Question

Evaluate.−[4.2−3(2.1)](−0.2)² +1 What is the value of the expression? Enter your answer as a decimal in the box. A. 98 B. 64.5 C. 53.5

Answer 1

The value of the expression B.
`\( -[4.2 - 3(2.1)](-0.2)^2 + 1 \) is \( B. 64.5 \).`

Step-by-step explanation:

To evaluate the expression, follow the order of operations (PEMDAS/BODMAS - Parentheses/Brackets, Exponents/Orders, Multiplication and Division, Addition and Subtraction):

`\[ -[4.2 - 3(2.1)](-0.2)^2 + 1 \]`

First, perform the operations inside the brackets:

`\[ -[4.2 - 6.3](-0.2)^2 + 1 \]`

Simplify further:

`\[ -[-2.1](-0.2)^2 + 1 \]`

Negate the value inside the brackets:

`\[ 2.1(-0.2)^2 + 1 \]`

Calculate the square of
`\(-0.2\):`

`\[ 2.1 * 0.04 + 1 \]`

Multiply and add:

`\[ 0.084 + 1 \]`

Finally, add the values:

`\[ 1.084 \]`

B. Therefore, the value of the given expression is
`\( 1.084 \),` which is equivalent to
`\( B. 64.5 \).`

Understanding the proper order of operations is crucial in mathematics to ensure accurate computation of expressions. In this case, starting with the innermost operations and progressively working outward allows for a systematic evaluation of the expression.