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Conics Homework 1
Given the following equations, which are not degenerate conics, tell whether the graph of each is a circle, an ellipse, a parabola, or a hyperbola. 1. $$ x^{2}-3xy+2y^{2}+2x-y+6=0$$ 2. $$3x^{2}-4xy+2y^{2}-3y=0$$ 3. $$ x^{2}-6xy+9y^{2}+x-y-1=0$$ 4. $$ 144x^{2}+144y^{2}-216x+96y-47=0$$ Find the e for each conic section. 5. $$x^{2}+y^{2}=25$$ 6. $$ \frac{(x-1)^{2}}{4} + \frac{(y+2)^{2}}{16}=1$$ Solve the system. 7. $$ x^{2}+y^{2}=9 $$ and $$(x+y)^{2}=9$$ 8. $$ 4x^{2}+4y^{2}=25$$ and $$ 2x+y^{2}=1$$

Homework 1
Pg. 15: 2-6 even, 14, 36, 38, 86-90 even Evaluate each algebraic expression for the given value or values of the variable(s): 2. $$ 8+6x$$, for $$x=5$$ 4. $$8x-y$$, for $$x=3 \ and \ y-4$$ 6. $$x^{2}+5x$$, for $$x=6$$ 14.$$\frac{7(x-3)}{2x-16}$$, for $$x=9$$ List all number from the given set that are a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. 36. $$\{ -7,-0.\overline{6},0, \sqrt{49}, \sqrt{50} \}$$ 38. $$\{ -5, -0.\overline{3}, 0, \sqrt{2}, \sqrt{4} \} $$ Simplify each algebraic expression. 86.$$ 2(5y+4)-3$$ 88.$$2(5x-1)+14x$$ 90.$$4(2y-6)+3(5y+10)$$

Homework 2
Pg. 31: 2-8 even, 24-36 even, 66, 68 94, 96 Evaluate each exponential expression. 2.$$ 6^{2} \times 2 $$ 4.$$ (-2)^{4} $$ 6.$$ -2^{4} $$ 8.$$ (-9)^{0} $$ Simplify each exponential expression. 24.$$ xy^{-3} $$ 26.$$ x^{7}y^{0} $$ 28.$$ x^{11}\times x^{5} $$ 30.$$ x^{-6}\times x^{12} $$ 32.$$ \left( x^{11} \right)^{5} $$ 34.$$ \left( x^{-6} \right)^{4} $$ 36.$$ \frac{x^{30}}{x^{10}} $$ Write each number in decimal notation without the use of exponents. 66.$$ 9.2 \times 10^2 $$ 68.$$ 7 \times 10^{-5} $$ Perform the indicated computations, Write the answers in scientific notation. 94.$$ (8.2 \times 10^{-8})(4.6 \times 10^{4}) $$ 96.$$ \frac{6.9 \times 10^8}{3 \times 10^5} $$

Homework 3
Pg. 46: 2-12 even, 24, 26, 34, 42, 46, 48, 102, 108 Evaluate or indicate that the root is not a real number. 2. $$ \sqrt{25} $$ 4.$$ -\sqrt{25} $$ 6.$$ sqrt{-25} $$ 8.$$ \sqrt{144+25} $$ 10.$$ \sqrt{144} + \sqrt{25} $$ 12.$$ \sqrt{(-17)^2} $$ Use the quotient rule to simplify. 24.$$ \sqrt{\frac{1}{49}} $$ 26.$$ \sqrt{\frac{121}{9}} $$ Add or subtract terms whenver possible. 34.$$ 8\sqrt{5}+11\sqrt{5} $$ 42.$$ 4\sqrt{13x}-6\sqrt{5} $$ Rationalize the denominator. 46.$$ \frac{2}{\sqrt{10}} $$ 48.$$ \frac{\sqrt{7}}{\sqrt{3}} $$ Simplify by reducing the index of the radical. 102.$$ \sqrt[4]{7^2} $$ 108.$$ \sqrt[12]{x^{4}y^{8}} $$

Homework 4
Pg. 58: 2, 6, 10, 12, 16, 42, 58, 60-64 even Is the algebriac expression a polynomial? If it is, write the polynomial in standard form. 2.$$ 2x+3x^{-1}-5 $$ Find the degree of the polynomial. 6.$$ -4x^{3}+7x^{2}-11 $$ Perform the indicated operations. Write the resulting polynomial in standard form and indicate its degree. 10.$$ (-7x^{3}+6x^{2}-11x+13)+(19x^{3}-11x^{2}+7x-17) $$ 12.$$ (18x^4 -2x^3 -7x+8)-(9x^4 -6x^3 -5x+7) $$ Find the product. 16.$$ (x+5)(x^2 -5x+25) $$ 42.$$ (x+5)^2 $$ 58.$$ (2x-3)^3 $$ Perform the indicated operations. Indicate the degree of the resulting polynomial. 60.$$ (-2x^{2}y+xy)+(4x^{2}y+7xy) $$ 62.$$ (7x^4 y^2 -5x^2 y^2 +3xy)+(-18x^4 y^2 -6x^2y^2 -xy) $$ 64.$$ (x^4 -7xy -5y^3 )-(6x^4 -3xy+4y^3 ) $$