Quiz # 6 Date: Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find all numbers not in the domain of the function. ) f(x) = x + None - 0 ) ) f(x) = x - 6 None -6 6 0 ) x - 6 ) f(x) = x + x - 4 0 -, 6, -6 4, -4 x 4) h(x) = -4x + 44-6, 0, 6 0-6, 6-6 ) 4) Find all numbers that are not in the domain of the function. Then give the domain using set notation. ) f(x) = x + 4x + 6 ) -, -; x x -, - ; x x - ; x x - none; (, ) 6 6) f(x) = x + x + 0; {x x 0} 0, -; {x x 0, -} -, -4; {x x -, -4} 4, ; {x x 4, } 6) ) f(x) = x - x + x - 49, ; x x, -, ; x x, - 49, 49 ; x x 49, - 49 ; x x ) ) f(x) = x - x + ; {x x } -, ; {x x -, } none; (, ) -; {x x -} )
9) f(x) = x - 6 4 6; {x x 6} none; (, ) 4; {x x 4} 0; {x x 0} 9) Express the rational expression in lowest terms. 0) 40m p mp mp m6p p m6 m 6 p 0) ) y + y - y + y + 6 ) y + y - - y + y - y + y + 6 y - y + 6 y - y + 4 ) x + 0x + 6x + 6 ) x + x + 6 x x + x + x + 0x + 6x + 6 ) x - y - bx + by x - y + bx - by ) - Already in lowest terms - b + b 4) ab + a - b - 6 bc - 4b + c - 4) a - c - 4 a - c + 4 b - c + 4 a + c - 4 Write the rational expression in lowest terms. 4k - ) 4-6k ) - - 6) m + n m - n m - n m + n m + n m - n m + n m + n Already in lowest terms 6)
Perform the indicated operation and express in lowest terms. (x - ) (x + 4) (x - 9) (x + ) ) (x + ) (x - ) (x + 4) (x + ) ) x + 9 x - - x - 9 x + x + 4 x - x - 9 x + ) k + k + 6 k + k + k + k k - k - ) k k - k k + k + k + k k - k - 9) p - p 9p - 9 p 9) 0p 9 9 0p 4p + 90p + 4 p 0p - 0p 9p - 9p 0) z + 6z + z + 9z + 0 z + z z + z - 0 0) z z + 9z + 0 z - z - z + z z - z ) k + kp + p 9k - kp + p 6k + kp + p 9k - 6p k + p k + p - k + 9p k - p k + 0p k - p ) Tell whether or not the rational expressions are equivalent. ) x (x + ) x(x + ), x(x - ) x - No Yes ) ) m + m -, m - No Yes ) Assume that the expressions given are the denominators of fractions. Find the least common denominator. 4) 6a - 4, a - a 6a - 4 6a(a - ) 6a - 6a - 4) ) 0xy, 90x4y, 4xy4 40 xy4 90 xy 0 xy4 x0y )
6) x + x - 0, x - 0 (x - )(x + ) (x - )(x - ) (x + )(x - ) (x + )(x + ) 6) ) q + r, q - r, q - r q(q - r) (q + r)(q - r) r(q + r) (q + r)(q - r) ) ) y + 0, y - 00, y y(y + 0)(y - 0) 0y(y + 0)(y - 0) y(y + 0)(y - 0) 0y(y + 0)(y - 0) ) Perform the indicated operation and express in lowest terms. 9) 9 r + 9 r - 6 9) r - 4 r(6 - r) 4r - r(r - 6) 4r - r(6 - r) r - 4 r(r - 6) 0) y - y + + 6 y - y - 0 (y - )(y - ) 0y - (y - )(y + )(y - ) y - 0 (y - )(y + )(y - ) 4y - 0 (y - )(y + )(y - ) 0) ) x x - 6 - x + x + 4 x + 6x + (x - 4)(x + 4)(x + ) x - 6 (x - 4)(x + 4)(x + ) x - 6x + (x - 4)(x + 4)(x + ) x - 6x + (x - 4)(x + 4) ) ) 4x + 9 0x ) 0 0x 4x + 0x (x + ) 0x 40x ) x - 4 x ) - x - 0x (x - 0) 0x - x + x 4) 9xy - xy 4) - x4y 9xy 6 - x 6 9xy - x 9xy - x y 9x6y 4
) x - + 6x + 4 ) x + (x - 6)(x + ) x + 4 6(x - 6)(x + ) x + 6(x - 6)(x + ) -x - 4 (x - 6)(x + ) 6) x - - - x 6) - x - - x + x - ) 9x - + - 9x ) - 9x - 9 9x - -9 9x - 9x - ) 9 x - - - x ) x - x - - x - - x - 9) 4 m - n + 9 n - m 9) - m - n 6 m - n m - n m - n 40) x x - 4 + x + 4 - x - 6 40) x - 6 x - 4 x + 6 x - 6 x + 6 x + 4 4) ab a - b - b a - b + 6 4) ab - b + a + b + a + 4b a + b a + 4b a - b (a - b)(a + 4b) a - b Simplify the complex fraction. x 4) x + 4 4) x(x + 4) x (x + 4) x + 4 x x(x + 4)
9 + x 4) x 4 + 4) x 6 6 6 x 44) k + k - 4 44) k - k - k - k + 4) - x + x 4) - x - x + - - x + x 46) 64p - q pq q - p 46) p + q p + q p + q pq pq p + q 4) 4 r - - 4 4 r - + 4 4) + r r - r r - r r r - r 4) - x + + x + x + - - x + 4 4) x + x x - x + 60 -(x + 4) x + x - x + 0 x - 6x + 60 x + x x + 44x + 60 6
49) m - + z- m- - z- 49) z + m z z + m m z - m z z + m z - m 0) x- x- - y- 0) y y - x y - x y y y - x y y + x ) mn - - nm- m - n ) m+n m+n mn mn Without actually solving the equation, list all possible numbers that would have to be rejected if they appeared as potential solutions. Then give the domain using set notation. ) x - - 0 x + 6 = 0 ), -6; {x x, -6} -, 6; {x x -, 6}, -6,, 0; {x x, -6,, 0} -, 6, -, -0; {x x -, 6, -, -0} ) 0x + - x = x - 0, - 0,, ; xx 0, - 0,, 0, - - 0,, -; xx - 0,, - - 0, 0, ; xx 0, - 0, ; xx - 0, ) 4) x - x - 4 + 9x - x - = x x - 4) 4,,,, 9 ; xx 4,,,, 9 4,, ; {x x 4,, } none;(-, ) -4, -, -; {x x -4, -, -} Solve the equation. ) + x = 0 x ) {4, } -, 4 {-4, } {-, 4} 6) y + - y - = y - 4 {-} {} {0} { } 6)
) - m - - m + = 0 m - 9 { } { 0 } { - } { 6 } ) ) y + y = ) {0} {-6} { } {6} 9) - x = 4 9) {} {-} - 60) x x + = -x 4x + 4 + x - x + 60) {-} - {} 6) x + x = - 0 {-6} {-} {} 6) 6) 4x - x - = x + x + 6) - 6 6) t = t -t - 4 6) {-, -4} 0, 4 {0, 6} 64) 6 x - 6 = + x + 6 {0, -} {-, } {-0, } 64) 6) -r - 69 r - = -r - r + 6 + r + r - r - { r r is a real number } 6) { r r -, r } -,, - 69, 66) x - + x = - x - x { -} { 0 } { 0, } 66)
Solve the problem. 6) The resistance, in ohms, of a -foot piece of wire is given by the function R(d) = 0.0, where d is d the diameter of the wire in inches. What is the resistance, rounded to the nearest hundredth of an ohm, if the wire has a diameter of 0.0 inches? 6.0 ohms 6. ohms 6.6 ohms 6.6 ohms 6) 6) The resistance, in ohms, of a foot piece of wire is given by the function R(d) = 0.0, where d is d the diameter of the wire in inches. What happens to the resistance of the wire as the diameter of the wire decreases? The answer cannot be determined without additional information. The resistance remains constant. The resistance decreases. The resistance increases. 6) 69) The distance of an object from a fulcrum is given by d = DW w. Find D if d = 4, w = 9, and W = 6. 69) 0. 6. 0.04 0) The formula s = a( - r 6) - r s = 6 04 and r =. gives the sum of the first six terms of a geometric series. Find a if 64 0) ) A formula for electric circuits is a = b +. If a = and b = 9, find c. c )..06.0 0.04 ) A formula for electric circuits is a = b +. If c = 9 and b =, find a. c ).60 64..6 0. Solve the formula for the specified variable. A ) P = + rt for r r = P - At r = P - ta r = P - A + t r = A - P Pt ) 4) F = 9 C + for C 4) C = 9 F - (F - ) C = 9 C = 9 (F - ) C = F - 9
) S = πrh + πr for h h = hs - r h = π(s - r) h = S πr - h = S - πr πr ) 6) A = h(b + b) for b 6) b = A - Bh h b = A - Bh h b = A + Bh h b = A - Bh Solve the problem. ) Dr. Wong can see patients in hours. At this rate, how long would it take her to see 44 patients? hours hours hours 4 hours ) ) Martha can rake the leaves in her yard in hours. Her younger brother can do the job in 6 hours. How long will it take them to do the job if they work together? ) hr hr 6 hr hr Answer the question. 9) Choose the equivalent form of the given formula for area of a regular polygon: A = nsa. 9) s = n aa S = na a a = ns A a = A ns Determine whether the equation represents direct, inverse, joint, or combined variation. 0) y = x 0) Direct Inverse Combined Joint Solve the problem. ) If m varies directly as p, and m = when p =, find m when p is 6. 4 6 49 ) ) If s varies directly as t, and s = 9 when t =, find s when t is 4. 4 96 4 ) ) If x varies inversely as v, and x = when v =, find x when v =. 9 ) 4) If f varies jointly as q and h, and f = 4 when q = and h =, find f when q = and h = 4. 0 6 4) ) If f varies jointly as q and h, and f = 96 when q = 4 and h =, find q when f = 4 and h = 6. 4 6 ) 0
6) If f varies jointly as q and h, and f = 00 when q = and h =, find h when f = 96 and q = 4. 4 6) ) If f varies jointly as q and h, and f = -96 when q = 4 and h =, find f when q = and h =. -0 - - -60 ) ) One maid can clean the house three times faster than another. Working together they can clean the entire house in hours. How long would it take the faster maid cleaning alone? ) hr hr 4 hr 4 hr 9) Frank can type a report in hours and James takes hours. How long will it take the two of them typing together? hr 4 0 hr hr 0 hr 9) 90) An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 4 hours. How long would it take the experienced accountant working alone? hr 0 hr hr 6 hr 90) 9) Maria and Charlie can deliver 60 papers in 4 hours. How long would it take them to deliver 9 papers? 6. hours 6 hours. hours.6 hours 9) 9) Sven can type 4 words per minute. How many words would he type in 4 hour (4 minutes)? 9) 60 words 4 words 0 words 9 words 9) A machine can fill 0 boxes of cereal in 0.6 hour. How many boxes of cereal can it fill per hour? 0 boxes 06 boxes 4 boxes boxes 9) 94) The weight of a liquid varies directly as its volume V. If the weight of the liquid in a cubical container cm on a side is 0 g, find the weight of the liquid in a cubical container cm on a side. g 6 g g 4 g 94) 9) The distance it takes to stop a car varies directly as the square of the speed of the car. If it takes feet for a car traveling at 40 miles per hour to stop, what distance is required for a speed of 6 miles per hour? 0.0 ft 9. ft 96.09 ft. ft 9) 96) The volume of wood in a tree varies jointly as the height of the tree and the square of the distance around the tree trunk. If the volume of wood is.4 cubic feet when the height is feet and the distance around the trunk is feet, what is the volume of wood obtained from a tree that is feet tall having a measurement of 4 feet around the trunk? 44.96 ft 49.96 ft 40.96 ft.96 ft 96)
Determine whether the equation represents direct, inverse, joint, or combined variation. 9) y = 4x Joint Direct Inverse Combined 9) 9) y = xz Joint Direct Combined Inverse 9) 99) y = x st Combined Direct Inverse Joint 99) Suppose the triangles shown are similar with angle A = angle D, angle B = angle E, and angle C = angle F. Answer the question. 00) 00) E B 4 6 A x - C D x + 4 F What is the value of x? 9 4