Answer: 3¼ hours
Step-by-step explanation:
Number of hours used in baking = 2¾ hours
Number of hours used in cleaning up the kitchen = ½ hour
Therefore, the time used in the kitchen will be the addition of the time used in baking plus the time used in cleaning the kitchen which will be:
= 2¾ + ½
= 2 3/4 + 2/4
= 2 5/4
= 2 + 1¼
= 3¼ hours
Therefore, 3¼ hours was used in the kitchen.
Answer: Option C
, 
Step-by-step explanation:
If the lines m and n are parallel then the large triangle and the small triangle are similar triangles, because they have equal angles.
By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a ', b' and c 'then:
In this case
So:
Therefore
if 
and then 
Finally
,
Answer:
f(x) = -4x + 80
Step-by-step explanation:
You are given two points,
(5, 60) and (10, 40)
in order to get the equation, let's use the form slope-intercept form
m = (y1 - y2) / (x1 - x2)
m = (60 - 40) / (5 - 10)
m = 20/-5
m = -4
Get the x intercept
y = mx + b
60 = (-4)(5) + b
b = 60+20
b = 80
so the equation is
y = -4x + 80
f(x) = -4x + 80
Answer:
(B) π/12 + π/6 k
Step-by-step explanation:
Points of inflection are where f"(x) = 0 and changes signs.
f(x) = cos²(3x)
f(x) = (cos(3x))²
f'(x) = 2 (cos(3x))¹ × -sin(3x) × 3
f'(x) = -6 sin(3x) cos(3x)
Using double angle formula:
f'(x) = -3 sin(6x)
f"(x) = -3 cos(6x) × 6
f"(x) = -18 cos(6x)
0 = -18 cos(6x)
0 = cos(6x)
6x = π/2 + 2πk or 6x = 3π/2 + 2πk
We can simplify this to:
6x = π/2 + πk
x = π/12 + π/6 k
