Answer:
See below.
Step-by-step explanation:
It isn't clear if the problem wants to know the number of video games sold, or the number remaining.
<h2><u>
Remaining Games</u></h2>
Let N be the number of video games in the store after d days. Assume none are replaced after they are sold.
N = 30 - 6d [Remaining games, N, are 30 minus the number of days, d, times 6 games/day] We need to also state 30 ≥ N ≥ 0. [No negative games are allowed. They are bad for morale].
<h2><u>
SOLD Games</u></h2>
Let N be the number of games sold over n days.
N = 6d [Games sold] Here, we need to state 0 ≤ N ≤ 30. [We can't sell more games than we have, unless you are a fast runner].
FORMULA:
- Pythagorean property —: h² = b² + p², where h = hypotenuse, b = base, p = perpendicular.
ANSWER:
By pythagorean property,
- x² = 25² + 100²
- x² = 625 + 10000
- x² = 10625
- x = √10625
- x = 103 cm rounded.
Hence, the length of x is 103 cm.
<span>4(3-2x)=22
4(3) - 4(2x) = 22
12 - 8x = 22
8x = 12 - 22
8x = -10
x = -10/8 = -5/4
or
x = -1.25</span>
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.
