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Questions in mathematics

📝 Answered - Given [tex]$\sin t=\frac{x}{x+1}$[/tex], find [tex]$\cos \left(\sin ^{-1}\left(\frac{x}{x+1}\right)\right)$[/tex]

📝 Answered - $\begin{array}{l} \rightarrow (-3)^2=9 \\ 2 x)^2=4 x^2(-3)^2=9 \\ (2 x-\underbrace{3)(2 x-3)}_{2(-3)(2 x)}=4 x^2-12 x+9 \end{array}$ 1) $(x+6)(x+6) \quad x^2+12 x+36$ 2) $(2 x+5)(2 x+5)$ $\qquad$ $4 x^2+20 x+25$ 3) $(3 x-4)(3 x-4) 9 x^2-24 x+16$ 4) $(x+8)^2 \quad x^2+16 x+64$ 5) $(4 x-3)^2 \quad 16 x^2-24 x+9$

📝 Answered - A hi-res stock $ABC$ is such that $/AC/ = 15 cm$, and the $\Varangle BAC = 48^{\circ}$. Calculate $/BC/$ in meters, correct to 3 decimal places. [Hint: $100 cm = 1 m, \tan 48^{\circ} = 1.1106$, $\left.\operatorname{Sin} 48^{\circ} = 0.7431, \operatorname{Cos} 48^{\circ} = 0.6691\right]$

📝 Answered - Fill in the blanks. (i) Zero has $\qquad$ reciprocal. (ii) The numbers $\qquad$ and $\qquad$ are their own reciprocals. (iii) The reciprocal of -5 is $\qquad$ . (iv) Reciprocal of $\frac{1}{x}$, where $x \neq 0$ is $\qquad$ . (v) The product of two rational numbers is always a $\qquad$ . (vi) The reciprocal of a positive rational number is $\qquad$ .

📝 Answered - If the discriminant of a quadratic equation is equal to -8, which statement describes the roots? A. There are two complex roots. B. There are two real roots. C. There is one real root. D. There is one complex root.

📝 Answered - Natalia is writing a recursive formula to represent the sequence. [tex]$8,12,18,27, \ldots$[/tex] What value should she use as the common ratio in the formula? A. [tex]$\frac{1}{4}$[/tex] B. [tex]$\frac{2}{3}$[/tex] C. [tex]$\frac{3}{2}$[/tex] D. [tex]$\frac{4}{1}$[/tex]

📝 Answered - Solve each polynomial equation in the complex numbers. [tex]2 x^4-7 x^3+38 x^2-47 x-34=0[/tex] Find the complex zeros of [tex]f[/tex]. [tex]x=[/tex] ____ (Type an exact answer, using radicals as needed. Express complex numbers in terms of [tex]i[/tex]. Use a comma to separate answers as needed.)

📝 Answered - Solve $6 x-17=k$ for $x$. A. $x=\frac{k+17}{6}$ B. $x=6 k+102$ C. $x=k+11$ D. $x=\frac{k}{6}+17$

📝 Answered - At which root does the graph of [tex]f(x)=(x+4)^0(x+7)^0[/tex] cross the [tex]x[/tex]-axis? A. -7 B. -4 C. 4 D. 7

📝 Answered - Determine whether the distribution is a discrete probability distribution. | x | P(x) | |---|-------| | 0 | 0.36 | | 1 | 0.24 | | 2 | 0.18 | | 3 | 0.13 | | 4 | 0.09 | Is the distribution a discrete probability distribution? A. Yes, because each probability is between 0 and 1, inclusive. B. Yes, because the sum of the probabilities is equal to 1 and each probability is between 0 and 1, inclusive. C. Yes, because the sum of the probabilities is equal to 1. D. No, because the sum of the probabilities is not equal to 1.