geno3141

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 

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