Maria E.

Tutored Over 65 Children 3rd - 12th grade, Primarily Math & English

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Geometry

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Question:

What if I can't recall if the formula for a (right) triangle is 1/2 base x height or 1/3 base x height? Is there an easy way to remember?

Maria E.

Answer:

The area of any rectangle may be found by multiplying the length x width of the rectangle. When a diagonal line is drawn across the rectangle from one upper corner to the opposite lower corner, the rectangle is split in half. Two (right) triangles sit side by side and share the same hypotenuse. We can still see the rectangle, but now we can also see the two equal sized triangles (same hypotenuse, same base and same height). This is a graphic way to prove that the area of 2 triangles x (1/2 b x h) = 1 rectangle (b x h)

Writing

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Question:

Please read the following text and answer the question that follows. "On Tuesday, Jaime walked to the grocery store to buy marshmallows, graham crackers and Hershey candy bars. While walking, he noticed dark clouds gathering overhead. Soon small raindrops began hitting his face. "Oh, no!" he thought. "We might not have the bonfire and s'mores this evening. And, I've been looking forward to this evening all week! I love the smell of bonfires. I love roasting marshmallows. And, I can eat s'mores all night long!" Still, he continued on to the store. He purchased the goodies and the cashier placed them in a paper bag. By the time he left the store, though, the rain had become a downpour. Jaime hadn't dressed for the downpour and he soon became drenched. His paper bag became drenched, too, and it started to tear. "This is definitely not turning out to be a very good day!" he thought to himself." Jaime's day was "not turning out" as he'd hoped. What did Jaime hope for most of all? (a) Most of all, Jaime didn't like getting wet on his walk to the grocery store. (b) Most of all, Jaime hoped that it wouldn't be raining for the cats and dogs on his way to the grocery store. (c) Most of all, Jaime hoped to have good weather for the bonfire, so that he could roast marshmallow over the fire, and eat s'mores. (d) Most of all, Jaime hoped that his paper bag would stay dry, because it contained his favorite candy bars, Hersheys!

Maria E.

Answer:

(b) is an incorrect answer. 'Cats and dogs' is an expression and does not refer to actual cats and dogs. While (a), (c), and (d) do describe Jaime's hopes for the day, the key words in the question are "most of all." What did Jaime hope for "most of all?" Regarding (a). When Jaime saw the cloudy, rainy weather, his thoughts went to the evening's bonfire. He showed no concern about getting wet on his walk to the grocery store. Regarding (d). Jaime hoped his bag would stay dry, but there was no mention that Hershey's were his favorite candy bar. Regarding (c). "All week" long, Jaime had been looking forward to a bonfire, marshmallows, and s'mores. If there were rainy weather that evening, there would be no bonfire, no marshmallows, and no s'mores. (c) describes what Jaime hoped for most of all.

Algebra

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Question:

In order to use the quadratic equation to solve an equation for 'x' mark which of the following equation(s) is(are) correct: (i) I must know the coefficient of xx. (ii) I must know the coefficient of xx and set the equation to = 0. (iii) I must know a, b, and c, and they cannot be fractions.

Maria E.

Answer:

To employ the quadratic equation so as to solve for 'x' our equation must be put in the standard axx + bx + c = 0 form. The a, b, and c numbers are "coefficients" to xx (to the power of 2), x (to the power of 1) and x (to the power of 0), respectively. If the equation is not set to = 0, then c will not be accurate. Therefore (i) is correct, because the coefficient of xx (a) is needed. In fact, both (i) and (ii) are correct, where (ii) contains additional correct information. While, (iii) is not correct. Coefficients may be whole numbers, negative numbers, decimals or fractions.

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