Check attached image file.
Answer:
A. a = 10
B. m<FNT = 120°
C. m<KTU = 60°
Step-by-step explanation:
A. (7a + 50)° and (14a - 20)° are corresponding angles. Therefore:
(7a + 50)° = (14a - 20)°
Use this equation to find the value of a
7a + 50 = 14a - 20
Combine like terms
7a - 14a = - 50 - 20
-7a = -70
Divide both sides by -7
-7a/-7 = -70/-7
a = 10
B. m<FNT = (14a - 20)° (alternate interior angles are congruent)
Plug in the value of a
m<FNT = 14(10) - 20
m<FNT = 140 - 20
m<FNT = 120°
C. m<KTU + (14a - 20)° = 180° (linear pair)
Plug in the value of a
m<KTU + 14(10) - 20 = 180
m<KTU + 120 = 180
m<KTU + 120 - 120 = 180 - 120
m<KTU = 60°
Answer: B
Explanation:
Use Pythagorean’s theorem to find it out:
A^2 + B^2 = C^2
8^2 + 15^2 = 17^2
64 + 225 = 289
289 = 289
So these side lengths create a right triangle
Answer:
Option A. 3.5x + 15 ≥ 55
Step-by-step explanation:
Points Rosh received for becoming a member = 15
Points Rosh received for visiting the moving theater = 3.5
Total points needed for a free movie ticket = 55
For each visit he receives 3.5 points, so for x visits he will receive 3.5x points.
Total points = Points received on becoming a member + Points received on x visits
So,
Total Points = 15 + 3.5x
These points must be at least 55 for a free movie ticket. At least means equal to or greater than. So the total points must be equal to or greater than 55 in order to earn a free movie ticket. This can be expressed as:
3.5x + 15 ≥ 55
So, option A gives the correct answer
I think the answer is 147
