Questions in mathematics

Questions in mathematics

📝 Answered - Solve the equation. [tex]\begin{array}{l} 2^{x-1}=31 \\ x=[?]\end{array}[/tex]

📝 Answered - Round to 4 significant figures. $0.00238866$

📝 Answered - Use synthetic division to decide whether the given number is a solution of the given equation. [tex]5 x^4-5 x^2+5 ; x=\frac{2}{5}[/tex]

📝 Answered - Helaine graphed the equation [tex]12 x-4 y=3[/tex]. What was the slope of Helaine's line?

📝 Answered - Type the correct answer in the box. Use numerals instead of words. What is the solution for $x$ in the equation? $10 x-4.5+3 x=12 x-1.1$ $x=\square$

📝 Answered - Find the solutions of the quadratic equation [tex]x^2+7 x+10=0[/tex] A) [tex]x=2,5[/tex] B) [tex]x=-7,-3[/tex] C) [tex]x=7,3[/tex] D) [tex]x=-2,-5[/tex]

📝 Answered - Solve: [tex]$3,125=5^{-10+3 x}$[/tex]

📝 Answered - 6. Find the exact value of [tex]$\lim _{x \rightarrow 0} \frac{x}{x}$[/tex]. A. [tex]$1 / \pi$[/tex] B. 0 C. 1 7. Which of the following functions is continuous? A. [tex]$f(x)=|x|$\qquad$[/tex] C. [tex]$f(x)=\frac{1}{x}$[/tex] B. [tex]$f(x)=\left{\begin{array}{ll}3 & text { if } x<4, \\ \frac{x}{2}+3 & text { if } x \geq 4,\end{array}\right.$[/tex] (D) [tex]$f(x)=\left{\begin{array}{ll}\ln (x) & text { if } x<0, \\ 0 & text { if } x=0,\end{array}\right.$[/tex] 8. If [tex]$[x]$[/tex] is the greatest integer not greater than [tex]$x$[/tex], then [tex]$\lim _{x \rightarrow 1 / 2}[x]$[/tex]. A. [tex]$1 / 2$[/tex] B. 1 C. 0 D. None of them 9. Let [tex]$f(x)=\left{\begin{array}{lll}x^2 & 1 & text { if } x \neq 1 . \\ 4 & text { if } x=1 .\end{array}\right.$[/tex] Which of the following statements is/are true? I. [tex]$\lim _{x \rightarrow 1} f(x)$[/tex] exists II. [tex]$f(1)$[/tex] exists III. [tex]$f$[/tex] is continuous at [tex]$x=1$[/tex]. A. only I B. only II C. I and II D. None of them 10. Find the acute angle between two straight lines having the equations

📝 Answered - Which statement about the following equation is true? [tex]2 x^2-9 x+2=-1[/tex] A. The discriminant is less than 0, so there are two real roots. B. The discriminant is less than 0, so there are two complex roots. C. The discriminant is greater than 0, so there are two real roots. D. The discriminant is greater than 0, so there are two complex roots.

📝 Answered - Solve the following logarithmic equation. $\log _4(s+21)-\log _4(s+5)=\log _4 s$ Select the correct choice below and, if necessary, fill in the answer box. A. The solution(s) is/are $\square$ (Simplify your answer. Type an integer or a fraction. Use a comma to separate answers as needed.) B. The solution is not a real number.