Self- assessment (Intermediate Algebra) If ou can work these problems using a scientific calculator, ou should have sufficient knowledge to demonstrate master of Intermediate Algebra and to succeed in a subsequent course. For the compound inequalit, give the solution set in both interval and graph forms. 1) 9-6 < 3 or -2-6 1) Graph the solution. 2) 3-2 -6 and - 1 < 0 2) Solve the given inequalit. Write the solution set in interval notation. 3) 8k + 1-1 3) 4) 2-1 - 8 < -12 4) ) k - 6-1 < 7 ) Solve the equation. 6) + 4 = - 6) Solve the sstem of equations. 7) 4 + 2 + z = -12 2-4 - z = - 3 + + 4z = -23 7) Solve the problem with three unknowns. 8) A manufacturer makes three models of ceiling fans, models A, B, and C. Production restrictions require it to make 20 more model-c fans than the total of the other models and 3 times as man model-b fans as model-a fans. The manufacturer must produce 740 fans per da. How man model-b fans will be made each da? 8) Solve the formula for the specified variable. 9) 1 a + 1 b = c for b 9) 1
Solve the sstem of equations. ) 2 + 4 + 4z = 60 + 2 + 2z = - + + z = -6 ) Solve the variation problem. 11) The resistance of a wire varies directl as the length of the wire and inversel as the square of the diameter of the wire. A 20 foot length of wire with a diameter of 0.1 inch has a resistance of 3 ohms. What would the resistance be for a 36 foot length, with diameter 0.01 inch, of the same kind of wire? 11) Decide whether the relation is a function, and give the domain and range. 12) 12) - - - - Determine whether the relation defines as a function of. Give the domain. 13) = -8 + 19 13) 14) = 3-2 14) Solve the problem. 1) Find f( 1 4 ) if f() = 32-2 - 3. 1) For the given pair of functions, find the indicated value or epression. 16) Given f() = 7 + 8 and g() = - 6, find (f - g)(-4). 16) Find (f g)() for the given functions f() and g(). 17) f() = 8 + 6 and g() = 2-17) Evaluate the composition of functions. 18) Let f() = 2 + 2 and g() = 3 + 6. Find (g f)(). 18) Find the center and radius of the circle. 19) 2 + 2 + 12-16 + 91 = 0 19) 2
Perform the indicated operation and epress in lowest terms. 20) 9s 2 + 6st + t 2 2s 2-9st - t 2 s2-26st + t 2 t 2 + 2st - 3s 2 1s2 + 2st - t 2 2s 2 + 3st + t 2 20) Epress the rational epression in lowest terms. ab + 4a - 3b - 12 21) bc - b + 4c - 20 21) Perform the indicated operation and epress in lowest terms. 2ab 22) a 2 - b 2 - b a - b + 6 2 22) Simplif the comple fraction. 23) 4 3 r - 1-4 4 3 r - 1 + 4 23) Solve the problem. 24) A jet plane traveling at a constant speed goes 1200 miles with the wind, then turns around and travels for 00 miles against the wind. If the speed of the wind is 0 mph and the total flight took 4 hours, find the speed of the plane. 24) Graph the given function as a solid line or curve and its inverse as a dashed line or curve on the same set of aes. 2) f() = + 2) - - - - Find the root if it is a real number. 26) 4 81 26 26) Evaluate the eponential. 27) - 27-4/3 64 27) 3
Use the rules of eponents to simplif the epression. Write the answer with positive eponents. Assume that all variables represent positive real numbers. t 28) -7/6 3 b -6/7 (t -1/2 b 1/2 ) -4 28) Simplif. Assume all variables represent positive real numbers. Give the answer in radical form. 29) 6 r r 2 29) Simplif. Assume that all variables represent positive real numbers. 30) 24 7-6 7 + 49 30) Perform the indicated operations and simplif. Assume that all variables represent positive real numbers. 31) 6 48 2-3 27 2-3 2 31) Simplif. Assume that all variables represent positive real numbers. 32) - 3 6 32) Rationalize the denominator. Assume that all variables represent positive real numbers and that the denominator is not zero. 33) - 2 + 3 33) Solve. 34) + 6 + 2 - = 4 34) Write the quotient in the form a + bi. 3) 6 + 2i 9-3i 3) Multipl or divide as indicated. 36) -36-64 36) Solve 37) (9t - 9) 2 = - 37) Solve the equation b completing the square. 38) 7 2 + 3-4 = 0 38) Use the quadratic formula to solve the given equation. 39) 3( - 3) = 39) 4
Solve the equation. 40) (m - 3) 2/3 + 3(m - 3) 1/3 - = 0 40) 41) 2 + 3z - 1 = -2 (3z - 1) 2 41) Solve the problem. Round to the nearest tenth, if necessar. 42) Ron takes two hr more time than Paul to mow the lawn. Working together the can mow the lawn in hr. How long does it take each of them working alone? 42) Solve the problem. Round answer to the nearest tenth, if necessar. 43) A to rocket is shot verticall upward from the ground. Its distance in feet from the ground in t seconds is given b s t = -16t 2 + 142t. At what times will the ball be 222 ft from the ground? 43) Graph. 44) f() = 3( - 2) 2 + 44) -1 - - 1 - - Find the verte of the given parabola. 4) f() = -4 2 + 8-9 4) Find the ais, domain, and range of the parabola. 46) = - 1 4 2 + 2 + 3 46) Approimate to the nearest thousandth. Use the change-of-base rule. 47) log 6.6 4.1 47) Solve the problem. 48) Find the amount of mone in an account after ears if $300 is deposited at 6% annual interest compounded monthl. 48)
49) A projectile is thrown upward so that its distance (in feet) above the ground after t seconds is h(t) = -t 2 + 420t. What is its maimum height? 49) Graph the eponential function. 0) = 3 0) 6 Solve the problem. 1) How long will it take a sample of radioactive substance to deca to half of its original amount, if it decas according to the function A(t) = 40e -0.13t, where t is the time in ears? Round to the nearest hundredth ear. 1) 2) 4 ( - 3) = 1 26 2) Solve the equation. 3) 6 3 = 8 + 1 (Round to the nearest thousandth.) 3) Solve the given equation. Give an eact solution. 4) log (2 + ) - log ( - 4 ) = log 3 4) ) log 2 ( + 7 ) = log 2 ( + 4 ) ) Graph the given logarithmic function. 6) = log 6) 6 6
Answer Ke Testname: SELF-ASSESSMENT 1) (-, 1) [3, ) 2) -7-6 - -4-3 -2-1 0 1 2 3 4 6 7 3) -, - 7 8 8, 4) ) - 2, 14 6) 1 1, 9 7) {(-3, 2, -4)} 8) 270 9) b = a ac - 1 ) 11) 40 ohms 12) Not a function; domain: (-, -1] ; range: (-, ) 13) Function; domain: (-, -19) (-19, ) 2 14) Function; domain: 3, 1) - 3 16 16) - 17) 8 2-34 18) 87 19) (-6, 8); r = 3 20) t + s t - s 21) a - 3 c - 22) 3a + 4b a + b 7
Answer Ke Testname: SELF-ASSESSMENT 23) 2-3 r 3 r 24) 0 mph 2) - - - - 26) 3 4 27) 26 81 28) b4/7 t 3/2 29) 30 r 17 30) 2 7 31) 14 3 32) - 3 6 2 33) 2-3 - 2 + 3 2-3 34) {-2} 8 3) 1 + 2 i 36) -48 37) 38) 39) 9 + i, 9 - i 9 9 4 7, -1 9 + 201, 9-201 6 6 40) -122, 11 8
Answer Ke Testname: SELF-ASSESSMENT 41) - 1 3, 1 6 42) Paul: 9.1 hr; Ron: 11.1 hr 43) 2 and 6.8 sec 44) - - - - 4) (1, -) 46) ais: = 4 domain: (-, 7] range: (-, ) 47) 0.748 48) $6367.89 49) 44 ft 0) 6 1) 4.3 r 2) 3 3) {0.631} 4) 7 ) 9
Answer Ke Testname: SELF-ASSESSMENT 6) 6