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360  - 150  =   210 degrees

sumfor(n, 1, 95, (1/n - 1/(n+5))==840322519 / 376437600
 

Find  sum of arithmetic sequence:    Sum =    209/2 ( 1 + 209)           then subtract   210   to get    21 735

Start with point slope form

y - -1  = -5/4 ( x- -4)      re arrange to slope intercept from     y = mx + b

y + 1 = -5/4(x+4)

y = -5/4 x -6

2 +16 = 18

3 o'clock   and  9 o'clock

If (x-y)/(x+y) = 5/2, find x/y.

x-y = 5/2 x  + 5/2 y

- 3/2 x = 7/2 y

x/ y = 7/2 * -2/3  = -14/6 = -2 1/3

12x

21x

x12

x21

1x2

2x1        6 ways for 1 and 2 to pbe in the number   the 'x' can be any of the remaining 8 numbers  (3 4 5 6 7 8 9 0)

6 * 8 = 48

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https://web2.0calc.com/questions/i-am-following-ep-s-suggestion

Find the value of  a so that the system has no solutions.

Hello Guest!

\(2x - 4 = ax + 7 - 3x\\ ax-3x-2x=-4-7\\ ax-5x=-11\\ x(a-5)=11\\ x=\dfrac{11}{a-5}\)

 The system has no solutions if a=5.

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6xy+10x2y=?

Hello Guest!

You can only factoring out.

\(6xy+10x^2y=2xy\cdot (3+5x) \)

  !

Answered.

C-7=3/4(P+7)

4(c-7)=3(P+7)

4C-28=3P+21

4C-3P=21+28

4C-3P=49       (1)

C-27=1/3(P+27)

3C-81=P+27

3C-P=108       (2)

check what I have done and then solve simultaneously.     

Robert is twice as old as Charlotte. Five years ago his age was three times Charlotte's age. Find their present ages.

Hello Guest!

\(r=2c\\ r-5=3(c-5)\\ 2c-5=3c-15\\ \color{blue}c=10\)

Charlotte is 10 years old.

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What us the easiest way to find the solution to 1+2-3+4+5-6+7+8-9+...+208+209-210 ?

Hello Guest!

The easiest way to do this is with the Gaussian empirical formula.

\(\sum\limits_{k=1}^{n} k =\dfrac{n(n+1)}{2}\)

\(\sum\limits_{k=1}^{209} k-210 ={\color{black}\dfrac{209(209+1)}{2}-210=}21735\)

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Rectangle ABCD is the base of pyramid PABCD. If AB=8, BC=4, PA perpendicular to AD, PA perpendicular to AB, and PB=15. Then what is the volume of PABCD?

Hello Guest!

\(h=\overline {PA} =\sqrt{15^2-8^2}\)

\(h=\sqrt{161}\)

\(V=\frac{1}{3}\cdot \overline {AB}\cdot \overline {BC}\cdot h=\frac{1}{3}\cdot 8\cdot 4\cdot \sqrt{161}\)

\({\color{blue}V=10.\overline 6\cdot\sqrt{161}}\approx135.345\)

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On the right-hand side make the denominator (x-2)(x+1) 

Then the bottoms will be the same and you can just equate the coefficients on the top.

Ok I answered

Suppose Nate's total money is $x and the cost of 1 curry puff is $y.

Since the cost of 1 apple pie is twice the cost of a curry puff.

Therefore the cost of 1 apple pie is $2y.

Now the cost of 6 curry puffs and 13 apple pies is $(6y + 26y) = $32y.

Since Nate spent 1/3 of his money on 6 curry puffs and 13 apple pies.

Therefore           

    32y = \({x \over 3}{}{}\)
 ⇒ x = 96y  .............. (1)

Now the remaining money is x - x/3 = 2x/3.

  3/4 of the remaining money is 3/4 * 2x/3 = x/2.

Since he bought more apple pies with 3/4 of the remaining money (^$\({x\over 2}{}{}\)) and he paid a total of $92.50 for all the apple pies.

Therefore

    26y + x/2 = 92.50

⇒ 26y + 96y/2 = 92.50    using equation (1)

⇒ 74y = 92.50 

⇒ 2y = 92.50/37

⇒ 2y = 2. 50

So Nate pay $2.50 for 1 apple pie.

Let, T 

he savings of Ramlan be x,

Savings of Brandon be y,

Savings of  Jonathan be z

Now in the question it is given that,

Ramian donated 2/3 of his savings,

Brandon donated 4/7 of his and

Johnathan donated 3/5 of his.

They had a total savings of $1652 

Total savings = x + y + z = $1652

Also the donation made by all is given to be equal, hence we can write,

                       2/3(x)=4/7(y)=3/5(z)
Now we get,

2/3x = 4/7y

x/y = 6/7

similary, 

                                 x/z = 9/10

To simplify we shall take the ratio of savings of all three from above equation,

                                         x : y : z = 18 : 21 : 20

Now let a be any constant, total saving is,

                  18a + 21a + 20a = 1692

                                      59a = 1692

                                          a = 28

Hence the donation by each is :

2/3(18)(28) = $336

4/7(21)(28) = $336

3/5(20)(28) = $336

Donation by each is $336.

If the tickets were the same amount of money, how much money does Bill have?

Hello Guest!

\(\dfrac{2\cdot 20€}{5}=\dfrac{4y}{15}\\ y=\dfrac{15\cdot 2\cdot 20€}{4\cdot5}\)

\(y=30€\)

Bill has 30 Dollars.

Bill has 15 dollars.

Mr and Mrs. Wilson have 3 children: Jessica, Jeremy, and Jenna. The average of Jessica and Jeremy's age is 11. The average of all three children's ages is 10 . How old is Jenna?

Hello Guest!

\(\frac{js+jr}{2}=11\ |\ \cdot 2\\ js+jr=22\\ \dfrac{js+jr+jn}{3 }=10\ |\ \cdot 3\\ js+jr+jn=30\ | -jn\\ js+jr=30-jn\)

\(22=30-jn\\ jn=30-22\)

\(jn=8\)

Jenna is 8.

  !

By method of partial fractions, A - B = 1 and 4A + B = 1.  Solving, we get (A,B) = (-3/5,2/5).