Answer
with
Step-by-step explanation:
Statement Reasons
1.∠1 ≅ 4 Given
2.∠1 = ∠2 Being Vertically opposite angles.
3.∠4 = ∠3 Being Vertically opposite angles.
4.∠2 = 3 From Statement no 2 & 3, Transitive property.
5.∠2 ≅ 3 From Statement 4
Proved.
Answer:
Step-by-step explanation:
1. no
2. yes
3. yes
4. yes
5. 5.2
6. 4.5
7. 2.5
8. 16
Answer:
Area of the shaded region = 6.88 cm²
Step-by-step explanation:
Area of the shaded region = Area of the rectangle - Area of the semicircle
Area of the rectangle = Length × Width
Length of the rectangle = AD = 8 cm
Width of the rectangle = OP = 4 cm [OP, OB and OC are the radii of the circle which are equal in measures]
Area of the rectangle = 8 × 4 = 32 cm²
Area of the semicircle = 
= 
= 
= 25.12 cm²
Area of the shaded region = 32 - 25.12
= 6.88 cm²
Answer:
-5 < x < 5
Step-by-step explanation:
|x| < 5
This can be split into two cases: x < 5 and -x < 5 because |x| could be either x or -x depending on whether x is positive, negative, or 0. Solving the second one we get x > -5 so the answer is -5 < x < 5.
Second one is correct, that is an identity.
Third one is a contradiction:
6x - 15 = 3 * (2x - 6) ------> 6x - 15 = 6x - 18
Fourth one:
5x - 3 * (x - 4) = 2 * (x - 6) ---> 5x - 3x + 12 = 2x - 12 ---> 2x + 12 = 2x -12
So this is a contradiction as well.