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That answer is correct.

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The value in the square root sign has to be greater than or equal to zero:



That is your domain.

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Should look like the parabola below:

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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=4 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 1, -1. Here's your graph:

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(3/4)x = 1.8
x = (4/3)1.8
The total demand will be 2.4 trillion metric tons.

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No ....

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We know that this is a parabola, so it is "U-shaped".
The length and width will always increase as the x-values increase.
The vertex is: (-b/2a , f(x)) = (1/2 , -1/2)
Latus Rectum (the distance from one point on the parabola across the foci to another point on the parabola) = |1/a| = |1/1| So we know this parabola is skinny.
The distance from the foci to the vertex (also known as the distance from the Directix to the vertex) = (1/(4a)) = (1/4)

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Yes, these are functions.
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series?
I would suggest an arithmetic series to be a linear function. In arithmetic sequences, you would either add or subtract to get the value. In linear functions, addition and subtraction is due to the slope.
Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the geometric series?
For this, I think it is represented by the exponential function. The standard form for the exponential function is: . The standard form for geometric sequences is: . They look quite alike.
An example of the arithmetic sequences could be to determine pay. If you get payed five bucks a week, you can determine how much you make a month or a year.
An example of the geometric sequences could be to determine height of a bouncy ball. If a ball's height after being dropped reduces (1/3) as a ratio to its previous bounce, you can determine its height after amount of bounces.

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Variables:



Equation:





or
Even though two is a possible answer, it is an even postive integer. Two is not the answer. Your answers are: 17,19,21

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The advantage would be that if the number has a radical sign, you would have to convert in order to solve faster. Also, its a faster way to multiply or add exponents.





Faster way:



or or

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After simplifying, you get:

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Year Sales Tax Revenue
2000 $19500
2001 $21000
2003 $24000
2004 $27300
2005 $31000
a) Using the two points defined by data from 2000 and 2005, develop a linear equation for the data.
2000 $19500 at this time (0 years from 2000)
2005 $31000 at this time (5 years from 2000)
y = ((31000-19500)/5)x + 19500
y = 2300x + 19500
b) Using the equation found in a), predict the tax revenue for 2006.
y = 2300(6) + 19500
y = 13800 + 19500 = 33300
c) Use the calculator to determine the "best fit" equation for the data.
I haven't done any equations dealing with the "best fit" line, but I will try my best. It seems right.
y = (31000-((19500 + 21000 + 24000 + 27300 + 31000)/5))x + 19500
y = 2205x + 19500
d) Using the equation found in c), predict the tax revenue for 2006.
y = 2205(6) + 19500 = 32730
e) Using the equation found in c), estimate tax revenue for the missing 2002 data
y = 2205x(2) + 19500 = 23910
.............................................................................

a) What is the maximum height attained by the rocket? How far has the rocket travelled horizontally at this point?
The highest point would be at the vertex.
((-b/2a),f(x))
10000/256 = 5000/128 = 2500/64 = 1250/32 = 625/16
f(x) = -0.0128(625/16)^2 + (625/16) + 60
v(39.0625,79.53125) Max height: 39.0625ft. Distance traveled: 79.53125ft.
b) At waht point(s) (after launch) is the rocket 70 feet high? (Horizontal displacement)



Use the quadratic formula to determine the root.

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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=0.488 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 11.7746106303547, 66.3503893696453. Here's your graph:

At about 11.8 ft. horizontally or about 66.4 ft.
c) How far away from the base of the cliff does the rocket land?
Again, use quadratic formula to determine the roots.

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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=4.072 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -39.762489097684, 117.887489097684. Here's your graph:

At about 117.9 ft. horizontally.

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The zeros are and

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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=4 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 4, 2. Here's your graph:

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4 7/9 - 2 11/18
4 14/18 - 2 11/18
86/18 - 47/18
39/18

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Since any number cannot equal zero, cannot equal .
<------ {2} ========= (-3) ------->
The shaded region (=======) is the location of the answers. (-3) means not equal to while {2} means equal to.

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3/8, 5/16, and 11/32
3(4)/8(4), 5(2)/16(2), and 11/32
12/32, 10/32, and 11/32
(3/8) is the largest drill bit

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Original:
length = 4w
width = w
Second rectangle:
length: 5 + 4w
width = 2 + w
Equations:
First triangle:





Second triangle:

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The perimeter is the sum of all the sides.

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Integers:



Equation:





The numbers are: 11,13,15

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The volume for a cube is: where is length, is width, and is height

The volume is 27 inches cubed.
The perimeter is the sum of all the sides:

The perimeter is 24 units.

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or

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and

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------------------------------------------------------------------------

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Number of Ways to Get More than 36:
5:8
6:7
6:8
7:6
7:7
7:8
8:5
8:6
8:7
8:8
There are eight different ways to achieve this:
10/(8*8)
(5/32)

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The values in the square root sign have to be greater than or equal to zero:


or
Domain: (x| or )
Range: {y|y >= 0}
Since you are not adding any numbers to your function, your range is equal or greater than zero.
I am sorry; I do not know how to graph using programs available to this web.

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(ideal area) - (real area) = (difference of area)
(157*157) - (159*155) = (difference of area)
(24649) - (24645) = 4ft. less than what he thought he originally had

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a) at what instant will it be back at the ground level?
Use quadratic formula to determine zeros.

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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=9216 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:

At 6 seconds, the ball will hit the ground.
b) for what time interval is the ball more than 384ft above the ground?



If you try to work this out, you will get an imaginery number. The ball will not reach this height. The highest the ball will go is about 144ft.