Questions: Evaluate the following expression for the given values of the variables: -4 sqrt(x+6)+y^2 for x=19 and y=-1

Transcript text: Evaluate the following expression for the given values of the variables: \[ -4 \sqrt{x+6}+y^{2} \text { for } x=19 \text { and } y=-1 \]

Solution

Solution Steps

Step 1: Substitute the given values into the expression

We are given the expression: \[ -4 \sqrt{x+6} + y^{2} \] with \( x = 19 \) and \( y = -1 \). Substitute these values into the expression: \[ -4 \sqrt{19 + 6} + (-1)^{2} \]

Step 2: Simplify the expression inside the square root

Simplify \( x + 6 \): \[ 19 + 6 = 25 \] Now the expression becomes: \[ -4 \sqrt{25} + (-1)^{2} \]

Step 3: Evaluate the square root and the exponent

Evaluate \( \sqrt{25} \) and \( (-1)^{2} \): \[ \sqrt{25} = 5 \quad \text{and} \quad (-1)^{2} = 1 \] Now the expression becomes: \[ -4 \cdot 5 + 1 \]

Step 4: Perform the multiplication and addition

Multiply \( -4 \) by \( 5 \): \[ -4 \cdot 5 = -20 \] Now add \( 1 \) to \( -20 \): \[ -20 + 1 = -19 \]