As consecutive odd numbers differ by two (example: 3, 5, 7), the first odd number can be expressed as 2n + 1, the next can be found by adding two to the first to get 2n + 1 + 2 which simplifies to 2n + 3. Finally the expression for the third consecutive odd integer can be found by adding two to the previous, 2n + 3, to get 2n + 5. Adding these three together and setting them equal to your sum gets the equation
2n + 1 + 2n + 3 + 2n + 5 = 63
Combine like terms and solve For n.
Once you have n, you must substitute it back into your three expressions (2n + 1, 2n + 3, 2n + 5) to find the three odd integers.
Hope this helps :)
Answer:
Step-by-step explanation:
A(7,1), B(5,-6)
(AB)² = (-6-1)² + (5-7)² = 53
AB = √53
Answer:
Step-by-step explanation:
Equation of a line:
The equation of a line has the following format:
In which m is the slope and b is the y-intercept.
Perpendicular lines:
When two lines are perpendicular, the multiplication of their slopes is -1.
Perpendicular to y=1/8x+2
This line has slope 
So, for the line we want to find the equation, we have that:
So
Find the equation of the line through point (1,−5)
This means that when 
. We use this to find b. So:
The equation of the line is:
Answer:
The correct options are;
1) Write tan(x + y) as sin(x + y) over cos(x + y)
2) Use the sum identity for sine to rewrite the numerator
3) Use the sum identity for cosine to rewrite the denominator
4) Divide both the numerator and denominator by cos(x)·cos(y)
5) Simplify fractions by dividing out common factors or using the tangent quotient identity
Step-by-step explanation:
Given that the required identity is Tangent (x + y) = (tangent (x) + tangent (y))/(1 - tangent(x) × tangent (y)), we have;
tan(x + y) = sin(x + y)/(cos(x + y))
sin(x + y)/(cos(x + y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y))
(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y) - sin(x)·sin(y)) = (Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y))
(Sin(x)·cos(y) + cos(x)·sin(y))/(cos(x)·cos(y))/(cos(x)·cos(y) - sin(x)·sin(y))/(cos(x)·cos(y)) = (tan(x) + tan(y))(1 - tan(x)·tan(y)
∴ tan(x + y) = (tan(x) + tan(y))(1 - tan(x)·tan(y)
