9514 1404 393
Answer:
99, 101, 103
Step-by-step explanation:
Let x represent the smallest. Then the sum of the first two is (x+x+2) and the third is x+4. The problem statement tells us the relation ...
5(2x +2) -(x +4) = x +798
10x +10 -x -4 = x +798
8x = 792
x = 99
The integers are 99, 101, 103.
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<em>Check</em>
5(99 +101) -103 = 99 +798
897 = 897 . . . . answer checks OK
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
The denominator is the bottom portion of the fraction. Example 4/6, the 6 is the denominator. The easiest way to start out in finding the common denominator is to see what number, 8 and 14, go into equally. Example: 1/4 and 1/3, 3 and 4 both go into 12. If you multiply 4 by 3 as well as 3 by 4 you get 12 both times. Now try it with 8 and 14.
What number can 8 and 14 go into equally? (56)
8x7=56...14x4=56