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Questions in mathematics

[Done] What is tan(d)? a. $\frac{15}{17}$ c. $\frac{8}{15}$ b. 8 d. 15

[Done] Find the derivative of $f(x)=2 x^3-5 x^2+3 x+2$ and place your answer below. Answer: $f^{\prime}(x)=$ $\square$

[Done] The function [tex]f(x)=-0.3(x-5)^2+5[/tex] is graphed. What are some of its key features? Choose three correct answers. * The domain is [tex] \{x \mid x[/tex] is a real number [tex]\}[/tex]. * The axis of symmetry is [tex]x=5[/tex]. * The minimum is (5, 5). * The range is [tex]\{y \mid y \geq 5\}[/tex].

[Done] If [tex]\theta=\frac{\pi}{6}[/tex], find the exact value of each expression below. (a) [tex]$\sin (-\theta)=$[/tex] [ ] (b) [tex]$\sin ^2 \theta=$[/tex] [ ] (c) [tex]$\sin 2 \theta=$[/tex] [ ]

[Done] The polynomials $a x^3+3 x^2-3$ and $2 x^3-5 x+a$ when divided by $(x-4)$ leave remainders $R_1$ & $R_2$ such that $R_1=R_2$. Then the value of $a$ is

[Done] If [tex]$f(x)=5 x-25$[/tex] and [tex]$g(x)=\frac{1}{5} x+5$[/tex], which expression could be used to verify [tex]$g(x)$[/tex] is the inverse of [tex]$f(x)$[/tex]? A. [tex]$\frac{1}{5}(\frac{1}{5} x+5)+5$[/tex] B. [tex]$\frac{1}{5}(5 x-25)+5$[/tex] C. [tex]$\frac{1}{(\frac{1}{5} x+5)}$[/tex] D. [tex]$5(\frac{1}{5} x+5)+5$[/tex]

[Done] Simplify $\sqrt{20}$. The simplified expression is $\square$.

[Done] Quadratic equations can be written in the form ax^2 + bx + c = 0. What is the maximum number of roots that a quadratic equation can have? A. one B. two C. three D. four

[Done] What is the common difference of an arithmetic sequence that starts with 3 and has subsequent terms of 5, 7, 9? (A) 3 (B) 6 (C) 1 (D) 2

[Done] For each expression, find: - The factors of the first term - The factors of the second term - The greatest common factor of the two terms Expressions: 1. 3x + 6y 2. 4a³ + 2a 3. 5x - 2x² 4. ax² - bx 5. 12a²b + 18ab² Example: Expression: 3x + 6y Factors of the first term: 3; x Factors of the second term: 2; 3; y Greatest common factor: 3 Factor form: 3(x + 2y)