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Questions in mathematics

[Done] Find the value of the expression: [tex]\frac{1}{21} x^2 y^2 \text { for } x=-\frac{1}{3}, y=4 \frac{1}{2}[/tex]

[Done] Factorise the equation [tex]$3 y(2 y+a)(5-y)=6$[/tex]

[Done] Which equation is quadratic in form? $3 x^5+8 x^3+6=0$ $6 x^4+7 x^2-3=0$ $5 x^6+x^4+12=0$ $x^9+x^3-10=0$

[Done] Which sample has a higher standard deviation? Sample A: 82, 85, 87, 88, 91, 93 Sample B: 68, 73, 74, 77, 81, 81 Select the correct answer below and fill in the answer box to complete your choice. A. Sample A has the higher standard deviation of [ ]. B. Sample B has the higher standard deviation of [ ].

[Done] Find the rate of change represented by the data in the table below. \begin{tabular}{l|lllll} $x$ & -8 & -4 & 0 & 4 & 8 \\ \hline $y$ & -5 & -2 & 1 & 4 & 7 \end{tabular} Is the rate of change positive or negative? a) positive b) negative Rate of Change: $\frac{\text { change in } y}{\text { change in } x}$

[Done] Use the substitution method to solve the system of equations. Choose the correct ordered pair. [tex]$\begin{array}{l} 2 x+2 y=16 \\ y=x-4 \end{array}$[/tex] A. (2,-2) B. (6,-2) C. (2,2) D. (6,2)

[Done] Given $y=(2 x+3)^2$, choose the standard form of the given quadratic equation. A. $0=4 x^2+10 x+6$ B. $0=25 x^2$ C. $0=4 x^2+9$ D. $0=4 x^2+12 x+9$

[Done] Each month, Kaisorn deposits $50.00 onto her public transportation card. It costs her $2.50 per trip to ride the subway. Thom deposits $40.00 on his public transportation card. It costs him $2.00 per trip to ride the subway. If [tex]$x$[/tex] represents the number of trips and [tex]$y$[/tex] represents the amount remaining in each account, which system of equations represents their transportation costs? [tex] \begin{array}{l} 50-2.5 x=y \\ 40-2 x=y \end{array} [/tex] [tex]$50+2.5 x=y$ $40+2 x=y$ [/tex] [tex]$50-2.5 y=x$ $40-2 y=x$ [/tex] [tex]$50+2.5 y=x$ $40+2 y=x$ [/tex]

[Done] $\int \tan ^2 x dx=$ A. $\sec ^2 x+c$ B. $2 \tan x+c$ C. $\tan x-x+c$ D. $2 \tan x-x+c$

[Done] A homeowner has an octagonal gazebo inside a circular area. Each vertex of the gazebo lies on the circumference of the circular area. The area that is inside the circle, but outside the gazebo, requires mulch. This area is represented by the function [tex]$m(x)$[/tex], where [tex]$x$[/tex] is the length of the radius of the circle in feet. The homeowner estimates that he will pay [tex]$\$1.50$[/tex] per square foot of mulch. This cost is represented by the function [tex]$g(m)$[/tex], where [tex]$m$[/tex] is the area requiring mulch. [tex]$\begin{array}{l} m(x)=8 x^2-2 \sqrt{2} x^2 \\ g(m)=1.50 m \end{array}$[/tex] Which expression represents the cost of the mulch based on the radius of the circle? A. [tex]$1.50\left(\pi x^2-2 \sqrt{2} x^2\right)$[/tex] B. [tex]$\pi(1.50 x)^2-2 \sqrt{2} x^2$[/tex] C. [tex]$1.50\left(\pi x^2-2 \sqrt{2} x^2\right)$[/tex] D. [tex]$1.50\left(\pi(1.50 x)^2-2 \sqrt{2}(1.50 x)^2\right)$[/tex]