Answer:
Step-by-step explanation:
The shortest distance d, of a point (a, b, c) from a plane mx + ny + tz = r is given by:
--------------------(i)
From the question,
the point is (5, 0, -6)
the plane is x + y + z = 6
Therefore,
a = 5
b = 0
c = -6
m = 1
n = 1
t = 1
r = 6
Substitute these values into equation (i) as follows;
Therefore, the shortest distance from the point to the plane is
Answer:
Step-by-step explanation:
Let x represent the number of attendees that it will take the company to break even.
The company pays a flat fee of $98 to rent a facility in which to hold each session. Additionally, for every attendee who registers, the company must spend $16 to purchase books and supplies. This means that the total cost that the company would pay for x attendees is
16x + 98
Each attendee will pay $65 for the seminar. This means that the total revenue that the company would generate from x attendees is 65x.
At the break even point,
total cost = total revenue
Therefore,
16x + 90 = 65x
65x - 16x = 98
49x = 98
x = 98/49
x = 2
It will take 2 attendees and the total expenses and revenues is
2 × 65 = $130
Answer:
m∠1 = 25° (opposite angles are congruent)
m∠2 = 87° ⇒ 180 - (25 + 68)
m∠3 = 68° ⇒ 180 - (87 + 25)
Hope this helps!
Answer:
(x + 3b)(3 + 5a)
Step-by-step explanation:
Assuming you require the expression factorised.
Given
3x + 9b + 5ax + 15ab ( factor the first/second and third/fourth terms )
= 3(x + 3b) + 5a(x + 3b) ← factor out (x + 3b) from each term
= (x + 3b)(3 + 5a) ← in factored form
Answer:
Step-by-step explanation:
Given
See attachment for triangle
Required
Find 
and 
of angle Y
For angle Y:
The 
of an angle is calculated as:
So:
The 
of an angle is calculated as:
So:
The of an angle is calculated as:
So:
