Please show how you got the answers if possible for better understanding.

All questions are in attachments.

49. Solve the following inequalities and express the solution in interval notation. 1 2-3x - 4 51. Use f(x) = 2x + 5 and g(x) = x2 + 1 to find the following expressions: (a) 3 2 : 3 (a) (f -g)(2) ( b ) (fg) (x) (b) 13 - 2x| +5 2 12 (c) (go f)(x) 50. Solve the following equations. (a) 62x-6 = 36 (d) f-1 (2 ) (b) 4 + 2e3x+1 = 16 52 Solve Va + 18 + 2 = x (c) 5 + In(2x + 3) = 253. The age of a tree t (in years) and its corresponding height H(t) (in feet) are given in the table. 55. Combine the expressions by writing them as a single logarithm with coefficient 1, and simplify as much as possible.. Age (years) 1 2 3 4 5 6 7 8 9 10 11 12 Height (ft) 5 8.3 11.6 14.6 15.4 16.5 17.5 18.3 19.4 19.7 2 (a) - logs ( 2 + 1) +-1095(x - 1) (a) Write a model of the form H(t) using regression. Round the coefficients to the nearest hundredth. (b) 2In(x2 - 1) + 4In(x - 2) - - Iny (b Using your model in part (a), predict the age of a tree if it is 25 ft. high. Round to the nearest year. 56. Expand the expressions as a sum and/or difference without exponents. Simplify each term as much as possible. (a) log8 \\ 2z + 1 54 Use the quadratic formula x = - -6 Vb2 - 4ac 2a to solve the following: (b) log4 (.25(x + 2) 3 ) (x - 1)2 = 2x + 3 57. Solve L = 10108 7. for I58.-Solve 2$1=5+ 2 :1: 131 59. A 300 gallon tank is initially empty and water is being added at a rate of 4 gallons per minute. (a) - Write a formula for a linear function D that models the number of gallons of water in the tank after t minutes. (b)- What is the appropriate domain for D? Provide your answer in interval notation. (c)-Identify the y-intercept and interpret it. ((1) - Does the intercept involving time have any physical meaning in this problem? Explain