Questions in mathematics

Questions in mathematics

📝 Answered - 13. [tex]\sqrt{3} \cos x + \cot^2 x = \frac{\sin^3 x + 1}{\sin^2 x}[/tex] 14. [tex]4 \sin^2 x = \sin 2x + 2 \sin x + 5 \cos x + 5[/tex]

📝 Answered - Wavelength varies inversely with frequency. Let [tex]$k$[/tex] be the product of wavelength and frequency. Complete the table using the inverse variation relationship. | Visible Light | Wavelength (m) | Frequency (THz) | [tex]$k$[/tex] | | :------------ | :------------- | :-------------- | :---------- | | Blue | 450 | [tex]$a$[/tex] | 301,500 | | Green | 520 | 580 | [tex]$b$[/tex] | | Yellow | [tex]$c$[/tex] | 540 | 302,400 | | Red | 635 | 480 | 304,800 | [tex]$a=\square$[/tex] [tex]$b=301, \square$[/tex] [tex]$c=\square$[/tex]

📝 Answered - Francesca drew point $(-2,-10)$ on the terminal ray of angle $\theta$, which is in standard position. She found values for the six trigonometric functions using the steps below.

📝 Answered - Consider the following two numbers: [tex]$x=0.649 \text { and } y=0 . \overline{649}$[/tex] Select all of the true statements below: [tex]$x$[/tex] is a larger value than [tex]$y$[/tex]. [tex]$y$[/tex] is a rational number. [tex]$x$[/tex] is a rational number. [tex]$y$[/tex] is an irrational number. [tex]$x$[/tex] is an irrational number. [tex]$y$[/tex] is a larger value than [tex]$x$[/tex].

📝 Answered - Which equation represents a line that is parallel to the line that passes through the points $(-6,9)$ and $(7,-17)$? A. $y=-\frac{1}{2} x+13$ B. $y=\frac{1}{2} x+13$ C. $y=2 x+13$ D. $y=-2 x+13

📝 Answered - Which equation represents a line that passes through $(-2,4)$ and has a slope of $\frac{2}{5}$? A. $y-4=\frac{2}{5}(x+2)$ B. $y+4=\frac{2}{5}(x-2)$ C. $y+2=\frac{2}{5}(x-4)$ D. $y-2=\frac{2}{5}(x+4)$

📝 Answered - Select the correct answer. On a television game show, contestants earn 5 points for each correct answer, but lose 2 points for each wrong answer. On last week's show, the winning contestant earned 80 points and answered 30 questions. Given that [tex]$x$[/tex] represents the number of questions answered correctly, and [tex]$y$[/tex] represents the number of questions answered incorrectly, determine which system of equations correctly represents this situation. A. [tex]$\begin{aligned} 5 x-2 y & =30 \\ x+y & =80 \end{aligned}$[/tex] B. [tex]$\begin{array}{r} 5 x-2 y=80 \\ x+y=30 \end{array}$[/tex] C. [tex]$\begin{aligned} 5 x+2 y & =30 \\ x-y & =80 \end{aligned}$[/tex] D. [tex]$\begin{array}{r} 5 x+2 y=80 \\ x-y=30 \end{array}$[/tex]

📝 Answered - If the point $G(-4,6)$ was moved horizontally 4 units to the left, which of the following is the correct mapping to define the translation? A. $(x, y) \rightarrow(x, y+4)$ B. $(x, y) \rightarrow(x+4, y)$ C. $(x, y) \rightarrow(x, y-4)$ D. $(x, y) \rightarrow(x-4, y)$

📝 Answered - $7.8 \frac{1}{6} \times 4 \frac{1}{2}$

📝 Answered - The two expressions below have the same value when rounded to the nearest hundredth. [tex]$\log _5 b \quad \log _9 48$[/tex] What is the approximate value of [tex]$\log b$[/tex] to the nearest hundredth? A. 0.93 B. 1.23 C. 9.16 D. 65.53