If Charlie runs 3 yards per second and there are 3600 seconds in an hour, then he runs
3 * 3600 = 10800 yards per hour.
There are also 1760 yards in one mile, so we need to divide 10800 by 1760 to find out how many miles it is:
10800 ÷ 1760 =
= 6,136363636363636
I think we should round it:
6,136363636363636 ≈ 6,1
Answer: Charlie runs with a speed of about 6,1 miles per hour.
Answer: exponential decay (choice B)
The variable x in the exponent tells us that this is an exponential function. The fact that the base 1/2 = 0.5 is between 0 and 1 indicates that the value of y will decay or get smaller as x increases. Visually, it graphs out a curve that goes downhill as you read from left to right.
side note: The function f(x) = 7*(1/2)^x can be written as y = 7*(0.5)^x. It has a horizontal asymptote of y = 0 meaning that the curve will get closer and closer to the x axis, but never actually touch it.
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.
