more math...?

Question

-determine the value of g so tht the line through the points (-6,4) and (g, 12) have a slope of 2

-QRST is a parrallelogram. if QR = 4x+6 and RS = 6x-8
a) for wht value of x is QRST a rhombus?
b) wht is the perimeter of the rhombus
c) if angle T is 60 degrees find the area of a rhombus

basically these are the questions i need to study so help me so i dont fail tomorrow!

Answer 1

Slope thru 2 points = y2-y1 / x2-x1.
If slope is 2, then 2 = 12-4 / g- (-6) . Then 2g+12=8 and g = -2

For QRST to be parallelogram, 4x+6 = 6x-8. Then x= 7.
If x= 7, each side = 34 and perimeter = 4 * 34 = 136
We can divide rhombus into 4 30/60/90 right triangles, each with a hypotenuse of 34 and a side of 17 opposite to the 30 degree angle. The altitude is 17 sqrt(3).
Area = 4 * (1/2) (17)*(17 sqrt(3) ) = 578 sqrt(3)
[there are other ways to do this]

Answer 2

so you have yourself a rise over run problem here with the (-6,4) and the (g,12)
slope =rise/run //this is your master equation.
add this equation with rise =(start point minus end point), and run=(same but with the other variable)
short hand for the rise I will use (yf-yi) and run is (xf-xi) i stands for initial f stands for final
so your slope =2 substitute this into your master equation
2=rise/run
now you know 3 of your points but xf=g (your going to need to solve for that.
yi=4
yf=12
xi=-6
now just plug those into the equations for rise and run
now you have
(12-4)/(g-(-6))=2
times bot sides by (g+6) cansling your (g+6) on the bottom note minusing a minus produces a +
so you get 12-4=2(g+6)
now just get g alone
8=2g+(2*6)
8-(2*6)=2g
-4=2g
-4/2=2/2g
so g=-2

Answer 3

Looks like Homework to me so i complete wont help you. Its a "do-it-yourself". But i'll give a hint

The Formula for Slope is S= (x2-x1) / (y2-y1)

For the parallelogram its the formulas that ur class teacher would have given . Its simple substitution. Dont try to cheat do it yourself.

Answer 4

(12-4)/(g+6) = 2, 8 = 2g + 12, g = -2

good luck on the 2nd part