Question 9 of 49intermediate🔧 ApplyShort Answer2 marks

We have learnt that to evaluate the value of an algebraic expression, we substitute a value of the variable in the given expression. Consider Example 3, where the wire is bent to form a rectangle. Here, the area of the rectangle, 10x−x210x - x^2, is a function of xx. Can you interpret this as an input-output process? What value does the expression take when x=6x = 6 cm?

Correct Answer

Yes, the area of the rectangle, 10x−x210x - x^2, can be interpreted as an input-output process. Here, the input is the value of the variable xx (the length of the rectangle), and the output is the corresponding value of the expression 10x−x210x - x^2 (the area). This means the area is a function of xx.

To find the value when x=6x = 6 cm, we substitute x=6x = 6 in the expression:

Value =10(6)−(6)2= 10(6) - (6)^2

=60−36= 60 - 36 =24= 24

Thus, the expression takes the value 24 when x=6x = 6 cm.

Exercise: Think and Reflect | Q: 1 | (Page 5)
For More Understanding

Explanation

The textbook context explains that evaluating an algebraic expression by substituting a variable can be viewed as an input-output machine, where the input is the variable's value and the output is the expression's value, representing a function. For the rectangle's area 10x−x210x - x^2, substituting x=6x = 6 yields:

10(6)−62=60−36=2410(6) - 6^2 = 60 - 36 = 24

Solution Steps

  1. Step 1: Interpret the expression as an input-output process where input is the value of xx and output is the value of 10x−x210x - x^2.

  2. Step 2: Substitute x=6x = 6 into the expression:

    10(6)−(6)210(6) - (6)^2

  3. Step 3: Calculate the value:

    60−36=2460 - 36 = 24

    ∴ The expression takes the value 24 when x=6x = 6 cm.

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