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Given y = -x + 4, determine the output value (y) when the input value is 9.
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| Point | x | y |
|---|---|---|
| y-intercept | 0 | 4 |
| x-intercept | 4 | 0 |
Step-by-step solution
19 stepsHere are the solutions to the questions:
QUESTION 8 [FUNCTIONS AND RELATIONSHIPS]
8.1.
Substitute the input value into the given equation .
Perform the subtraction.
The output value is .
8.2.
To find , substitute into the rule .
To find , substitute into the rule .
The values are and .
8.3.
Examine the input and output values to find a pattern.
Inputs: 2, 3, 8, 10
Outputs: 16, 22, 52, 64Test a linear relationship of the form .
Using the first two pairs (2, 16) and (3, 22):
For (2, 16): (Equation 1)
For (3, 22): (Equation 2)Subtract Equation 1 from Equation 2 to find .
Substitute into Equation 1 to find .
Formulate the rule and verify with other input-output pairs.
The rule is .
Check for : (Matches)
Check for : (Matches)
The rule is .QUESTION 9 [ALGEBRAIC EXPRESSIONS]
9.1. Given the expression:
9.1.1.
Identify the terms in the expression.
Terms are separated by addition or subtraction signs.
The terms are , , and .
There are terms in the expression.9.1.2.
Identify the term containing .
This is .
The coefficient of is the numerical factor multiplying .
The coefficient of is .
9.1.3.
Identify the term that does not contain any variables.
The constant term is .
9.1.4.
Identify the power of the variable in each term.
For , the power is 2.
For , the power is 1 (since ).
For , the power is 0 (since ).The degree of the expression is the highest power of the variable in any term.
The highest power is 2.
The degree of the expression is .9.1.5.
Substitute into the expression .
Calculate the square of .
Perform the multiplication.
Substitute these values back into the expression and perform the additions/subtractions.
The value of the expression if is .
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