F (x) = 4x ⇒ y = 4x
↓
x = 4y Divide by 4 on both sides
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x / 4 = y ⇒ Inverse function = x / 4
Answer:
1) X stands for individual acts and y, group acts. 2) Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). 3)
Step-by-step explanation:
Completing with what was found:
<em> 1) Here is a summary of the scenario your classmate presented for the talent show:Main show The main show will last two hours and will include twelve individual acts and six group acts.Final show The final show will last 30 minutes and will include the top four individual acts and the top group act.The equations he came up with are: 12x+ 6y= 120, 4x+ y= 30</em>
1. What do x and y represent in this situation?
X stands for individual acts and y, group acts.
Besides that, In the system of equation, they represent the time for x, and the time for y.
2. Do you agree that your classmate set up the equations correctly? Explain why or why not.
Yes, that's right. Each scenario describes a different period in minutes, but each one respecting their different amounts (individual and group acts). Either for 120 minutes or 30 minutes length. And their sum totalizing the whole period.
3. Solving the system by Elimination
1 < x < 5
Left side is 1 and right is 5
Greater than 1 because left side is a fraction less than 1 and right side is a number greater than 1.
The left side being a fraction less than 1 could only mean that you have to multiply a number greater than 1 to the other side. And since the other side is a number greater already than 1 then multiplying the left side to the right side must result in a number greater than 1.
The sum of the first n terms in a geometric sequence given the first term (a1) and the common ratio (r) is calculated through the equation,
<span>Sn </span>= (<span><span><span>a1</span>(1−<span>r^n</span>) / (</span><span>1−r)
Substituting the known terms,
Sn = (20)(1 - (1/4)^4)) / (1 - 1/4)
Sn = 26.5625
Thus, the sum of the first four terms is 26.5625. </span></span>