x= 5
12 squared + b squared = 13 squared
144+ b squared = 169
b squared = 25
b squared= √25
b=5
Answer: Purchase Price: $85. Discount: (85 x 24)/100 = $20.40
Final Price:
85 - 20.40 = $64.60
The percentage of this plane that's enclosed by the pentagons is closest to: D. 56.
<h3>How to determine the percentage?</h3>
Since the side of the small square is a, then the area of the tile is
given by:
Area of tiles = 9a²
<u>Note:</u> With an area of 9a², 4a² is covered by squares while 5a² by pentagons.
This ultimately implies that, 5/9 of the tiles are covered by pentagons and this can be expressed as a percentage as follows:
Percent = 5/9 × 100
Percent = 0.555 × 100
Percent = 55.5 ≈ 56%.
Read more on area of square here: brainly.com/question/8902873
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Complete Question:
The plane is tiled by congruent squares of side length a and congruent pentagons of side lengths a and a²/a, as arranged in the diagram below. The percent of the plane that is enclosed by the pentagons is closest to (A) 50 (B) 52 (C) 54 (D) 56 (E) 58
Answer:
<h2>
11</h2>
Step-by-step explanation:
n, n + 1, n + 2 - three consecutive integers
The equation:
n(n + 1) = 8(n + 2) + 2 <em>ust the distributive property</em>
n² + n = 8n + 16 + 2
n² + n = 8n + 18 <em>subtract 8n from both sides</em>
n² - 7n = 18 <em>subtract 18 from both sides</em>
n² - 7n - 18 = 0
n² - 9n + 2n - 18 = 0
n(n - 9) + 2(n - 9) = 0
(n - 9)(n + 2) = 0 ⇔ n - 9 = 0 or n + 2 =0
n - 9 = 0 <em>add 9 to both sides</em>
n = 9
n + 2 = 0 <em>subtract 2 from both sides</em>
n = -2 < 0
n + 2 = 9 + 2 = 11