All Answers 352881 Answers

Exactly the same as equalities 

except you have to turn the sign around if you do any of these things

1) swap sides

2) Multiply or divide by a negative number.

3) Take the reciprocal of both sides.   (turn entire fractions on each side upside down)

Huh?   

$$6^{-4}$$

gets entered as 6^(-4)  =

YES I DO  !!!

I MAKE SCOOBY SNACKS WITH OR WITHOUT THE SNARKY COMMENTS.

MY SPECIALTY IS TREACLE SANDWICHES THAT DRIP ALL OVER THE FLOOR.

THAT INCREASES THE FRICTION RATIO SOMEWHAT, I DON'T NEED ALAN TO TELL ME THAT.

BUT

I DO NEED ALAN'S HELP TO WORK OUT THE PHYSICS OF IT ALL!!          ROF  LOL

Hmm i wonder...

Perhapes 2?!?

1. 8/15= 16/30
2. 5/6= 25/30

So -9/30

inverse cos is the same as arc cos

so press

[2nd] [acos]

2x^2-3y^2=5xy and-3x+y=5     rearranging the second equation, we have y = 3x + 5

And putting this into the first equation, we have

2x^2 - 3(3x + 5)^2 = 5x(3x + 5)  simplify

2x^2 - 3(9x^2 + 30x +25) = 15x^2 + 25x

2x^2 -27x^2 - 90x - 75  = 15x^2 + 25x

-13x^2 - 27x^2 - 115x - 75  = 0   multiply through by -1

13x^2 + 27x^2  + 115x + 75 = 0

40x^2 + 115x + 75 = 0      divide through by 5

8x^2 + 23x + 15 = 0    factor

(x + 1 )(8x + 15) = 0

And setting each factor to 0, we have that x = -1 and x = -15/8

And using y = 3x + 5 when x = -1, y = 2  and when x = -15/8, y = -5/8

So....our solutions are (-1, 2) and (-15/8, -5/8)

Ok, I don't know why we have been avoiding this one.  Sorry.

There are 180 degrees in pi radians.  so rather than memorising foruma I start from there.

$$\begin{array}{rll}
180\;degrees &=& \pi\; radians\\\\
180\times \frac{50}{180} \;degrees &=& \pi \times \frac{50}{180} radians\\\\
50\; degrees &=& \pi \times \frac{5}{18} radians\\\\
50\; degrees &=& \frac{5\pi}{18}\; radians\\\\
\end{array}$$

By alpha of 400 degrees I assume you mean chantge 400 degrees to radians  

400-360=40degrees

$$\begin{array}{rll}
180\;degrees &=& \pi\; radians\\\\
180\times \frac{40}{180} \;degrees &=& \pi \times \frac{40}{180} radians\\\\
40\; degrees &=& \pi \times \frac{2}{9} radians\\\\
40\; degrees &=& \frac{2\pi}{9}\; radians\\\\
\end{array}$$

Umm well it could 2/5 or -2/5 but I don't think you refer to slopes like this as negative.

I am going fot the 2/5 answer.   Sorry Chris 

Yes that is true :)

it = 4 7

Hi Shaniab :)

Well I think that Guildenstein should stop going into Horatio's phone and that there should be no bet!!! LOL

When will  the last 2 digits be greater than 49

Well, the second last digit can be 5,6,7,8 or 9    That is 5 choices

and the last digit can be anything at all.

P(last 2 digits are great than 49)= (5/10)*1 = 0.5

So yes this has the same odds as a fair coin toss.   

Does that answer the question?

$${\mathtt{10}}{\mathtt{\,\small\textbf+\,}}{\mathtt{9}} = {\mathtt{19}}$$

x-y=3 and xy-5x+y=-13

Using the first equation we can rearrange it as y = x -3    and substituting this in the second, we have

x(x -3) - 5x + (x -3) = -13   simplify

x ^2  - 3x - 5x + x -3 = -13

x^2 - 7x + 10  = 0      factor

(x -5) ( x-2) = 0   and setting each factor to 0, we have that x = 5 and x =2

And using y = x -3, when x = 5, y = 2   and when x = 2 , y = -1

So...our solutions (intersection points) are (5,2) and (2, -1)

2x^2-px+q=0

x=1/2, -2

what is p-q?

We have that

2(1/2)^2 -(1/2)p + q = 0  →  (1/2) - (1/2)p + q = 0       (1) 

And .... 2(-2)^2 - (-2)p + q  = 0     →     8 + 2p  + q  = 0   (2)

And subtracting (1) from (2) we have  15/2 + (5/2)p = 0    →  15 + 5p =0  → p = -3

And using (2), we have 8 - 6 + q = 0   → 2 + q  = 0    →  = -2

So, our function is ..y =  2x^2 -3x - 2

So....p - q  = -3 - (-2)  = -1

x=0

She does a good job of making Scooby snacks from snarky comments, too!

y ≤ -2x^2

x^2+y^2=24 and y=2x+3  

Substituting  for y in the first equation, we have

x^2 + (2x + 3)^2  = 24    simplify

x^2 + 4x^2 + 12x + 9 = 24

5x^2 + 12x  - 15  = 0     this won't factor..so using the onsite solver, we have

$${\mathtt{5}}{\mathtt{\,\times\,}}{{\mathtt{x}}}^{{\mathtt{2}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{12}}{\mathtt{\,\times\,}}{\mathtt{x}}{\mathtt{\,-\,}}{\mathtt{15}} = {\mathtt{0}} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = {\mathtt{\,-\,}}{\frac{\left({\sqrt{{\mathtt{111}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{6}}\right)}{{\mathtt{5}}}}\\
{\mathtt{x}} = {\frac{\left({\sqrt{{\mathtt{111}}}}{\mathtt{\,-\,}}{\mathtt{6}}\right)}{{\mathtt{5}}}}\\
\end{array} \right\} \Rightarrow \left\{ \begin{array}{l}{\mathtt{x}} = -{\mathtt{3.307\: \!130\: \!750\: \!570\: \!547\: \!8}}\\
{\mathtt{x}} = {\mathtt{0.907\: \!130\: \!750\: \!570\: \!547\: \!8}}\\
\end{array} \right\}$$

Let's round these to -3.31 and .91

And using y = 2x+ 3,  when x = -3.31, y = -3.614 and when x =.91, y = 4.814

So the solutions are (-3.31, -3.614) and ( .91, 4.814)

Let's try this a slightly different way...

12 x 1/8   =  12/1 x 1/8 =  12/8   = [ 4 x 3 ] / [4 x 2 ]  =  3 / 2

The fractions you're adding just have the denominators of 4, 6 and 8

We only need worry about the 6 and the 8 because 4 is already a factor of 8

So 8 factors as 2^3 and 6 factors as 2 x 3

So...taking the highest power of each different factor, the  common denominator = 2^3 x 3 = 8 x 3 =  24

So we have

3/4 = 18/24

-5/6  = - 20/24   and

-3/8 = -9/24

Now...just add.subtract the fractions on the right side of the equal signs...

1 1/2    Just put in the calculator 12*(1/8), you will get 1.5, which equal 1 1/2

(2-1/x))/(x+3)  ....we could use the quotient rule here, but I always tend to forget it, so I prefer to write the denominator as a ( -1 ) power and just use  the product / chain rules....so we have

 y = (2 - x^-1) (x + 3)^-1

y ' =  x^-2(x + 3)^-1 - (2 - x^-1)(x +3)^-2

Which we could simplify as  (x+ 3)^-2 [ x^-2 (x + 3) - 2 + x^-1 ] = (x+ 3)^-2 [ 2x^-1 + 3x^-2 - 2 ]

[Note....there are several other acceptable forms ]

y =  (2 - x^-1) / (x + 3)

Using the quotient formula:

y'  =  [ (x + 3)(x^-2) - (2 - x^-1)(1) ] / (x + 3)²

y'  =  [ x^-1 + 3x^-2 - 2 + x^-1 ] / (x + 3)²

y'  =  ( 2x^-1 + 3x^-2 - 2 ) / (x + 3)²

Let Jenny's age be N

And Manuel's age = N + 5

So we have

3/4 (N + 5)  = N  simplify

(3/4)N + 15/4  = N    subtract (3/4)N from both sides

15//4 = (1/4)N    multiply both sides by 4

15 = N 

And  Manue's age  is 15 + 5 = 20