Questions in mathematics

Questions in mathematics

📝 Answered - Find the value of the expression \( \frac{\sin x + \cos x}{\cos^3 x} \). Which of the following is correct? (A) \( 1 + \tan x + \tan^2 x - \tan^3 x \) (B) \( 1 + \tan x + \tan^2 x + \tan^3 x \) (C) \( 1 - \tan x + \tan^2 x + \tan^3 x \) (D) \( (1 + \tan x) \sec^2 x \)

📝 Answered - Select the correct answer. Given the following formula, solve for [tex]$l$[/tex]. [tex]$P=2(l+b)$[/tex] A. [tex]$l=4(P+b)$[/tex] B. [tex]$l=\frac{P-2 b}{2}$[/tex] C. [tex]$l=\frac{P-b}{2}$[/tex] D. [tex]$l=\frac{P-b}{4}$[/tex]

📝 Answered - What is the determinant of the coefficient matrix of the system $\left\{\begin{array}{l}-x-y+2 z=5 \\ 3 x+2 y-z=3 \\ 4 x+4 y-8 z=-2\end{array}\right.\$? A. 0 B. 16 C. 18 D. 40

📝 Answered - Rewrite the following equation in logarithmic form. [tex]$64=4^3$[/tex] Rewrite the following equation in exponential form. [tex]$\log _{49}(7)=\frac{1}{2}$[/tex]

📝 Answered - Which is the simplified form of [tex]m^{-8} p^0[/tex] ? A. [tex]\frac{1}{m^8 p}[/tex] B. [tex]\frac{1}{m^8}[/tex] C. [tex]\frac{p}{m^8}[/tex] D. [tex]m^8[/tex]

📝 Answered - Consider functions [tex]$f$[/tex] and [tex]$g$[/tex]. [tex] \begin{array}{l} f(x)=\sqrt{x^2+24 x+144} \\ g(x)=x^3-216 \end{array} [/tex] Which expression is equal to [tex]$f(x)+g(x)$[/tex]? A. [tex]$x^3+x^2+24 x-72$[/tex] B. [tex]$x^3+x-204$[/tex] C. [tex]$x^4-204$[/tex] D. [tex]$x^3+x-228$[/tex]

📝 Answered - Chin was shown the graph of a line that contained point (1,7). He wrote $f(x)=4 x+3$ to correctly represent the line. Which of these equations could represent the same line? $y-7=3(x-1)$ $y-1=3(x-7)$ $y-7=4(x-1)$ $y-1=4(x-7)$

📝 Answered - Give the slope and the $y$-intercept of the line with the given equation. Then, graph the linear equation. $y=3 x+7$ What is the slope? Select the correct choice below and fill in any answer boxes within your choice. A. The slope is $\square$ . (Simplify your answer.) B. The slope is undefined.

📝 Answered - Mrs. Carlyle bought a bag of peanuts for her children. When Phillip, Joy, Brent, and Preston came home from school, they each took some peanuts from the bag. - Phillip took [tex]$\frac{1}{3}$[/tex] of the peanuts from the bag. - Joy took [tex]$\frac{1}{4}$[/tex] of the remaining peanuts. - Brent took [tex]$\frac{1}{2}$[/tex] of the remaining peanuts. Preston took 10 peanuts. There were 71 peanuts remaining in the bag. 1. How many peanuts were originally in the bag? 2. How many peanuts did each child take?

📝 Answered - A square has a side that measures 11 units. What is the area of a circle with a circumference that equals the perimeter of the square? Use 3.14 for [pi], and round your answer to the nearest hundredth. A. 1,519.76 units² B. 379.94 units² C. 616.56 units² D. 154.14 units²