Answer:
Surface area of the wood to be painted = (
+ r 
)
- 16
Step-by-step explanation:
Surface area of a cone is given as the sum of the surface area and the area of its base.
i.e Surface area = + Lr
where: L is the length of its slant height and r is the radius.
Applying the Pythagoras theorem,
L =
Thus,
Surface area = r (r + )
The given cylindrical hole has a radius of 4 cm and depth 2 cm.
The area of one of its circular surfaces =
= × 
= 16 
The surface area of the piece of wood to be painted = surface area of cone - area of cylindrical circular surface.
Surface area of the wood to be painted = r (r + ) - 16
We can represent the base as z and the height as 2z+6. We are going to use the formula A=1/2*b*h and solve for z
180=1/2*z*(2z+6)
360=2z^2+6z
0=2z^2+6z-360
0=2(z^2+3z-180)
0=(z+15)(z-12)
So z=-15 and 12 but it must be positive so then the base is equal to 12
When we plug this into 2z+6 we get 30 for the height
2(12)+6=30
Hope this helps
Answer:
f(5) = 13
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
- Function notation and substitution
Step-by-step explanation:
<u>Step 1: Define</u>
f(x) = x² - 12
x = 5
<u>Step 2: Evaluate</u>
- Substitute: f(5) = 5² - 12
- Exponents: f(5) = 25 - 12
- Subtract: f(5) = 13
Answer:
Step-by-step explanation:
Given
Represent Babysitting with B
Represent Gas Station with G
Total workhours = At most 15
Earnings = At least $90
First, we need to represent the work hours as inequality
B + G = At most 15
At most 15 means less than or equal to 15.
So, we have:
Next, we represent the earnings as inequality.
6 hours of babysitting is: 6B
10 hours at gas station is: 10G
So:
6B + 10G is at least 90
At least 90 means greater than or equal to 90
So, we have:
