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700,000 + 5,000x = y

and 

600,000 + 10,000x = y

So

600,000 + 10,000x = 700,000 + 5,000x

Solve for x:

10,000x = 100,000 + 5,000x

5,000x = 100,000

x = 20

Plug in x to find y:

700,000 + 5,000(20) = y

700,000 + 100,000 = y

800,000 = y

See Cavalieri's Principle here :

http://www.cut-the-knot.org/Curriculum/Calculus/Cavalieri.shtml

\(7\frac{3}{8} = \frac{59}{8} = 7.375\)

Maybe we can take out a patent on a new math term, Melody....

I hereby declare that  GHCD  =  "Greatest Highest Common Denominator "

Wonder if they'll buy it....???

this button: ÷

or type in: /

Don't forget to put parenthesees around it if necessary.

A rectangular lawn has dimensions of 24 ft by 32 ft. A sidewalk will be constructed along the inside of all four sides. The remaining lawn will have an area of 425 square ft. How wide is the walk? Please show your work

Assuming that the sidewalk has a uniform width......call the width, x

And we have that

(24 - 2x) (32 - 2x) = 425    simplify

4x^2 - 112x + 768 = 425

4x^2 - 112x + 343  = 0  factor

(2x - 7) (2x - 49)  = 0       set each factor to 0

2x - 7   = 0                                2x - 49   =  0         

add 7  to both sides                  add 49 to both sides

2x = 7                                       2x =  49        divide both sides by 2

x = 7/2 ft  = 3.5 ft                        x = 49/2  ft  = 24.5 ft

24.5 ft sounds pretty wide for a sidewalk!!!......besides......it's an impossible answer

3.5  ft. seems more reasonable.....

\(4\frac{1}{2} + 9\frac{1}{8} \\ = 4\frac{4}{8} + 9\frac{1}{8} \\ = 13\frac{5}{8}\)

what is the the square root of 5 squared plus 2 squared?

Sorry! Thanks CPhill!

\(\sqrt{5^2+2^2}=\sqrt{25+4}=\sqrt{29}=5.38516\) !

The answer is 2,000.

I think we need one more piece of information about the triangle.

The answer is +12.

Yes they are equal. When you have a negative exponent on a term in the numerator you can move that term to the denominator and get rid of the negative sign on the exponent. 2^-3 = 1/2³

cos(39)=22/x solve for x?

rad:

\(cos(39)=\frac{22}{x}\)

\(x=\frac{22}{cos(39)}=\frac{22}{0.2666}=82.50734\)

deg:

\(cos(39grd)=\frac{22}{x}\)

\(x=\frac{22}{cos(39grd)}=\frac{22}{0.7771}=28.3087\)

!

what is ghcd

Well GCD could be greatest common denominator and 

HCD could be highest common denominator.   (which is the same thing)

What is the context?

Solve for x over the real numbers:
2^(4 x + 16) = 6^(5 - 7 x)

Take the natural logarithm of both sides and use the identity log(a^b) = b log(a):
log(2) (4 x + 16) = log(6) (5 - 7 x)

Expand out terms of the left hand side:
4 log(2) x + 16 log(2) = log(6) (5 - 7 x)

Expand out terms of the right hand side:
4 log(2) x + 16 log(2) = 5 log(6) - 7 log(6) x

Subtract 16 log(2) - 7 x log(6) from both sides:
(4 log(2) + 7 log(6)) x = 5 log(6) - 16 log(2)

Divide both sides by 4 log(2) + 7 log(6):
Answer: |x = (5 log(6) - 16 log(2))/(4 log(2) + 7 log(6))  = - 0.139181898....

x - y  = 7

x - y = 5

This has no solution.......the difference of two numbers can't have two possible answers....

No.......this used to confuse me, too....

The power [exponent] on the variables remains the same.....thus

1x + 2x   = 3x

It's when we are multiplying that the powers change.....thus

1x * 2x   =  [1 *2] * [x * x ]   = 2x^2

probability to get a number six on rolling 2 dice.

1 1 2 1 3 1 4 1 5 1 6 1
1 2 2 2 3 2 4 2 5 2 6 2
1 3 2 3 3 3 4 3 5 3 6 3
1 4 2 4 3 4 4 4 5 4 6 4
1 5 2 5 3 5 4 5 5 5 6 5
1 6 2 6 3 6 4 6 5 6 6 6 = 1 - (5/6)^2 =1 - 25/36 =11/36 =~30.56%

what is the the square root of 5 squared plus 2 squared?

\(\sqrt{5^2+2^2}=\sqrt{34}=5.831\)

!

We can use the Law of Cosines to solve this.....the horizontal distance, D, is given by:

D   =  sqrt  [ 18^2 + 18^2  - 2(18)(18)cos(72) ]  ≈ 21.16 inches

The best answer is 4. If you add 2 plus 2, it will become 4.

tan x = 18/22

arctan(tan x) = arctan(18/22)

x ≈ 39.289º

its 22

The answer is 4. 

If....... by "measure of center" you mean the median......arrange the values in increasing order

60,70,45,60,80,35,45  =

35, 45, 45, 60, 60, 70, 80 =

The median in an odd number of values is the middle number.....in this case, 60