12 to the power of 1 is 12
To solve for the measure of angle m, use the cosine law formula.
c^2 = a^2 + b^2 - 2ab cos(C)
in the given situation
( LN )^2 = ( LM )^2 + ( MN)^2 - 2(LM)(MN)cos(m)
substitute the given values
7^2 = 6^2 + 9^2 - 2(6)(9)cos(m)
-68 = 2(6)(9)cos(m)
cos(m) = -0.6296
m = arcos ( -0.6296)
m = 129.0 degrees
Answer:
How To Find The Area Of The Shaded Region?
Step 1: Find area of inner shape.
Step 2: Find area of outer shape.
Step 3: Area of shaded region = area of outer shape – area of inner shape
Example 2:
Find the area of the shaded region:
area of shaded region
Solution:
Step 1: Find area of inner square = 2 cm × 2 cm = 4 cm2
Step 2: Find area of outer shape = (2 cm × 3 cm) + (10 cm × 3 cm)
= 6 cm2 + 30 cm2
= 36 cm2
Step 3: Area of shaded region = area of outer shape – area of inner square
= 36 cm2 – 4 cm2
= 32 cm2
Step-by-step explanation: There you go :)
Answer = 6
Explanation:
I'm guessing there's a simpler solution, but let's give it a shot.
The two roots are provided by using the quadratic equation:
x = [-b ± √(b2 - 4ac)] / (2a)
For x2 - 10x + q = 0
a = 1
b = -10
c = q
Substituting these values in:
x = [-b ± √(b2 - 4ac)] / (2a)
= [-(-10) ± √((-10)2 - 4(1)(q))] / (2(1))
= [10 ± √(100 - 4q)] / 2
= 0.5 [10 ± √(100 - 4q)]
The first root, x1
x1 = 0.5 [10 + √(100 - 4q)]
= 5 + 0.5√(100 - 4q)
The second root, x2
x2 = 0.5 [10 - √(100 - 4q)]
= 5 - 0.5√(100 - 4q)
The difference in the roots is 6.
6 = x1 - x2
= [5 + 0.5√(100 - 4q)] - [5 - 0.5√(100 - 4q)]
= 5 + 0.5√(100 - 4q) - 5 + 0.5√(100 - 4q)
6 = √(100 - 4q)
(6)2 = [√(100 - 4q)]2
36 = 100 - 4q
-64 = -4q
q = 16
Do a little more work to determine the roots.
x2 - 10x + q = 0
x2 - 10x + 16 = 0
(x - 8)(x - 2) = 0
x = {2, 8}
8 - 2 = 6
Answer:
total area = 99m² + 39.4m²
= 138.4m²