Answer:
Length of the room is 180 ft
Step-by-step explanation:
We have a rectangular room with dimensions:
width = 70 ft and length "x" (unknown)
Perimeter of a rectangle is 2*w + 2*x and according to problem statement 500 ft of lights will fit exactly in room perimeter then:
2*70 + 2*x = 500
140 + 2*x = 500
2*x = 500 - 140
2*x = 360
x = 360/2
x = 180 ft
Minimum value is equal to x=8, y=-4
First find the derivative of the original equation which equals= d/dx(x^2-16x+60) = 2x - 16
at x=8, f'(x), the derivative of x equals zero, so therefore, at point x = 8, we have a minimum value.
Just plug in 8 to the original equation to find the answer for the minimum value.
Here, in order to find the solutions to the quadratic equation - x² + x - 30 = 0, we will use factorization method.
In the method, we will split 30, in such factors, which when added or subtracted gives us 1, and when multiplied gives us -30.
So, we will use, -5 and 6. When they are added they will give us 1 and when multiplied they will give us -30 as answer.
Now, the equation will be written as -
x² - 5x + 6x - 30 = 0
Taking common, we get
x(x - 5) +6(x-5) = 0
(x-5)(x+6) = 0
So, x - 5 = 0 and x +6 = 0, we will get, x = 5 and x = - 6
<u>Thus, the correct option is C). x = 5 and -6</u>
7miles---------1hr
11.2miles------- x
cross multiply;
11.2 × 1 = 7 × x
x= 11.2÷7
x=1.6hr
