Answer:
x ≈ - 5.32, x ≈ 1.32
Step-by-step explanation:
Given
x² + 4x - 7 = 0 ( add 7 to both sides )
x² + 4x = 7
To complete the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(2)x + 4 = 7 + 4
(x + 2)² = 11 ( take the square root of both sides )
x + 2 = ± ( subtract 2 from both sides )
x = - 2 ±
Thus
x = - 2 - ≈ - 5.32 ( to 2 dec. places )
x = - 2 + ≈ 1.32 ( to 2 dec. places )
Answer:
Part a) The area of the figure is
Part b) The perimeter of the figure is
Step-by-step explanation:
Step 1
Find the area of the figure
In this problem we have that
The figure ABC is the half of a square and the other figure is a semicircle
<u>Find the area of the figure ABC</u>
we have
The area of the half square ABC is equal to find the area of triangle ABC
so
<u>Find the area of the semicircle</u>
The area of the semicircle is equal to
we have that
substitute
The area of the figure is equal to
Step 2
Find the perimeter of the figure
The perimeter of the figure is equal to
we have
Applying Pythagoras theorem
Remember that
the circumference of a semicircle is equal to
The perimeter of the figure is equal to
Simplify