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Math homework help please!!?
1.) given a rectangle with the area of 126 squarre feet, and side lengths (x+2) and (x-3), find the value of x and the dimensions of the sides
2.) samanthas dining room has a length 6 feet wider than the width. The area of the dining room is 280 square feet. What are the dimensions of the dining room.
3.) a cylindrical tank used for oil storage has a height that is half the length of it's radius. If the volume of the tank is 1,122,360 what is the tanks radius
2 Answers
- 1 decade ago
1) rectangle area = b * h
b = x + 2
h = x - 3
Area = 126
so, 126 = (x+2)(x-3)
multiplied out
126 = x^2 + 2x -3x -6
combine
0 = x^2 -x -132
factor
0 = (x - 12)(x + 11)
set each to zero
x - 12 = 0 or x + 11 = 0
x = 12 or x = -11
can you have a -11 length on a rectangle? No. So...
x = 12 then substitute back to your sides (x + 2) and (x - 3)
Base: 12 + 2 = 14
Height 12 - 3 = 9
do the same thing for 2 and 3 essentially...
- 1 decade ago
1)
(x+2)*(x-3)=126
x^2-x-6=126
x^2-x-132=0
*ac method*
a=x^2
b=-x
c=-132
a*c= -132
find 2 factors of -132 that equals b or -1
-12+11=-1
-12*11=-132
add it
x^2-12x+11x-132=0
(x^2-12x)(11x-132)=0
x(x-12)11(x-12)=0
(x+11)(x-12)=0
x= -11 or 12
for length you cant use a negative
so x=12
dimensions: 14x9 feet
2)
width= x
length= x+6
x(x+6) = 280
x^2+6x= 280
x^2+6x-280= 0
ac method
ac= -280
-14 and 20
x^2-14x+20x-280=0
(x^2-14x)(20x-280)=0
x(x-14)20(x-14)=0
(x+20)(x-14)=0
x= -20 or 14
dimensions is always positive
x=14
dimensions= 20x14feet
3)
volume of a cylinder is calculated by pi(3.14)*height(radius/2)*radius squared(radius^2)
i'm confused on this one.
but that's how to set it up
