Answer: B. 5root(3)
Use Pythagorean’s theorem to solve this problem. We know one side and the hypotenuse, so we can solve for the other side.
a² + b²= c²
5² + b² = 10² (plug in 5 for one side, and 10 for the hypotenuse)
25 + b² = 100 (square 5 and 25)
b² = 75 (subtract 75 from both sides)
b=√(75) (take the square root of both sides)
b=√(25*3) (factor out a square)
b=5√(3) (simplify radical)
Answer:
27
Step-by-step explanation:
note that tanx cotx = tanx × = 1
Given
tanx - cotx = 5 ( square both sides )
(tanx - cotx)² = 5² = 25 ← expand left side using FOIL
tan²x - 2tanxcotx + cot²x = 25
tan²x - 2 + cot²x = 25 ( add 2 to both sides )
tan²x + cot²x = 27
Answer:
Step-by-step explanation:
To write an equation, use the slope-intercept equation:
M is the slope and b is the y-intercept.
First, find the slope by using the slope formula for when you have two points:
Rise over run is the change in the y-axis over the change in the x-axis. Substitute values:
Simplify parentheses (two negatives make a positive) and simplify:
The slope, m, is 4. Insert this information into the equation:
Now, take one of the points and insert into the slope-intercept formula:
Solve for b, the y-intercept. Simplify multiplication:
Add 20 to both sides and simplify:
The y-intercept, b, is 20. Insert this value into the equation:
Done.