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Thanks to both of you!

There isn't one exact number but there is an infinite amount of numbers opposite to -twelve

The inverse of -12 is 12.

Let y be the number of years until the mother is twice as old.....so we have......

The mother's age at that time   =  2 times the son's age at that time

34 +  y   =  2 ( 6 + y)    simplify

34 + y =  12  + 2y     subtract y, 12 from both sides

22  = y

The mother will be twice as old in 22 more years

And in 22 years, the son  will be 6 + 22  = 28 years old

Check :

34 + 22  =  56

6 + 22  =  28

And 56  is twice as old as 28   !!!!

34 = mothers age

6 = son's age   

in 'x' years mom will be 34 + x     son will be 6+x    ALSO   two times sons age is equal to mom's    34+x = 2(6+x)   solve for x = 22 years  

so sone will be 6 + 22 = 28 and mom will be  34 + 22 = 56

Hello guest!

3x+(-4)=2v+9

3x + (-4) = 2v + 9                    dissolve clip

3x - 4 = 2v + 9                        [ + 4

3x = 2v + 9 + 4

3x = 2v + 13                           [ / 3

x = (2/3)v + 13/3 

Greeting asinus :- )

  !

We want to make sure that any 20 of 40 questions are correct....so the number of possible different sets of correct questions  =  C(40, 20)

We have a 25%  =.25  probability of answering each question correctly and a 75%  = .75 probability of an incorrect answer.....so......the probability of getting any 20 questions correct is given by :

C(40,20) * (.25)^20 * (.75)^20   = 0.0003976  =  about   .03976%

Mmmm......doesn't seem that guessing is going to help much !!!!

Hello guest!

how do you find the hypotenuse with only the opposite and relevance angle?

sin alpha = opposite side / hypothenuse

Hypothenuse = opposite side / sin alpha

Greeting asinus :- )

  !

Use the  x^y button right next to the ' 7 '       Eaxmple :  For    4^3        Enter   ' 4'   then the x^y button then ' 3 '         

100

h = height of building

d = horizontal distance

h - 20.75 = d*tan(18+16/60)

h+ 20.75 = d*tan(56+28/60)

Subtract the first from the second to find d, then substitute the result into either one of the above to find h.

Solve for n over the real numbers:
1000 = 50 1.00125^n+10 (1.00125^n-1.99875)

50 1.00125^n+10 (1.00125^n-1.99875) = 2^(1-5 n) 25^(1-n) 801^n+10 ((801/800)^n-1601/801):
1000 = 2^(1-5 n) 25^(1-n) 801^n+10 ((801/800)^n-1601/801)

1000 = 2^(1-5 n) 25^(1-n) 801^n+10 ((801/800)^n-1601/801) is equivalent to 2^(1-5 n) 25^(1-n) 801^n+10 ((801/800)^n-1601/801) = 1000:
2^(1-5 n) 25^(1-n) 801^n+10 ((801/800)^n-1601/801) = 1000

2^(1-5 n) 25^(1-n) 801^n+10 ((801/800)^n-1601/801)  =  -16010/801+2^(1-5 n) 5^(1-2 n) 801^n+2^(1-5 n) 25^(1-n) 801^n:
-16010/801+2^(1-5 n) 5^(1-2 n) 801^n+2^(1-5 n) 25^(1-n) 801^n = 1000

2^(1-5 n) 5^(1-2 n) 801^n = e^(log(2^(1-5 n))) e^(log(5^(1-2 n))) e^(log(801^n)) = e^((1-5 n) log(2)) e^((1-2 n) log(5)) e^(n log(801)) = exp((1-5 n) log(2)+(1-2 n) log(5)+n log(801)) and 2^(1-5 n) 25^(1-n) 801^n = e^(log(2^(1-5 n))) e^(log(25^(1-n))) e^(log(801^n)) = e^((1-5 n) log(2)) e^((1-n) log(25)) e^(n log(801)) = exp((1-5 n) log(2)+(1-n) log(25)+n log(801)):
-16010/801+exp(log(2) (1-5 n)+log(5) (1-2 n)+log(801) n)+exp(log(2) (1-5 n)+log(25) (1-n)+log(801) n) = 1000

Simplify and substitute x = exp((1-5 n) log(2)+(1-2 n) log(5)+n log(801)):
 -16010/801+exp((1-5 n) log(2)+(1-2 n) log(5)+n log(801))+exp((1-5 n) log(2)+(1-n) log(25)+n log(801))  =  6 e^((1-5 n) log(2)+(1-2 n) log(5)+n log(801))-16010/801  =  6 x-16010/801  =  1000:
6 x-16010/801 = 1000

Add 16010/801 to both sides:
6 x = 817010/801

Divide both sides by 6:
x = 408505/2403

Substitute back for x = exp((1-5 n) log(2)+(1-2 n) log(5)+n log(801)):
exp(log(2) (1-5 n)+log(5) (1-2 n)+log(801) n) = 408505/2403

Take the natural logarithm of both sides:
log(2) (1-5 n)+log(5) (1-2 n)+log(801) n = log(408505/2403)

Expand and collect in terms of n:
(-5 log(2)-2 log(5)+log(801)) n+log(2)+log(5) = log(408505/2403)

Subtract log(2)+log(5) from both sides:
(log(801)+(-5 log(2)-2 log(5))) n = log(408505/2403)+(-log(2)-log(5))

Divide both sides by -5 log(2)-2 log(5)+log(801):
Answer: |  n = (-log(2)-log(5)+log(408505/2403))/(-5 log(2)-2 log(5)+log(801))=~2268

IT DOES BALANCE, BUT THERE MUST BE A SIMPLER WAY!!. MAYBE CPhill has one.

Assuming you need the 54th root of 1.11894   = 1.002083312     that is:  (1.002083312)^54 = 1.11894

1 2/3

First Arc csc (-3.1379280)  = -18.5832 degrees     then cos (-18.58329)  = .94786

kathh22......this one is a little difficult for me to picture the exact situation.......can you upload a photo???  [if it's from a textbook]

Even if you meant  2^(2/2) + 2     the answer is still  '4'

Assuming you need to solve for x,y:

From the FIRST equation: 4x + 10y = 40           4x= 40 - 10y        x= 10 - 10/4 y   Sustitute THIS value for 'x' into the SECOND equation:

3(10 - 10/4 y) - 10y = 37

30 - 30/4 y - 10y  = 37

-70/4 y = 7

y = 7 (-4/70)= -28/70 = - 4/10

Susbstitue this value fo y into one of the equations    x = 10 - 10/4 (-4/10) =  10 + 20/20 = 11

so (x,y) = (11, -4/10)

Check   4x + 10y = 40    4 (11) + 10(-2/5) =40

                                       44 -4 = 40                       Check!

         Another check   3x - 10y = 37

                                   3(11) - 10(-4/10) = 37

                                    33+ 40/10 = 37                    Check !

2^2/2+2=

= 4/2 + 2

= 2+2

= 4

The answer is 4.

SOLVING BY ELIMINATION

4x+10y=40  → equation 1               

3x-10y=37 → equation 2

add both equations:

7x=77

  x=11

substitute for x in equation 1:

4(11)+10y=40

44 + 10y = 40

10y= -4

y= -4/10

therefore,

x= 11

y= -4/10

From A.......we know a side (6.56)   and an opposite angle = 46°10'  = [46 + 1/6]°

And OA  is the  adjacent side   [ the distance from O to A ]......so we have

tan[46 + 1/6] = 6.56 / OA   solve for OA

OA = 6.56 / tan [ 46 + 1/6]  = about 6.3 miles

From B.....this will be the hypotenuse of a right triangle

We can use the Pythagorean Theorem to solve this

OB   = sqrt [  6.56^2 + 6.3^2 ]   = about 9.1 miles

I will ASSUME you meant:    Whats -16t^2 + 16T+ 480   =0

Let's simplify by dividing through by  -16 to get

t^2 -t - 30 = 0

(t-6)(t+5) = 0       reults in t = 6 or -5