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Questions in mathematics

[Done] What is the axis of symmetry of [tex]h(x)=-2 x^2+12 x-37[/tex]? A. [tex]x=-15[/tex] B. [tex]x=-3[/tex] C. [tex]x=3[/tex] D. [tex]x=15[/tex]

[Done] The perimeter of a rectangular pool is more than 62 meters, and the width is at least 10 meters less than the length. Which system of inequalities represents the possible length in meters, [tex]l[/tex], and the possible width in meters, [tex]w[/tex], of the pool? A. [tex] \begin{aligned} w & \leq 10-1 \\ 21+2 w & \geq 62 \end{aligned} [/tex] B. [tex] w \leq 10-1 2 l+2 w\ \textgreater \ 62 [/tex] C. [tex] w \leq I-10 2 l+2 w \geq 62 [/tex] D. [tex] w \leq 1-10 2 l+2 w\ \textgreater \ 62 [/tex]

[Done] Consider the functions [tex]f(x)=\left(\frac{4}{5}\right)^x[/tex] and [tex]g(x)=\left(\frac{4}{5}\right)^x+6[/tex]. What are the ranges of the two functions? [tex] \begin{array}{l} f(x):\{y \mid y\ \textgreater \ [/tex] [tex]g(x):\{y \mid y\ \textgreater \ [/tex] [tex]\end{array} [/tex]

[Done] A right pyramid with a square base has a base length of $x$ inches, and the height is two inches longer than the length of the base. Which expression represents the volume in terms of $x$? A. $\frac{x^2(x+2)}{3}$ cubic inches B. $\frac{x(x+2)}{3}$ cubic inches C. $\frac{x^3}{3}+2$ cubic inches D. $\frac{x^3+2}{3}$ cubic inches

[Done] A box contains white, milk, and dark chocolates. The ratio of white to milk chocolates is [tex]$2: 3$[/tex] A chocolate is picked at random. The probability that it is a white chocolate is [tex]$\frac{2}{11}$[/tex] What is the probability that it is a dark chocolate? Give your answer as a fraction in its simplest form.

[Done] Solve the system of equations and enter the solution as an ordered pair in the box below. [tex]\begin{array}{l} 3 y=2 x+1 \\ 5 y=2 x+3 \end{array}[/tex] Solve the system of equations and enter the solution as an ordered pair in the box below. [tex]\begin{array}{c} 5 x+3 y=11 \\ 2 x-y=0 \end{array}[/tex]

[Done] Mark the statements that are true. A. An angle that measures $\frac{\pi}{6}$ radians also measures $30^{\circ}$. B. An angle that measures $180^{\circ}$ also measures $\frac{\pi}{2}$ radians. C. An angle that measures $\frac{\pi}{3}$ radians also measures $60^{\circ}$. D. An angle that measures $30^{\circ}$ also measures $\frac{\pi}{3}$ radians.

[Done] If [tex]$f(x)=5x$[/tex], what is [tex]$f^{-1}(x)$[/tex]?

[Done] Solve the quadratic equations. Find the value/values of x (use extracting square roots). Show your solution. 1. x² - 49 = 0 2. 9x² - 25 = 0 3. 4x² + 1 = 5

[Done] Sudha had 8 3/4 meters long rope. She cut it into 7 equal parts. Find the length of each piece of the rope?