31/36 is the correct answer
To find Ken's speed divide total distance by total time:
174 miles / 3 hours = 58 miles per hour.
In the equation for Brenda, the 57 is the miles per hour because you would multiply that by x ( hours) to get total miles (y).
Ken had the faster driving speed.
3 | x+12 |=6
Start by distributing 3 to both x and 12
You get 3x+36=6
Subtract 36 from both sides
You then get 3x=-30
Divide 3 from both sides getting
x= -10
Explanation:
It helps to understand the process of multiplying the binomials. Consider the simple case ...
(x +a)(x +b)
The product is ...
(x +a)(x +b) = x² +(a+b)x + ab
If the <em>constant</em> term (ab) is <em>negative</em>, the signs of (a) and (b) are <em>different</em>.
If the constant term (ab) is <em>positive</em>, the signs of (a) and (b) will both match the sign of the coefficient of the linear term (a+b).
___
Of course, the sum (a+b) will have the sign of the (a) or (b) value with the largest magnitude, so when the signs of (a) and (b) are different, the factor with the largest magnitude will have the sign of (a+b), the x-coefficient.
<u>Example</u>:
x² -x -6
-6 tells you the factors will have different signs. -x tells you the one with the largest magnitude will be negative.
-6 = -6×1 = -3×2 = ... (other factor pairs have a negative factor with a smaller magnitude)
The sums of these factor pairs are -5 and -1. We want the factor pair that has a sum of -1, the coefficient of x in the trinomial.
x² -x -6 = (x -3)(x +2)
The answer should be 2.12