Answer:
x=6
Step-by-step explanation:
12x + 6= 78
-6 -6
12x = 72
(Divide by 12)
72 divided by 12 is 6.
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Divide the number of fast balls by the total number of pitches:
240 / 384 = 0.625
Answer:
Lines are parallel.
Step-by-step explanation:
The given lines are
Rearrange the equation in the slope intercept form that is
where
is the slope.
<em>First Line:</em>

compare it with 
slope (
) of first line 
<em>Second Line:</em>

divide both by 

compare it with 
slope
of second line 
Since slope of two lines are equal

hence these lines are parallel.
Answer:
a. 277.3 m²
b. $307.86
Step-by-step explanation:
a. Area of the wall to be painted = area of rectangle - area of triangle
= L × W + ½×a×b×sin θ
L = 17 m
W = 14 m
a = 8.7 m
b = 9.5 m
θ = 72°
Plug in the values into the equation
Area of the wall = (17×14) + (½*8.7×9.5×sin 72)
Area of the wall = 238 + 39.3024105
Area of the wall to paint ≈ 277.3 m²
b. 20 liters of paint of 1 container cost $21.99
If 1 liter of paint covers 1m², therefore,
277.3 m² will need = 277.3 × 1 = 277.3 liters of paint.
20 liters = 1 container of paint
277.3 liters = 277.3/20 = 13.865 ≈ 14 containers
1 container = $21.99
14 containers = 21.99 × 14 = $307.86
It is known

and

(if you want to determine cosine of 30° you should draw the perpendicular line to the x-axis and find the point of intersection, the value of x-coordinate is the cosine of 30°).
The angle

and

(see image).
The angle

and

(see image).