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the time in hours and minutes between 12:20 and 23:00

\(\begin{array}{rcl} 23:00 &=& 22:60 \\\\ \hline 22&:&60 \\ -12&:&20 \\ \hline =10&:&40 \end{array}\)

Is your calculator stupid too?

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Can someone show me how to solve this? x/8-(10-3/2x)=x+5 I know that x is 24, but how do i solve it?

\(\frac{x}{8}-(10-\frac{3}{2}x)=x+5\\ \frac{x}{8}-10+\frac{3x}{2}=x+5\\ \frac{x}{8}-10+\frac{3x}{2}+10=x+5+10\\ \frac{x}{8}+\frac{3x}{2}=x+15\\ 8*(\frac{x}{8}+\frac{3x}{2})=8*(x+15)\\ x+12x=8x+120\\ 13x=8x+120\\ 13x-8x=8x+120-8x\\ 5x=120\\ x=24 \)

If x>2 then (x^2-x-6)/(x^2-4)=

\(\frac{x^2-x-6}{x^2-4}\\ =\frac{(x-3)(x+2)}{(x-2)(x+2)} \qquad x\ne-2\qquad \mbox{because it has to be greater than 2}\\ =\frac{x-3}{x-2} \)

how to factor 5s^2 +19s -4?

You need to find 2 numbers that multiply to 5*-4=-20   (so one is neg and one is pos)

and add to +19        (so the 'big' one is positive)

they would be +20 and -1

split   19s up into  20s-1s

\(5s^2+19s-4\\ =5s^2+20s-1s-4\\ \mbox{factorise in pairs}\\ =5s(s+4)-1(s+4)\\ =(5s-1)(s+4)\)

That is as far as you can go :))

x/8 -10 +3/2x = x + 5   Add 10 to both sides

x/8 + 3/2x = x + 15       Add left side and subtract x from both sides

x/8 + 12/8x -x =15

13/8x -x =15

13/8x - 8x/8 =15

5x/8 =15

5x= 15 (8)

5x= 120

x= 120/5 = 24

What is 0.125 as a percent?   =  0.125*100%   =  12.5%

Inverse tan is the same as arc tan

on this calc press [2nd] [atan]

in a motor race the winning car travels 231 miles in 2 hours 45 minutes. What is the average speed in miles per hour?

231 /  2.75

As below:

Music frequency

This means -1.885x10^-5, or -0.00001885

The "E" is often used in text-based computer programs.

Usually, to find the turning points of a function you need to differentiate it and set the result to zero.  If the function has two minima it must have at least one maximum so you might have to solve a cubic equation to find the turning points.

This would probably be clearer if you gave a specific example.

how can i calculate 6 foot 3 minus 5 foot 9

6-5=1

so you have 

1 foot 3 inch - 9 inch

=15inch - 9 inch

= 6 inch 

List a series of values for x and then calculate the corresponding values of 5x/(x-2), so you have pairs (x, 5x/(x-2)).

Note that you should avoid using x = 2 as this will result in a singularity. The graph will consist of two separate lines; one to the right of x=2 and one to the left.

If tan(x) = 2 then x =  tan^-1(2) ≈ 63.4°  This is in the first quadrant where sin(x) and cos(x) are both greater than 0.

\(\sqrt{X+\sqrt{X+\sqrt{X+...}}}=5\\ Let\\ Y= \sqrt{X+\sqrt{X+\sqrt{X+...}}}\qquad where\;\;\;Y=5\\ Now\\ \sqrt{X+Y}=5\\ X+Y=25\\ but\; Y=5\\ X+5=25\\ X=20\)

a)   4 / 8 = L / 3      where L is the length of the strut .....cross- multiply

12 = 8L      divide both sides by 8

12/8 =  L   =  1.5 ft

b)   I can't see a picture....but........the rafter and the top of the wall form vertical angles inside and outside the structure......the rafter will be as far below the top of the wall 1.5 ft outside the wall as it is above the wall  1.5 ft inside the structure........so we have

4 /  8 =  H / 1.5      where H is the height pf the rafter 1.5 from the wall on the inside of the structure.....cross-multiply

6 = 8H      divide both sides by 8

3/4 ft  = H   

So....the rafter will be  [8 - 3/4] ft     = 7.25 ft from the floor at its tip on the outside of the building

We can use similar triangles to solve this.

At 3 feet east of the west wall, the ceiling rises 2.5 ft.  So....we want to know how far we are from the wall when the ceiling rises 4ft above 8 ft   [12 ft is 4ft more than the 8 ft at the wall ] :

3 / 2.5  =  d / 4      where d is the distance from the west wall where the ceiling ht = 12ft

Cross-multiply

12  = 2.5 d         divide both sides by 2.5

12 / 2.5 = d  = 4.8 ft from the west wall

If mx^3+(n-5)x^2+3x-1 is divided by (x-2) , the remainder is -11 and it has a factor of (x-1), find the values of m and n

If x - 1 is a factor, then 1 is a root.....and we have.....

m + n - 5 + 3 - 1  = 0     simplify

m + n  - 3 = 0    →   n = 3 - m

And we know that  f(2) = 11   .....so....

m(2)^3 + ( 3 - m -  5)(2)^2  + 3(2) - 1 = 11   simplify

8m  + (-2 - m)(4)  + 6  - 1   = 11

8m -8 - 4m  + 6 - 1   = 11

4m - 3 = 11      →  m  = 7/2      and  n = 3 - 7/2 =  -1/2

Here's a graph of the function :    https://www.desmos.com/calculator/vsp5mk19bj

x^3-144x<0   .....let's factor the left side as

x(x -144) < 0  =  x( x + 12) (x - 12) < 0

The solution comes from one, or more, of these intervals :

(-inf, -12) (-12, 0) (0, 12) (12, inf)

If we pick the test points,  - 13, -3, 3, and 13   and put them in the factored equation, -3 and 13 make the inequality true, but -13 and 3 make it false

So.....the solution intervals are (-12, 0) and (12, inf)

Here's a graph that will show this is true :   https://www.desmos.com/calculator/uc5lu7mmsj