Answer:
460 USD
Step-by-step explanation:
monthly earnings = 250 x 4 = 1000
monthly bills = 135 x 4 = 540
end of month = 1000 - 540 = 460 USD
9514 1404 393
Answer:
b = 20/7
Step-by-step explanation:
The slope of the first line can be found by solving for y:
by = -5x +6 . . . . . . add 6-5x
y = -5/b +6/b . . . . . divide by b
The slope is -5/b.
The slope of the second line can be found by solving for y:
7y = 4x +7
y = 4/7x +1 . . . . . . divide by 7
The slope is 4/7.
For the lines to be perpendicular, the product of these slopes must be -1:
(-5/b)(4/7) = -1
-20/(7b) = -1 . . . . simplify
b = 20/7 . . . . . . . multiply by -b
The lines will be perpendicular when b = 20/7.
Given that the area is equal to twice the perimeter and the dimensions are:
length=4x ft, width=(x+6) ft
the perimeter will be:
P=2(L+W)
P=2(4x+(x+6))
P=2(4x+x+6)
P=2(5x+6)
P=(10x+12)
Area of the rectangle is:
A=4x(x+6)
A=4x²+24x
but:
2P=A
thus
2(10x+12)=4x²+24x
20x+24=4x²+24x
thus
4x²+4x-24=0
x²+x-6=0
x²-2x+3x-6=0
x(x-2)+3(x-2)=0
(x-2)(x+3)=0
thus the answer is:
x=-3 or x=2
thus
length=4x=4*2=8 ft
width=(x+6)=(2+6)=8 ft
We are dealing with monomial function so we just focus on end behavior.
5x¹⁰ has both ends going up so it would have minimum value
-4x¹¹ has one end going down and other end going up so no minimum value
-x¹² has both ends going down so it opens downward thus no minimum value. Just maximum.
6x⁷ has one ends going up and other going down so no minimum value.
So final answer is y = 5x¹⁰