Define a variable and write an expression for the phrase.
1 answer:
Answer:
The expresion for the phrase is:
Step-by-step explanation:
In order to get the expression for the phrase, we have to understand the described operations in it.
The phrase starts with "the quotient of...", therefore the expression must be a fraction:
To get what is the numerator (A) and the denominator (B), we have to analyze carefully the rest of the phrase: "...2 times a number and 8"
In this case, the word "and" separates the numerator from the denominator:
Numerator: "2 times a number"
This unknown number is called x
Therefore, numerator of the fraction (A) is:
And the Denominator: "8"
Therefore:
Finally, replacing values:
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This equation can be solved graphically by plotting the equations
f(x) = 3^x
and
g(x) = 5x-1.
The x-coordinate of the point(s) of intersection is the solution.
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On my graphing calculator, I find it easier to locate x-intercepts, so I would rewrite the equation as
3^x -(5x -1) = 0
and plot the function
h(x) = 3^x -(5x -1)
The x-intercept(s) would be the solutions. (There are two: x≈0.577, x=2.)
f(x) = 3^x
and
g(x) = 5x-1.
The x-coordinate of the point(s) of intersection is the solution.
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On my graphing calculator, I find it easier to locate x-intercepts, so I would rewrite the equation as
3^x -(5x -1) = 0
and plot the function
h(x) = 3^x -(5x -1)
The x-intercept(s) would be the solutions. (There are two: x≈0.577, x=2.)