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Questions in mathematics

[Done] Solve for $x$. $2 \ln (5 x)=-2$ Do not round any intermediate computations, and round your answer to the nearest tenth. $x=$

[Done] If [tex]$f(x)=3^x+10$[/tex] and [tex]$g(x)=2 x-4$[/tex], find [tex]$(f-g)(x)$[/tex] A. [tex]$(f-g)(x)=3^x+2 x+6$[/tex] B. [tex]$(f-g)(x)=3^x-2 x+14$[/tex] C. [tex]$(f-g)(x)=-3^x+2 x-14$[/tex] D. [tex]$(f-g)(x)=x+14$[/tex]

[Done] 19. The inverse of [tex]f(x)=2 x-1[/tex] is A. [tex]x-1[/tex] B. [tex]\frac{x+1}{2}[/tex] C. [tex]\frac{1}{x+2}[/tex] D. [tex]x^2[/tex] 20. Find the inverse of [tex]f(x)=x^3-2[/tex]. A. [tex](x+2)^{\frac{1}{2}}[/tex] B. [tex](x-2)^{\frac{1}{3}}[/tex] C. [tex](x-2[/tex] [tex](x+2)[/tex]. 21. If [tex]h(x)=\frac{x+1}{2 x-5}[/tex], find [tex]h^{-1}(0)[/tex]. A. o B. -1 C. 1 D. [tex]\frac{\pi}{2}[/tex]. 22. Find the range of [tex]f(x)=\frac{x-2}{x-3}[/tex], A, [tex]R \{0,1\}[/tex] B, R C, [tex]R \{2,3\}[/tex] D, [tex]R \[/tex] 23. The [tex]y[/tex]-intercept of [tex]y=a x^3+b x^2+c x+d[/tex] is A. [tex](y(0), 0)[/tex] B. [tex](y(0), y[/tex] C. [tex](0,0)[/tex] D. [tex](0, y(0))[/tex]. 24. Evaluate [tex]\lim _{h \rightarrow 0} \frac{1}{h} \ln \left(\frac{2+h}{2}\right)[/tex]. A. [tex]e^2[/tex] B. 1 C. [tex]\frac{1}{2}[/tex] D. 0 . 25. Evaluate the lett-hand limit [tex]\lim _{x \rightarrow-3}\left(-\frac{5}{x+3}\right)[/tex], A. [tex]-\infty[/tex] B. [tex]x[/tex] C. 2 D. 26. Evaluate [tex]\lim _{x \rightarrow-2} \frac{x+2}{\ln (x+3)}[/tex]. A. Does not exist B. 2 C. o D, 1 .

[Done] Arrange the following numbers in ascending order. a) 75211 b) 741200 c) 412440 d) 4127894 e) 2451845

[Done] The area of a rectangular park is given by the algebraic expression 6xy. What are the possible expressions for the dimensions of the park?

[Done] (18) Out of 120 students in SSS 3, [tex]\frac{5}{8}[/tex] like football and [tex]\frac{2}{5}[/tex] like swimming. Every student like at least one of these sports. (a) What fraction of the students in [tex]SSS _3[/tex] like both subjects? (b) What fraction of the students like football but not swimming? (c) What fraction of the students like swimming only?

[Done] Simplify the expression: $4\left(x^2\right)^4 \cdot(-x)^3$

[Done] Write one trigonometric equation that can be used to find the value of $x$ by replacing the variable $a$ with the correct value. $x=\sin ^{-1}(a)$

[Done] Which value is a solution to the inequality $5x - 1 \leq -11$? A) $x=-1$ B) $x=0$ C) $x=5$ D) $x=-2$

[Done] Which explains how to find the radius of a circle whose equation is in the form $x^2+y^2=z$? A. The radius is the constant term, $z$. B. The radius is the constant term, $z$, divided by 2. C. The radius is the square root of the constant term, $z$. D. The radius is the square of the constant term, $z$.