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3x - 4x  =  (3 - 4)x  =  -1x   or just   -x

To solve for x, you need to know the value of f(x).

Distance = Rate x Time

April:                                                                                Tim:

3/4 mi = (Rate) x (1/8 hr)                                               2/3 mi = (Rate) x (2/9 hr)

Divide both sides by (1/8 hr)                                           Divide both sides by (2/9 hr)

(3/4 mi) ÷ (1/8 hr)  =  Rate                                            (2/3 mi) ÷ (2/9 hr)  =  Rate

3/4 ÷ 1/8  =  3/4 x 8/1  =  6                                           2/3 ÷ 2/9  =  2/3 x 9/2  =  3

   Rate = 6 mi/hr                                                                    Rate = 3 mi/hr

What is the equation?

What problem?

To solve -15y < 3 divide both sides by -15

 --- WARNING! if you multiply or divide both sides of an inequality, you MUST change the direction of the inequality ---

---?  -15y / -15  >  3/-15                 notice the change of direction of the inequality

                     y    > -1/5

It is a quadratic equation that reduces to  3x² + 5x - 1

For -4 ≤ x ≤ -1   --->  f(x) = -(3/4)x + 1/4   --->  f( f(x) ) =  -(3/4)( -(3/4)x + 1/4) + 1/4 = (9/16)x + 1/16

    --->  3  =  (9/16)x + 1/16   --->   x  =  47/9   (not in the domain)

For -1 ≤ x ≤ 3   --->  f(x) = x + 2   --->   f( f(x) )  =  (x + 2) + 2  =  x + 4

    --->   3  =  x + 4   --->  x = -1      --->  one point

For 3 ≤ x   --->  f(x) =  -x + 8   --->   f( f(x) )  =  -(-x + 8) + 8  =  x - 8

    --->   3  =  x - 8   --->  x = 11      --->  one point

Formula to find the future value:  F = P·( (1 + i)^n - 1 ) / i 

F = future value         P = payment = 220        n = number of payments = 5.250 x 4 =  22

i = interest rate per period (as a decimal) = 0.0325/4  =  0.008125

F = 220·( (1 + 0.008125)^22 - 1 ) / 0.008125  =  5276.17 

-11/3 is your answer because when you add negatives, it is basically like adding regular numbers, but with a negative sign. Same denominator so it is simple.

OK! sorry to bother you, Melody

If the equation is of this form:  y = mx + b, then the slope is m.

Examples:

y = 2x + 7   --->   slope = 2

y = x - 4   --->   y = 1x + 7   --->   slope = 1

y = -6x    --->  slope = -6

y = (1/3)x + 12   --->   slope = 1/3

y = x   --->   y = 1x   --->   slope = 1

19.208543761633543

just type it into a calculator...

Thank you so much

I'm not certain that this is the easiest way, but ...

I'm going to find the inverse of y  =  3x + b

--->  x  =  3y + b

--->  x - b  =  3y

--->  y  =  (x - b)/3

Since they intersect at the point (-3, a), set the two equations equal to each other:

--->  3x + b  =  (x - b)/3

--->  9x + 3b  =  x - b

--->  8x  =  - 4b

Since x = -3 at that point:

--->  8(-3)  =  -4b

--->   -24  =  -4b

--->  b  =  6

Original equation is y  =  3x + 6

At the point (-3, a) --->  a  =  3(-3) + 6   --->   a  =  -9 + 6   --->   a = -3

=4[3^3-5(8-6)]/2+11

=4[3^3-5(2)]/13

=4[27-10]/13

=4[17]/13

=68/13

=approx. 5.23

Sorry 

I am on the road today.

It is nice to be wanted/needed though.

Thank you.  :)

to find the vertex, go from standard form to vertex form by "completing the square". (look up the process)

then graph using the vertex, and label two other points

For the graph shown, each box has a width and height of 1.

The graph of f(2x) would be identical to the graph of f(x) if you change the scale on the x-axis, so that the width of each box would be ½ (but keep the height the same as it was).

a)  On the original graph, there is the point (-4, 4). On the graph of f(2x), the coordinates of the point are                    (-2,4), so a = -2.

      On the original graph, there is the point (4, -4). On the graph of f(2x), the coordinates of the point are                    (2, -4), so b = 2. 

b) See the note above part a.

c)  f(2x - 8)  =  f( 2(x - 4) )  This graph makes a horizontal shift of the graph of f(2x) 4 spaces to the right.                    The graph of f(2x - 8), which is f( 2(x - 4) ), is congruent to the graph of f(2x), just move it 4                          spaces to the right.

     Moving (-2,4) four spaces to the right creates (2,4), so c = 2.

     Moving (2,-4) four spaces to the right creates (6, -4), so d = 6.

d)  Draw the graph of f(2x), then move that graph 4 spaces to the right to create f(2x - 8).

For the graph shown, each box has a width and height of 1.

The graph of f(2x) would be identical to the graph of f(x) if you change the scale on the x-axis, so that the width of each box would be ½ (but keep the height the same as it was).

a)  On the original graph, there is the point (-4, 4). On the graph of f(2x), the coordinates of the point are                    (-2,4), so a = -2.

      On the original graph, there is the point (4, -4). On the graph of f(2x), the coordinates of the point are                    (2, -4), so b = 2. 

b) See the note above part a.

c)  f(2x - 8)  =  f( 2(x - 4) )  This graph makes a horizontal shift of the graph of f(2x) 4 spaces to the right.                    The graph of f(2x - 8), which is f( 2(x - 4) ), is congruent to the graph of f(2x), just move it 4                          spaces to the right.

     Moving (-2,4) four spaces to the right creates (2,4), so c = 2.

     Moving (2,-4) four spaces to the right creates (6, -4), so d = 6.

d)  Draw the graph of f(2x), then move that graph 4 spaces to the right to create f(2x - 8).

-3/-3 simplifies to +1

y=x2-x1=

    y2-y1=  Ypu will then get a fraction then divide it

He still has 2. Because he never lost his lollies. He only looses his lollies.

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