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Crazy boy [7]
4 years ago
12

Write the expression -3x 2 + 2y 2 + 5xy - 2y + 5x 2 - 3y 2 in simplest form. Then, answer the following questions using complete

sentences.
How many terms are in the simplified expression?
How many of the terms in the simplified expression are negative?
Mathematics
2 answers:
mixas84 [53]4 years ago
7 0
-3x^2 + 2y^2 + 5xy - 2y + 5x^2 - 3y^2....combine like terms
2x^2 + 5xy - y^2 - 2y

u have 4 terms in the simplified expression......and 2 of them r negative.
ASHA 777 [7]4 years ago
7 0
= -3x² + 2y² + 5xy - 2y + 5x² - 3y²
= (5x² - 3x²) + (2y² - 3y²) + 5xy - 2y
= 2x² - y² + 5xy - 2y

In short, simplified form would be: 2x² - y² + 5xy - 2y

a) There are four terms in simplified expression.

b) Only two term is negative.

Hope this helps!
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2 years ago
Please help me!!!!!!!!!!!!!​
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Answer:  see proof below

<u>Step-by-step explanation:</u>

Use the following Half-Angle Identities:    tan (A/2) = (sinA)/(1 + cosA)

                                                                     cot (A/2) = (sinA)/(1 - cosA)

Use the Pythagorean Identity: cos²A + sin²B = 1

Use Unit Circle to evaluate: cos 45° = sin 45° = \frac{\sqrt2}{2}

<u>Proof LHS → RHS</u>

Given:                       cot\ (22\frac{1}{2})^o-tan\ (22\frac{1}{2})^o

Rewrite Fraction:     cot\ (\frac{45}{2})^o-tan\ (\frac{45}{2})^o

Half-Angle Identity:   \dfrac{sin(45)^o}{1-cos(45)^o}-\dfrac{sin(45)^o}{1+cos(45)^o}

Substitute:                  \dfrac{\frac{\sqrt2}{2}}{1-\frac{\sqrt2}{2}}-\dfrac{\frac{\sqrt2}{2}}{1+\frac{\sqrt2}{2}}

Simplify:                      \dfrac{\frac{\sqrt2}{2}}{\frac{2-\sqrt2}{2}}-\dfrac{\frac{\sqrt2}{2}}{\frac{2+\sqrt2}{2}}

                               =\dfrac{\sqrt2}{2-\sqrt2}-\dfrac{\sqrt2}{2+\sqrt2}

                               =\dfrac{\sqrt2}{2-\sqrt2}\bigg(\dfrac{2+\sqrt2}{2+\sqrt2}\bigg)-\dfrac{\sqrt2}{2+\sqrt2}\bigg(\dfrac{2-\sqrt2}{2-\sqrt2}\bigg)

                               =\dfrac{2\sqrt2+2}{4-2}-\dfrac{2\sqrt2-2}{4-2}

                               =\dfrac{4}{2}

                               = 2

LHS = RHS:  2 = 2  \checkmark

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