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The 120 feet of fencing will form 3 sides of the outdoor room.  Thw two sides touching the museum will have width W; the third side, joining these will have length L (which is what you are asked to find).

So we must have:  2W + L = 120  or  W = 60 - L/2

The enclosed area is given by A = W*L  or  A = (60 - L/2)*L  or 60*L - L²/2

To find the maximum area we differentiate A with respect to L and set the result to zero:

dA/dL = 60 - L

For dA/dL to be zero we must have L = 60

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-16m+5(2m+3)=15-6m     OK.....let's simplify this

-16m + 10m + 15 = 15 - 6m

-6m + 15 = 15- 6m

15 - 6m = 15 - 6m        this is an identity.......any m will wwork......!!!

If I wanted to take......

log₈ 64     ....   on the calculator....just  type .... log(64, 8)

-16m+5(2m+3)=15-6m

I thought the rectangles are equal in length.  8*10=80

7*11.4=80. (11.4 is rounded)

Tackle as follows:

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We have

8/10 = 7/x     cross-multiply

8x = 70         divide each side by 8

x = 70/8 = 8.75 = 8.8 (rounded)

It goes 20 miles per hour.  So 60/20=3.  15+3=18.  So mishforever21 is correct.

We have

11/8 = x/3      cross-multiply

33 = 8x          divide by 8 on both sides

33/8 = x = 4.125 = 4.1 (rounded)

A googol is a 1 with 100 zeros.  1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000  is a googol. Thank you everyone.  I wasted my time.  Whatever. I don't care. I study math for fun.  That is just how weird I am

You got it Forest!  The answer is 69.

cross multiply

13(x - 9) = 15

13x - 117 = 15        add 117 to each side

13x = 132               divide by 13 on both sides

x = 132/13

1/sin(49) = sin(20)/sin(r)    cross multiplying, we have

sin(r) = sin(49)*sin(20)

sin(r) = 0.2581258787973758     and using the sine inverse, we have

sin^-1(0.2581258787973758) = r =  about 14.96°

Good try forest304.  (S)he mean what is 3 1/2+ 2 6/7 as fractions.  The answer is 6 5/14

Combine like terms by following order of operations.

Let the time Carlos drove = x  ....then the time that Maria drove = (5-x)

And Rate * Time = Distance   ....so we have

53x + 51(5-x) = 258    simplify

53x + 255 - 51x = 258

2x + 255 = 258      subtract 255 from both sides

2x = 3         divide both sides by 2

x = 3/2        and Maria drove (5 - x)   =  5 - 3/2   = 3.5 hs.

I'm not sure what you are asking, so here are two possibilities:

3 x 1/2 + 2 x 6/7

=1.5 + 1.7

=2.2

If you meant

3.5 + 2.86

approx = 6.36

Direct Variation is the Direct Variations

(5 x 6) (2) + 18/2

(30) (2) + 18/2

(30) (2) + 9

60 + 9

69!

It's 8 Hun.

Pi is equivalent  to approx 3.1415926535....

Pi is used to find the circumference by multiplying it to the diameter or 2x the radius.

Pi is also used in many other math problems, but can also be used to crack codes, and locks. Any compination of letters or numbers can be found in Pi because it is a sequence that never ends. Example: If I have a passwork for my computer, 1369, If you have a device that could run Pi through the system, eventually those number, in that sequence, would be found in Pi and the password would be cracked!

We can use the tangent function for this...let x be the opposite side...so we have

tan(20) = x / 18   multiply both sides by 18

18* tan (20) = x = about 6.55 units

Similar means that they have the same ratio. Simply put, as you stretch the width of the rectangle the length with stretch accordingly. The first rectangle has a ratio of 12:9 or reduced to 4:3 so a second rectangle with a width of 8 would still have a ratio of 4:3 or 8:6 so the length would be 6!

21

Just playin its 2

Go ahead soldier.