Answer:
See attached image and explanation below.
Step-by-step explanation:
We notice that any quadrilateral abed can be divided into two triangles by drawing one of the quadrilateral's diagonals. See the attached picture where the quadrilateral is noted with a green perimeter, the diagonal is pictured in red, and the triangles that are form are shaded in light blue and beige.
Each of the triangles in which the quadrilateral is divided, has the property that the addition of its internal angles equals 180 degrees. From the picture we understand that in order to find what the addition of the internal angles of the quadrilateral is, all we need to do is to add all the angles in both triangles.
Such addition will render 360 degrees. And since the diagonal division can be done with a quadrilateral of any shape, we conclude that the addition of the internal angles of any quadrilateral should result in 360 degrees.
Answer:
9h + 18
Step-by-step explanation:
9 multiplyed by h is 9h. 9 multiplyed by 2 is 18. Therefore it is 9h + 18.
Answer:
Step-by-step explanation:
Check attachment for solution
Answer:
1. From sin²θ +cos²θ =1 and sinθ=-2/3, we see that cosθ=√(1-sin²θ) or cosθ=√5/3, where the sign of cosine is positive as it is in Quadrant IV. x lies in 4th quadrant , cos x is +ve. , cos x = √5/3. Answer.
answer : cos x = √5/3
2. 4/3
3. sin (- theta) = - sin (x) so sin x = 1/6
tan = sin / cos = 1/6 / cos = - sqrt35/35 solve for cos
cos = 1/6 * (-35/sqrt35)
= -35 sqrt35 /210
answer : −35/√210
4. The cosine function is an even function, so cos(θ) = cos(-θ).
The relationship between sin(θ) and cos(θ) is sin(θ) = ±√(1 -cos(θ)^2)
For sin(θ) < 0 and cos(θ) = (√3)/4, sin(θ) = -√(1 -3/16) = -√(13/16)
sin(θ) = -(√13)/4 For sin(θ) < 0 and cos(0) = √(3/4), ...
sin(θ) = -√(1 -3/4) = -√(1/4) sin(θ) = -1/2
answer : -13/√4
5. answer : tan^2 θ ⋅ cos^2 θ = 1 − cos^2 θ would be the first step
We know that
the equation of a vertical parabola in vertex form
y=a*(x-h)²+k
(h,k)------> (0,5)
y=a*(x-0)²+5
y=a*x²+5
substitute the point (2,9) in the equation
9=a*(2)²+5------> 9=4*a+5-------> 4*a=9-5-----> 4*a=4-----> a=1
the equation of the vertical parabola is
y=x²+5
the equation of a horizontal parabola in vertex form
x=a*(y-k)²+h
(h,k)------> (0,5)
x=a*(y-5)²+0
x=a*(y-5)²
substitute the point (2,9) in the equation
2=a*(9-5)²------> 2=16*a------> a=1/8
the equation of the horizontal parabola is
x=(1/8)*(y-5)²
the answer isthe equation of the vertical parabola is y=x²+5
the equation of the horizontal parabola is x=(1/8)*(y-5)²
see the attached figure
