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Kevin L.

Middle School Math Teacher and Tutor for 12 years

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Question:

If a@b = (a - b) + (b - a), find 5@6.

Kevin L.

Answer:

These funky formula problems are just about substitution! The 5 replaces the a and the 6 replaces the b in the formula. 5@6 = (5 - 6) + (6 - 5). 5@6 = (-1) + (1) = 0

Geometry

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Question:

Can a triangle be formed with side lengths 12 cm, 12 cm, and 24 cm?

Kevin L.

Answer:

According to the Triangle Inequality Theorem, two sides of a triangle must add to a sum greater than the 3rd side. In this case, 12 cm + 12 cm is equal to the third side, but not greater. Therefore, no triangle is possible!

Algebra

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Question:

The sum of the first and fourth consecutive even integer is equal to the third integer subtracted from 70. Find the integers.

Kevin L.

Answer:

Let the first integer = x. The other integers become: x + 2, x + 4, and x + 6 as even integers are always two units apart. The sum of the first and fourth integer means: x + x + 6 = 2x + 6 The equation is: 2x + 6 = 70 - (x + 4) (be careful - Subtract from is a backwards phrase!) now distribute the negative! 2x + 6 = 70 - x - 4 2x + 6 = 66 - x 3x = 60 x = 20 So the integers are 20, 22, 24, and 26.

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