FIRST PARTWe need to find sin α, cos α, and cos β, tan β
α and β is located on third quadrant, sin α, cos α, and sin β, cos β are negative
Determine ratio of ∠α
Use the help of right triangle figure to find the ratio
tan α = 5/12
side in front of the angle/ side adjacent to the angle = 5/12
Draw the figure, see image attached
Using pythagorean theorem, we find the length of the hypotenuse is 13
sin α = side in front of the angle / hypotenuse
sin α = -12/13
cos α = side adjacent to the angle / hypotenuse
cos α = -5/13
Determine ratio of ∠β
sin β = -1/2
sin β = sin 210° (third quadrant)
β = 210°

SECOND PARTSolve the questions
Find sin (α + β)
sin (α + β) = sin α cos β + cos α sin β



Find cos (α - β)
cos (α - β) = cos α cos β + sin α sin β



Find tan (α - β)


Simplify the denominator


Simplify the numerator


Simplify the fraction

The factored form is (3x-4)(x+9)
Answer
48,000
Step-by-step explanation:
base(x)
1,200(40)
<u>Answer:</u>
The cost of one gallon of gas in Toronto, Canada is $3.458.
<u>Solution:
</u>
Given, One gallon of gasoline in buffalo, New York costs $2.29.
In Toronto, Canada, one liter of gas costs $0.91.
There are 3.8 liters in one gallon.
We have to find how much does one gallon of gas cost in Toronto?
Now, cost of one gallon of gas in Toronto = cost of one litre of gas in Toronto x 3.8 liters for 1 gallon.
Cost of one gallon of gas = 0.91 x 3.8 = 3.458
Hence, the cost of one gallon of gas in Toronto, Canada is $3.458.
Answer:
130/l in where l is the length of the rectangle
Step-by-step explanation:
The formula for area of a rectangle is length by width where the width is the height of the rectangle
Given that area=130 in²
Lets assume the length of this rectangle is =l inches
Then ;
A=l*w
130 =l*w
130/l = w
130/l in = height