ElectricPavlov

x^2 - 8x = -65.

x^2 -8x+65 = 0      Now use Quadratic Formula      a =1    b= -8     c = 65

\(x = {-(-8) \pm \sqrt{(-8)^2-4(1)(65)} \over 2(1)}\)        Continue to find the two values of 'x'

Just equate the two expressions

(3r - 2)/5  =   (5 + 2r)/8.      Now cross multiply

8 ( 3r-2) = 5 ( 5+2r)      <=====   now just solv for 'r'    ....you can do that yah?

a point & a slope

two points

a table of values MIGHT be true.....but it could result in multiple lines ....or curves....

What is the question?

You can use the equation to find these values.....but the graph would be much easier.....you didn't include it, but here it is

Two points of intesection

x = first piece

3x = second piece

8x + 5 = third piece        summed , they equal = 65

x + 3x + 8x+5 = 65       <=======   can you take it from here?

Complete the square for x and y

(x+3)^2     +   (y-2)^2    =   - c  +9  +4             The red part = radius²    ( which = 14²)       solve for c

2/3 of them were local stamps and the rest

were foreign stamps     So L = 2F     or  F = 1/2L

then

(L-5/6L) + (F-125) = 1/6 (L+F)     sub in the red equation for F then solve for  L = 300     so   F = 150 stamps

    You should be able to figure out the answers with this...........

Circle equation    x^2 + y^2 = 2500

Line equation between cities     y = -61/56 x  -61     sub this into the circle equation to solve for x

x^2  +  ( -61/56 x  +61 ) ^2   -2500 = 0

2.18654x^2 -132.8928x +1221 =0     Now use quadratic Formula  ( or a quadratic formula calculator available online)

                                                                    to find   x =   49.4938  and  11.2825      

                                                                               total x distance = 38.211 miles out of     56  'x' direction miles

38.211 / 56 = 68.23% of the route