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RoseWind [281]
3 years ago
11

Marcus states that the polynomial expression 3x3 – 4x2y + y2 + 2 is in standard form. Ariel states that it should be y2 – 4x2y +

3x3 +2. Explain which student is correct and why.
Mathematics
2 answers:
garri49 [273]3 years ago
7 0

Answer:

I know that ariel is wrong because 3x^3 is higher power than y^2

3x^3 goes first

then the mixed term -4x^2y

then the y^2

then the 2

marcus is right

Step-by-step explanation:

lora16 [44]3 years ago
4 0

Answer:

Here Ariel is wrong because 3x^3 is higher power than y^2

3x^3 goes first

then the mixed term -4x^2y

then the y^2

then the 2

So, Marcus is right

Standard form means that you write the terms by descending degree. here's main rules how to write polynomial expression in the standard form:

1. write the term with the highest exponent first (terms of third degree in our case 3x^3 );

2. write the terms with lower exponents in descending order (term -4x^2y followed by y^2 );

3. remember that a variable with no exponent has an understood exponent of 1 (here are no such terms);

4. a constant term (a number with no variable) always goes last (term 2).

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Answers:

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===============================================

Explanation:

For these questions, we'll use the inscribed angle theorem. This says that the inscribed angle is half the measure of the arc it cuts off. An inscribed angle is one where the vertex of the angle lies on the circle, as problem 1 indicates.

For problem 1, the arc measure is 80 degrees, so half that is 40. This is the measure of the unknown inscribed angle.

Problem 2 will have us work in reverse to double the inscribed angle 42 to get 84.

-------------------

For problem 3, we need to determine angle DEP. But first, we'll need Thales Theorem which is a special case of the inscribed angle theorem. This theorem states that if you have a semicircle, then any inscribed angle will always be 90 degrees. This is a handy way to form 90 degree angles if all you have is a compass and straightedge.

This all means that angle DEF is a right angle and 90 degrees.

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(angle DEP) + (35) = 90

angle DEP = 90 - 35

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The inscribed angle DEP cuts off the arc we want to find. Using the inscribed angle theorem, we double 55 to get 110 which is the measure of minor arc FD.

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