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Missing data in the question!

https://web2.0calc.com/questions/trapezoid_25

The perimeter of a particular rectangle is eight times its width. If the area of the rectangle is 24 in^2, what is the width of the rectangle, in inches?    

Call the perimeter P, the length L, and the width W.  

P = 8W                              given  

P = 2L + 2W                      perimeter is L+W+L+W  

8W = 2L + 2W  

6W = 2L  

3W = L  

A = L • W  

A = 3W • W  

A = 3W²  

24 = 3W²  

8 = W²  

W = sqrt(8)  =  2•sqrt(2)  

The problem doesn't ask for the length, but by the way L = 6•sqrt(2)  

_.

Philip rec'd 8 out of (8+3 )    = 8 /11 of the prize

    Terry received 3/ 11 of the prize        the difference , 5/11 of the prize  = 20 dollars   

        or    5/11 x  = 20      solve for 'x'

2.17 times thicker would be a   117 % thicker

say it is   5 mil thickness      100% thicker would be 10 mil thickness   BUT it is twice as thick..... do you see?

Find how long will Ajay take to finish the work alone ?​

Hello Guest!

\(4(\frac{1}{8day}+\frac{1}{20day})=\frac{1}{x}\\ \frac{1}{2day}+\frac{1}{5day}=\frac{1}{x}\\ \frac{5+2}{10day}=\frac{1}{x}\\ x= \color{blue}\frac{10}{7}day\)

\(1\frac{3}{7}\) day it will be Ajay take to finish the work alone.​

  !

Let there were x boxes of apple at first.

 Monday sold :  \( {3\over7 }x + 7{}{}\)
 Remaining  :   \( x -({3 \over 7}x + 7) = {}{}\)\({4 \over 7}x - 7{}{}\)
 Tuesday sold:     \({3\over 5}({}{}\)\( {4 \over 7}x-7)+5 ={}{}\)\( {12 \over 35}x+{}{}\)\( {4 \over 5}{}{}\)
 Remaining:      13
 Set and equation :

        x - \( ({3 \over 7}x+7)-{}{}\)\( ({12 \over 35}x+{}{}\)\( {4 \over 5}){}{}\) =13

        x - \( {3 \over 7}x-7-{}{}\)\( {12 \over 35}x-{}{}\)\( {4\over 5}=13{}{}\)

                                      \({8 \over 35}x ={}{}\)\( {104\over 5}{}{}\)
                                           \(x\) = 91 (boxes)

There were 91 boxes of apples at first 

{  Total boxes -- Monday sold -- Tuesday sold = 13 }

Law of sines

sin A / a  = sin C / c       to find C          then you can find angle B    because B = 180 - A - C

The question easy by

includes apple:

 1 + 2 + 1 + 2 + 2 + 2 + 2 + 1 + 2 = 15

only banana:    1

 only  banana + cherry:   4

 =>  15+1+4=20

(x+4) *2          =       4 * (x-6)           solve for 'x'

Pythag theorem  for the right triangle

10^2 = 6^2 + s^2        solve for     s = shadow length

1/8   +  1/20  + 1/X   =   1/4

x = ajay time  

Find how much the coins are worth altogether.   

So value of the nickels + value of the quarters

then

divide the answer by 40 because you have 40 coins.

Solution: x^2+2x=(x^2+2x)^2+2(x^2+2x)

               x^2+2x=x^4+2(x^2)(2x)+(2x)^2+2x^2+4x

               x^2+2x=x^4+4x^3+6x^2+4x

               0=x^4+4x^3+5x^2+2x

               Dividing everything by x gives: x^3+4x^2+5x+2=0

               Using the rational root theorem, you can check if any of these values make the equation equal to 0: 1, -1, 2, -2

               And -1 and -2 both check out.

x=-1 or x=-2

Need more info.....

x=-1 or x=-2

x = -2   -1   0

Its 96/5. The formula for sum of an infinite geometric series is      A₁/1-r         Where  A₁ is the first term in the series and r is the common ratio. Plugging in your values, you have  A₁/1-(-1/5)=16------------>  A₁/(6/5)=16 Solving for  A₁ you get 96/5. No clue where my guy got 64/5 from.

9x^2 +6x+ x^2 + 4x + ?

10x^2 +10x +?

10 *(x^2 +x)

10 (x+1/2)^2

10 ( x^2 + x + 1/4 )

10x^2 + 10x + 2.5          =   ( sqrt 10 x   + 1/2 sqrt(10) )^2 

g(x) =  7 x⁷  + a x⁵ .........         Degree 7 cancels the degree 7 in f(x)   and the a x⁵   makes the result of adding them degree 5      

There are 340 numbers that are circles with only one number.

From the formula, the first term is a = 64/5.

Imaginary roots alwas come in pairs    a +- bi        so the other root would be   2 - 3i sqrt3