Answer:
so im gonna help you gte the answer how many quarts are in a gallon thne you wil find your answer
Step-by-step explanation:
The <u>correct answer</u> is:
B) A 90° counterclockwise rotation about the origin, followed by a reflection across the x-axis, followed by a translation 8 units right and 1 unit up.
Explanation:
The coordinates of the <u>points of the pre-image</u> are:
(3, 1)
(3, 4)
(5, 7)
(6, 5)
(6, 2)
The coordinates of the <u>points of the image</u> are:
(7,-2)
(4,-2)
(1,-4)
(3,-5)
(6,-5)
A 90° counterclockwise rotation about the origin negates the y-coordinate and switches it and the x-coordinate. Algebraically,
(x,y)→(-y,x).
When this is applied to our points, we get:
(3, 1)→(-1, 3)
(3, 4)→(-4, 3)
(5, 7)→(-7, 5)
(6, 5)→(-5, 6)
(6, 2)→(-2, 6)
A reflection across the x-axis negates the y-coordinate. Algebraically,
(x, y)→(x, -y).
Applying this to our new points, we have:
(-1, 3)→(-1, -3)
(-4, 3)→(-4, -3)
(-7, 5)→(-7, -5)
(-5, 6)→(-5, -6)
(-2, 6)→(-2, -6)
A translation 8 units right and 1 unit up adds 8 to the x-coordinate and 1 to the y-coordinate. Algebraically,
(x, y)→(x+8, y+1).
Applying this to our new points, we have:
(-1, -3)→(-1+8,-3+1) = (7, -2)
(-4, -3)→(-4+8,-3+1) = (4, -2)
(-7, -5)→(-7+8,-5+1) = (1, -4)
(-5, -6)→(-5+8,-6+1) = (3, -5)
(-2, -6)→(-2+8,-6+1) = (6, -5)
These match the coordinates of the image, so this is the correct series of transformations.
Answer: C
Step-by-step explanation:
We can say that the equaiton of the line is -1/6x+1, considering that is in each answer choice. Than main part is the shading and inequality. If you look closely at the graph, the shading line is a dashed/dotted line. This means the shaded part does not equal the actual line. We can eliminate B and D.
Now, we are left with A and C. A is saying y< while C is saying y>. C is the correct answer because if you look at the shading, it it above the line, which is greater than. Therefore, the answer is C.
To find the lateral surface area of this triangular prism, you will find the area of the three congruent rectangles that form the lateral faces.
A = lw
6 x 12
A = 72 in.²
72 in.² x 3 (lateral faces)= 216 in.²
