Answer:
The solution is x = 10 and x = -6. This quadratic could be represented in factored form as (x - 10)(x + 6) or on a graph with x-intercepts at (10,0) and (-6,0).
Step-by-step explanation:
To solve the quadratic, write the quadratic in standard form and factor the equation.
x² - 4x = 60
x² - 4x - 60 = 0
(x - 10)(x + 6) = 0
x = 10 and x = -6
I'm going to assume that the room is a rectangle.
The area of a rectangle is A = lw, where l=length of the rectangle and w=width of the rectangle.
You're given that the length, l = (x+5)ft and the width, w = (x+4)ft. You're also told that the area, A = 600 sq. ft. Plug these values into the equation for the area of a rectangle and FOIL to multiply the two factors:

Now subtract 600 from both sides to get a quadratic equation that's equal to zero. That way you can factor the quadratic to find the roots/solutions of your equation. One of the solutions is the value of x that you would use to find the dimensions of the room:

Now you know that x could be -29 or 20. For dimensions, the value of x must give you a positive value for length and width. That means x can only be 20. Plugging x=20 into your equations for the length and width, you get:
Length = x + 5 = 20 + 5 = 25 ft.
Width = x + 4 = 20 + 4 = 24 ft.
The dimensions of your room are 25ft (length) by 24ft (width).
Answer:
y = 2x - 12
Step-by-step explanation:
To find the inverse of a function, you switch x and y and solve for y.
x = 1/2 y + 6 switch x and y
x - 6 = 1/2 y subtract 6 from both sides
2x - 12 = y multiply both sides by 2
Valdez Company opened a special checking account. The charge for each check written was either $.55 or a $6-a-month minimum service charge (whichever is greater). At the beginning of the month, the company checkbook balance was $695.18. Valdez Company wrote 14 checks totaling $312.88. Deposits of $188.10 and $195.10 were made during the month. What's Valdez's checkbook balance to start the next month (including the cost of check writing)?