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HInts:

1)  XU · UY  =  UF · UE     --->   XU · UY  =  56

     GV · VH  =  XV · VY     --->   XV · VY  =  80

2)  UY  =  UV + VY

     XV  =  XU + UV

3)  Combining 1) and 2):  XU · UY  =  56     --->     XU · (UV + VY)  =  56

                                        HV · VY  =  80     --->     (XU + UY) · VY  =  80

4)  To make the notation simpler:  x = XU   and  y = VY

5)  So:  x · (8 + y)  =  56     --->     x  =  56 / (8 + y)

            (x + 8) · y  =  80     --->     x  =  80 / y  - 8

6)  Combining these two equations:  56 / (8 + y)  =  80 / y  - 8

     Multiply each term by the least common denominator and solve, using the quadratic formula.

7)  So:  x · (8 + y)  =  56     --->     y  =  56 / x - 8

            (x + 8) · y  =  80      --->     y  =  80 / (x + 8)

8)  Combine the two equations of step 7) and solve in a way similar to how step 6) was solved.

9) You now have the values for x and y and you know the value of UV; add.

10) The answer isn't 24.

The remainder is 2x^2 - 7x + 1.

XY = 24.

We first divide 2y = f(2x)/2 + 2 by 2 to get y = f(2x)/4 + 1.  Next we graph the point (9,7).  Then we scale towarards the y-axis by a factor of 2 giving us the point (9,7/2).  Next we scale towards the x-axis by a factor of 4 giving us (9/4,7/2).  Lastly, we translate in the positive y-direction (up) by 1 giving us (13/4,7/2).

The answer is then 13/4 + 7/2 = 27/4.

What is angle RPK, in degrees?

Hello Guest!

\(arc\ RK={\color{black}360^o-2\cdot arc\ KM=360^o-2\cdot 138^o}=84^o\)

\(\angle KMR=42^o\\ \angle MKQ=8.5^o\\ \angle KPM =180^o -8.5^o -42^o =129.5^o\\ \angle RPK =\dfrac{360^o-2\cdot 129.5^o}{2}\)

\(\angle RPK = 50.5^o\)

  !

Suppose Peter can finish painting the fence in x hours. That means he can paint 1/x of the fence in 1 hour, John can paint 1/6 of the fence in 1 hour, and Paul can paint 1/8 of the fence in 1 hour. We can write the following equation:

1/6 + 1/8 + 1/x = 1/2

Solving, we get x = 24/5, so it takes Peter 24/5 hours to paint the fence alone.

this is what I tried.

I am not sure if it is riight

Chose which color to give out first  2 choices

Dole out the red cards first   

person one could get any of 3 cards

person 2 can get ether of the other 2

person 3 gets the last on

So that is 3! ways to dole out the red cards.  There will be 3! ways to dole out the yellw cards   2* 3!*3!=6*6 = 72

Now you need to work out how many ways they can be given out if there are no restrctions.

(for this method getting a R1Y1 is different from   Y1R1)

6! i think  

72/ 6! = 0.1  or 10%  

Dolphinia,   in answer to your question

They all get a yellow one too,  So what?   

Thank You! I get it now.

In triangle(ABD), angle(B) = 35^o, so AD is the shortest side.

In triangle(ACD), angle(CAD) = 55^o, so CD is the shortest side.

Since CD is shorter than AD, CD is the shortest.

[Using the idea that, in a triangle, the shortest side is opposite the smallest angle.]

S  =  sugar

F  =  flour

2S + 3F  <=  40

          F  <=  2S + 8

2S + 3(2S + 8)  <= 40

2S +   6S + 24  <=  40

          8S + 24  <= 40

                  8S  <=  16

                    S  <= 2

F  <=  2S + 8     --->     F  <=  2(2) + 8  <=  4 + 8  <=  12

2/x  =  y/3     --->     xy  =  6

2/x  =  x/y     --->     x²   =  2y     --->   y  =  ½x²

xy  =  6   and   y  =  ½x²     --->     x( ½x²​ )  =  6     --->     x³  =  12

Here is a graph

https://www.desmos.com/calculator/qhtvyyhrio

I think we need to get it in the correct form:

(x-6)^2     + (y+7)^2          - 80   = 0  

x^2 -12x + 36    + y^2 + 14y + 49    - 80 = 0         THEN  - C  = 36 + 49 - 80 =   + 5       so    C = -5     

Shaded area is greater than the line....but does not include the line

find the equation of the line to be    2(x) + 1                  so the shaded area is    y > 2x+1      rearrange to     2x - y + 1 <0

1 hour at 10 miles per hour  =  10 miles

1 hour at 24 miles per hour  =  24 miles

Total:   10 miles + 24 miles  =  34 miles

10 + 24 = 34 miles       If biking takes one hour and train takes one hour .

Natural numbers less than 3 include  2   1    and  sometimes  zero.

It says it's wrong.

gee thanks for the elaborate and 100% correct answer 

x^2 -12x       + y^2 + 14y        = C

(x-6)^2          + (y+7)^2          =     C                       Circle centered at   6, -7 

                                                                                 distance fomula to 10,1 is the radius

                                                                                           4^2 + 8^2 = d^2 = r^2

                                                                                            80 = r^2         C needs to equal 80

(x-6)^2     + (y+7)^2          - 80   = 0   

Thanks!

Rewrite as  :

1/ (a^3 + 7)  +  a^3 / (a^3 + 7)   =   7

(1 + a^3 ) /  (a^3 + 7)   =  7

Multiply both sides  by a^3 + 7

1 + a^3   = 7 ( a^3 + 7)

1 + a^3  = 7a^3  + 49

1 - 49  = 7a^3  - a^3

-48  =  6a^3

-8  = a^3       take the cube root

-2  = a    ( only real solution)

You need to sample at least 2x the frequency to avoid losing data.....higher rates are better

2 x 7.25 kHz = 14.5 kHz sampling rate

14 500 samples per second   and each requires 2048 levels   2048 = 2 ¹¹     So you need 11 bits to quantisize 2048 levels

14500 * 11 = 159500 bits per second   159.5 kbps      or   ~~  1.6 x 10²  kbps

Assuming  yearly compounding.....

A = 201  ( 1.09)^4   ≈   $283.73

Because   ABFE  = ABFE  and  triangle  BDF  =  triangle  ECF

Then  right triangle ADE   must have the same area as triangle  ABC

Area of triangle BDF  = (1/2)(DB + BA) ( AE)  =   (1/2) (2 + 3)  ( 5) =   12.5

Since triangle  ECF  has the same area we  have that

(1/2)  ( BA )  ( AE  + EC )   =12.5     multiply both sides by 2

(BA) ( AE +  EC)  = 25

(3)   ( 5 + EC)  =  25      divide both sides by 3

EC + 5  = 25/3

EC  =   25/3   - 5

EC  =  25/3  = 15/3   =    10/3