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Questions in mathematics

[Jawaban] What is the standard form of the equation of a circle given by $x^2+y^2-18 x+8 y+5=0$?

[Jawaban] Mr. Capuano, an art teacher, surveyed his students to find out whether they are satisfied with his classes. He also noted which class each student had taken. Oil-painting Satisfied: 17 Not satisfied: 3 Sculpture Satisfied: 25 Not satisfied: 5 Art Classes \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} Oil \ Painting \end{tabular} & Sculpture & Total \\ \hline Satisfied & $34 \%$ & & $84 \%$ \\ \hline$\ldots \ldots$ & & & \\ \hline \end{tabular} What is the value of $x$ in the relative frequency table for the survey results? Round the answer to the nearest percent. $3 \%$ $6 \%$ $8 \%$ $15 \%

[Jawaban] Which statement can be written as a biconditional statement? A. If a polygon has 4 sides, then the figure is a quadrilateral. B. If an angle measures $46^{\circ}$, then it is an acute angle. C. If $x=-4$, then $x^2=16$. D. If two angles are supplementary, then one is obtuse and one is acute.

[Jawaban] Which expression is equivalent to $(3 x^2+4 x-7)(x-2)$? A. $(3 x^2+4 x-7)+2(3 x^2+4 x-7)$ B. $2 x(3 x^2+4 x-7)$ C. $(3 x^2+4 x-7)(x)+(3 x^2+4 x-7)(-2)$ D. $x(3 x^2+4 x-7)-2

[Jawaban] Solve for $r$ in the proportion: [tex]$\frac{r}{56}=\frac{33}{22}$[/tex]

[Jawaban] How many 4-digit personal identification numbers are possible if the number cannot contain a zero? A. 5,040 B. 6,561 C. 9,000 D. 10,000

[Jawaban] What is the value of $x$ in the equation $-\frac{5}{8} x=-160$? A. -256 B. -100 C. 100 D. 256

[Jawaban] Show that $\frac{d}{d x}\left(2 \tan ^{-1} \theta\right)=\frac{d}{d \theta}\left[\tan ^{-1}\left(\frac{2 \theta}{1-\theta^2}\right)\right]$

[Jawaban] $6 \frac{1}{4} + \frac{2}{3} =$

[Jawaban] A student solved the following system of equations incorrectly using these steps: $\begin{array}{r} 2 x+5 y=13 \\ -x+4 y=13 \\ 2 x+5 y=13 \\ +-2 x+8 y=13 \\ \hline 13 y=26 \\ y=2 \end{array}$ $\begin{array}{r} 2 x+5(2)=13 \\ 2 x+10=13 \\ 2 x=3 \\ x=1.5 \end{array}$ What error did the student make? A. In line 2, the student forgot to multiply the right side of the equation by 2. B. In line 3, the student should have subtracted the equations instead of adding them. C. In line 3, the student added the two equations incorrectly. D. In line 5, the student used an incorrect equation when solving for $x$.