All posts by mathconfidence

January 2019 Brain Puzzler Solution

Q: On the way to catch an international flight, Sabina drives 35 miles per hour for an hour and realizes she will be an hour late if she continues at this speed. If she increases her speed by 15 miles per hour for the remaining part of the drive she will arrive 30 minutes early. How far is her home from the airport?

A: 210 miles
She already covered 35 miles.  She has d miles left at 50 miles an hour.

Her time left to travel would be d/50 and because she will arrive an hour late vs a half hour early, there is a 1.5 hour difference between her time this faster speed and her time at the slower speed.  So the time of d/50 is 1.5 less than d/35.

We can write this as d/50 = d/35 – 1.5    OR        d/50 + 1.5 = d/35

When you solve this, you will get that the remaining distance is 175 miles plus we have to add the original 35 miles.  It would have taken Sabina 6 hours in total at 35 mph to cover the 210 miles but instead takes her only 4.5 hours — the first hour that she drove at 35 mph (35 miles) and the next 3.5 hours at 50 mph (175 miles).

Get the Math and the Points Aug 18 CC Algebra I Regents #30

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The left hand side of the equation is almost a perfect square:
In order for it to be a perfect square:  x^2 + 4x + ____ = 2 + ____
To find the number that completes the square take 1/2 of 4 and square it
So 4 gets added to both sides
Then the right side becomes 6
Then we can write the left side like this: (x + 2) ^2
So (x + 2)^2 = 6
then take the sqrt of both sides but do not forget the +/- with the sqrt
Then subtract 2 from both sides:
You will have two answers a plus and a minus and you can check your work by using the quadratic formula 🙂


Get the Math and the Points Aug 2018 CC Alg I Regents #28

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To solve a quadratic equation ax^2 + bx + c = 0, wecan use the quadratic formula above given on the Regents Reference Sheet.

In order to find out if a solution is rational or irrational, we focus on the algebra under the radical: b^2 – 4ac: If b^2 – 4ac is a perfect square, then when we take the square root, we will get a rational number but if b^2 – 4ac is not a perfect square (like 4, 9, 16 etc), then the solution will be irrational.

In the equation 2x^2 + 3x – 10 =0, a=2, b=3 and c = -10
Once you substitute in those numbers into b^2 – 4ac, do you get a perfect square or not?