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Questions in mathematics

[Done] A group of 2 adults and 4 children spent $38 on tickets to a museum. A group of 3 adults and 3 children spent $40.50 on tickets to the museum. Based on this information, how much is an adult ticket, and how much is a child ticket? [tex]2a + 4c = 38.00[/tex] [tex]3a + 3c = 40.50[/tex] What values of [tex]a[/tex] and [tex]c[/tex] represent the solution to the system? [tex]a = 8, c = 5.5[/tex] What does the solution (8, 5.5) mean in the context of this problem? A. The cost of 8 child tickets is $5.50. B. The cost of 8 adult tickets is $5.50. C. A child ticket costs $8, and an adult ticket costs $5.50. D. An adult ticket costs $8, and a child ticket costs $5.50.

[Done] Find the area of this triangle. Round to the nearest tenth. The triangle has a base of 12 cm, a side of 5.5 cm, and an angle of 33°.

[Done] Identify the equation that translates [tex]y=\ln (x)[/tex] five units down. [tex]y=\ln (x-5)[/tex] [tex]y=\ln (x)+5[/tex] [tex]y=\ln (x+5)[/tex] [tex]y=\ln (x)-5[/tex]

[Done] Show that: $\operatorname{cosec} 10^0-\sqrt{3} \sec 10^0=4$

[Done] Complete the working below to show that [tex]\frac{12 x^4}{9 x^2-36} \div \frac{4 x^5}{3(x-2)}[/tex] simplifies to [tex] \frac{1}{x(x+p)}[/tex] where [tex]p[/tex] is an integer. [tex]\begin{array}{l} \frac{3}{\square} \\ \frac{1}{\square} \end{array}[/tex]

[Done] A credit card bill for $856.25 was due on July 15. The next due date was August 15. The table below shows purchases and payments made during that time. | Date | Purchase or payment | Date | Purchase or payment | | :----- | :------------------ | :----- | :------------------ | | 7/19 | 115.54 | 8/6 | 126.94 | | 7/24 | 29.09 | 8/7 | 60.00 | | 7/25 | 110.66 | 8/7 | 107.65 | | 7/26 | 36.02 | 8/8 | 141.25 | | 7/26 | 53.64 | 8/8 | 51.91 | | 7/27 | 86.41 | 8/9 | 141.99 | | 7/29 | -450.00 | 8/10 | 48.14 | | 7/30 | 29.17 | 8/11 | 85.55 | | 8/4 | 73.01 | 8/13 | 144.54 | | 8/5 | 21.72 | 8/14 | 105.59 | Calculate the finance charge based on the average daily balance and an annual interest rate of 20.5%. (Round your answer to the nearest cent.)

[Done] Write the expression as an exponent with the base of 3: [tex]$81 \cdot 3^6$[/tex]

[Done] a) $y=\frac{3}{5} x-2$

[Done] What is the degree of $12 x^4-8 x+4 x^2-3$? A. 4 B. 3 C. 12 D. 8

[Done] The expression [tex]$5 x -7$[/tex] represents the time it takes a commuter to travel in the morning to work. The expression [tex]$11 x -1$[/tex] represents the time it takes a commuter to travel in evening from work. What is the total travel time? A. [tex]$16 x-6$[/tex] B. [tex]$16 x+8$[/tex] C. [tex]$16 x-8$[/tex] D. [tex]$6 x-6$[/tex]