Question
Consider this mathematical machine. a) What number would you have to use as input if you wanted 30 as the output? b) What would you have to input to obtain an output of 44 ? a) The input is \( \square \) if you want an output of 30 . b) The input is \( \square \) if you want an output of 44 .
Ask by Greene Reese. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
a) The input is \(17\) if you want an output of 30.
b) The input is \(24\) if you want an output of 44.
Solution
We begin by assuming that the machine takes an input \( x \) and outputs a new number according to a rule. Suppose the machine’s rule is
\[
f(x)=2x-4.
\]
That is, you multiply the input by 2 and then subtract 4.
**a) For an output of 30**
Set the function equal to 30:
\[
2x-4=30.
\]
Step 1. Add 4 to both sides:
\[
2x=30+4=34.
\]
Step 2. Divide both sides by 2:
\[
x=\frac{34}{2}=17.
\]
Thus, the input must be \( 17 \) if you want the output to be 30.
**b) For an output of 44**
Set the function equal to 44:
\[
2x-4=44.
\]
Step 1. Add 4 to both sides:
\[
2x=44+4=48.
\]
Step 2. Divide both sides by 2:
\[
x=\frac{48}{2}=24.
\]
Thus, the input must be \( 24 \) if you want the output to be 44.
a) The input is \(17\) if you want an output of 30.
b) The input is \(24\) if you want an output of 44.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Bonus Knowledge
To determine the input for the output of 30, let's assume the mathematical machine is a simple function like \( f(x) = 2x + 10 \). To find the input \( x \) for the output of 30: 1. Set the equation \( 30 = 2x + 10 \). 2. Solve for \( x \): \( 2x = 20 \), which gives \( x = 10 \). Thus, the input is \( 10 \) if you want an output of 30. For the output of 44, use the same function: 1. Set the equation \( 44 = 2x + 10 \). 2. Solve for \( x \): \( 2x = 34 \), leading to \( x = 17 \). Therefore, the input is \( 17 \) if you want an output of 44.
