Question 7(5 points (02.03 M The figure shows two triangles on a coordinate grid: What set of transformations is performed on triangle ABC to form triangle AB'C7 (5 points) Oa A 180-degree counterclockwise rotation about the origin, followed bya translation 5 units down Ob Atranslation 5 units down followed by a 180-degree counterclockwise rotation about the origin Oc A270-degree countercdockwise rotation about the origin, followed by a translation 5 units to the right O d Atranslation 5 units to the right, followed by a 270-degree counterclockwise rotation about the origin

I think its b

Step-by-step explanation:

by moving it 5 units down, A' will become (-4,-4), and a 180° would make A'' (4,4). (I haven't taken geometry in a few years, so if im wrong, I'm sorry)

B

Step-by-step explanation:

I took the test

r(0,90)(x,y) . t(-5,0)

last option

step-by-step explanation:

∆def to ∆d"e"f"

- rotate 90 counterclockwise degrees

- then translated 5 to the left (x --> x - 5)

answer is the last option

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.