i'm thinking of two consecutive even integers. the sum of their squares is 100. find the numbers.
the base of a triangle is 5 cm less than its height and base if the area of the triangle is 63 cm^2.
2007-01-26 01:53:08 · 8 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
n^2+(n+2)^2=100
2n^2+4n+4=100
n^2+2n+2=50
n^2+2n-48=0
(n+8)(n-6)=0
n=-8 or n=6
n+2=-6 or 8
2007-01-26 03:48:55 · answer #1 · answered by cow 1 · 0⤊ 0⤋
10
2007-01-26 10:01:16 · answer #2 · answered by Lolo 1 · 0⤊ 0⤋
Integer 1 is x
Integer 2 is (x+2)
I#1's square is x^2
I#2's square is (x^2 + 4x + 4)
x^2 + x^2 + 4x + 4 = 100
2x^2 + 4x + 4 = 100
x^2 + 2x + 2 = 50
x^2 + 2x -48 = 0
(x+8)(x-6) = 0
x = -8 or 6
Integer #1 is -8 or 6
Integer #2 is -6 or 8
---------------
Height = h
Base = h-5
Area = I/2 * b * h
63 = 1/2 * (h-5) * h
126 = (h-5)(h)
126 = h^2 - 5h
0 = h^2 - 5h -126
0 = (h-14)(h+9)
h = -9 or 14... since you can't have a negative measurement, h=14
So, b = h-5 = 9
2007-01-26 10:00:34 · answer #3 · answered by Mathematica 7 · 1⤊ 0⤋
x^2+x^2+4x+4=100 2x^2+4x+4=100 2x^2+4x-96 2(x^2+2x-48) 2(x+8)(x-6) 6 and 8 are the awnsers to the first
x(x-5)/2=63 x^2-5X=126 x^2-5x-126 (x-14)(x+9) the hieght is 14 the base is 9
2007-01-26 10:04:29 · answer #4 · answered by ??? 4 · 0⤊ 0⤋
6, 8 - 6^2 + 8^2 = 36 + 64 = 100
2007-01-26 09:58:20 · answer #5 · answered by eriq p 4 · 0⤊ 1⤋
Not sure what the second question is, (is an extension of the first?), but the first question, the numbers are six and eight, who's roots are 36 and 64. 36+64=100!!
2007-01-26 09:59:32 · answer #6 · answered by Dr Z 2 · 0⤊ 0⤋
6 and 8
the height is 14 and base is 9
2007-01-26 10:03:27 · answer #7 · answered by Anonymous · 0⤊ 0⤋
its a challenge for u:
(100-100)dividedby(100-100)=2or 1/2
2007-01-26 10:03:16 · answer #8 · answered by RAKESH Y 1 · 0⤊ 0⤋