The option D) x + x+2 + x+4 = 53 represents the exact equation of sum of three consecutive odd integers which is equal to 53.
<u>Step-by-step explanation:</u>
The sum of the three consecutive odd integers = 53
<u>To frame the equation :</u>
- Let us consider any of the three consecutive odd integers.
- Let us take 1,3,5 as the three consecutive odd integers.
Assume the first odd integer as 'x'. In this case, (x=1)
- The second consecutive odd integer is 3.
- The difference between 1 and 3 is 2.
Therefore, the second consecutive odd integer is x+2.
- The third consecutive odd integer is 5.
- The difference between 1 and 5 is 4.
Therefore, the third consecutive odd integer is x+4.
This means that, the sum of any three consecutive odd integers are given as x + x+2 + x+4.
Given that,
Sum of the three consecutive odd integers is 53.
The first odd integer + second odd integer + third odd integer = 53
x + x+2 + x+4 = 53.
The option D) x + x+2 + x+4 = 53 represents the exact equation of sum of three consecutive odd integers which is equal to 53.
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
%error=(6.5g/mol - 7g/mol)/(7g/mol) * 100= 7.14% error
