ANSWER :
The answer is :
EXPLANATION :
Note that cotangent is only positive when the angle is in the first or third quadrant.
Since y is not in the first quadrant, it must be in the third quadrant.
So the x and y are both negative.
An angle with a terminal point (x, y)
The cotangent is x/y
We can equate :
Since x and y are both negatives, x = -9 and y = -13
We can have the triangle :
The hypotenuse will be :
We are asked to find the value of sec y.
In an angle with a terminal point (x, y)
The secant is :
The hypotenuse is 5√10 and x = -9
The value of sec will be :
Area of a rectangle
is LxW. We let x = width and x+20 = length. Using the formula we will evaluate;
A = LxW
4800 =
(x+20)(x)
x² + 20x –
4800 = 0
We will get
the factors of it to determine x values, in this case, we are only looking at
the positive x value since are dealing with the area.
x² + 20x +
4800 = 0
(x+80)(x-60)
= 0
(x + 80) = 0 | (x-60) = 0
x = - 80 | x = 60
x = 60, this is the width
x +20 = 80, this is the length
Get the x terms by themselves on one side and a constant on the other side of the equal sign...
4x^2-8x=1 make the leading coefficient equal to one...
x^2-2x=1/4 now halve the linear coefficient, -2 in this case, square it, and add that value to both sides of the equation...-2/2=-1, -1^2=1 so
x^2-2x+1=1+1/4
x^2-2x+1=5/4 now the left side is a perfect square...
(x-1)^2=5/4 take the square root of both sides...
x-1=±√(5/4) add 1 to both sides
x=1±√(5/4)
Answer: (-3,-4)
Step-by-step explanation:
4x-y=-8
y=2x+2
4x-(2x+2)=-8
2x-2=-8
y=2x+2
x=-3
y=2(-3)+2
y=-4
x=-3 , y=-4