Questions in mathematics

Questions in mathematics

📝 Answered - $\triangle R S T \sim \triangle R Y X$ by the SSS similarity theorem. Which ratio is also equal to $\frac{R T}{R X}$ and $\frac{R S}{R Y}$ ? $\frac{X Y}{T S}$ $\frac{S Y}{R Y}$ $\frac{R X}{X T}$ $\frac{S T}{Y x}$

📝 Answered - A knitting pattern for a shawl calls for 8 stitches in the first row. Each row after that has 2 more stitches than the previous row. The explicit rule [tex]a_k=8+(k-1) 2[/tex] gives the number of stitches in the nth row. Which summation is equal to [tex]S_{20}[/tex], the number of stitches in the first 20 rows of the shawl? [tex] \begin{array}{l} \sum_{k=1}^{20}(2+6 k) \\ \sum_{k=1}^{20}(2+8 k) \end{array} [/tex] What is the first term of the arithmetic series? [tex]a_1=8[/tex] What is the 20th term of the arithmetic series? [tex]a_{20}=46[/tex] How many stitches are in the first 20 rows of the shawl?

📝 Answered - Select whether the equation has a solution or not. [tex]2 \sqrt{5 x-4}-3=-11[/tex]

📝 Answered - Hayden had $\frac{5}{8}$ of a pizza left in the fridge. He ate $\frac{1}{4}$ of the leftover pizza. How much of the pizza did he eat? A. $\frac{1}{6}$ B. $\frac{5}{32}$ C. $\frac{12}{10}$ D. $\frac{10}{32}$

📝 Answered - Solve the rational inequality and graph the solution set on a real number line. Express the solution set in interval notation. [tex]$\frac{x-9}{x+5}\ \textgreater \ 0$[/tex] Solve the inequality. What is the solution set? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is (9,-5). (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) B. The solution set is the empty set.

📝 Answered - A soccer match lasted 94 minutes (including injury time). If team A was in possession for [tex]$65 \%$[/tex] of the match, for how many minutes and seconds was team A in possession?

📝 Answered - The yearly cost in dollars, $y$, at a video game arcade based on total game tokens purchased, $x$, is $y=\frac{1}{10} x+$ 60 for a member and $y=\frac{1}{5} x$ for a nonmember. Explain how the graph of a nonmember's yearly cost will differ from the graph of a member's yearly cost.

📝 Answered - Use the drawing tool(s) to form the correct answers on the provided answer space. Giles is making tacos for dinner and bought some beef and chicken. At the store, he bought twice as much beef as chicken. The chicken costs $1.85 per pound, and the beef costs $3.70 per pound. Before sales tax, Giles spent a total of $12.95 on beef and chicken. The system of equations below represent the pounds of chicken, [tex]$x$[/tex], and pounds of beef, [tex]$y$[/tex], that Giles purchased. [tex]\begin{array}{c} y=2 x \ 1.85 x+3.7 y=12.95 \end{array}[/tex] Part A: Use the ray tool to graph the system of equations on the coordinate plane. Part B: Use the point tool to select the approximate pounds of beef Giles purchased.

📝 Answered - 1. Tell what property allows you to compute [tex]\frac{1}{3} \times (6 \times \frac{4}{3}) = (\frac{1}{3} \times 6) \times \frac{4}{3}[/tex] a) Associative property of addition b) Associative property of multiplication c) Commutative property of multiplication d) Commutative property of addition 2. [tex]42(4 + 2) = (42 \times 4) + (42 \times 2)[/tex] is an example of a) commutative property b) distributive property c) associative property d) closure property 3. Solve: [tex]3m = 5m - \frac{8}{5}[/tex] a) 4 b) 5 c) [tex]\frac{3}{5}[/tex] d) [tex]\frac{4}{5}[/tex]

📝 Answered - Tom ran 1 1/2 kilometers on Tuesday and 1 1/4 kilometers on Wednesday. How many kilometers did he run in two days? How many more kilometers did he run on Tuesday than on Wednesday?