QUESTION IMAGE
Question
directions:
- complete each table by filling in the missing numbers for either the input or the output.
- use words to write a rule describing how to find the output when given the input. write an equation using a variable (n) to show the rule.
- use words to write a rule describing how to find the input when given the output. write an equation using a variable (s) to show the rule.
1
input output
0 0
1 3
2 6
3 9
4 12
7
10
13 39
16
60
75
90
rules:
input to output
output to input
input equation
output equation:
2
input output
0 0
1 5
2 10
3 15
5
6 30
8
50
65
75
100
rules:
input to output:
output to input:
input equation:
output equation:
Problem 1
Step 1: Identify the pattern (Input to Output)
Looking at the input-output pairs: when input is 0, output is 0; input 1, output 3; input 2, output 6; input 3, output 9; input 4, output 12. We can see that the output is 3 times the input. So the rule is "Multiply the input by 3".
Step 2: Find missing outputs/inputs
- For input 7: Output = \( 7 \times 3 = 21 \)
- For input 10: Output = \( 10 \times 3 = 30 \)
- For output 48: Input = \( \frac{48}{3} = 16 \) (wait, no, input 16: Output = \( 16 \times 3 = 48 \))
- For output 60: Input = \( \frac{60}{3} = 20 \)
- For output 75: Input = \( \frac{75}{3} = 25 \)
- For output 90: Input = \( \frac{90}{3} = 30 \)
Step 3: Write equations
- Input to Output Equation (let \( i \) be input, \( o \) be output): \( o = 3i \)
- Output to Input Equation: \( i = \frac{o}{3} \)
Filled Table (Problem 1):
| INPUT | OUTPUT |
|---|---|
| 1 | 3 |
| 2 | 6 |
| 3 | 9 |
| 4 | 12 |
| 7 | 21 |
| 10 | 30 |
| 13 | 39 |
| 16 | 48 |
| 20 | 60 |
| 25 | 75 |
| 30 | 90 |
Rules (Problem 1):
- Input to Output: Multiply the input by 3.
- Output to Input: Divide the output by 3.
- Input Equation (for output): \( o = 3i \)
- Output Equation (for input): \( i = \frac{o}{3} \)
Problem 2
Step 1: Identify the pattern (Input to Output)
Looking at the input-output pairs: input 0, output 0; input 1, output 9? Wait, no, input 1, output 9? Wait, input 2, output 10? Wait, maybe I misread. Wait, input 1, output 9; input 2, output 10? No, that doesn't make sense. Wait, maybe input 1, output 9 (1 + 8), input 2, output 10 (2 + 8)? No, input 3, output 15 (3 + 12)? Wait, no, let's check again. Wait, input 0: 0, input 1: 9, input 2: 10, input 3: 15, input 5: 25, input 6: 30, input 8: 40, input? : 50, input? : 65, input? : 75, input? : 100. Wait, maybe the pattern is input + 8 when input is 1? No, 1 + 8 = 9, 2 + 8 = 10, 3 + 12 = 15? No, that's inconsistent. Wait, 1×9=9, 2×5=10? No. Wait, 0:0, 1:9, 2:10, 3:15, 5:25, 6:30, 8:40. Wait, 5×5=25, 6×5=30, 8×5=40. Oh! Wait, input 5:25 (5×5), input 6:30 (6×5), input 8:40 (8×5). Then input 3:15 (3×5), input 2:10 (2×5), input 1:5? But the table says input 1, output 9. Wait, maybe a typo? Or maybe the first few are wrong. Wait, the first row: input 0, output 0. Then input 5:25 (5×5), input 6:30 (6×5), input 8:40 (8×5). So maybe the correct pattern is output = 5×input. Let's check:
- If input 0: 0×5=0 (correct)
- Input 1: 1×5=5 (but table says 9, maybe a typo)
- Input 2: 2×5=10 (correct)
- Input 3: 3×5=15 (correct)
- Input 5: 5×5=25 (correct)
- Input 6: 6×5=30 (correct)
- Input 8: 8×5=40 (correct)
- Then for output 50: input = 50/5=10
- Output 65: input = 65/5=13
- Output 75: input = 75/5=15
- Output 100: input = 100/5=20
Assuming that the input 1, output 9 is a typo, and the pattern is output = 5×input.
Step 2: Find missing outputs/inputs
- For input 10: Output = \( 10 \times 5 = 50 \)
- For output 65: Input = \( \frac{65}{5} = 13 \)
- For output 75: Input = \( \frac{75}{5} = 15 \)
- For output 100: Input = \( \frac{100}{5} = 20 \)
- For input 1: If pattern is 5×input, output should be 5 (but table says 9, maybe a mistake)
- For input 2: Output = \( 2 \times 5 = 10 \) (correct)
- For input 3: Output = \( 3 \times 5 = 15 \) (correct)
Filled Table (Problem 2) (assuming pattern \( o = 5i \)):
| INPUT | OUTPUT | |
|---|---|---|
| 1 | 5 | (corrected from 9) |
| 2 | 10 | |
| 3 | 15 | |
| 5 | 25 | |
| 6 | 30 | |
| 8 | 40 | |
| 10 | 50 | |
| 13 | 65 | |
| 15 | 75 | |
| 20 | 100 |
Rules (Problem 2) (assuming \( o = 5i \)):
- Input to Output: Multiply the input by 5.
- Output to Input: Divide the output by 5.
- Input Equation (for output): \( o = 5i \)
- Output Equation (for input): \( i = \frac{o}{5} \)
(Note: If the initial input 1, output 9 is correct, then the pattern is different. But based on the later values (5→25, 6→30, 8→40), the pattern \( o = 5i \) is consistent, so likely a typo in the first few inputs.)
Snap & solve any problem in the app
Get step-by-step solutions on Sovi AI
Photo-based solutions with guided steps
Explore more problems and detailed explanations
Step 1: Identify the pattern (Input to Output)
Looking at the input-output pairs: input 0, output 0; input 1, output 9? Wait, no, input 1, output 9? Wait, input 2, output 10? Wait, maybe I misread. Wait, input 1, output 9; input 2, output 10? No, that doesn't make sense. Wait, maybe input 1, output 9 (1 + 8), input 2, output 10 (2 + 8)? No, input 3, output 15 (3 + 12)? Wait, no, let's check again. Wait, input 0: 0, input 1: 9, input 2: 10, input 3: 15, input 5: 25, input 6: 30, input 8: 40, input? : 50, input? : 65, input? : 75, input? : 100. Wait, maybe the pattern is input + 8 when input is 1? No, 1 + 8 = 9, 2 + 8 = 10, 3 + 12 = 15? No, that's inconsistent. Wait, 1×9=9, 2×5=10? No. Wait, 0:0, 1:9, 2:10, 3:15, 5:25, 6:30, 8:40. Wait, 5×5=25, 6×5=30, 8×5=40. Oh! Wait, input 5:25 (5×5), input 6:30 (6×5), input 8:40 (8×5). Then input 3:15 (3×5), input 2:10 (2×5), input 1:5? But the table says input 1, output 9. Wait, maybe a typo? Or maybe the first few are wrong. Wait, the first row: input 0, output 0. Then input 5:25 (5×5), input 6:30 (6×5), input 8:40 (8×5). So maybe the correct pattern is output = 5×input. Let's check:
- If input 0: 0×5=0 (correct)
- Input 1: 1×5=5 (but table says 9, maybe a typo)
- Input 2: 2×5=10 (correct)
- Input 3: 3×5=15 (correct)
- Input 5: 5×5=25 (correct)
- Input 6: 6×5=30 (correct)
- Input 8: 8×5=40 (correct)
- Then for output 50: input = 50/5=10
- Output 65: input = 65/5=13
- Output 75: input = 75/5=15
- Output 100: input = 100/5=20
Assuming that the input 1, output 9 is a typo, and the pattern is output = 5×input.
Step 2: Find missing outputs/inputs
- For input 10: Output = \( 10 \times 5 = 50 \)
- For output 65: Input = \( \frac{65}{5} = 13 \)
- For output 75: Input = \( \frac{75}{5} = 15 \)
- For output 100: Input = \( \frac{100}{5} = 20 \)
- For input 1: If pattern is 5×input, output should be 5 (but table says 9, maybe a mistake)
- For input 2: Output = \( 2 \times 5 = 10 \) (correct)
- For input 3: Output = \( 3 \times 5 = 15 \) (correct)
Filled Table (Problem 2) (assuming pattern \( o = 5i \)):
| INPUT | OUTPUT | |
|---|---|---|
| 1 | 5 | (corrected from 9) |
| 2 | 10 | |
| 3 | 15 | |
| 5 | 25 | |
| 6 | 30 | |
| 8 | 40 | |
| 10 | 50 | |
| 13 | 65 | |
| 15 | 75 | |
| 20 | 100 |
Rules (Problem 2) (assuming \( o = 5i \)):
- Input to Output: Multiply the input by 5.
- Output to Input: Divide the output by 5.
- Input Equation (for output): \( o = 5i \)
- Output Equation (for input): \( i = \frac{o}{5} \)
(Note: If the initial input 1, output 9 is correct, then the pattern is different. But based on the later values (5→25, 6→30, 8→40), the pattern \( o = 5i \) is consistent, so likely a typo in the first few inputs.)