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I am sorry, I didn't see where. I am also not posting this question because I want someone to do my homework. I am doing it truely to see what ways people can solve it!

Acid of ingredients added together = acid in final solution

.10a      +    .20 ( f-a)   = .16 f               a = amount of X      f-a = amount of Y    f = final amount

.10a + .20f-.20a = .16f

-.1 a = - .04 f

a = .4 f        ( this is the amount of X)

then      Y = f - a = f - .4f = .6 f

then X:Y =    .4  :  .6 =   2 :3                         

Ill give you some hints:

sqrt(45) = sqrt(9*5) = 3 sqrt(5)

sqrt(36) = 6

sqrt(27) = sqrt(3*3*3) = 3 sqrt(3)

sqrt(18) = sqrt(9*2) = 3 sqrt(2)

sqrt(9) = 3

It should be easy from here, just plug in the simplified version in for the unsimplifiied, and then you will see what to do from there! 

no problem! 

Bike store

 1.30 x = 125     solve for 'x' the wholesale price of the bike

1.87 / 22 = .085 = 8.5% tax

66 * .085 = $ 5.61 tax

Another way:   66 dollars is 3 times 22, so the  tax will be 3 times the 22meal tax    1.87 * 3 = $ 5.61

Please post multiple questions seperately....you are more likely to get a response....

   I answered ONE of your questions.....people will see there is a response and not look at your post to realize there are more questions!

a - 1200 * 1.0925 =1,311 dollars

b - 1200 * 0.75 =900 dollars - after 25% discount

900 * 1.0925 =983.25 - cost of the sewing machine.

c - 1,311 * 0.75 =983.25 - same as "b"

d - 1200 * 0.75 =900 dollars

1,311 - 900 =411 dollars in savings compared to "a"

411 / 1311 =31.35% =~31% in savings comapared to "a"

e - No, you saved the percentage in "d" or about 31%

lol, but very true indeed...

"How many ordered pairs of positive integers (x,y) satisfy the equation x/y = 100/(xy) + y/x?"

Multiply both sides by xy

x² = 100 + y²  

Rearrange

x² - y² = 100

Rewrite as 

(x + y)(x - y) = 100

100 can be expressed as  

50x2   For this we set

x+y = 50

x-y = 2

Add to get 2x = 52 so x = 26, hence y = 24

100 can also be expressed as 

25x4

20x5

10x10

I'll leave you to find the x and y values corresponding to these products.

3. Hint: Simplify both equations to its simplist.

4x + 15 > -9

4x > -24

x > -6

4. Hint: Plug in the answers from the multiple choice list.

I 4x + 3 I = 3

I 4(0) + 3 I = 3

I 3 I = 3 

As follows (I think!):

I don't know if the following is what is wanted or not (I'm guessing, based on what the vectors looked like to me!).  a, b and k are constants (not necessarily the same for each matrix).

1 -  compute   12121_3 * 1222_3 =101222102 (in base 3)

2 - compute 1980_16 / 18_16 =110 (in base 16)

Expand the sequence:

1, 1/3, 1/9, 1/27, 1/81, 1/243. If you sum them up, you should get =364 / 243. Therefore, just count the number of terms, which = 6 terms.

Because the numbers involved are very small, just by inspection, we can come to the conclusion that the smallest x that will satisfy the 3 congruences is 22, since:

22 mod 3 = 1

22 mod 5 = 2

22 mod 7 = 1. 

To this we can add the LCM[3, 5, 7] = 105 for a genral solution:

x = 105n  + 22, where n =0, 1, 2,3 .........etc. So, if you we use the smallest x, we have:

22 mod 105 = 22. Or:

[105 + 22] =127 mod 105 =22

It is generally much easier to caculate the VOLUME of the final mixture, in this case 16% acid, if that volume is given. But, we can make up a theoretical volume of say, 10 c.c.

Let the amount of 10% acid needed = T

Then, the amount of 20% acid needed = 10 - T

0.10T + 0.20*[10 - T] =0.16 * 10, solve for T

T = 4 cc of 10% acid will be needed

10 - 4 = 6 cc of 20% acid will be needed.

So, the ratio needed to make a mixture of 16% acid will be:

4 : 6 = 2 : 3 . In other words, you will need to mix 2 parts of 10% acid with 3 parts of 20% acid to make a mixture that is 16% acid.

Thanks guest,

I just want to have a quick look too.

For what value of c will the circle with equation x^2 + 8x + y^2 + 4y + c = 0 have a radius of length 7?

$x^2 + 8x + y^2 + 4y + c = 0\\ x^2 + 8x + y^2 + 4y = -c\\ x^2 + 8x +16+ y^2 + 4y +4 = -c+16+4\\ (x+4)^2+(y+2)^2=20-c\\~\\ 20-c=49\\ 20-49=c\\ c=-29$

That is what I get   

Firstly there is no x in the question.   Use the pronumerals that you are given.

I asked you for    $g=? \qquad v_0=? \qquad h_0=?$

You have not given them to me. But you have obviously done it.

what you have done is not exactly wrong.

Can you please present it properly though, as an equation, and with the correct letters. Then I will look at it with you.

Hi Melody, I tried the question by my self and got -2(x-2)^2 +18. I got this from -1/2(4)x^2+8x+10 and after I solved that I got what I first said.

There probably is some simple rule but I don't know it.

I just looked at x=1 mod 7, found a list of values, and looked for the first one that made the first two equations true as well.

Then I found the mod105  of that number.

It didn't take all that long for find the answer.

hi Finace,

First you need to determine the value of the constants

$g=? \qquad v_0=? \qquad h_0=?$

then substitute the values into the formula and simplify it.

now you have height as a concave down parabola function in terms of time.

Now factorize the quadratic and sketch the parabola.

See how much of it you can do by yourself? 

Get back to us with your contribution.

A request to other answerers:

This is a teaching answer please do not override it.

m∠CXA = 23 + 113 

angle CXA = 136 degrees 

7/4    and    15/8