Can you please help me with my review # 20 it's multiple answers?

Question

1 The five fastest roller coasters in the world are the Fujiyama(Japan), Goliath(CA), Millennium Force (OH), Steel Dragon 2000(Japan), and Superman the Escape(CA). The speeds, in miles per hour, of the first four coasters are 83, 85, 92, and 95, respectively. How fast can Superman the Escape travel if the average speed of all five coasters is no more than 91miles per hour?

a no more than 100 mph

b at least 93 mph

c at least 100 mph

d no more than 93 mph

2 find the coordinates of the vertices's of the figures formed by y<x+2, x+y<6, and y>-2

a (0,0), (2,4), (8,-2)

b (-4,-2), (2,4),(8,-2)

c (-4,-2),(4,2),(8,-2)

d (-2,-4),(2,4),(8,-2)

3 solve [2x+5y/x+3y] = [1,0] for y

a 1

b 3

c -3

d -1

4 the vertices's of ABC are A(-3,-4), B(-1,3) C(3,-2). the triangle is rotated 90 degrees counterclockwise. Use the rotation matrix [0,-1]/[1,0] to find the coordinates of C'.

a (-3,2)

b (4,-3)

c (-3,-1)

d (2,3)

5 if g(x) = 3x-8, find g[g(-4)]

a -68

b 4

c -20

d -52

6 write an equation for an ellipse if the if the end point of the major axis are at (-8,1) and the end points pf the minor axis are at (0,-1) and (0,3).

a x^2/16+(y-1)^2/4=1

b (x-1)^2/64+y^2/4=1

c (x-1)^2/16+y^2/4=1

d x^2/64+(y-1)^2/4=1

Answer 1

1) The sum of the four given is 355.  If the average of the five is not to exceed 91, that&#039;s the same as saying the sum cannot exceed 455.  Therefore, Superman the Escape cannot travel at more than 100 mph, answer choice (a)

2) The figure bound by the three lines is a triangle.  Since one of the lines is y = -2, the y-coordinate of two of the vertices must be -2.  That immediately eliminates answer (a) &amp; (d).  The lines y = x + 2 and y = 6 - x intersect at (2, 4), so the correct answer is (b)

3) Something about the notation is incorrect here.  The expression on the left side is a single dimensional algebraic expression, and the expression on the right appears to be a coordinate point.  I suspect this question has not been typed correctly.  

4) You really don&#039;t need the matrix at all, just basic geometric thinking.  Point (C) has a positive x and a negative y, so it&#039;s in the fourth quadrant.  When it rotates 90° ccw, C&#039; will land in the first quadrant.  The only first quadrant point among the answer is (d), the correct answer.  

5) g(-4) = 3(-4) - 8 = -12 - 8 = -20

   g(g(-4)) = g(-20) = 3(-20) - 8 = -60 - 8 = -68

answer choice (a)

6) The center of the ellipse is at the midpoint of the minor axis, the point (0, 1).  This means we need an ellipse of the form:

(x^2)/a^2 + (y - 1)^2/b^2 = 1

That eliminates answers (b) &amp; (c)

The y-direction has the semi-axis of 2, and the x-direction has the semi-axis of 8, so the squares of those numbers have to be in the denominators of those respective terms.  

(x^2)/64 + (y - 1)^2/4 = 1, answer choice (d)