Questions in mathematics

Questions in mathematics

[Free] If the quadratic equations, ax^2 + bx + c = 0 and bx^2 + cx + a = 0, where a, b, c are distinct, have one common root, then what is the common root?

[Free] The domain of the piecewise function is $(-\infty, \infty)$. a. Graph the function. b. Use your graph to determine the function's range. [tex]f(x)=\left\{\begin{array}{rll} 6 x & if & x \leq 0 \\ 6 & if & x \ \textgreater \ 0 \end{array}\right.[/tex] a. Choose the correct graph below. A. B. C. D.

[Free] Given that [tex]$\tan \theta=-1$[/tex], what is the value of [tex]$\sec \theta$[/tex], for [tex]$\frac{3 \pi}{2}\ \textless \ \theta\ \textless \ 2 \pi$[/tex] ? A. [tex]$-\sqrt{2}$[/tex] B. [tex]$\sqrt{2}$[/tex] C. 0 D. 1

[Free] Which expression is equivalent to $\left(x^{\frac{1}{4}} y^{16}\right)^{\frac{1}{2}}$ ? A. $x^{\frac{1}{2}} y^4$ B. $x^{\frac{1}{8}} y^8$ C. $x^{\frac{1}{4}} y^8$ D. $x^{\frac{1}{4}} y^4$

[Free] How are the graphs of the functions [tex]$f(x)=\sqrt{16}^x$[/tex] and [tex]$g(x)=\sqrt[3]{64}^x$[/tex] related? A. The functions [tex]$f(x)$[/tex] and [tex]$g(x)$[/tex] are equivalent. B. The function [tex]$g(x)$[/tex] increases at a faster rate. C. The function [tex]$g(x)$[/tex] has a greater initial value. D. The function [tex]$g(x)$[/tex] decreases at a faster rate.

[Free] If you are given the graph of [tex]g(x)=\log _2 x[/tex], how could you graph [tex]f(x)=\log _2 x+5[/tex]? A. Translate each point of the graph of [tex]g(x)[/tex] 5 units up. B. Translate each point of the graph of [tex]g(x)[/tex] 5 units down. C. Translate each point of the graph of [tex]g(x)[/tex] 5 units left. D. Translate each point of the graph of [tex]g(x)[/tex] 5 units right.

[Free] What is the highest common factor (HCF) of 15 and 22?

[Free] Explain how to graph the given piecewise-defined function. Be sure to specify the type of endpoint each piece of the function will have and why. [tex]f(x)=\left\{\begin{array}{ll} -x+3, & x\ \textless \ 2 \\ 3, & 2 \leq x\ \textless \ 4 \\ 4-2 x, & x \geq 4 \end{array}\right.[/tex]

[Free] Read the table and answer the questions. | | Flock X | Flock Y | Flock Z | |---|---|---|---| | Total Pieces of Food Eaten | 57 | 153 | 90 | | Food Percentage* | $\square$ % | $\square$ % | $\square$ % | | Simulated Number of Birds in Flock for 2nd Generation** | $\square$ | $\square$ | $\square$ | * Divide each flock's total pieces of food by 300, the total number of pieces of food eaten. ** Multiply the food percentage for each flock by the total number of birds (30).

[Free] Evaluate the function for the given value. [tex] \begin{array}{c} y=4 \cdot 3^x \text { for } x=3 \\ y=[?] \end{array} [/tex]