Answer:
x= 60°, y = 80°, z = 40°
Step-by-step explanation:
Look at the line substending 40° and Z°; you would see that both lines are parallel and so their angles are they the same.
Hence z= 40° { corresponding angles of parallel lines}
Similarly;
Look at the line substending 60° and x°; you would see that both lines are parallel and so their angles are they the same.
60° = x° { corresponding angles of parallel lines}
Now looking at the angle between x and y; let's call the angle between them r
And you would observe closely that r = z° = 40°{ vertically opposite angles are equal}
Note that x + r + y = 180°{ angle on a straight line}
y = 180° - ( x + r)
y = 180 - (60+40)
y = 180° - 100°
= 80°
Answer:
240 miles
Step-by-step explanation:
Given that:
Charges offered by Prestige car rentals for renting a midsize vehicle:
Fixed charges = $47
Per mile charges for renting a midsize vehicle = $0.07
Charges offered by Gateway Auto for renting a midsize vehicle:
Fixed charges = $35
Per mile charges for renting a midsize vehicle = $0.12
To find:
Number of miles for which both the companies charge the same price?
Solution:
Let the number of miles for which both the companies will charge the same price =
miles
Charges for one mile by Prestige car rentals = $0.07
Charges for
miles by Prestige car rentals = $0.07
Total charges by Prestige Car rentals = $47 + $0.07
Charges for one mile by Gateway Auto = $0.12
Charges for
miles by Gateway Auto = $0.12
Total charges by Gateway Auto = $35 + $0.12
As per question statement, the charges are same:

Answer:
b
Step-by-step explanation:
Answer:
s = 22.5 m
Step-by-step explanation:
the equation for the speed change of a coach moving along a straight section of the road and starting braking at a speed of 20 m / s has the form v (t) = 25-5t. Using integral calculus, determine the coach's braking distance.
v (t) = 25 - 5 t
at t = 0 , v = 20 m/s
Let the distance is s.

Let at t = t, the v = 20
So,
20 = 25 - 5 t
t = 1 s
So, s = 25 x 1 - 2.5 x 1 = 22.5 m
Answer:
1. H = 29 cm
2. θ = 44°
Step-by-step explanation:
1. We can find the height of the triangle by considering the isosceles triangle as two right triangles. The height can be found by using Pitagoras:

Where:
L: is the sides of the isosceles triangle = 42 cm
B: is the base = 30 cm
H: is the height =?
Then, the height is:

2. The two equal angles (θ) can be found using the following trigonometric identity:


Hence, the two equal angles are 44°.
I hope it helps you!