The difference of two positive numbers is 5 and the sum of their squares is 233. Which pair of numbers is the solution to this word problem?
a) The two numbers are 8 and 13.
b) The two numbers are 7 and 12.
c) The two numbers are 6 and 11.
d) The two numbers are 9 and 14
The length of a rectangle is 6 cm less than twice its width. Find the dimensions of the rectangle if its area is 108 cm2. Which equation can you use to solve this problem?
a) w(2w + 6w) = 108
b) w(2w – 6w) = 108
c) w(2w – 6) = 108
d) w(2w + 6) = 108
2007-12-21 12:31:45 · 5 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
a. just square 8 and 13 and add, if they add up to 233, it is a. If not, keep on checking until you get it right.
b. area=l(w). l=2w-6, so you get w(2w-6), C.
2007-12-21 12:38:50 · answer #1 · answered by Mother Pucker 3 · 0⤊ 0⤋
1.
The difference of two positive numbers is 5 and the sum of their squares is 233. Which pair of numbers is the solution to this word problem?
The answer is :
a) The two numbers are 8 and 13.
2.
The length of a rectangle is 6 cm less than twice its width. Find the dimensions of the rectangle if its area is 108 cm2. Which equation can you use to solve this problem?
The answer is :
c) w(2w – 6) = 108
2007-12-22 05:02:53 · answer #2 · answered by An ESL Learner 7 · 0⤊ 0⤋
The pair of numbers:
x = greater number, x - 5 = lesser number
Value of greater number:
x^2 + (x - 5)^2 = 233
x^2 + (x^2 - 10x + 25) = 233
x^2 + x^2 - 10x + 25 = 233
2x^2 - 10x = 208
x^2 - 5x = 104
x^2 - 5x - 104 = 0
(x - 13)(x + 8) = 0
x - 13 = 0
x = 13
Value of lesser number:
= 13 - 5
= 8
Answer: a) The two numbers are 8 and 13.
Dimension of a rectangle:
w = width, 2w - 6 = length
Answer: c) w(2w - 6)
Proof:
Finding the width:
w(2w - 6) = 108
2w^2 - 6w = 108
w^2 - 3w = 54
w^2 - 3w - 54 = 0
(w - 9)(w + 6) = 0
w - 9 = 0
w = 9
Finding the length:
= 2(9) - 6
= 18 - 6
= 12
Area:
= 9 * 12
= 108
2007-12-21 21:30:40 · answer #3 · answered by Jun Agruda 7 · 4⤊ 0⤋
1: 13 - 8 = 5 8^2=64 13^2= 169 64+169= 233
2007-12-21 20:55:05 · answer #4 · answered by Aubs 3 · 1⤊ 0⤋
i hope this could help... if you really want to know the answer for #1, just get the sum of the squares of the number from the given choices.. in this case the answer is 8 & 13
for #2, formula of an area is L * W, then you got to find the value (rather assignment) of these W & L
W = w , L = 2w - 6
the answer is c
2007-12-22 09:43:47 · answer #5 · answered by ces 3 · 0⤊ 0⤋