Questions in mathematics

Questions in mathematics

📝 Answered - What is the simplified value of the exponential expression $16^{\frac{1}{4}}$? A. $\frac{1}{2}$ B. $\frac{1}{4}$ C. 2 D. 4

📝 Answered - How many meters are in 1 centimeter? [tex]1 cm=[?] m[/tex]

📝 Answered - Given [tex]$\lim _{x \rightarrow 0} f(x)=4$[/tex]. What is [tex]$\lim _{x \rightarrow 0} \frac{1}{4}[f(x)]^4$[/tex]? A. 0 B. 4 C. 64 D. 128

📝 Answered - Let $f(x)=\left\{\begin{array}{lll}7 x-6 & \text { if } & x<8 \\ \frac{3}{x+9} & \text { if } & x \geq 8\end{array}\right.$ Show that $f(x)$ has a jump discontinuity at $x=8$ by calculating the limits from the left and right at $x=8$. $\lim _{x \rightarrow 8^{-}} f(x)=$ $\square$ $\lim _{x \rightarrow 8^{+}} f(x)=$ $\square$

📝 Answered - Simplify $\sqrt[4]{16} : 2^3$

📝 Answered - $25 \overline{)178}$

📝 Answered - Select the correct answer. Given: RSTU is a rectangle with vertices $R (0,0), S (0, a ), T ( a , a )$, and $U ( a , 0)$, where $a \neq 0$. Prove: RSTU is a square. | Statements | Reasons | | ----------- | ----------- | | 1. RSTU is a rectangle with vertices R(0,0), S(0, a), T(a, a), and U(a, 0). | 1. given | | 2. $R S= a$ units | 2. ? | | 3. $S T= a$ units | 3. distance formula | | 4. $\overline{ RS } \cong \overline{ ST }$ | 4. ? | | 5. RSTU is a square. | 5. ? | What is the correct order of reasons that complete the proof? A. If two consecutive sides of a rectangle are congruent, then it's a square; distance formula; definition of congruence B. distance formula; definition of congruence; if two consecutive sides of a rectangle are congruent, then it's a square C. distance formula; if two consecutive sides of a rectangle are congruent, then ir's a square; definition of congruence D. definition of congruence; distance formula; if two consecutive sides of a rectangle are congruent, then it's a square

📝 Answered - Which graph is the graph of this function? [tex]f(x)=\left\{\begin{array}{ll}5 & \text { if }-3 < x < -2 \\-\frac{3}{2} & \text { if }-2 \leq x < 3 \\ \frac{1}{2} & \text { if } 3 \leq x \leq 4\end{array}\right.[/tex] A. graph A B. graph B C. graph C D. graph D

📝 Answered - Given the function [tex]$f(x)=-2(x+5)^2+6$[/tex]: a) Determine the equation of the inverse of [tex]$f(x)$[/tex]. Note: do not use the quadratic formula. b) Is the inverse of [tex]$f(x)$[/tex] a function? If not, restrict the domain of [tex]$f(x)$[/tex] such that its inverse is a function. Include all possibilities.

📝 Answered - 9. $AB$ is parallel to $EC$ and $AB=(1+3 \sqrt{5}) cm$. $E$ is a point on $AD$ such that $AE:ED=\sqrt{5}:3$. Find (a) $\frac{EC}{AB}$ in the form of $p+q \sqrt{5}$, where $p$ and $q$ are rational numbers.