Answer:
The graph in the attached figure
Step-by-step explanation:
we have
This is a vertical parabola open upward
The vertex is a minimum
step 1
Find the x-intercepts
The x-intercepts are the values of x when the value of the function is equal to zero
For f(x)=0
Factor x
The x-intercepts are (0,0) and (-4,0)
step 2
Find the y-intercept
The y-intercept is the values of the function when the value of x is equal to zero
For x=0
The y-intercept is (0,0)
step 3
Find the vertex
Convert the equation into vertex form
Complete the square
Rewrite as perfect squares
The vertex is the point (-2,-4)
therefore
using a graphing a graphing tool
The graph in the attached figure
Answer: 1.) 180 cubic meters
2.) 302 square centimeters
3.) 16.33 centimeters
Step-by-step explanation:
1.) Volume of pyramid is bh/3
Base is 6×6 Height is 15/3
Multiply to get 180.
2.) Two sides are 5×11=55 each. Two sides are 6×11=66 each, and the two ends are each 5×6=30.
Add 55+66+30=151 then multiply 151×2=302.
3.) V=bh.
Triangular base is ab/2. Given a is 10 and base (edge of square side) is 12.
10×12/2= 60. Divide that into the given Volume: 1080cm^3
1080÷60= 16.33cm^2
Answer:
The door has a width of 6.26 feet, with a height of 12.52 feet.
Step-by-step explanation:
You can solve this by taking two pieces of information we're given:
1) the diagonal size of the doorway is 14 feet
2) the height of the doorway twice its width
First lets describe the width and height using the diagonal length. We can do that with the Pythagorean theorem:
w² + h² = 14²
Now we can use the relationship between the width and height to eliminate one variable:
w² + (2w)² = 14²
w² + 4w² = 14²
5w² = 196
w² = 39.2
w ≈ 6.26
So the door has a width of 6.26 feet, with a height of double that, 12.52 feet.
Answer:
Step-by-step explanation:
Given inequality is 
Simplifying the inequality by rearranging the terms:
=> 
=> 
=>
So the given inequality can be simply expressed as
Hence x can take all values in the domain which are less than 2.
