Answer:
x < 88
Step-by-step explanation:
ΔCED and ΔCEF
DE = EF CE = CE CF < CD
∠FEC < ∠DEC
x - 13 < 75
x < 88
I agree with the person that commented first
The sum of the 3 inside angles of a triangle needs to equal 180:
11x-5 + 6x + 5 + c = 180
Combine like terms:
18x = 180
Divide both sides by 18:
X = 10
Solve for Q:
11x -5= 11(10) -5 = 110-5 = 105 degrees
Answer:
1) x = 40° & y = 50°
2) x = 100° & y = 80°
Step-by-step explanation:
1)
ABCD is a cyclic quadrilateral (∵ all the vertices of the quadrilateral are touching on the circle). As it is a cyclic quadrilateral , sum of it's opposite angles will be 180°.
⇒ ∠ADC + ∠ABC = 180°
⇒ 130° + y = 180°
⇒ y = 180 - 130 = 50°
In ΔABC ,
∠ACB = 90° (∵ AB is the diameter of the circle and a diameter subtends an angle of 90° on any point on circle.)
Using angle sum property of triangle ,
∠ABC + ∠ACB + ∠CAB = 180°
⇒ y + 90° + x = 180°
⇒ x + 50° + 90° = 180°
⇒ x + 140° = 180°
⇒ x = 180 - 140 = 40°
2)
ΔABC is an isosceles triangle (∵AB = AC). As it is an isosceles triangle , it's base angles will be equal. So , ∠ABC = ∠ACB = 50°
Using angle sum property of triangle ,
∠ABC + ∠ACB + ∠BAC = 180°
⇒ 50° + 50° + y = 180°
⇒ y + 100° = 180°
⇒ y = 180 - 100 = 80°
ABEC is a cyclic quadrilateral (∵ all the vertices of the quadrilateral are on the circle.). As it is a cyclic quadrilateral , sum of it's opposite angles will be 180°.
⇒ ∠BAC + ∠BEC = 180°
⇒ y + x = 180°
⇒ x + 80° = 180°
⇒ x = 180 - 80 = 100°
Cost = 300 x + 750 , where x is the number of the scooters;
Price = 900 - x
Profit = x ( 900 - x ) - ( 300 x + 750 ) =
= 900 x - x² - 300 x - 750 = - x² + 600 x - 750
d (Profit) = - 2 x + 600
- 2 x + 600 = 0
x = 600 : 2
x = 300
The company must produce 300 scooters to maximize the profit.
The maximum profit is:
- 300² + 600 · 300 - 750 = $89,250
