Answer:
Step-by-step explanation:
The wording, "the quotient of a number and 4," can be displayed as c/4. C would be our variable for the number because the question asks specifically for it. 5 more would demonstrate that we're adding 5 more to our equation. Which would result in c/4 + 5. However, since it equals 7, just add that portion to create the following equation:
Answer: The domain of the function is:
Interval Notation: (-∞ , -7) ∪ (-7 , 0) ∪ (0 , 7) ∪ (7, ∞)
Set-Builder Notation: { x | x ≠ 0 , 7 , -7 }
All real numbers besides 0, 7, and -7.
Step-by-step explanation:
In order to find the domain of your rational function, we need to simplify it:
Remember, most of the time, the domain of a rational function consists of all real numbers besides zero.
To find the domain, we equal the equations in the denominator to zero.
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So all real numbers except for 0, -7, and 7 are in the domain of this rational function.
Answer:
Step-by-step explanation:
Length = x
width = x - 7
height = x - 10
volume = 600 in^3
Volume = L * w * h
600 = x * (x - 7)*(x - 10)
600 = x * (x^2 - 17x + 70)
600 = x^3 - 17x^2 + 70x
x^3 - 17x^2 + 70x - 600 = 0
There is a genius somewhere that could solve this using algebra. The rest of us have 2 choices. We can graph it (see below) or we could use a program that solves it for us. I'll do both for you.
a = 1
b = - 17
c = 70
d = - 600
There is only 1 real solution: x = 15
L = 15
w = 8
h = 5
That has to be one of the ugliest graphs made. It does into the hundreds of thousands and it still looks like a straight line. Trust me. It's not.
