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Questions in mathematics

📝 Answered - Sketch the function [tex]f(x)=-2(x+5)^2+6, x \geq-5[/tex], and its inverse on the same graph. All graphs must be done by hand. No graphing software. Use different colours for each curve. d) State the domain and range of the function and its inverse using set notation: | | [tex]f(x)[/tex] | Inverse | |------------|----------------|---------| | Domain | | | | Range | | |

📝 Answered - What is the product of $-\frac{5}{6} \times \frac{2}{3}$? A. $-\frac{7}{9}$ B. $-\frac{5}{9}$ C. $\frac{5}{9}$ D. $\frac{7}{9}$

📝 Answered - Simplify, using the associative property of multiplication. $ = 48x - 30y - \square$

📝 Answered - What is the slope of a line parallel to [tex]$y=\frac{5}{2} x-7$[/tex]?

📝 Answered - Convert the equation $y+5=-2(x-3)$ to general form.

📝 Answered - Use the Graphing tool to graph the functions [tex]f(x)=\log _4 x[/tex] and [tex]g(x)=\log _{0.25} x[/tex]. Then identify the key features of each graph. Drag each feature to the correct location on the table. | Features of f only | Features of both [tex]f[/tex] and [tex]g[/tex] | Features of [tex]g[/tex] only | | --- | --- | --- | | | | | domain of [tex](0, \infty)[/tex] range of [tex](-\infty, \infty)[/tex] positive over the interval [tex](0,1)[/tex] negative over the interval [tex](0,1)[/tex] asymptote of [tex]x = 0[/tex] [tex]x[/tex]-intercept of [tex](1,0)[/tex] increasing as [tex]x[/tex] increases decreasing as [tex]x[/tex] increases

📝 Answered - Prove that: [tex]\frac{\sin 20^{\circ}-\sin 10^{\circ}}{1-\cos 10^{\circ}+\cos 20^{\circ}}=\tan 10^{\circ}[/tex]

📝 Answered - Which statement is true about the circumference of a circle? A. The circumference is equal to the radius of the circle. B. The circumference is equal to the diameter of the circle. C. The circumference is found by multiplying by the radius. D. The circumference is found by multiplying by the diameter.

📝 Answered - Solve the equation [tex]$12 x+6 y=24$[/tex] for [tex]$x$[/tex]. A. [tex]$x=24-6 y$[/tex] B. [tex]$x=\frac{1}{2} y+2$[/tex] C. [tex]$x=2-\frac{1}{2} y$[/tex] D. [tex]$x=12(24-6 y)$[/tex]

📝 Answered - Given that [tex]$\log _a x=3, \log _a y=4$[/tex], and [tex]$\log _a z=5$[/tex], find the following [tex]$\log _a \frac{\sqrt[4]{y^3 z^4}}{\sqrt[4]{x^4 z^{-4}}}$[/tex]