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\[ 400,000 + 100,000 = 500,000 \]
A car travels 150 miles in 3 hours. What is the average speed of the car in miles per hour?
Average speed is calculated by dividing the total distance by the total time:
\[ \text{Average Speed} = \frac{150 \, \text{miles}}{3 \, \text{hours}} = 50 \, \text{miles per hour} \]
A quadratic equation \( ax^2 + bx + c = 0 \) has roots 4 and -3. If \( a = 1 \), what are the values of \( b \) and \( c \)?
Using Vieta's formulas, the sum and product of the roots are given by:
Sum of roots: \( 4 + (-3) = 1 = -\frac{b}{a} \)
Since \( a = 1 \),
\[ -b = 1 \Rightarrow b = -1 \]
Product of roots: \( 4 \times (-3) = -12 = \frac{c}{a} \)