Answer:
The answer is "a" 5x-4(-3x+5)=-3
Answer:
an = -1.3n -2.4
Step-by-step explanation:
The formula for an arithmetic sequence is
an = a1 +d (n-1)
where a1 is the first term and d is the common difference
an = -3.7 - 1.3(n-1)
Distribute
an = -3.7 -1.3n +1.3
an = -2.4 - 1.3n
an = -1.3n -2.4
Using the recurrence relation, we can find a couple more values in the sequence:
- a3 = 3a2 -3a1 +a0 = 3(4) -3(2) +2 = 8
- a4 = 3a3 -3a2 +a1 = 3(8) -3(4) +2 = 14
First differences are 0, 2, 4, 6, ...
Second differences are constant at 2, so the function is quadratic.
The sequence can be described by the quadratic ...
... an = n² -n +2
_____
We know the value for n=0 is 2, so we can find <em>a</em> and <em>b</em> using the given values for a1 and a2.
... an = an² +bn +2
... a1 = 2 = a·1² +b·1 +2 . . . . for n=1
... a + b = 0
... a2 = 4 = a·2² -a·2 +2 . . . . for n = 2; using b=-a from the previous equation
... 2 = 2a
... a = 1 . . . . so b = -1
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
