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Questions in mathematics

[Jawaban] 3 years ago from now, the age of the father was 14 years more than twice his son's age. After how many years from now will he be twice his son's age? 1. 11 2. 12 3. 8 4. 14

[Jawaban] Find the coordinates of the focus and equation of the directrix for the parabola given by $y^2=-4 x$. The general formula for this parabola is $y^2=4 p x$. Therefore, the value of $p$ is $\square$ . The coordinates of the focus are $\square$ . The equation of the directrix is $\square$ .

[Jawaban] What is the simplified form of [tex]$\sqrt{400 x^{100}}$[/tex] ? A. [tex]$200 x^{10}$[/tex] B. [tex]$200 x^{50}$[/tex] C. [tex]$20 x^{10}$[/tex] D. [tex]$20 x^{50}$[/tex]

[Jawaban] Select the correct answer. What is this expression in simplified form? [tex]$\frac{\sqrt{32}}{\sqrt{2}}$[/tex] A. 16 B. 2 C. [tex]$\sqrt{30}$[/tex] D. 4

[Jawaban] Select the correct answer. What is the justification for step 4 in the solution process? Step 1 : [tex]\frac{9}{2} b+11-\frac{5}{6} b=b+2[/tex] Step 2 : Step 3 : Step 4 : [tex]\frac{22}{6} b+11=b+2[/tex] [tex]\frac{8}{3} b+11=2[/tex] [tex]\begin{aligned}\frac{8}{3} b & =-9 \\b & =-\frac{27}{8}\end{aligned}[/tex] A. the multiplication property of equality B. combining like terms C. the addition property of equality D. the subtraction property of equality

[Jawaban] Find the value of the expression: $\frac{3^7 \cdot 27}{\left(3^4\right)^3}$

[Jawaban] What is the solution to the following equation? $x^2+5 x+7=0$ A. $x=\frac{-3 \pm \sqrt{-7}}{2}$ B. $x=\frac{3 \pm \sqrt{25}}{2}$ C. $x=\frac{-5 \pm \sqrt{53}}{2}$ D. $x=\frac{-5 \pm \sqrt{-3}}{2}$

[Jawaban] Two percent of mobile phones produced at a factory are defective. Which of the following is a binomial experiment? A. Selecting phones randomly until a non-defective phone is chosen B. Selecting phones randomly until 200 defective phones are chosen C. Selecting 200 phones randomly and recording whether each phone is defective D. Selecting a group of phones randomly and recording the number of defective phones in the group

[Jawaban] Perform the indicated operations, and write the result in the form $a+b i$. (Simplify your answers completely.) $i^{44}$

[Jawaban] Evaluate the following limits: 38. Evaluate [tex]$\lim _{x \rightarrow 1^{-}} \frac{|x-1|}{x-1}$[/tex]. A. 2 B. 1 C. 0 D. -1 39. Evaluate [tex]$\lim _{x \rightarrow \infty} \frac{4-x^2}{4 x^2-x-2}$[/tex]. A. -2 B. 1 C. 2 D. -[tex]$\frac{1}{4}$[/tex]. 40. Evaluate [tex]$\lim _{x \rightarrow 0} \frac{\sin ^2 x}{x}$[/tex]. A. 0 B. [tex]$\infty$[/tex] C. 1 D. -1 41. If [tex]$\lim _{x \rightarrow 0} \frac{1-\cos x}{3 x \sin x}=\frac{1}{k}$[/tex], find the value of [tex]$k$[/tex]. A. 3 B. -1 C. 6 D. -3 42. Evaluate [tex]$\lim _{x \rightarrow 0} x^2 \cos \left(\frac{1}{x}\right)$[/tex]. A. i B. [tex]$\infty$[/tex] C. 0 D. Undefined.