Final answer:
The quotient of z and 7 is 9 is represented by the equation z / 7 = 9. This is obtained by understanding that 'quotient' means the result of division, and it can be algebraically translated and solved for z.
Step-by-step explanation:
The equation that represents the sentence 'the quotient of z and 7 is 9' is z / 7 = 9. To express this mathematically, you perform the following steps:
- Identify the terms involved: the 'quotient' refers to the result of division between two numbers.
- Translate the sentence to an algebraic expression: Since 'z' is being divided by 7, and the result is 9, the equation becomes z / 7 = 9.
- Solve for z if required: To find the value of z, you would multiply both sides of the equation by 7 to isolate z, yielding z = 63.
This simple linear equation can be useful in various mathematical contexts, especially in solving word problems and understanding algebraic expressions.