Which relationships could have a negative correlation? Select three options. number of hours on video games and test scores speed of a car and minimum stopping distance average running speed and total race time adult’s head circumference and age outside temperature and amount of a heating bill

- number of hours on video games and test scores

- average running speed and total race time

- outside temperature and amount of a heating bill

Step-by-step explanation:

1. number of hours on video games and test scores (negative correlation - as you spend more hours on video games, test scores might decrease)

2. speed of a car and minimum stopping distance (positive correlation - as the distance to the next stop increases, the speed of the car should increase)

3. average running speed and total race time (negative correlation - as you run for longer, your speed should decrease)

4. adult’s head circumference and age (positive correlation - as your age increases, your head size increases, too)

5. outside temperature and amount of a heating bill (negative correlation - as temperature increases, the heating bill decreases)

Since we want to solve for the variable x, we want to isolate x

a²x + (a - 1) = (a + 1)x ⇒ Distribute x to (a+1). Also, remove parentheses

a²x + a - 1 = ax + x ⇒ Subtract a from both sides

a²x - 1 = ax + x - a ⇒ Add 1 to both sides

a²x = ax + x - a + 1 ⇒ Subtract (ax + x) from both sides

a²x - (ax + x)= ax + x - a + 1 - (ax+x) ⇒ Simplify. Remember that multiplying positive by negative = negative

a²x - ax - x = ax + x - a + 1 - ax - x ⇒ Simplify

a²x - ax - x = -a + 1 ⇒ Factor out the x from a²x - ax - x

x(a² - a - 1) = -a + 1 ⇒ Divide both sides by (a² - a - 1)

x = (-a + 1) / (a² - a - 1)

However, we need to make sure that the denominator does not equal 0. Therefore, you set the denominator = 0 (just use the quadratic formula for this), and it gives that the denominator =0 when a = (1+√5)/2 AND (1-√5)/2

Therefore, the final answer is

x = (-a + 1) / (a² - a - 1) given that a ≠ (1+√5)/2, a ≠ (1-√5)/2