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Your doing good Melody, Keep up the good work 

Can you please show your work?

Thanks, Guest 

Solve the following system:
{2 x + 2 y = 36 | (equation 1)
y + 1 = x + 3 | (equation 2)

Express the system in standard form:
{2 x + 2 y = 36 | (equation 1)
-x + y = 2 | (equation 2)

Add 1/2 × (equation 1) to equation 2:
{2 x + 2 y = 36 | (equation 1)
0 x+2 y = 20 | (equation 2)

Divide equation 1 by 2:
{x + y = 18 | (equation 1)
0 x+2 y = 20 | (equation 2)

Divide equation 2 by 2:
{x + y = 18 | (equation 1)
0 x+y = 10 | (equation 2)

Subtract equation 2 from equation 1:
{x+0 y = 8 | (equation 1)
0 x+y = 10 | (equation 2)

Collect results: x=8            and               y=10 
 

Yes he was asking for 5/7, I explained all of the steps, It took me 10 mins 

your problem after combining like terms is 3.8125?

I got -2/3 anyone else

16,581,375^67=

5.1829410256 3232253910 3775186805 8024724297 6214535865 5666377512 0823027807 3616248456 9103932942 3626448489 8267556795 9992756527 5232823052 5219435345 9702283029 6503882097 2465303426 4425161532 3741089104 3340795997 9495458367 8254930491 5055601238 4844968841 8666708099 2619477003 1581864553 1899593518 6040825404 7240121438 8560437075 3468299003 1296009357 7289596249 1746179818 9152986650 9940041559 5249624817 7756798363 3582842305 2983722629 6275024038 2135531854 0380019366 6555562455 0449920207 0292085409 1644287109 375 E+483

I believe your equation is a TVM(Time Value of Money) formula for finding a loan payment and it should  be written like this:

$3,000=$500,000* i*{[1 + i]^360 / ([1 + i]^360 - 1)}, solve for i

When you raise (1+i) to 360, that means your interest rate is already divided by 12. This appears to be a mortgage for $500,000 amortized over 30 years, or 360 months, with a monthly payment of $3,000 @ i% compounded monthly. 

If I'm correct in my assumption, then there is no DIRECT solution for i%. You can only find i% through iteration and interpolation. When I plug your numbers into my computer, it comes up with a rate of 6% compounded monthly. That means the i% in your formula would be 6% / 12 =0.005, which is the monthly interest rate.

How did you know to make the hypotenuse sqrt5  ?

5/7 right

1/2 usually

19-4c=17

Subtract 19 from both sides

-4c=-2

Divide by 4 on both sides

c=1/2

What's 5 divide seven??

5/7

7 cannot go into 5

add a 0 after the 5

50/7

7 can go in 7 times

7*7=49

50-49=1

7 cannot go into 1

add a 0 after the 1

10/7

7 can go in once

10-7=3

7 cannot go into 3

add a 0 after the 3

30/7

7 can go in 4 times

30-28=2

7 cannot go into 2

add a 0 after the 2

20/7

7 can go in 2 times

20-14=6

7 cannot go into 6

add a 0 after the 6

60/7

7 can go in 8 times

60-56=4

7 cannot go into 4

add a 0 after the 4

40/7

7 can go into 5 times

40-35=5

And we are back were we started your answer is 0.714285... Repeating 

Let's go with 19.

It might be interesting to see if we can discover a pattern here.

Note

Three elements....two at  time  (1,2) (1,3) (2,3)....sum  =   12

Four elements .... two at a time  (1,2) (1,3) (1,4) (2,3) (2,4) (3,4)  .....sum  =  30

Five elements....two at a time  (1,2) (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) (3,4) (3,5) (4,5)  ....sum  = 60

Note that for N elements taken  2 at a time......the pattern of sums seems to be

(N - 1) ( N ) ( N+ 1)  / 2  

So....for 6 elements taken 2 at a time.....the sum should be

(5) (6) (7)  / 2  =     210 / 2  =   105

Verify for yourself that this is true.......!!!!!!

heureka answers is (of course!) correct; but, if you don't have that formula at hand, you might think about it this way:

Since the highest common factor of 140 and x is 20, x must contain 20 as a factor.

Since the lowest common multiple of 140 and x is 420: because 140 divides into 420 three times, x must contain a 3.

Since x contains both 20 and 3 as factors, x is 20 · 3 = 60.

3.1x + 2.51y  =  43.97

x + y  =  15

I don't know if these are the two correct equations; but, if they are, one way to solve them is by solving the second equation for x and then substituting that value in the first equation:

x + y  =  15     --->     x  =  15 - y

3.1x + 2.51y  =  43.97     --->     3.1(15 - y) + 2.51y  =  43.97

                                                   46.5 - 3.1y + 2.51y  =  43.97

                                                   46.5 - 0.59y  =  43.97

                                                   -0.59y  =  -2.53

                                                    y  =  4.29

Substituting that value into the equation  x = 15 - y     --->     x  =  15 - 4.29      --->     x  =  10.71

Since AO is ll to QR then PR is a transversal that cuts parallel lines

Thus angle POA  = angle PRQ

And angle QPR  = angle APO

Thus, by Angle-Angle congruency....triangle QPR  is similar to triangle APO

But similar triangles are similar in all respects.....

So........  PQ / PR  = PA / PO    which also implies that     PA / PQ  = PO / PR

But.....PA  = AQ.....so.....PA  = (1/2)PQ

Then....by substitution.......

(1/2) PQ / PQ  =  PO / PR

Simplifying.....we have that    

(1/2)  = PO  / PR    whicih implies that

PO  = (1/2)PR

And since PR is the diameter of the circle and PO is (1/2)  of PR.....O must be the center of the circle

affirmatively 21... but truthfully 19

There was a rock. And then another rock formed. So now there were 2 rocks! 

That is how math was formed.

Ok then. I got the answer. 

In an equilateral triangle, all the side lengths are the same.

So that means 7x = 5x + 16.

Subtract 5x to both sides to get 2x = 16.

Divide both sides by 2 to get x = 8.

But that's not our answer. We need to plug in 8 instead of  x to one of the 'sides equations.'

Let's plug it into 7x. 

7(8)  = 56. Remeber, we substituted 8 for x.

So we know a side of the equilateral triangle is 56 cm. 

And we know that all the side lengths are the same.

So the last side length would be 56 cm.

Hi Melody,

well, honestly....I went about the whole thing a different way...The reason I believe I cannot make use of ratio's, is because I do not have any values. I do not know how one can use ratio's if there are no values....so I did this:

In triangle PQR:

AOIIQR     Given

PA=AQ     Given

Therefore AO runs through the middel of triangle PQR

Therefore AO devides PR     Midpoint theorem

Thus PO=OR

Since PR is the diameter,     Given

PO must equal OR

Thus "O" is the middle of the circle.

Is this wrong?..Thanx for your assistance!!