we have that
7) points F(-8,4) H(-4,-4) and G(6,-2)
step 1--------> find the slope of a line FG
m=(y2-y1)/(x2-x1)---> (-2-4)/(6+8)=-6/14=-3/7
step 2
the altitude of triangle FGH is perpendicular with the line FG
therefore
m1*m2=-1 (If two straight lines are perpendicular they have their slopes reversed and changed sign)
m1=slope line FG
m2=slope altitude
m2=-1/(-3/7)=7/3
step 3
find the equation of the line that passes through the point H with slope m2
H(-4,-4) m2=7/3
y=mx+b---------- > -4=(7/3)*(-4)+b
b=(28/3)-4=(28-12)/3=16/3
y=(7/3)x+16/3--------> y=(7x+16)/3----------> 3y=7x+16
the answer is the option D (3y=7x+16)
8) eraser has the shape of a rectangular prism
Volume V=l*w*h
if l=3l and w=3w
then
V2=(3l)*(3w)*(h)=9(l*w*h)--------> V2=9V (the volume will be 9 times larger)
the answer is the option C the volume will be 9 times larger
9) The median of a trapezoid is the segment that joins the midpoints of the non-parallel sides
the non parallel sides are AD and BC
midpoint side AD---------------- > M (-4,0.5)
A(-7,2) D(-1,-1)
xm=(-7-1)/2=-4
ym=(-1+2)/2=0.5
midpoint side BC---------------- > N (3,4)
B(3,7) C(3,1)
xm=(3+3)/2=3
ym=(7+1)/2=4
the length of median MN is
M (-4,0.5) N (3,4)
d=√(3+4)²+(4-.5)²=√(49+12.25)=7.826--------> 7.83 units
the answer is the option B 7.83 units
10) hight of the kite=4+50*sin(38)=34.78 ft----->34.8 ft
the answer is the option B 34.8 ft