The algebraic expressions given by the three students which was derived using the tiles represented in the figure are all correct.
<u>Patti's algebraic expression</u> :
2 - 1 + 2x - 3 could be broken down as follows :
- 2 = two shaded tiles with each having a +1 value
- -1 = white tile which has a - 1 value
- 2x = two shaded tiles labeled x
- -3 = 3 shaded tiles in the negative portion of the rectangle, with each having a - 1 value.
<u>Carla's Expression</u> :
2x + 2 - 4 could be explained thus :
- Carla builds on Patti's expression by summing up the negative values of the tiles.
- 2x + 2 - 1 - 3 = 2x + 2 - 4
<u>Emile's expression</u> :
2x - 2 could be explained thus ;
- Emile simplified the expression further by adding all the constant values to produce a simplified expression
2x + 2 - 1 - 3
2x + 2 - 4
2x - 2
Therefore, all the algebraic representation of the tiles given by the students are all correct.
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∠ a: x
∠ b: x
∠ c: x + 21
∠ d: x - 53
∠ a + ∠ b + ∠ c + ∠ d = 360 <em>sum of the angles of a rectangle is 360° </em>
(x) + (x) + (x + 21) + (x - 53) = 360
4x - 32 = 360
4x = 392
x = 98
∠ c: x + 21 = (98) + 21 = 119
∠ d: x - 53 = (98) - 53 = 45
Answer: ∠ a = 98°, ∠ b = 89°, ∠ c = 119°, ∠ d = 45°
-2(x + 3) = -2(x + 1) - 4
-2x - 6 = -2x - 2 - 4 <em>distributed -2 on the left and on the right</em>
-2x - 6 = -2x - 6
<u>+2x </u> <u>+2x </u>
-6 = -6
TRUE
Since this is a true statement, there are infinite solutions (aka All Real Numbers)
Answer: C
The answer would be 10. I know this because I got it right on my assignment. Have a great day!
Answer:
91, 81, 72, 63, 55, 48, 42, 37, 33, 30, 28, 27.
Step-by-step explanation:
its going down starting with a difference of 10 and ending with a difference of 1.