DESPERATELY need Math Help...test tomorrow...here are some examples. can anyone help me work them out?

PLEASE explain to me how you got the answer!( I separated the problems with lines) ________47.) Rhombus ABCD has an angle of 120 and a side of length 6. What is the area? _________48.) The line produced by the equation y=3 intersects the parabola y=x squared - 4x + 7 at one point. What is the vertex of the parabola? ________ 49. a courtyard has dimensions of x times y feet, and surrounded by a flower bed of 2 feet wide and with a 2 foot wide walkway into the courtyard. What is the area of the flower bed in square feet? _________ 50. A particular brand of lemonade is made by mixing concentrate with water. How many gallons of concentrate should be mixed with 5 gallons of water so that 18 percent of the resulting lemonade is concentrate? _____%26lt;br%26gt; PLEASE HELP ME...Im so lost!! Thanks guys!

DESPERATELY need Math Help...test tomorrow...here are some examples. can anyone help me work them out?
47. The rhombus. With a lot of these problems it helps if you try to draw a picture, so that you can see what you're looking at.



The height of the rhombus (imagine it lying on its side)

is 6 sin 120 = (6 * sqrt3)/2 = 3 sqrt 3.



So, to get the area, multiply this by 6, the length of the base.



So the area is 18 sqrt 3.



48. The equation for the parabola is y = x^2 - 4x + 7, so this intersects the line y = 3 when

x^2 - 4x + 7 = 3, or

x^2 - 4x + 4 = 0 (subtract 3 from both sides)



Solve for x using the formula to find the roots of a quadratic, and you get

x = [4 +/- sqrt(16 - 16)]/2 = 2.



Since we know that y = 3 when this is true, we know that the y value of the vertex must be 3, and therefore the vertex is at (2,3).



49. Do you have a drawing of the set up for the courtyard? I can't visualise the problem.



50. Let the amount of concentrate be l, and the amount of water be w. The ratio of concentrate in the final mixture is 18 : 82.



So 18/82 = l/w, where, in this case, w = 5.



So 18/82 = l/5, so l = 5*18/82 = 90/82 = 1.098 (to 3 sig fig).



Hope this helps.
Reply:question 47:

since all sides in a rhombus are equal therefore all other sides in the rhombus are of length 6. From there you split the rhombus in half to find side AC by using cosine rule. if you didnt know cosine rule is Asquared = Bsquared + Csquared - 2bccosA where B and C are the two given sides. therefore Asquared = 36 + 36 - 72cos120. you can work out the result of AC from there therefore BDsquared = 36 + 36 - 72 cos60 u times the two sides together and divide by 2 to get the result



sorry i cant help with the other questions, they are too hard to explain by just typing you need diagrams