<span>The diagonals of a parallelogram bisect each other.
So we just equate the two equations BE and DE
2x^2 - x = x^2 + 6
2x^2 - x - x^2 - 6 = 0
x^2 - x - 6 = 0
This is quadratic eqn. So we obtain.
(x - 3) ( x + 2) = 0
Setting each to 0 and solving for x, we have that x = 3 and x = -2
So we have two possible values for BD.
But Since BE = DE then we can simply double each
If x = 3 BD = 2 (2(3)^2 - 3) = 2 ( 18 - 3) = 30 units
If x = - 2 BD = 2((-2)^2 -3 ) = 2 (8 - 3) = 10 units</span>
Answer:
this is a required answer.
Answer:
x = 1
Step-by-step explanation:
8x - 5(x - 3) = 18
8x - 5x + 15 = 18 <em>[Expand the brackets]</em>
3x = 3 <em>[Separate variables and constants]</em>
<u>x = 1</u>
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
