Tutor profile: Qijia Z.
Subject: SAT II Mathematics Level 2
A line has parametric equations x = 5 + t and y = 7 + t, where t is the parameter. The slope of the line is?
From the question, we know that as t changes, both x and y change. So to rewrite x = 5 + t, we can get t = x - 5; Rewrite y = 7 + t, we can get t = y - 7. So combining these two equations, we can get t = x - 5 = y - 7, Ignore the parameter t, we get y = x - 5 + 7 = x + 2. So the slope of the line is 1.
Subject: SAT II Mathematics Level 1
What are all values of x for which 4 - x^2 >= x - 2?
Rearranging the inequality above, we can get x^2 + x - 6 <= 0 If we factor the left side, we can get x^2 + x - 6 = (x + 3)(x - 2) So the inequality is further written as (x + 3)(x - 2) <= 0 Since when x=-3 or x=2, (x + 3)(x - 2) = 0, the number -3 and 2 must be the "boundaries" of the range of values What we are not sure right now is whether the values we want are inside or outside this boundary, so we can just plug in a random number within this boundary to test it. If it satisfy the inequality, then the range within the boundary contains all the possible values. So if we try x=0, we get (0+3)(0-2)=-6 < 0, which satisfies the inequality. So the values of x should be any number within the boundary, which is the interval [-3, 2]
In a certain store, the regular price of a refrigerator is $600. How much money is saved by buying this refrigerator at 20 percent off the regular price rather than buying it on sale at 10 percent off the regular price with an additional discount of 10 percent off the sale price?
A. If you buy it with 20% off-- the money you save: $600*0.2=$120 B. If you buy it with 10% off the regular price with an additional 10% off the sales price-- the money you save from the first 10% off the regular price: M1=$600*0.1=$60; then the discounted price will be: $600*0.9=$540; the money you save from the 10% off the discounted price: M2=$540*0.1=$54; so the total money you save from this plan is: M1+M2=$60+$54=$114 So the difference between these two methods will be-- $120-$114=$6
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