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 gcd(7788,1386)=66 is correct. I don't know if this calculator does "gcd" and "lcm". You can try "WolframAlpha" and it should give you the answer.

To factor, we need to find 2 numbers that add to 2 and multiply to -15.
5 seems like it could fit with -3 to match the requirements.
Ima go wtih d here.

A short cylinder made of a piece of paper will hold more than a tall one. You are taking the square of the longer side versus the shorter one.

\(11\pi(\frac{8.5}{2\pi})^{2}=\frac{794.75}{4\pi}\ \textrm{vs.}\ 8.5\pi(\frac{11}{2\pi})=\frac{1028.5}{4\pi}\)

Is a definition given for how tall one story is?

I need to know how to get each of them

never mind i found the answer its 1 btw

9 = (r-2)(2r+sqrt5)(2r-sqrt5)

10 = (7k+6)(3k^2+8)

11 = (6x+7)(sqrt7x+sqrt6)(sqrt7x-sqrt6)

12 = (p+6)(p+sqrt3)((p-sqrt3)

See Alan's answer No.#2 here. Make sure to adjust for the time difference of 20 minutes instead of 10 minutes in this particular question: p=1 - (1/2(60 - 20)^2/60^2 =(1/2*40^2)/60^2 =1 - 2/9 =7/9:

https://web2.0calc.com/questions/alex-needs-to-catch-a-train-the-train-arrives-randomly-some-time-between-1-00-and-2-00-waits-for-10-minutes-and-then-leaves-if-alex-also

Last one

x + 3y - z  = 6    

4x - 2y + 2z = -10    

6x + z  = -12

Sorry..Johnny...but I gotta' go in just a minute

The answer to  this is   (x ,y , z)   = ( -3, 5, 6)

When I get back on...I'll give you a complete run through...if you need it  !!!

Thanks man :D

2x - 3y  = -27     multiply through by 3   ⇒   6x - 9y = -81    (1)

-3x + 2y  = 23   multiply through  by  2 ⇒   -6x + 4y  =  46    (2)

Add (1)  and (2)  and we get

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

y  = 7

And  using   2x  -  3y = -27  to  find x we get

2x - 3(7)  = -27

2x - 21  = -27     add 21 to  both sides

2x = -6    divide both sids by  2

x  = -3

So  (x ,y )  =  ( -3, 7)

x + y  = 6

x  =  y + 4        sub the second into the first for  x

(y + 4) + y  = 6

2y + 4  = 6

2y  = 2

y = 1

And   x   =  y + 4  =  1 + 4   = 5

So   (x, y)  = ( 5 , 1)

x + 5y  = -15

y  = (1/5) x + 1        sub the second into the first for y  and we have

x + 5 ( 1/5 x + 1)  = -15

x + x + 5  = -15

2x + 5  = -15     subtract 5 from  both sides

2x  = -20     divide both sides by 2

x  = -10

And using    y  = (1/5)x + 1  to find  x, we have   y  =(1/5) (-10) + 1  = -2 + 1   =  -1

So   (x , y)   = ( -10 , -1)

These are a little tougher, RP...  

7) 42m^4  - 48 m^3  - 42m^2  + 48m

GCF 42m^4 and 48m^3 =  6m^3

GCF 42m^2 + 48  = 6m

So we have

6m^3 ( 7m - 8)  - 6m (7m - 8)

(7m - 8) ( 6m^3 - 6m)        ....we can factor 6m out of the second factor

(7m - 8 ) * 6m ( m^2 - 1)    .....m^2 - 1   factors as a difference of squares  = (m + 1) (m -1)

6m ( 7m - 8)(m + 1) (m - 1)

8) 56v^4  - 98v^3  - 64v^2 + 112v 

GCF   56v^4  and  98 v^3   =  14v^3

GCF  64 v^2 and 112v  = 16v

So we have

14v^3 ( 4v - 7)  - 16v ( 4v - 7)   

(4v - 7) ( 14v^3 - 16v)   ....we can factor  2v  out of the second factor

(4v - 7)  *2v *  (7v^2 - 8)

2v (4v - 7) (7v^2 - 8) 

Could you please repost this question? We can't see your numbers for the problem.

John has a 100% chance of being there if he arrives at 2:20 or earlier. Add 1/3.

At 3:00, he has a 1/3 chance. We can take this and take the average from 2:20 and 3:00 to get 2/3 for this 40 minute period. Multiply this by the portion of time. Add 4/9 to the probability.
Result: He has a 7/9 chance of catching the train.

The diagram not being shown might be the reason that you are struggling with this problem... You're welcome.

No prob  !!!

% change  =   [   ( New Mass - Old Mass ) / (Old Mass ) * 100 ] %

So...for the first one we have

 [   ( 86.6 - 92.0 ) / 92.0   *   100  ] %  =   [ - 5.4 / 92  * 100 ] %  ≈ [ -5.87] %    (decrease )

Second one

[  (94.4 - 89.3 )  / 89.3   * 100 ] %  =  [ 5.1 / 89.3  * 100 ] %  ≈   [5.71 ]%    (increase)

Thank you for all your help!! Have a wonderful day/night!

Thank you so much!! I was very confused about these questions and now I understand it! I appreciate your help!

No diagram is shown....

Excellent, RP  !!!

42) A trapezoidal prism of height 12 cm. The parallel sides of the base have lengths 12 cm and 6 cm. The other sides of the base are each 6 cm. The trapezoid's altitude measures 5.2 cm.

The key here is to  find the area of the trapezoidal base and then multiply this area by the height of the prism...note that info concerning "the other sides of the base" isn't really needed

Area of the trapezoid  =  [ base area ] =   (1/2) (altitude of the trapezoid) * (sum of the base lengths)  =

                                                                  (1/2) ( 5.2) (12 + 6) =

                                                                  (1/2) (5.2) (18) =

                                                                    9 * 5.2  =   

                                                                     46.8 cm

Now....the volume =   base are * height of the prism =   46.8 * 12   =  561.6 cm^3

45) A trapezoidal prism of height 6 yd. The parallel sides of the base have lengths 9 yd and 4 yd. The other sides of the base are each 5 yd. The trapezoid's altitude measures 4.3 yd

This one is similar

Area of the trapezoid =  (1/2) (4.3) (9 + 4)  = (1/2) (4.3) (13)   = 27.95 yd

Volume of the prism  =   6 (27.95)  = 167.7 yd^3

BTW...here's a website that might help : https://study.com/academy/answer/how-do-you-find-the-volume-of-trapezoidal-prism.html

-3*-4y=12y

-3*3=-9

12y+(-9)+7y

12y+7y=19y

19y-9