The function p is defined as p(x)=`x^2-3x`. If the function q is defined as q(x)=p(x)-4, what is the value of q(10)?

Options

A. -30
B. 6
C. 66
D. 70

Answer

To solve the problem, we need to find the value of the function \( q(x) \) at \( x = 10 \). The function \( q(x) \) is defined in terms of the function \( p(x) \).

1. **Step 1: Define the function \( p(x) \)**
The function \( p(x) \) is given as:
\[ p(x) = x^2 - 3x \]

2. **Step 2: Define the function \( q(x) \)**
The function \( q(x) \) is defined as:
\[ q(x) = p(x) - 4 \]

3. **Step 3: Substitute \( p(x) \) into \( q(x) \)**
We can substitute the expression for \( p(x) \) into the equation for \( q(x) \):
\[ q(x) = (x^2 - 3x) - 4 \]
Simplifying this gives:
\[ q(x) = x^2 - 3x - 4 \]

4. **Step 4: Calculate \( q(10) \)**
Now, we need to find \( q(10) \):
\[ q(10) = 10^2 - 3(10) - 4 \]
Calculating each term:
\[ 10^2 = 100 \]
\[ 3(10) = 30 \]
Now substituting these values back into the equation:
\[ q(10) = 100 - 30 - 4 \]
Simplifying this gives:
\[ q(10) = 100 - 30 = 70 \]
\[ q(10) = 70 - 4 = 66 \]

5. **Final Answer**
Therefore, the value of \( q(10) \) is:
\[ \boxed{66} \]