Answer:
Part 1) The domain of the quadratic function is the interval (-∞,∞)
Part 2) The range is the interval (-∞,1]
Step-by-step explanation:
we have
This is a quadratic equation (vertical parabola) open downward (the leading coefficient is negative)
step 1
Find the domain
The domain of a function is the set of all possible values of x
The domain of the quadratic function is the interval
(-∞,∞)
All real numbers
step 2
Find the range
The range of a function is the complete set of all possible resulting values of y, after we have substituted the domain.
we have a vertical parabola open downward
The vertex is a maximum
Let
(h,k) the vertex of the parabola
so
The range is the interval
(-∞,k]
Find the vertex
Factor -1 the leading coefficient
Complete the square
Rewrite as perfect squares
The vertex is the point (7,1)
therefore
The range is the interval
(-∞,1]
Answer:
Step-by-step explanation:
Have in mind the definition of the term 
, and now work on what the term 
is based on the previous definition:
In the next step do NOT combine the numerical values, but try to identify the 
term (
) in the expression (notice the use of square brackets to group the relevant terms):
![a_{n+1}=4\,n+4-1\\a_{n+1}=[4\,n-1]+4\\a_{n+1}=a_n+4](https://tex.z-dn.net/?f=a_%7Bn%2B1%7D%3D4%5C%2Cn%2B4-1%5C%5Ca_%7Bn%2B1%7D%3D%5B4%5C%2Cn-1%5D%2B4%5C%5Ca_%7Bn%2B1%7D%3Da_n%2B4)
So now we have the term "" defined in a recursive manner based on the previous term ""
The <em>correct answer</em> is:
400,000.
Explanation:
The third digit in 399 is 9. To round to this place value, we inspect the digit behind it. If the digit is 5 or greater, we round up; if it is less than 5, we round down.
The digit behind 9 is 7. Since it is greater than 5, we round up. This would ordinarily put the number up 1; however, doing that makes the 9 a 10, which in turn makes the next number 10, and the next number 4. This gives us 400,000.
Answer:
0.3334 ft
Step-by-step explanation:
Measure the height and radius of the tank. The radius is the distance from the center of the tank to its outer edge. Another way to find the radius is to divide the diameter, or width, by two. Square the radius by multiplying the radius times itself and then multiply it by 3.1416, which is the constant pi.
- Given height and volume: r = √(V / (π * h)),
- Given height and lateral area: r = A_l / (2 * π * h),
- Given height and total area: r = (√(h² + 2 * A / π) - h) / 2,
- Given height and diagonal: r = √(h² + d²) / 2,
- Given height and surface-area-to-volume ratio: r = 2 * h / (h * SA:V - 2),
- Given volume and lateral area: r = 2 * V / A_l,
- Given base area: r = √(A_b / (2 * π)),
- Given lateral area and total area: r = √((A - A_l) / (2 * π)).
First of all, 2400=0.6x is the equation
Now, we use cross multiplication
2400/1 = 3/5x
2400*5 = 3x
12,000 = 3x
12000/3= 4000
<u>The total fundraiser goal is $4,000.</u>
