1. 103-22 = 81
2 10.2-3y+2x is already in simplest form
It should be a 100 degree angle as well.
Let the number of hotdogs sold = X
Soda was 2 times the amount so soda = 2x
The total of both was 225:
2X + x = 225
Simplify:
3x = 225
Divide both sides by 3:
x = 225/3
x = 75
Hot dogs = 75
Soda = (75 x 2) = 150
Answer:
See below
Step-by-step explanation:
The graph is formed from f(x) = |x|.
f(x) = |x| is shaped like a V with the vertex at the origin and the slope of each arm = 1. Then f(x) = |x + 3| will have the same shape but will be moved 3 units to the left so the vertex is at (-3,0). The - 1 ( to give f(x) = |x + 3| - 1) translates the whole graph 1 unit down so the vertex is at the point (-3, -1).
The domain is All Real x and the range = All real values of f(x)
equal or greater than -1.
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°
