Answer:
a) ∠TVZ= 95°
Step-by-step explanation:
3a) ∠STY= ∠QTV (vert. opp. ∠s)
3x°= 120°
x°= 120° ÷3
x°= 40
∠TVZ= ∠RVW (vert. opp. ∠s)
∠TVZ= (2x +15)°
∠TVZ= [2(40) +15]°
∠TVZ= (80 +15)°
∠TVZ= 95°
b) Since ∠TVZ and ∠WVZ lies on a straight line,
∠TVZ +∠WVZ= 180° (adj. ∠s on a str. line) -----(1)
∠WVZ= (2x +5)°
∠WVZ= [2(40) +5]°
∠WVZ= (80 +5)°
∠WVZ= 85°
Substitute ∠WVZ= 85° into (1):
∠TVZ +85°= 180°
∠TVZ= 180° -85°
∠TVZ= 95°
Thus, ∠TVZ is indeed 95°.
Notes:
• What is vert. opp. ∠s?
It is an abbreviation used for a property of angles, vertically opposite angles. When two lines intersect each other, the angles facing each other (or the angles on the opposite side of each other) are equal.
• What is adj. ∠s on a str. line?
It is an abbreviation for 'adjacent angles on a straight line'. The sum of all the angles on a straight line is 180°.
Answer:
Associative
Step-by-step explanation:
3 x 4 =12 and 12 x 2 =24
Since there aren't any exponents the x,y, and z gets added together giving you 24 xyz
Solve for x over the real numbers:
2 x^2 - 4 x - 3 = 0
Divide both sides by 2:
x^2 - 2 x - 3/2 = 0
Add 3/2 to both sides:
x^2 - 2 x = 3/2
Add 1 to both sides:
x^2 - 2 x + 1 = 5/2
Write the left hand side as a square:
(x - 1)^2 = 5/2
Take the square root of both sides:
x - 1 = sqrt(5/2) or x - 1 = -sqrt(5/2)
Add 1 to both sides:
x = 1 + sqrt(5/2) or x - 1 = -sqrt(5/2)
Add 1 to both sides:
Answer: x = 1 + sqrt(5/2) or x = 1 - sqrt(5/2)
Answer: The answer is x = 20 feet
Step-by-step explanation: I am right because there is 4 feet below the ground and 16 feet above the ground so if you add 4 + 16 = 20 which is the total feet of the pole.
