Questions in mathematics

Questions in mathematics

📝 Answered - In 30-40 words, construct an algebraic proof for the given statement. Give a property from Theorem 6.22 for every step. For all sets [tex]$A, B$[/tex], and [tex]$C$[/tex], [tex]$(A \cap B) \cup C=(A \cup C) \cap(B \cup C)$[/tex] (1) If all sets [tex]$A$[/tex] and [tex]$B$[/tex], [tex]$A \cup(B-A)=A \cup B$[/tex].

📝 Answered - Which statement about the following equation is true? [tex]3 x^2-8 x+5=5 x^2[/tex] A. The discriminant is less than 0, so there are two real roots. B. The discriminant is greater than 0, so there are two real roots. C. The discriminant is less than 0, so there are two complex roots. D. The discriminant is greater than 0, so there are two complex roots.

📝 Answered - Select all the correct answers. Which expressions are equivalent to the given expression? [tex](-\sqrt{9}+\sqrt{-4})-(2 \sqrt{576}+\sqrt{-64})[/tex] * -51-6i * -3+2i -2(24)-8i * 45+10i * -51+6i * -3+2i +2(24)+8i * -3-2i-2(24)+8i

📝 Answered - Complete the table by squaring each negative [tex]$x$[/tex]-value listed: [tex] \begin{array}{cc} x & x^2 \\ -2 & \\ -3 & \\ -4 & \\ -5 & \\ -6 & \\ -7 & \\ -8 & \\ -9 & \\ -10 & \\ -11 & \\ \end{array} [/tex]

📝 Answered - Multiply: $(-4+i)(2-3 i)$

📝 Answered - Use the drawing tools to form the correct answer on the number line. Graph the solution to this inequality on the number line: [tex]$0.3(x-4)\ \textgreater \ -0.3$[/tex]

📝 Answered - Which statement best describes how to determine whether [tex]f(x)=x^2-x+8[/tex] is an even function? A. Determine whether [tex]-x^2-(-x)+8[/tex] is equivalent to [tex]x^2-x+8[/tex] B. Determine whether [tex](-x)^2-(-x)+8[/tex] is equivalent to [tex]x^2-x+8[/tex]. C. Determine whether [tex]-x^2-(-x)+8[/tex] is equivalent to [tex]-(x^2-x+8)[/tex]. D. Determine whether [tex](-x)^2-(-x)+8[/tex] is equivalent to [tex]-(x^2-x+8)[/tex]

📝 Answered - Which gives the best estimate and the exact product of $(5.9)(8.28)$? A. estimate: 40 ; exact product: 48.852 B. estimate: 48; exact product: 48.852 C. estimate: 400; exact product: 488.52 D. estimate: 480; exact product: 488.52

📝 Answered - $z=\frac{(\sqrt{3}+1)+(\sqrt{3}-1)}{4}

📝 Answered - Compute. $8-9-1+12-1$