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Monday and Tuesday: 4.5 + 2.4 = 6.9

Monday and Tuesday than Wednesday: 6.9 - 1.7 = 5.2

Cooper hiked 5.2 miles on Monday and Tuesday together.

Janet spent 2/7 of her money on 4 pencils and 8 books. She then spent the remaining amount of money on 6 pencils, 10 toys and 12 books. How many toys could she buy with 6/7 of her money?

Let the price of 1 pencil ==P

Let the price of 1 book==B

Let the price of 1 toy==T

4P  +  8B ==2/7,

6P  +  12B ==5/7 - 10T, solve for T

T ==1/35

1/35T ==6/7

T==30 - number of toys she could buy with 6/7 of her money.

Let the number of button in box B ==B
Then the number of button in box A==B + 64
Let the number of buttons added to box A==C
Then the number of buttons removed from box B =2C

Now box A  has ==B + 64 + C
And box B now has=B - 2C

B - 2C ==B - 28......................................(1)
[2B - C + 64] / [B - 28] ==4 / 1.............(2), solve for B, C
Solve the 2 simultaneous equations (1) and (2) above.

B ==81   and  C==14
A==81 + 64 ==145 - buttons - what box A had at first.

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...........

BD = 4 

AD/2 = 2/40

AD = 1/10

Angle EDF = 1/2(180 - 71)

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

3x + y = 34

5x-y   = 38        add the two equations

8x = 72

x = 9       then y = 7

x = -y^2 - 3y - 5    is  a sideways parabola that opens to the left

        to intersect at only one point, the line x = k must intersect at the vertex

              arrange the equation to vertex form to find the vertex at  -2.75 , -1.5         x = - 2.75

You must remember  SOH CAH TOA        SIN = OPP/HYP = 4/5    CSC = 1/SIN = 5/4

      SEE IF YOU CAN DO THE REST 

          CAH    COS = ADJ/HYP     ETC ....

2x² +28x +98       =    (sqrt(2)x + sqrt (98))²

Initially    j = 4/5 k       or     k = 5/4 j

Then

j - 5/8j     +  108    =   k  + 5/8 j       sub in red equation

  3/8 j      + 108     =  5/4j  + 5/8 j

                   108   = 12/8 j

                       j = 72

2x - 4y = 9 + 3x - y.      arrange to   y = mx+b form      m = slope     parallel slope is ths same

3y =- x -9

y = -1/3 x  - 3 

a and b are unknown.

you keep saying a=10 and b=10 but that is only one of an infinite number of possibilities.

a could be 8 and b 12

or a could be 5.3 and b could be 14.7

or a could be pi and b could be 20-pi

What you know is that a+b=20    which means   b=20-a

You want the sum of their squares is  a^2 +b^2   but we have to replace b with  20-a

so

\(a^2+b^2\\ =a^2+(20-a)^2\\ =a^2+400+a^2-40a\\ =2a^2-40a+400\)

the factors multiplied together = -18    added together = t

                           t

-18      1           -17

18      -1            17

-6        3            -3

6        -3             3

-9        2            -7

9        -2             7            multiply all of the t's together for your answer

Here is the first one....you try the similar second one....

a-3 = sqrt (5a-9)        square both sides

a^2 - 6a + 9 = 5a-9    re-arrange

a^2 -11a +18 = 0

(a-9)(a-2) = 0      a = 9   or   2        test both answers.....you will find that only x = 9 works   (throw out '2')

a^2+b^2 would be 10^2+10^2 which is 100+100 and the answer is 200. Its wrong. 

The equation of the line AB is     \(y=\frac{-31}{32}x+31\)

The equation of the circle is     \(x^2+y^2=23^2\)

I want to find the intersection.

So I need to solve

\(x^2+(\frac{-31}{32}x+31)^2=23^2\)

You can solve this as a standard quadratic if you want to but it is pretty awful so I used the wolframalpha calculator and go the the approx answers of     x=11.351 and x=19.635

So between these values of x, the signal will be available    19.635-11.351 = 8.284

8.284/32 = 0.2588

So the signal will be available for approximately  25.88% of the drive.

calculation:

[AEF] = 4/9 

k = 27/5.

Angle RPG = 71 degrees.