A couple 8-9th grade level math questions?

Question

Please show work/give explanation

1. The slope of a line parallel to the line 3y+2x=6 is?

2. What is the solution set to the equation X/5 + X/2 = 14?

3. The graph of y=2^x lies in which quadrants?

4. When the angle of elevation of the sun is 62•, the shadow on the ground cast by a pole is 85' long, how tall is the pole

Answer 1

1. get it to slope intercept form (y=mx+b)

3y=-2x+6

y=(-2/3x)+2

m is your slope, and -2/3 is m so -2/3 is the slope of the original line

parallel lines have the same slope, so -2/3 is your answer

thats all i can do

Answer 2

Reorder your equation to the form y=Ax+B, where A and B are constants.  A will be the slope.

You have to add the fractions.  Same stuff you did in 6th grade.  Find a lcd (10).  Then you have (2X+5X)/10= 14.

Sure you can solve THAT.

It lies in quadrants I (for x>0) and II (for x<0).  

I trust you know trig functions, because you will need one.

The pole and shadow are sides of a right triangle.  The angle of elevation starts at the end of the shadow and goes to the top of the pole.   You want the trig gunction that involves the opposite side(the pole)/adjacent side(the shadow) for an angle of 62 degrees.  

Answer 3

1. first you must put the equation in y=mx +b form

subtract  2x from both sides to get 3y=-2x+6

then divide both sides by 3 to get y= -(2/3)x+6

m is the slope so the slope is negative two thirds, all parallel lines have the same slope

2. first you want to make the denominator of both fractions the same, the lowest common denominator is ten. so multipy (x/5) by 2/2 and multiply (x/2) by 5/5. then you should get (2x)/10 +(5x)/10 = 14

so now that the denominator of both fractions are the same you can add them and get (7x)/10 = 14

so now you want to mulitply both sides of the equation by 10 and this will get you 7x=140 and then you divide both by 7 and the answer is x=20

3.  well first you should know where each quadrant is on a graph.  so if you draw a vertical line for y and a horizontal line for x will will come up with a t.  the upper right portion is quadrant 1 or I (where both x and y are positive), then you go around the graph counter-clockwise. the upper left is 2 (where x is neg and y is pos), bottom left is 3 (where both x and y are negative), and bottom right is 4 (where x is pos and y is neg).  with that in mind if you graph this you will find that the graph only lies in quadrant 1 and 2, because no matter what x is (neg or pos or even 0), y will always be positive

4. well try to draw it out as a right triangle.  

like this > http://www.intmath.com/Trigonometric-fun...

im gonna assume you know sine, cosine, and tangent, otherwise im not sure there is a way to solve the problem without more information.  so we will call the 85ft side, side b. now we want to find the height of the pole and we will call that side a and the angle across from it (62 deg) is angle A.  

we know that tan A = (side a/ side b)  so tan 62 = (a/85)

if you put tan 62 deg in your calculator you should get ~1.88073

so now we have the equation 1.88073 = 85/a so multiply b on both sides and we should then get 1.88073a = 85 and then divide by 1.88073 on both sides and a equals 45.2ft

hope this helps, i probably should of organized this better, any questions please ask