The described picture frame can be visualized into two separate parts. The first area is equal to the area using the outermost dimensions for the length and width.
Area = Length x Height
Area = (20 in) x (14 in)
Area = 280 in²
We are given that the area is only equal to 192 in². We subtract this value from the computed area.
Difference = 280 in² - 192 in²
difference = 88 in²
This area is equal to the area of the hollow space inside the frame. That is equal to,
height = 20 in - 2x
length = 14 in - 2x
The area,
88 = (20 - 2x)(14 - 2x)
Simplify the right hand side of the equation.
88 = 280 - 68x + 4x²
Divide the equation by 4,
22 = 70 - 17x + x²
Transposing,
x² - 17x - 48 = 0
The factors of the equation is 58.2.
Thus, the thickenss is equal to 58.2 in
The answer is '<span>f(x) is an odd degree polynomial with a positive leading coefficient'.
An odd degree polynomial with a positive leading coefficient will have the graph go towards negative infinity as x goes towards negative infinity, and go towards infinity as x goes towards infinity.
An even degree polynomial with a negative leading coefficient will have the graph go towards infinity as x goes toward negative infinity, and go towards negative infinity as x goes toward infinity.
g(x) would have a a positive leading coefficient with an even degree, as the graph goes towards infinity as x goes towards either negative or positive infinity.
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If we know that 30% of the time is used after 9 minutes we can write this mathematically as:
By solving for x we can determine the total time allowed to play games and so:
The total time allowed to play games is 30 minutes. Since 9 minutes have lapsed 30-9=21 minutes left to play.
Answer:
n = 1 second formula
n = 0 first formula
Step-by-step explanation:
I answer this in the other question you put, here it is again.
This is easy to get. We know the sequence cause it follows a pattern of 8, so let's try some values of n from 1 to 4, to get those numbers with the first formula:
n = 1,2,3,4
f(1) = 8(1) + 2 = 10
f(2) = 8(2) + 2 = 18
f(3) = 8(3) + 2 = 26
f(4) = 8(4) + 2 = 34
As you can see, with the first formula, the first term is 10, and not 2. The only way to get 2 with n = 1 is with the second formula:
f(1) = 8(1) - 6 = 2
f(2) = 8(2) - 6 = 10
f(3) = 8(3) - 6 = 18
f(4) = 8(4) - 6 = 26
With n = 1, the second formula was better and correct.
The first formula could be right only beggining with n = 0. Here is the proof:
f(0) = 8(0) + 2 = 2
