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Questions in mathematics

📝 Answered - If x^2 + y^2 = 34xy, then prove that 2log(x + y) = 2log(6) + log(x) + log(y).

📝 Answered - A given line has the equation [tex]$2 x+12 y=-1$[/tex]. What is the equation, in slope-intercept form, of the line that is perpendicular to the given line and passes through the point [tex]$(0,9)$[/tex]? A. [tex]$y=-6 x+9$[/tex] B. [tex]$y=-\frac{1}{6} x+9$[/tex] C. [tex]$y=\frac{1}{6} x+9$[/tex] D. [tex]$y=6 x+9$[/tex]

📝 Answered - Consider the following system of equations: [tex]\begin{aligned} 2 x-y & =12 \ -3 x-5 y & =-5 \end{aligned}[/tex] The steps for solving the given system of equations are shown below: [tex]\begin{array}{rlrl} & \text { Step 1: } & -5(2 x-y) & =-5(12) \ & -3 x-5 y & =-5 \ & \text { Step 2: } & -10 x+5 y & =-60 \ & -3 x-5 y & =-5 \ & \text { Step 3: } & -13 x & =-65 \ & \text { Step 4: } & x & =5 \ & \text { Step 5: } & 2(5)-y & =12 \ & \text { Step 6: } & y & =-2 \end{array}[/tex] Solution: (5,-2) Select the correct statement about step 3.

📝 Answered - Aiko is finding the sum $(4+5 i)+(-3+7 i)$. She rewrites the sum as $(-3+7) i+(4+5) i$. Which statement explains the error Aiko made by using a mathematical property incorrectly? A. Aiko incorrectly used the commutative property by changing the order of the two complex numbers. B. Aiko incorrectly used the distributive property by combining the real number and the coefficient of the imaginary part. C. Aiko incorrectly used the associative property by changing the order of the two complex numbers. D. Aiko incorrectly used the identity property by combining the real number and the coefficient of the imaginary part.

📝 Answered - $\begin{array}{c} GCF=[?] \ \frac{3}{25} \times \frac{5}{9}= \ \square \end{array}$

📝 Answered - Write the given equation in the form $(x-h)^2+(y-k)^2=r^2$. Identify the center and radius. 7) $x^2+y^2+12x-6y-55=0$ A) $(x+6)^2+(y-3)^2=100$ Center: $(-6,3) ; r=10$ B) $(x+6)^2+$ C) $(x+12)^2+(y-6)^2=55$ Center: $(6,$ Center: $(12,-6) ; r=55$ D) $(x+12)^2$ Center: (- Find the domain in interval notation. 8) $f(x)=\frac{8}{\sqrt{7-x}}$ A) $(-\infty, 7]$ B) $[7, \infty)$ C) $(7, \infty)$

📝 Answered - The table represents a linear equation. | x | y | | --- | ---- | | -4 | -11 | | -2 | -6 | | 6 | 14 | | 10 | 24 | Which equation correctly uses point $(-2,-6)$ to write the equation of this line in point-slope form? A. $y-6=\frac{5}{2}(x-2)$ B. $y-6=\frac{2}{5}(x-2)$ C. $y+6=\frac{2}{5}(x+2)$ D. $y+6=\frac{5}{2}(x+2)$

📝 Answered - What is the solution in interval notation to $-4 \leq 3 x-7<8$?

📝 Answered - If [tex]$\csc \theta=\frac{1}{\sin \theta}$[/tex] and [tex]$\sin \theta=\frac{1}{\sqrt{2}}$[/tex], for the angle 450 what is [tex]$\operatorname{Csc} \theta$[/tex]? A. [tex]$\frac{2}{\sqrt{22}}$[/tex] B. [tex]$\frac{2 \sqrt{2}}{2}$[/tex] C. [tex]$\frac{\sqrt{2}}{1}$[/tex]

📝 Answered - Solve the polynomial inequality and graph the solution set on a real number line. Express the solution set in interval notation. [tex]x^3+4 x^2-16 x-64 \textgreater \ 0[/tex] Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is [ ]. (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) B. The solution set is the empty set.