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Questions in mathematics

📝 Answered - Which coordinate pair represents the reflection of $(-4,6)$ across the $x$-axis? (A) $(4,-6)$ (B) $(-4,6)$ (C) $(-4,-6)$ (D) $(4,6)$

📝 Answered - Four cups of pure water are added to a 20-cup bowl of punch that is $75 \%$ juice. What percentage of the new punch is juice? \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} Original \\ (Cups) \end{tabular} & \begin{tabular}{c} Added \\ (Cups) \end{tabular} & \begin{tabular}{c} New \\ (Cups) \end{tabular} \\ \hline Amount of Juice & 15 & 0 & \\ \hline Amount of Punch & 20 & 4 & \\ \hline \end{tabular} $27 \%$ $37.5 \%$ $62.5 \%$ 75\%

📝 Answered - Which binomial is a factor of [tex]$9 x^2-64$[/tex]? A. [tex]$3 x-8$[/tex] B. [tex]$9 x-32$[/tex] C. [tex]$3 x+32$[/tex] D. [tex]$9 x+8$[/tex]

📝 Answered - -2y + 2y^2 + 2y^2 - y

📝 Answered - If [tex]$y=-7 x$[/tex] and [tex]$x=-6$[/tex], what is the value of [tex]$y$[/tex]?

📝 Answered - Find the value of the expression. [tex]3^2[(13+5)-12][/tex] [tex]3^2[(13+5)-12]=\square[/tex] (Simplify your answer.)

📝 Answered - The vet said that Eva's cat, Chuckles, needs a special diet. So, Eva feeds Chuckles dry food in the morning and [tex]$\frac{3}{4}$[/tex] of a cup of wet food in the evening. In all, Eva feeds Chuckles [tex]$1 \frac{1}{4}$[/tex] cups of food each day. Which equation can you use to find the amount of dry food [tex]$d$[/tex] Eva feeds Chuckles? [tex]$\frac{3}{4} d=1 \frac{1}{4}$[/tex] [tex]$d+\frac{3}{4}=1 \frac{1}{4}$[/tex] [tex]$d-\frac{3}{4}=1 \frac{1}{4}$[/tex] [tex]$d+1 \frac{1}{4}=\frac{3}{4}$[/tex] Solve this equation for [tex]$d$[/tex] to find the amount of dry food Eva feeds Chuckles. To write a fraction, use a slash ( / ) to separate the numerator and denominator. cups

📝 Answered - $\frac{8^3-4 \cdot 5^3}{(4-4 \cdot 15) \div 7}$

📝 Answered - Match the expressions with their equivalent simplified forms. Tiles [tex]$10 x+6$[/tex] [tex]$2 x-8$[/tex] [tex]$3 x-5$[/tex] [tex]$2 x+14$[/tex] [tex]$2 x+6$[/tex] [tex]$10 x+14$[/tex] Pairs [tex]$\begin{array}{l} (-2 x+4)+2(2 x+1) \\ 2(3 x+5)-4(x-1) \\ 2(x-7)+(8 x+20) \longrightarrow \end{array}$[/tex]

📝 Answered - Directions: For the following piecewise functions, find the value of $k$ that makes the function continuous, or state that no such value exists. 26. $f(x)=\left\{\begin{array}{cc}\frac{9 x^2-4}{3 x+2}, & \text { if } x \neq-\frac{2}{3} \\ k, & \text { if } x=\frac{2}{3}\end{array}\right.$ 27. $g(x)=\left\{\begin{array}{ll}x^2-2, & \text { if } x<3 \\ k x+4, & \text { if } x \geq 3\end{array}\right.$ 28. $h(x)=\left\{\begin{array}{ll}3 x-1, & \text { if } x<2 \\ \ln (k), & \text { if } x \geq 2\end{array}\right.$ 29. $p(x)=\left\{\begin{array}{cc}\frac{x^2-x-6}{x^2-4}, & \text { if } x \leq-2 \\ k x^2, & \text { if } x>-2\end{array}\right.$