All Answers 358108 Answers

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.

The meaning of life is a philosophical and spiritual question concerning the significance of life or existence in general. It can also be expressed in different forms, such as "Why are we here?", "What is life all about?", and "What is the purpose of existence?" It has been the subject of much philosophical, scientific, and theological speculation throughout history. There have been a large number of proposed answers to these questions from many different cultural and ideological backgrounds.

The meaning of life is in the philosophical and religious conceptions of existence, social ties, consciousness, and happiness, and borders on many other issues, such as symbolic meaning, ontology, value, purpose, ethics, good and evil, free will, the existence of one or multiple gods, conceptions of God, the soul, and the afterlife. Scientific contributions focus primarily on describing relatedempirical facts about the universe, exploring the context and parameters concerning the 'how' of life. Science also studies and can provide recommendations for the pursuit of well-being and a related conception of morality. An alternative, humanistic approach poses the question "What is the meaning of my life?" The value of the question pertaining to the purpose of life may coincide with the achievement of ultimate reality, or a feeling of oneness, or even a feeling of sacredness.

-Wikipedia