Answer:
t = 1.667 s
Step-by-step explanation
The distance traveled since the warning flag in feet is characterized by
d = 30*t^2 + 40*t
Where t is the time in seconds after the car starts accelerating.
We can easily solve this question by plotting the equation using a graphing calculator or plotting tool.
We need to find the time for which the distance d = 150 ft
150 = 30*t^2 + 40*t , t > =0
We can see that this value in the graph is approximately
t = 1.667 s
We can verify
30*(1.667)^2 + 40*(1.667 ) ≈ 150
Answer:
53 teachers
Step-by-step explanation:
Basically, what we need to do here is to find how many teachers there need to be, first. If there are 6,734 students in the school district and if maximum class size is 25, then the number of teachers needed is:
6,734 / 25 = 269.36
Of course, it's obvious that we can't have a decimal number of teachers, so we need to find integer (269 or 270).
If we take 269 teachers and 25 students per class, we get:
269 • 25 = 6,725 students, which is not enough, since there are 6,734 students.
That means that the number of teachers needed is 270.
It is given that there are already 217 teachers, meaning that 270-217=53 teachers have to be supplemented.
Answer:
Option A. <A and <B are complementary angles
Option D. 
Step-by-step explanation:
we know that
If ABC is a right triangle
then
------> by complementary angles
and
Remember that
so
A.
h = 14 ft · sin 30° = 14 ft · 0.5 = 7 ft.
b.
From the bottom of the height to the bottom of the slide:
y² = 14² - 7² = 196 - 49 = 147
y = √147 = 12.12 ft
15 ft - 12.12 ft = 2.88 ft ( from the bottom of the stairs to the bottom of the height )
tan x = 7 / 2.88 = 2.43
∠x = tan^(-1) 2.43
∠x = 67.63° ≈ 68°.
