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Good job, tertre  !!!

No ordered pairs shown....but...no prob

x+5y = −15   

 y =  1/5x+1

Rearrange the first as  x  = -15  - 5y

Sub this into the second for  x

y  =  (1/5)(-15 - 5y) + 1  simplify

y = -3 - y + 1    add y to both sides

2y  =  -3 + 1

2y = -2    divide both sids by 2

y  = -1

So

x  = -15 - 5(-1)  =  -15 + 5  =   -10

So   (x, y)  = ( -10, -1)

Tomorrow lol

What happens if you multiply the first equation by -3 and the second equation by 2? Let's try it!

If we follow what I said, we will get: 6x+-18y=114 and 6x-8y=64. Now, we can subtract, to attain -10y=50, so y=-5. We can plug the value of y back in the second equation, to get: 3x-4(-5)=32, 3x+20=32, 3x=12, x=4. Thus, the answer is : (4,-5).

Thank you so much! I appreciate your help! 

That's a lot to chew on  at one time....when do you need this by  ??

Last one....this is the most difficult

We have a trapezoidal prism

The area of the two trapezoids forming the sides  = 

2 * (1/2) (height) ( sum of the base lengths )  =

2 *(1/2) (7.8) ( 17 + 8 )    =  195 m^2

We have two other congruent sides that are rectangles  with height  = 9m  and width  = 8 m

So..their combined area  =  2 * 9 * 8    = 144 m^2

And the top is a rectangle  with dimensions of  8 and 17

So its area is  8 * 17  = 136m^2

And the bottom is a square with a side of  8  ...so its area  = 8^2  = 64 m^2

So...the total surface area  is  195  + 144 + 136 + 64  = 539  m^2

Third one

Another triangular prism

The top/bottom  are  triangles with a base of 15m  and a height  of 11.2 m

So...the area of the top/bottom  is  15 * 11.2  = 168 m^2

The sides are rectangles  each with a height of 7m  and  widths of  [ 13, 14 and 15 ] m

So...the total area of the sides  =  7 [ 13 + 14 + 15  ] = 294 m^2

So...the total surface area  is   168 + 294   =  462 m^2

Second one

This is a hexagonal prism

The top and bottom are hexagons...comprised of 6 congruent triangles...each with a base  of 11  ft and a height of 9.5 ft

So...the area of the top/bottom  =  6 (1/2)(11)(9.5)  =  313.5 ft^2

The sides are 6 congruent rectangles   each with a height of  6ft and a width of 11 ft...so the area of the sides is

6 * (11) ( 6)  =396 ft^2

So...the total surface area  =   [313.5 + 396 ] ft^2   =  709.5 ft^2 

First one

We have two triangles comprising the top/bottom  each with a base of 17 cm and a height of 4.9 cm

The area of these  =  17 (4.9)  = 68.6 cm^2

The sides are three rectangles...each with a height of  9cm  and  widths of  [ 7 , 13 and 17 cms]

The total area of these  is  [ 9 ] * [ 7 + 13 + 17  ] =  9 [ 37]  =  333 cm^2

So...the total surface area of the first  figure [ a triangular prism ]  is  [ 68.6 + 333 ] cm^2  =  401.6 cm^2

3√-50  =

3√  [ -1  *  25  * 2 ]  =

(3 *i * 5 )√ 2  =

15i√2

Negative price tickets will happen for musicals when the singing is really, really bad. Free ear plugs are included.

1.)   (4x^3 y^2) ^3/10  =

¹⁰ √  ( [ 4x^3 y^2 ]^3 )  =

¹⁰ √ [64 x^9 y^6 ]

HAHAHA!!!....we didn't really do anything  !!!!

In the sample problem...I think 

p  = If you go to school

q  = You must make a right turn

r  = You must use a turn signal

So

Law  of Detachment  says

p → q    and  q  → r    [ both are true ]

Law of  Syllogism says [ since both of these are true ]

p →  r

I could use a smarter force to check my work. :D

Do you know what they are talking about when they say "P" "Q" and "R?"

Thank you both!

See if this helps, Owen  :

https://www.shmoop.com/logic-proof/detachment-syllogism.html

Ok then... Good job!

The obvious approach is to define \(h(x)=g(f(x))\) and then apply \(h(x)\) to the number 12 just 8 times.

First you need to work out \(h(x)\) algebraically by replacing the x in \(g(x)\) by the formula for \(f(x)\). Nobody will complain if you do a bit of Mathematics before you do the calculation! The result turns out to be simpler than you might expect, because the setter tried to make things easy for you! Now apply \(h(x)\) to 12 just 8 times. You don't need a calculator.

To say any more would be to give the game away (or to score points).

Other one is 6√14

Nope...no better answer......good job  !!!

Great! I felt good doing this lol

10√(4x^3y^2)^3