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Sin is defined as opposite/hypotenuse.
Draw a right triangle with one point at the origin. Draw the hypotenuse (h) with an angle of 9 degrees above the x axis. The "altitude" gained is given by
At 2 miles, we have = 0.312 miles
How far must one go to be an altitude of 1 mile?

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The way to solve these types of problems is to get all the constants on one side and all the terms with x in them on the other. Then simplfy.
Let's do the first one
41: 4(3+x)+10= -11(x-6)+1
First expand both sides using distribution
12+4x + 10 = -11x + 66 + 1
Now combine like terms
22 + 4x = 67 - 11x
Now get the constants on one side and the x terms on the other
4x + 11x = 67 - 22
Combine like terms again
15x = 55
Now isolate x by diving both sides by 15
x = 55/15 = 11/3
Check you answer by using 11/3 as x in the original problem and verifying that both sides are equal
43 is easier.
3x+21 = -2x + 11
same steps. get constants on one side, x term on the other
3x + 2x = 11 - 21
combine like terms
5x = -10
x = -2
I bet you can do 45 now. Give it a go and ing me if you cant get it

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Th easiest thing to do is find the tangent of 52. Then realize that is sin/cos or y/x. Thus the slope of a line through the origin will be equal to the tangent(52).
Tangent(52) = 1.28
y = 1.28x

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See --> http://www.calc101.com/webMathematica/long-divide.jsp#topdoit

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a) A ∩ B means what is in both A and B. {3} is in both
b) A ∩ C means what is both A and C. Again only {3} is in both
c) A U C means what is in either A or C. {1 2 3 5 7}
d) B U C means what is in either B or C {3 4 5 6 7}
e) (A U B) ∩ C means what is in either A or B and also in C
AUB = {1 2 3 4 5 6} what is also in C? {3 5}
f) A U (B U C) what is in any of the three {1 2 3 4 5 6 7}
g) (A ∩ B) ∩ C what is in each of the three {3}
h) (A ∩ B) U C look at answer a above. Now what either in that or in C? {3 5 7}
does this help any?

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Given

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You need to break the trip into two parts.
The total trip is 220. The total time is 3 hours.
Let the distance from Albuquerque to Roswell be x (watch out for aliens in Roswell).
Then the distance from Roswell to Carlsbad is
The time for each leg is given by
The time to Roswell is
The time to Carlsbad is
The total time is 3 hours.







So the distance to Roswell is 150 miles.
At an average speed of 75 mph, the drive to roswell takes 2 hours.

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This is a classic algebra problem.
Let the two numbers be represented as x and y.
You are given:
the sum is 27
their difference is 20
You can use substitution or elimination to solve these. See http://collabvsl.wetpaint.com/page/Solving+Systems+of+Equations for a nice video that covers different ways to solve systems like this.
We'll use elimination to solve

add these two equations
-----------------





Now that you know one number, use that to solve for the other one




You can verify the answers by substituting back into the original two equations.

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Find the factors for the quadratic terms and then cancel to simplify.
=
=
=
Now cancel what you can, remembering that dividing by a fraction is just the same as multiplying by that fractions inverse.
Ping if you cant get it

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I'll show you how to do question 1. Questions 2 and 3 are use the same technique - so you can solve them.
1) (The points A(1,6), B(6,6), C(4,3), D(-1,3) are vertices of a quadrilateral. Prove that the quadrilateral is a parallelogram.
You need to remember that parallel lines have the same slope and perpendicular lines have slopes that are negative reciprocal (the product of the slopes of two perpendicular lines equals -1.
So find the slopes is the segments AB and CD. Then find the slopes of segments BC and DA.
slope when given two points.
Slope of AB is given by =
Slope of CD is given by =
Both are 0, so they are parallel

Slope of BC is given by =
Slope of DA is given by =
Both are -2/3, so they are parallel too.
A figure with two sets of parallel lines is a a prallelogram

2) For problem two, find the slopes of the three segments. Then verify that two of those slopes have a product of -1.
3)For problem three, find the slopes of the segments LV and OE. The show they have a product of -1
4) Solve for x


Solve when y = 3, m=4 and b = -5

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The future value of money using compound interest is given by:

Where
F is the future value
P is the present value
r s the annual interest rate
n is the number of compounding per year
t is the total number of compoundings
This problem asks for the present value (P)of a future sum (F=5000), when the interest is 8%(r=0.08) compounded semi-annually (n=2) for a length of 8 years (t = 8*n = 16).
Solving for P:







The answer is C
Read this for more info -->http://www.purplemath.com/modules/expofcns4.htm

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We know the sum of the angels in a triangle is 180.
Given: A = 2B + 20
Then C = 180 - A - B
C = 180 - (2B+20) - B
C = 180 - 2B - 20 - B
C = 160 - 3B
So, the angles are:
A = 2B+20
B = B
C = 160 - 3B
Make sense?

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Assume you have double angle and half angle identities already 'in your bag of trick'. See http://homepage.mac.com/shelleywalsh/MathArt/DoubleHalf.html
Namely
sin(2x) = 2sin(x)cos(x)
cos(2x) = 2cos^2(x)-1
tan(x/2) = sin(x)/(1+cos(x))
Now let's start at the top
(sin2x/ 1+cos2x) * (cosx/1+cosx) =
((2sin(x)cos(x)) / (1 + (2cos^2(x)-1)) * (cosx/1+cosx) =
((2sin(x)cos(x)) / (2cos^2(x)) * (cosx/1+cosx) =
((sin(x)cos^2(x)) / (cos^2(x)) * 1/(1+cosx) =
sin(x) * 1/(1+cosx) =
sin(x)/(1+cosx) =
tan(x/2)

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so far so good.
2p = 1b (p=pencil; b=blue pen)
15= 10p + 5b
Now substitute using 2p=b
15 = 10p + 5(2p)
15 = 10P + 10p
15 = 20p
3/4 = p
pencils are $0.75 each
pens are 2p = 2*(0.75) = $1.50
Check your answer.
Is 10*0.75 + 5*(1.50) = 15?

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Given
Evaluate at x=3
Remember that subtracting a negative is the same as adding a positive

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To find percent grade, divide the part by the whole and multiply by 100.
% =
% =
% grade

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1) Pour from 20 into 14 filling it. Leaves 6 in the 20
2) Pour from 14 into 8 filling it. Leaves 6 in the 14
3) Drink the 8 oz contents
4) Pour 6 from the 20 into the 8
If you cant drink any
1) pour from 20 into the 8. leaves 12 and 8
2) Pour from other 20 into the 14. leaves 6 and 14
3) Pour 12 into 6. leaves empty and 18
4) Pour 8 into empty. Leaves empty 8 and 8 in 20
5) Pour from 14 into 8 until 8 is full. leaves 8 and 14 with 6 in it (one done)
6) Pour from 8 into 18 until full. Leaves 6 in 8 (other one done) and a full 20.
When we are done, we have a full 20, 6 in 8, 6 in 14 and 8 in the other 20. total 40. we are golden.

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These two lines can be represented by the same line. So they are dependent

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Let p be the pennies and n be nickles


Use elmination, subtract these two equations


So you have 5 nickles and pennies

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Let the two angels be a and b
a+b = 215
We are also given a second set of information
The supplement of an angle plus the angle is always 180.
We are told



Now solve using

Solved by pluggable solver: Solving a System of Linear Equations by Elimination/Addition

Lets start with the given system of linear equations In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for y, we would have to eliminate x (or vice versa). So lets eliminate x. In order to do that, we need to have both x coefficients that are equal but have opposite signs (for instance 2 and -2 are equal but have opposite signs). This way they will add to zero. So to make the x coefficients equal but opposite, we need to multiply both x coefficients by some number to get them to an equal number. So if we wanted to get 9 and 1 to some equal number, we could try to get them to the LCM. Since the LCM of 9 and 1 is 9, we need to multiply both sides of the top equation by 1 and multiply both sides of the bottom equation by -9 like this: Multiply the top equation (both sides) by 1 Multiply the bottom equation (both sides) by -9 So after multiplying we get this: Notice how 9 and -9 add to zero (ie ) Now add the equations together. In order to add 2 equations, group like terms and combine them Notice the x coefficients add to zero and cancel out. This means we've eliminated x altogether. So after adding and canceling out the x terms we're left with: Divide both sides by to solve for y Reduce Now plug this answer into the top equation to solve for x Plug in Multiply Subtract from both sides Combine the terms on the right side Multiply both sides by . This will cancel out on the left side. Multiply the terms on the right side So our answer is , which also looks like (, ) Notice if we graph the equations (if you need help with graphing, check out this solver) we get graph of (red) (green) (hint: you may have to solve for y to graph these) and the intersection of the lines (blue circle). and we can see that the two equations intersect at (,). This verifies our answer.

To get a = 95 and b = 120

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Given the function
evaluate that function when a = 33
Take the function and plug in the value for a.
Now do the arithmetic. What is 33-13?


I don't understand the second one. 2=3y when y=8 doesn't make sense

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I don't think so.
Start with a right triangle.
At the non-right angle vertices, double the angles. What are the resulting angles?
Let's say that one angle was alpha, then the other angle must be 90-alpha.
If we double alpha, we get 2alpha.
If we double (90-alpha), we get (180-2alpha).
The sum of the anlges inside a triangle is 180.
Let's add our two angles so far. 180-2alpha + 2alpha = 180. So we already have 180 degrees. The other vertex doesn't exist (the lines are parallel).

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I am thinking this:
We are being asked to find the largest value of n such that is an integer
=




2 will never factor into 3, since both are prime. So the largest number for n is the largest one that still results in being an integer. What is the smallest number that still is a positive integer? well, that's 1. So what value of n results in is 1? n = 20

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Draw the picture. Mark the two sets of congruent sides in the rectangle. Then layout the two equilateral triangles and mark the sides that are congruent with the two different sets in the rectangle. You end up with a rectangle with two triangles and only two different lengths for the various segments.
Remember that side-angle-side (SSA) is one means to establish congruent triangles.
Now:
The angles in the original rectangle are all 90 degree each.
The angles in equilateral triangles are 60 degrees each.
Triangles ADP, ABQ and CPQ are all congruent using SSA. How do we get that? Angle ADP is 90+60 = 150. Segment AD and DP as sides
Angle ABQ is also 90+60. Again BC and AB as sides
Angle PCQ = 360 - 60 - 90 - 60 = 150. Sides are CQ and CP
So we have 3 congruent triangles. Hence the thrid side of each is the same length. And the triangle composed of those three sides must be equilateral.
Not so for parallelogram

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You did. well done.
Use this to check if you need to
http://www.hostsrv.com/webmab/app1/MSP/quickmath/02/pageGenerate?site=quickmath&s1=equations&s2=solve&s3=basic

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Use solid lines when there is an equal sign as part of the expression. None of these equations have an equal sign, so none use solid lines

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Use this --> http://www.calc101.com/webMathematica/long-divide.jsp

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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: 7, 1. Here's your graph:

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I think that's a trick question. Sure it will ... if you park it at a 60 degree angle.
If you have to park it 'straight', then we have to do a little math.
Draw your parallelogram, 45 feet and 30 feet with 60 degree angle between the 30 and 45 sides.
Drop a line from one end of the a 45 foot side down. Make it perpendicular to the 30 foot base line.
Now take 45 *cos(60) to see how long the side of the resulting right triangle is. Take 45*sin(60) to see how long the other side is. Then make the call about whether the rv can fit

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Earning is the flat 350 + $10 for each oil change