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Here is a plot
http://www.wolframalpha.com/input/?i=-3%28-2x-v%29-3%28-v%2Bx%29

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so p=0 or p+6=0
thus p=0 or p =-6

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=36 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 0, -6. Here's your graph:

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given l = 405, find v



90 mph, tisk tisk tisk :(

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The length of one side is
The area of a square is given by the





http://www.wolframalpha.com/input/?i=%281%2Bsqrt%282%29%29^2

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Just plug and play.
Pick a value for x, then use that value of x to find y
for instance, pick x = 0



So one ordered pair is (0,5)
Pick another value for x. Let's pick x = 1



A second ordered pair is (1,2)
Use the same process to find as many ordered pairs as you want

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Your value for x is correct
Let's do y

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use wolframaplha to plot this type of thing
http://www.wolframalpha.com/input/?i=|x|%2Fx

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add 2 to both sides
divide both sides by 4

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zx +5x
you got it the first time :)

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subtract 3 from each side

divide both sides by 4
{{4x/4 = 4/4}}}

Veerify your answer
Does ???

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is percent

%

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Do this one backwards
After the last fence, he has 1 apple.
Before the fence he had x apples
You are told

so he hads 3 apples before the last fence.
Now go back to fence 2


He had 7 apples before he hopped the second fence
Now all the way back to the fence closest to the tree



He started with 15 apples
He had to give 8 apples to the first farmer
4 apples to the second farmer
2 apples to the last farmer
and he ges one lousy apple for all his hard work and fence jumping
I hope it was worth it.
How about THEM apples :)

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Let's pick from type A first.
We need to pick 4.
First pick has 6 choices
Second one now has 5
Third 4
Fourth 3
That leaves 2 extra type As
Now let's pick 4 from type B
Fifth pick has 7 choices
Sixth has 6
Seventh 5
Eight 4
That leaves 3 more type B.
We have two more picks to make and 5 question left to pick from
Ninth has 5 choices
Tenth has 4
Now, do the math

Solve that and there you go!

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See this URL for a plot
http://www.wolframalpha.com/input/?i=-3x^7%2B42x^3

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Find the roots.


root at x = 4 and x = -4
Now pick a value less than -4. let's say -10.
When x=-10, then which is > 0
Pick a value between the two root. Say x=0
When x=0 which is < 0
Pick a value greater than 4, say 10
Again which is greater than 0.
So points to the left of -4 and to the right of 4 do not satisfy the inequality.
The plot will be all points above the curve x^2-16 and below the x axis, between -4 and 4
See this URL for a plot
http://www.wolframalpha.com/input/?i=x^2-16%3C%3D0

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expand using power to power


reorder using commumutation
collect like terms and use power times power rule

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Use the info provided to create a linear model of Life Expenctency.
You are given two points. With that data you have enough information to create the equation for a line.
First let's find the slope of the line
Slope =
You are given the two data points (1991,63.2) and (1996, 65.7)
So the slope is =
The problem says to model the Life Expectancy where t is the 'number of years since 1991"
So
that uses the slope we found above as the rate of change year to year. It also uses the expectency in the year 1991 as the starting point.
Check this now. In year 1991, t = 1991-1991 = 0. So which is correct
IN 1996, t = 1996-1991 = 5. So which is correct
You are then asked to use the equation to extrapolate the data to the year 2006
So, 2006-1991 = 15

Again, this is just a model. There is nothing to suggest that Life expectency is linear. But that is all the data you have, so you have to go with that.
Make sense?

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solve for y

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multiply thru by 5

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Not sure if this is what you wrote. If not, try again and use lots of parens to make sure

Hope it is. Because that is what we will solve here :)

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expand
collect like terms

isolate variable
remember to flip the sign when dividing or multiplyig an inequality by a negative number

see here for a plot
http://www.wolframalpha.com/input/?i=4n+-+24+%3C%3D+3+%284n+%2B+8%29

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collect like terms on each side

collect like terms and simplify

isolate variable


Look here for a plot
http://www.wolframalpha.com/input/?i=0.6x%2B14%2Bx%3E2x%2B15-0.5x

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If you have a question, post it.

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You can factor this or use the quadratic equation


w = 10 or w=-5

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=225 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 10, -5. Here's your graph:

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x=1 and x= -1
Check your answers by pluggin in those 2 values for x, one at a time, and verifying the equality is 'true'