Answer:
x = 30
Step-by-step explanation:
The angle in the bottom right is 120
Call is y
y+60 = 180
y = 180-60
y =120
Opposite angles in a parallelogram are equal so the upper left angle is 120
Call the 3x +z = 120
We also know that 2x+90 +z = 180 since it forms a straight line
Subtract 90 from each side
2x+z = 90
Using 3x+z = 120 and 2x+z =90 and subtracting the second equation
3x+z = 120
-2x-z =-90
------------------
x = 30
Answer:
Isolate the variable by dividing each side by factors that don't contain the variable.
Exact Form:
x
=
1
3
Decimal Form:
0.3
this is the first one I'm not to good with area
Answer:
units cubed
Step-by-step explanation:
The volume of a sphere is: 
We know the radius r = 1/4, so we just plug this into the equation:
(4/3)*
*(1/4)^3 = (4/3)*
*(1/64) = 
So, the answer is
units cubed.
Answer: 11.5 ft
Step-by-step explanation:
The length of the shadow of the building = length of the shadow - distance of the building
= 52 - 32
= 20
Let the height the shadow strike the side of the building be h
then by similar shape rule
h / 20 = 30 / 52
52h = 30 x 20
52h = 600
h = 600/52
h = 11.53846154
h ≈ 11.5
Answer:
cos(θ) = 3/5
Step-by-step explanation:
We can think of this situation as a triangle rectangle (you can see it in the image below).
Here, we have a triangle rectangle with an angle θ, such that the adjacent cathetus to θ is 3 units long, and the cathetus opposite to θ is 4 units long.
Here we want to find cos(θ).
You should remember:
cos(θ) = (adjacent cathetus)/(hypotenuse)
We already know that the adjacent cathetus is equal to 3.
And for the hypotenuse, we can use the Pythagorean's theorem, which says that the sum of the squares of the cathetus is equal to the square of the hypotenuse, this is:
3^2 + 4^2 = H^2
We can solve this for H, to get:
H = √( 3^2 + 4^2) = √(9 + 16) = √25 = 5
The hypotenuse is 5 units long.
Then we have:
cos(θ) = (adjacent cathetus)/(hypotenuse)
cos(θ) = 3/5