Questions in mathematics

Questions in mathematics

[Done] What is the value of x if: \[ x + 4y = 7 \] and \[ x - 4y = 8? \]

[Done] Use double angle formulas to find the exact values of \(\sin(2x)\), \(\cos(2x)\), and \(\tan(2x)\). Given: \(\sin(x) = \frac{12}{13}\), \(0 < x < \frac{\pi}{2}\)

[Done] If the area of the base of a rectangular solid is tripled, what is the percent increase in its volume?

[Done] What is the sales tax rate on a $750 computer at J & M Computers if the sales tax is $48.75?

[Done] What fraction of 130 is 80?

[Done] What is the experimental probability of rolling an odd number on a standard number cube? For 50 rolls of the number cube, predict the number of rolls that will result in an odd number.

[Done] What shape has only one pair of parallel lines?

[Done] Calculate the surface area of a cube with a side measurement of 3.2 inches.

[Done] The employees from maintenance go for coffee together every day at 9 AM. On Monday, Hector paid $5.45 for three cartons of milk, four cups of coffee, and seven doughnuts. On Tuesday, Guillermo paid $5.30 for four milks, two coffees, and eight doughnuts. On Wednesday, Anna paid $5.15 for two milks, five coffees, and six doughnuts. On Thursday, Alphonse had to pay for five milks, two coffees, and nine doughnuts. How much change did he get back from his $10 bill?

[Done] Find \( f(a) \), \( f(a+h) \), and the difference quotient \(\frac{f(a+h) - f(a)}{h}\), where \( h \neq 0 \). Given \( f(x) = \frac{2x}{x-1} \).