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Questions in mathematics

[Done] What is the solution of the matrix equation? [tex] \left[\begin{array}{l} x \\ y \end{array}\right]=\left[\begin{array}{ll} -3 & 5 \\ -1 & 2 \end{array}\right]\left[\begin{array}{l} 0 \\ 2 \end{array}\right] [/tex]

[Done] Select the correct answer. What is this expression in simplified form? [tex]2 \sqrt{2} \cdot 7 \sqrt{18}[/tex] A. [tex]$18 \sqrt{5}$[/tex] B. 84 C. [tex]$84 \sqrt{2}$[/tex] D. [tex]$14 \sqrt{6}$[/tex]

[Done] Determine the equation of a circle with a center at $(-4,0)$ that passes through the point $(-2,1)$ by following the steps below. 1. Use the distance formula to determine the radius: $d=\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}$. 2. Substitute the known values into the standard form: $(x-h)^2+(y-k)^2=r^2$. What is the equation of a circle with a center at $(-4,0)$ that passes through the point $(-2,1)$? A. $x^2+(y+4)^2=\sqrt{5}$ B. $(x-1)^2+(y+2)^2=5$ C. $(x+4)^2+y^2=5$ D. $(x+2)^2+(y-1)^2=\sqrt{5}$

[Done] Select the equation for the line crossing the point $(1,4)$ and with slope $=2$. A. $y-1=4(x-2)$ B. $y+1=2(x+4)$

[Done] A basketball player is shooting a basketball toward the net. The height, in feet, of the ball [tex]$t$[/tex] seconds after the shot is modeled by the equation [tex]$h=6+30 t-16 t^2$[/tex]. Two-tenths of a second after the shot is launched, an opposing player leaps up to block the shot. The height of the shot blocker's outstretched hands [tex]$t$[/tex] seconds after he leaps is modeled by the equation [tex]$h=9+25 t-16 t^2$[/tex]. If the ball was on a path to reach the net 1.7 seconds after the shooter launches it, does the leaping player block the shot? A. yes, exactly 0.6 seconds after the shot is launched B. yes, between 0.64 seconds and 0.65 seconds after the shot is launched C. yes, between 0.84 seconds and 0.85 seconds after the shot is launched D. no, shot not blocked

[Done] $3^8 \div 3^{-2}=$ A. $1^{-4}$ B. $6^6$ C. $3^{10}$ D. $3^{-4}$

[Done] Identify all of the following solutions of [tex]$\sqrt{x+8}-6=x$[/tex]. A. None of the above B. [tex]$x=-7$[/tex] C. [tex]$x=-4$[/tex] D. [tex]$x=-4$[/tex] and [tex]$x=-7$[/tex]

[Done] Select the correct answer. Consider the first four terms of the sequence below. $-3,-12,-48,-192, \ldots$ What is the $8^{\text {th }}$ term of this sequence? A. $-12,288$ B. $-49,152$ C. -768 D. $-196,608

[Done] Simplify the expression. [tex]i^{37}=[/tex]

[Done] Which equation represents a line which is perpendicular to the $y$-axis? A. $y=-6$ B. $x=-6$ C. $x=\frac{1}{2} y$ D. $x=-y$