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7.15  total

x = nickel             amount in nickles    .05 x

91 -x  = dimes      amount in dimes     .10 (91-x)      these two amounts summed together = 7.15

.05 x       +     .10 (91-x)     =       7.15

                                                                     solve for 'x' the number of nickels       then  #dimes =  91-x

Your teacher is wrong.  The answer is 16/3.

The area of triangle ACD is 25.

I think what your question is asking is what equal number of movies would equal the same amount for both of the plans  ?

($ 30  + 1.95 x ) = 7.95x      Solve for x = 5 movies would be the same amount $ 39.75

Since triangle(ACB) is a right triangle with base AC, point E will be the midpoint of the base.

Look at right triangle(AEB). The hypotenuse is AB = 5; one side is AE = 3, so the other side, BE = 4 (Pythagorean Theorem).

Therefore, the area of triangle(ABC) = ½·AC·BE  =  ½·6·4  =  12  and the area of triangle(BEC)  =  6.

Now I want to find the length of AD.

AD is the height of triangle(ABC) if BC is the base.

Area of triangle(ABC)  =  12  =  ½·BC·AD     --->     12  =  ½·5·AD     --->     12  =  2.5·AD     --->     

AD  =  4.8

I will use the length of AD to find the length of BD.  

Triangle(ABD) is a right triangle with hypotenuse AB = 5 and side AD = 4.8. 

Therefore, using the Pythagorean Theorem, BD  = 1.4.

Since BC  =  5  and  BD  =  4,  CD  =  3.6.

If you look at triangle(BCE) with base BC, triangle(DCE) with base DC, and tiangle(BDE) with base BD, they all have the same height.  (It isn't drawn, but you can draw it from point E perpendicular to BC.

Area of triangle(BCE)  =  area of triangle(DCE)  + area of triangle(BDE)

Since the length of DC = 3.6 and the length of BD = 1.4 and length of CD = 5, the length of CD = 3.6/5 the length of BC.

So, the area of triangle(DCE)  =  3.6/5 · area of triangle(BCE)

--->       area of triangle(DCE)  =   3.6/5 · 6  =  4.32                   

Consider all points in the plane that solve the equation x^2 + 2y^2 = 16. Find the maximum value of the product xy on this graph.

Doing it graphically I get approx  5.66

A LOT of similar questions posted here of late.....

total bills   14

x = 5 dollar bills       $ 5x  = amount in $ 5 denominations

  then   14-x   = number of 10 dollar bills       $ 10 ( 14-x)   = amount in $10 denominations

         both amounts must sum to $ 95

5x     +     10 (14-x)   = 95      solve for x , the number of $5 bills     then # 10's =   14 - x   

It was good that guest2 found the site and good that guest1 looked for his/her own solution.

Thanks to both of you.

Maybe you are the same guest lol

Sounds very logical to me   

x/4 - y/5 =1

Put it into y= mx + b form     slope will be  'm'   perpindicular slope is  - 1/m

y/5 = x/4 -1

y =  5/4 x - 5       slope is    5/4      perpindicular   is  -1/(5/4)   = - 4/5

My teacher said it was wrong.

Explain why it is right. Show steps.

yes, its 39

Walter rate  = 1job / 4 hr

Bill      rate   = 1 job /4hr

Tome rate    = 1 job /3 hr

1 job / (rates) = time for all three working to complete the jub

1 job / ( 1/4 + 1/4 + 1/3)   =         ?      Hours

First train get s a head start  

rate  x  time = distance

45    x   2     = 90 mile head start

Second train is travelling 30 m/hr faster and will close this 90 mile difference in   90 m/30m/hr = 3 hours

The second train will have travelled 3 hours at 75 m/r  = 225 miles when they meet

The area of triangle DEC is 25/4.

Explain why this is wrong.

The number = x

Multiply it by 2       2x

Subtract 11            2x-11

This equals   3x

2x-11 = 3x     SUbtract 2x from both sides

-11 = x

x = -11

Adult tix =  a

Child tix  =  (275 - a)

Amount from adult tix   = $ 5 a

Ammount for child tix    = $ 3 (275-a)        these amounts sum to $ 1025

5 a     +    3 ( 275 - a)   = 1025         solve for 'a' = adult tix     then child tix  =   275 - a   

WHAT quadratic ??? 

Increase price 1   2 fewer pairs sold

   for 'x' dollar increase:

       Price         *     pairs sold                         = revenue

     (60 +  x)      *      (200-2x)                          = revenue

         12000 -120x + 200x -2x^2                     = revenue

                        -2x^2+80x+12000                   = revenue       This will be an upside down parabola  (due to the -2x^2)

Maximum will be at   -b/2a       a = -2   b = 80

                               80/4 = $ 20     this is the mumber of 1 $ increases.....so   $80 per pair will maximize profit

Plug in that price    x       pairs sold 

         $80                x        ( 200 - 2(20))     =    max revenue

I agree with the above Guest #1. This is a job for a computer code. I wrote a short code and it gives the following result:

116035  125116  161440  170521  188683  197764  232070  241151  250232  268394  277475  286556  295637  357186  366267  375348  384429  429834  438915  455059  491383  509545  518626  527707  554950  571094  580175  607418  625580  634661  643742  652823  661904  705291  714372  723453  732534  741615  759777  768858  777939  803164  812245  821326  830407  839488  848569  884893  893974  901037  910118  919199  973685  982766  991847  Total =  55 such numbers

"The maximum value is 16/3, which you get when x = y = 4/sqrt(3)." 

This is wrong. Show steps.

Two buses leave a station at the same time and travel in opposite directions. One bus "A" travels 18 miles per hour faster than "B" the other. If the two buses are 280 miles apart after 2 hours, what is the rate of each bus?

Hello Guest!

\((b+b+18)2=280\\ 4b+36=280\\ b=61\\ a=79\)

Bus A travels 79 miles an hour,
Bus B runs 61 miles an hour.

  !

Pretty sure it would just be 250000*10^0 on a scientific calculator.