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3(x+y) - 5(x-y)  =

3x + 3y  - 5x + 5y  =

-2x + 8y

3x+23=54       subtract 23 from both sides

3x =  31         divide by 3 

x   = 31 / 3

The had a total of  $28/.20 = 140 coins...so...

A + B + C + D  = 140   ( 1)

A + D  = B + C   →  A + D - B - C  = 0  (2)

A - C - D = 2    →  A - 2  = C + D   (3)

B + D - 8  = A + C      (4)

Add (1)  and (2)   →  2A + 2D  = 140  →  A + D  = 70 →  D  = 70 - A   (5)

Put (5)  into (3)  →   A - 2  = C + ( 70 - A)  →   2A  - 72  = C   (6)

Put  (5)  and (6)  into (4)

B + [70 - A] - 8  =  A + [2A - 72]   →   B  =  4A - 134

So we have

A + B + C + D  = 140

A + [4A - 134] + [2A - 72] + [70  - A]  = 140

6A =   276  →  A  = 46  →   $9.20    =  $2.20 profit

D = 70 - 46  =   24   →  $4.80   =  $2.20  loss

C  = 2(46) - 72  = 20  →  $4.00 → $3.00 loss

B = 4(46) - 134  = 50   →  $10.00 → $3.00 profit

Notice that this is a "zero sum" game with regard to profit and losses...just as we would expect !!!!

Well, it depends what sides or angles are given. 

If you're finding cosine of an angle, you would first have to figure out the type of triangle you are dealing with in order to find the unknown angle or theta. 

If your triangle is a right triangle and you're trying to find another angle, you would use SOHCAHTOA. Cosine would be used if you have the adjacent and hypotenuse sides. 

If your triangle is not a right triangle, use cosine law. For example, if you are trying to find angle A, you would use the first formula, and the second formula for angle B and third for angle C.

cos(A) = b² + c² − a²  / 2bc

cos(B) = c² + a² − b²  / 2ca

cos(C) = a² + b² − c²  / 2ab

I hope this answered your question LOL or if you understood any of it. I literally just finished grade 10 math last week and I'm pretty sure I did this right but you could check ofc. I recommend www.mathsisfun.com if you need more help! 

Have a great evening and good luck! 

Sara

More important than knowing the decimal expansion of pi is knowing how you derive pi because that tells you why it is important.

If you divide the circumference of any circle by its diameter, you will get pi.

The constant  willl occur at the 5th  term in the binomial expansion of this  =

C(6,4) * (2x^2)^2 * (1/x)^4  =

15 (4x^4) (1/x^4)  =

15* 4   =

60

a + 14d  = 9a    →  8a   = 14d  →   d = [8/14]a   =  (4/7)a

So

S₃₅  = (35/2) [2a + 34 (4/7) a ]

S₃₅   = (35/2) [ 2a + (136/7)a ]

S₃₅  = (35/2) [ (150/7)a ]

S₃₅ = ( 35/7)(150/2) a  = (5)(75) a   =  375 a

A sales manager has weekends off and has 20 paid vacation days per year, including holidays that fall on weekdays. If her salary is $93,600 per year, what is her pay per workday?

It's    60.

Using the binomial theorem,the fifth term is (6)(5)(4)(3)(2x^2)^2(1/x)^4    /  4!

=(6)(5)(4)(3)(4x^4)(1/x^4)     /4!

=(6)(5)(4)(3) (4)       /4!

= (6)(5)(4)(3)  (4)/     (4)(3)(2)

=(6)(5)(4)  /(2)     = (6)(5)(2)  = 30 x 2  = 60

I would say there are NINE significant figures (since there is a .8 after the '0')

From the web:

There are three rules on determining how many significant figures are in a number:

Non-zero digits are always significant.

Any zeros between two significant digits are significant.

A final zero or trailing zeros in the decimal portion ONLY are significant.

Arc cos (12/15) = x = 36.87 degrees

degrees of arc / 360  x pi x dia  = arc length

We have

-7  = a₁ + (14)d     → 14d  = -7 - a₁      (1)

210  = (15/2) (2a₁ + 14(d) )      (2)

Sub (1)  into (2)

210 = (15/2) ( 2a₁ -7 - a₁ )

210 ( 2 / 15) =  a₁ - 7

28  = a₁ -  7     

a₁   = 35

And

14d  = -7 - 35   →    14d  = - 42   →   d  = -42/14  =  -3

a₁   = 35      a₂  =   32    a₃  = 29

12 minutes at 15 mph covers 3 miles to the store

3 miles /30mph =  .1 hr travel time coming home (6 minutes)

6 miles / (12 minutes + 6 minutes) =  6 /18 = 1/3 miles / minute = 20 m/hr average

Since all three are prime numbers, therefore their LCM =2 x 5 x 7 =70

 x^2 + y^2=169   (1)

5x+12y=169     (2)

The slope of any tangent line to the circle will be  =  -x /y

The slope of the line  =   -5/12

Equating slopes, we have

-x /y  = -5/12    →  y = 12/5 x       sub this into (1)  

x^2 +[ (12/5)x]^2  = 169

x^2 + (144/ 25)x^2  = 169

169x^2 / 25  = 169

x ^2 / 25   = 1

x^2  =25

x =  ± 5

When x = 5, y= (12/5) *5   = 12

When x  = -5, y  = (12/5) * -5  = - 12

Only   (5,12)   will  saitsfy  5x+12y=169

Here's a graph :

x =

Thank you