1+sin²x=2-cos²x
Remenber: sin²x+cos²x=1 ⇒sin²x=1-cos²x
1+sin²x=1+(1-cos²x)=2-cos² x (this is true)
I'll write in the format (x;y) where x is the salad dressings amount, and y is the amount of servings.
We can see the line goes through the points (1;2) , (2;4) , (3;6) ...
So, the amount of servings are doubled the amount of salad dressings she need to use. (1 cup every 2 servings, 2 cups every 4 servings, etc.)
-> Leslle used half a cup of salad dressing for every serving of salad (B)
Joseph was swimming faster because 1/12 of a mile per minute is around 5 miles per hour so Joseph was swimming 0.5 miles per hour faster than Joe.
Perpendicular lines have slopes that are opposite and reciprocal. Therefore, the line we are looking for has a -3 slope.
y= -3x+b
Now, we can substitute in the point given to find the intercept.
2= -3(4)+b
2= -12+b
b=14
Finally, put in everything we've found to finish the equation.
y= -3x+14
Given
Brian's house: (-7, 9)
Sue's house: (-7, -2)
Find
The number of units between Brian's house and Sue's house.
Solution
Both Brian and Sue live on the "street" x=-7, so the distance between their houses is the distance between -2 on that street and +9 on that street. We always consider distance to be positive, so it doesn't matter whether we start at Brian's house and go -11 units to Sue's house, or start at Sue's house and go +11 units to Brian's house. Either way, we travel 11 units.
_____
"Displacement" is another matter. That has a sign associated with it and there is always a reference direction that is positive. Movement in the opposite direction results in a negative displacement. "Distance" is always positive.
