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the length of PQ   +   the length of QR   =   the length of PR

(5x - 2)   +   (x + 12)   =   40

                                                   We can take off the parenthesees since there is only addition between them

5x - 2 + x + 12   =   40

                                                   Rearrange the terms

5x + x + 12 - 2   =   40

                                                   Combine like terms

6x + 10   =   40

                                Subtract  10  from both sides of the equation.

6x   =   30

                                Divide both sides of the equation by  6

x   =   5

Now that we know what  x  is, plug it into each expression to find  PQ  and  QR

PQ   =   5x - 2   =   ?

QR   =   x + 12   =   ?

As follows:

I'll leave you to round to the nearest hundredth.

Like so:

The link works, thank you! I'm normally not amazing at understanding the concept behind what I'm calculating but I think I do this time. So for c. it would be

-0.042017002/0.001 = -42.017002

right? This might be me being confused again but since they're asking for me to approximate the slope would that even be correct?

I'm also not completely understanding what you said at b. Is a just 0?

a + 1/a = 9.

x/y = 8.

x + 1/x = 12.

b/a = 2 - sqrt(2).

x           y

56        8
14       14
8        56

In a rectangle ABCD, point E is on side CD. The area of triangle ADE is one-fifth of the area of quadrilateral ABCE. What is the ratio of the length of segment DE to the length of segment DC? Express your answer as a common fraction.

The ratio of DE to CD is 1/3  

I've noticed that after I solved that ()angle. 

This is everything less than and ncluding the line

Line slope = - 3/2

y = -3/2 x + b       b = -2

y <= -3/2 x - 2

I don't like incomplete questions.  This is NOT solvable!!!

But, we can make it solvable by adding this:  BC = CF

∠AFC = arctan(AB / BF) = 26.56505118º                ∠AFC = ∠ABG = β

AG = sin( β ) * AB = 0.894427191

AH = cos( β ) * AG = 0.8

DH = AD - AH = 1.2 units  

Hi could you expand on this? I don't understand how it's 3/5 and 7/20

I think we need a picture of angle WXY

jugoslav solved the question for TRIangle WXY    .....  but is that what your question meant to ask?

switch x's and y's  

x = (y-1)^1/3 +5       solve for y

y =  (x-5)^3 +1      

Here is a graph:

https://www.desmos.com/calculator/9vvejdlwbt

Arrange given line into   y = mx+b    form  to find slope , m

    m = -2/5    parallel slope is the same

Here is your new line equation in POINT-SLOPE form

(y-1) = -2/5 (x-4)        now re-arrange this into y = mx + b form

A second method:

new line is slope intercept form:

   y = -2/5 x + b     sub in the point given

   1 = -2/5 (4) + b      solve this for 'b'

     then your new line is    y = -2/5 x + b

In angle WXY, if m∠W is five less than twice m∠Y and m∠X is 21 more than m∠Y, find the measure of each angle.

(2Y - 5) + Y + (Y + 21) = 180

Y = 41

2*41 - 5 + 41 + 41 + 21 = 180 

[(3x1) +(5 x2) + (3 x 4) + (1 x 3) ] / (3+5+3+1)  = 2.33     (kinda weak! )

Expand  (2x  +  3)^15

32768 x^15 + 737280 x^14 + 7741440 x^13 + 50319360 x^12 + 226437120 x^11 + 747242496 x^10 + 1868106240 x^9 + 3602776320 x^8 + 5404164480 x^7 + 6304858560 x^6 + 5674372704 x^5 + 3868890480 x^4 + 1934445240 x^3 + 669615660 x^2 + 143489070 x + 14348907
 

$ 3.88 / 4 bottles   =   3.88/4    dollars per bottle  = ......... $/bottle