Question

evaluate and match each expression on the left to its value on the right, when \\(x = 6\\) and \\(y = 5\\).

\\(12 + x\\) \t 10
\\(3x + y\\) \t 15
\\(4y - 10\\) \t 18
\\(\frac{1}{2}xy\\) \t 23

Explanation:

Identify the given values and expressions

We are given the variable values:
\(x = 6\)
\(y = 5\)

We need to evaluate the following four expressions:

1. \(12 + x\)
2. \(3x + y\)
3. \(4y - 10\)
4. \(\frac{1}{2}xy\)

We will match each result to one of the values on the right: \(10\), \(15\), \(18\), or \(23\).

Evaluate the first expression

Substitute \(x = 6\) into the expression:

$$12 + x = 12 + 6 = 18$$

This matches the value \(18\).

Evaluate the second expression

Substitute \(x = 6\) and \(y = 5\) into the expression:

$$3x + y = 3(6) + 5 = 18 + 5 = 23$$

This matches the value \(23\).

Evaluate the third expression

Substitute \(y = 5\) into the expression:

$$4y - 10 = 4(5) - 10 = 20 - 10 = 10$$

This matches the value \(10\).

Evaluate the fourth expression

Substitute \(x = 6\) and \(y = 5\) into the expression:

$$\frac{1}{2}xy = \frac{1}{2}(6)(5) = 3(5) = 15$$

This matches the value \(15\).

Answer:

Expression	Value
\(3x + y\)	\(23\)
\(4y - 10\)	\(10\)
\(\frac{1}{2}xy\)	\(15\)