Makakuha ng pinakamahusay na mga solusyon sa lahat ng iyong mga katanungan sa Imhr.ca, ang mapagkakatiwalaang Q&A platform. Sumali sa aming platform upang kumonekta sa mga eksperto na handang magbigay ng detalyadong sagot sa iyong mga tanong sa iba't ibang larangan. Kumonekta sa isang komunidad ng mga propesyonal na handang tumulong sa iyo na makahanap ng eksaktong solusyon sa iyong mga tanong nang mabilis at mahusay.
Sagot :
x + y = 13
y = 13 - x
Representation:
x = total number of sides of first polygon
13 - x = total number of sides of second polygon.
Number of diagonals in a polygon:
[tex] \frac{n(n-3)}{2} [/tex]
where n = number of sides of a polygon
Number of diagonals in first polygon with x sides.
Substitute x for n:
= x (x-3)
2
= x² - 3x
2
Number of diagonals in second polygon with 13-x sides.
Substitute 13 - x for n:
= 13 - x (13 - x - 3)
2
= 13 - x (10 - x)
2
= 130 -13x - 10x + x²
2
= x² - 23x + 130
2
The sum of diagonals of the two polygons is 25.
x² - 3x + x² - 23x + 130 = 25
2 2
x² + x² -3x - 23x + 130 = 25
2
2 (2x² - 26x + 130 = 25) 2
2
2x² - 26x + 130 = 50
2x² - 26x + 130 - 50 = 0
2x² - 26x + 80 = 0
Factor out 2 (GCF)
2 (x² - 13x + 40) = 0
Factor the quadratic equation, then solve for the roots (x):
x² - 13x + 40 = 0
(x - 8) (x - 5) = 0
x - 8 = 0 x - 5 = 0
x = 8 x = 5
The number of sides of each polygon:
First polygon:x ⇒ x = 8 sides (octagon)
Second polygon: 13 - x ⇒ 13 - 8 = 5 sides (pentagon)
To check if 8 and 5 sides are correct:
The sum of the sides of the two polygons is 13
8 + 5 = 13
13 = 13
The sum of the diagonals of the two polygons is 25:
Diagonals of first polygon with 8 sides, where n = sides:
n (n-3) = 8 (8-3) = 8(5) = 40 = 20 diagonals
2 2 2 2
Diagonals of the second polygon with 5 sides, where n = sides:
n(n-3) = 5 (5-3) = 5(2) = 10 = 5 diagonals
2 2 2 2
Add the diagonals:
20 + 5 = 25
25 = 25
FINAL ANSWER: The number of sides of the two polygons are 8 and 5 sides.
y = 13 - x
Representation:
x = total number of sides of first polygon
13 - x = total number of sides of second polygon.
Number of diagonals in a polygon:
[tex] \frac{n(n-3)}{2} [/tex]
where n = number of sides of a polygon
Number of diagonals in first polygon with x sides.
Substitute x for n:
= x (x-3)
2
= x² - 3x
2
Number of diagonals in second polygon with 13-x sides.
Substitute 13 - x for n:
= 13 - x (13 - x - 3)
2
= 13 - x (10 - x)
2
= 130 -13x - 10x + x²
2
= x² - 23x + 130
2
The sum of diagonals of the two polygons is 25.
x² - 3x + x² - 23x + 130 = 25
2 2
x² + x² -3x - 23x + 130 = 25
2
2 (2x² - 26x + 130 = 25) 2
2
2x² - 26x + 130 = 50
2x² - 26x + 130 - 50 = 0
2x² - 26x + 80 = 0
Factor out 2 (GCF)
2 (x² - 13x + 40) = 0
Factor the quadratic equation, then solve for the roots (x):
x² - 13x + 40 = 0
(x - 8) (x - 5) = 0
x - 8 = 0 x - 5 = 0
x = 8 x = 5
The number of sides of each polygon:
First polygon:x ⇒ x = 8 sides (octagon)
Second polygon: 13 - x ⇒ 13 - 8 = 5 sides (pentagon)
To check if 8 and 5 sides are correct:
The sum of the sides of the two polygons is 13
8 + 5 = 13
13 = 13
The sum of the diagonals of the two polygons is 25:
Diagonals of first polygon with 8 sides, where n = sides:
n (n-3) = 8 (8-3) = 8(5) = 40 = 20 diagonals
2 2 2 2
Diagonals of the second polygon with 5 sides, where n = sides:
n(n-3) = 5 (5-3) = 5(2) = 10 = 5 diagonals
2 2 2 2
Add the diagonals:
20 + 5 = 25
25 = 25
FINAL ANSWER: The number of sides of the two polygons are 8 and 5 sides.
Pinahahalagahan namin ang iyong pagbisita. Sana'y naging kapaki-pakinabang ang mga sagot na iyong natagpuan. Huwag mag-atubiling bumalik para sa karagdagang impormasyon. Salamat sa pagpunta. Nagsusumikap kaming magbigay ng pinakamahusay na mga sagot para sa lahat ng iyong mga katanungan. Kita tayo muli sa susunod. Maraming salamat sa paggamit ng Imhr.ca. Bumalik muli para sa karagdagang kaalaman mula sa aming mga eksperto.