Let a function of 2 variables be defined by `h(x, y)=x^(2)+3xy-(y-x)`, what is the value of `h(5, 4)`?

Options

A. 76
B. 84
C. 85
D. 86

Answer

To find the value of the function \( h(x, y) = x^2 + 3xy - (y - x) \) at the point \( (5, 4) \), we will follow these steps:

### Step 1: Substitute the values of \( x \) and \( y \)
We need to substitute \( x = 5 \) and \( y = 4 \) into the function.

\[ h(5, 4) = 5^2 + 3(5)(4) - (4 - 5) \]

### Step 2: Calculate \( 5^2 \)
Calculate the square of \( 5 \):

\[ 5^2 = 25 \]

### Step 3: Calculate \( 3(5)(4) \)
Now calculate \( 3 \times 5 \times 4 \):

\[ 3 \times 5 \times 4 = 60 \]

### Step 4: Calculate \( (4 - 5) \)
Now calculate \( 4 - 5 \):

\[ 4 - 5 = -1 \]

### Step 5: Substitute the calculated values back into the equation
Now substitute the calculated values back into the equation:

\[ h(5, 4) = 25 + 60 - (-1) \]

### Step 6: Simplify the expression
Now simplify the expression:

\[ h(5, 4) = 25 + 60 + 1 \]

### Step 7: Perform the final addition
Now perform the final addition:

\[ h(5, 4) = 86 \]

Thus, the value of \( h(5, 4) \) is \( 86 \).

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