The triangles ABC and EDF are congruent, meaning they have the same side lengths and angles measures.
The measure of DF, as both triangles are congruent, is equal to the measure of BC.
We can calculate the length of BC using the distance formula:
As BC is congruent with DF and BC=5, the length of DF is 5 units.
Answer
Find out the original side length of the square .
To prove
Let us assume that the original length of the square be x.
Formula
As given
The dimensions of a square are altered so that 8 inches is added to one side while 3 inches is subtracted from the other.
Length becomes = x + 8
Breadth becomes = x -3
The area of the resulting rectangle is 126 in²
Put in the formula
(x + 8) × (x - 3) = 126
x² -3x + 8x -24 = 126
x ²+ 5x = 126 +24
x² + 5x - 150 = 0
x² + 15x - 10x - 150 = 0
x (x + 15) -10 (x +15) =0
(x + 15)(x -10) =0
Thus
x = -15 , 10
As x = -15 (Neglected this value because the side of the square cannot be negative.)
Therefore x = 10 inches be the original side of the square.
Answer: Option D
Step-by-step explanation:
By definition if we have a function F (x) and perform a transformation of the form
Then it is true that:
If c is negative the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the right
If c is positive, the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the left.
Note that in this case the transformation is:
Then and
Therefore the graph of G(x) will be equal to the graph of F(x) displaced horizontally <em>9 units to the left</em>
The answer is the option D.