  = 24 min

6 hours +   24 min before 3 PM  =

8 : 36  AM ⇒   time you started  

Tom will travel 14 mph which means he will have traveled 14*2=28 miles in the two hours. 
Juanita will have travelled 20*2=40 miles in the two hours. Since they're going in the opposite directions simply add upp their distances (40+28) and you will find how far apart they are after two hours.

Cheers

The easiest way, if you understand what you are doing is to say the top of the buliding is the point (0,0)

later the whole graph will be translated up 25m.

So the parabola goes through (0,0)  (4,0) and (2,20)

\(h=k(t)(t-4)\\ sub\; in (2,20)\\ 20=2k*-2\\ 20=-4k\\ k=-5\\ h=-5t(t-4)\\ h=-5t^2+20t\\ \text{now translate it up 25 metres and I have}\\ h=-5t^2+20t+25 \)