Questions in mathematics

Questions in mathematics

📝 Answered - A security alarm requires a four-digit code. The code can use the digits 0-9 and the digits cannot be repeated. Which expression can be used to determine the probability of the alarm code beginning with a number greater than 7? [tex]$\frac{\left(2 P_1\right)\left(9 P_3\right)}{10 P_4}$[/tex] [tex]$\frac{\left(2 C_1 M C_3\right)}{{ }_{10} C_4}$[/tex] [tex]$\frac{\left(10 P_1\right)\left({ }_9 P_3\right)}{10 P_4}$[/tex] [tex]$\frac{\left(10 C_1\right)\left(C_3\right)}{{ }_{10} C_4}$[/tex]

📝 Answered - Which line is perpendicular to a line that has a slope of [tex]\frac{1}{2}[/tex]? line AB line CD line FG line HJ

📝 Answered - Given: [tex]AB =12[/tex] [tex]A C=6[/tex] Prove: C is the midpoint of [tex]\overline{ AB }[/tex]. Proof: We are given that [tex]A B=12[/tex] and [tex]A C=6[/tex]. Applying the segment addition property, we get [tex]AC + CB = AB[/tex]. Applying the substitution property, we get [tex]6+C B=12[/tex]. The subtraction property can be used to find [tex]C B=6[/tex]. The symmetric property shows that [tex]6=A C[/tex]. Since [tex]C B=6[/tex] and [tex]6=A C, A C=C B[/tex] by the [ ]. property. So, [tex]\overline{ AC } \cong \overline{ CB }[/tex] by the definition of congruent segments. Finally, C is the midpoint of [tex]\overline{ AB }[/tex] because it divides [tex]\overline{ AB }[/tex] into two congruent segments.

📝 Answered - Find the value of [tex]$c$[/tex] so that the polynomial [tex]$p(x)$[/tex] is divisible by [tex]$(x-3)$[/tex]. [tex]$p(x)=-x^3+c x^2-4 x+3$[/tex]

📝 Answered - Simplify $\frac{54 k^2-6}{3 k+1}$

📝 Answered - Which of the following describes the domain of the piecewise function [tex]g(x)=\left\{\begin{array}{lll}\frac{x^2+4 x}{x^2+2 x-8} & \text { for } & x\ \textless \ 4 \\ \log _3(x+5) & \text { for } & x \geq 4\end{array} ?\right.[/tex] A. [tex](-\infty, 2) \cup(2,4) \cup(4, \infty)[/tex] B. [tex](-\infty,-4) \cup(-4,2) \cup(2, \infty)[/tex] C. [tex](-\infty, 2) \cup(2, \infty)[/tex] D. [tex](-\infty, \infty)[/tex]

📝 Answered - Which statement best describes how to determine whether [tex]f(x)=x^2=x+8[/tex] is an even function? A. Determine whether [tex]-x^2-(-x)+8[/tex] is equivalent to [tex]x^2-x+8[/tex]. B. Determine whether [tex](-x)^2-(-x)+8[/tex] is equivalent to [tex]x^2-x+8[/tex]. C. Determine whether [tex]-x^2-(-x)+8[/tex] is equivalent to [tex]-(x^2-x+8)[/tex]. D. Determine whether [tex](-x)^2=(-x)+8[/tex] is equivalent to [tex]-(x^2-x+8)[/tex].

📝 Answered - Solve the proportion. [tex]\frac{r}{81}=\frac{1}{9}[/tex]

📝 Answered - Let v = <3, -2>. What is the approximate direction angle of v? A. 34° B. 56° C. 146° D. 326°

📝 Answered - A farmer has 200m of wire fencing from which to build a rectangular enclosure. He intends to use an existing wall for one of the sides. Find the dimensions that will result in a maximum enclosed area. Wall Length = x metres Breadth = y metres