Straighterline MAT201 PRECALCULUS MIDTERM GRADED EXAM (New Version August 2024)

Question 1 Correct 5.00 points out of 5.00 Subtract the polynomials and simplify. Select one: a. b. c. d. ( 2 7 p2 − 1 2 pq + 134 q 2 + 14) − ( 194 p2 + 4 7 pq − 154 q 2 + 11) − 5 − pq + + 25 14 p2 15 14 4 7 q 2 13 + pq − + 25 14 p2 1 14 1 7 q 2 − 5 − pq + + 3 14 p2 15 14 4 7 q 2 − 5 + pq − + 25 14 p2 1 14 1 7 q 2 Straighterline PRECALCULUS MIDTERM GRADED EXAM (New Version August 2024) We are a team of experts offering course/class attendance (including final proctored exams!!) for all Straighterline, Online ATI, HESI, NCLEX, Portage Learning, Sophia, Nursing, Business etc courses. We also write essays, discussion posts, research papers and school assignments. Should you need any of these services, Contact us via email: or : +1 (540) 753-5914. Guaranteed Passing!Question 2 Correct 5.00 points out of 5.00 Question 3 Correct 5.00 points out of 5.00 Factor completely. Select one: a. b. c. d. Solve the inequality. Write the solution set in interval notation. and Select one: a. b. c. d. (8 − x2)1/2 + x ⋅ 1 (8 − (−8x) 8 x2)−1/2 − 2(x − 2)(x + 2) (8 − x2)1/2 x2 (8 − x2)1/2 − x2 (8 − x2)1/2 2(x2 − 4) (8 − x2)1/2 20 3x 11 + 2x ≥ 2 ( − ∞, − 9 2 ) ∪ [ 230 , ∞) [ − 9 2 , 230 ) {} [ − 230 , 9 2 ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Question 5 Correct 5.00 points out of 5.00 Solve the problem. A train ride is per ride. A commuter can purchase an unlimited-ride card for per month. How many rides are required for a commuter to save money by buying the card? Select one: a. rides b. rides c. rides d. rides Solve the problem. The daily profit in dollars made by an automobile manufacturer is where is the number of cars produced per shift. Find the maximum possible daily profit. Select one: a. b. c. d. $2.85 $45 22 18 16 20 P(x) = −40x2 + 2240x − 17, 000 x $1 3, 642 $31, 360 $14, 360 $13, 211 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Question 7 Correct 5.00 points out of 5.00 Solve the equation. Select one: a. b. c. d. Simplify the expression. Select one: a. b. c. d. √−1−1−−−−p − √−2−+−−p = −1 {±2} {7, 2} {2} {7} √−−−1−4−4 √−−−−3−6 2i 2 − 2i 1 2 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Write the equation in slope-intercept form. Then, graph the line using the slope and - intercept. Select one: a. b. y −3x + 5y = −15 y = 5 x − 3 3 y = − 3 x − 3 5 8/21/24, 6:11 PM Midterm Exam: Attempt review d. y = 3 x − 3 5 y = 3 x + 3 5 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Solve the problem. The following figure represents the average hourly wage for employees of MegaMart from to . Let represent the hourly wage and let represent the year, where corresponds to the year , represents , and so on. Then the average wage can be approximated by the equation , where . Use the linear equation to approximate the average wage for the year and compare it to the actual wage of per hour. Select one: a. per hour; the calculated wage was less than the actual wage. b. per hour; the calculated wage was more than the actual wage. c. per hour; the calculated wage was less than the actual wage. d. per hour; the calculated wage was more than the actual wage. y x x = 0 1980 x = 1 1981 y = 0.17x + 3.02 0 ≤ x ≤ 25 1990 $5.05 $3.87 $1.18 $5.57 $0.52 $4.72 $0.33 $3.87 $0.12 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Evaluate as indicated. If , find and simplify . Select one: a. b. c. d. f(x) = 4x2 + 4x − 5 f(2 + x) 4x2 + 2x + 19 4x2 + 4x − 7 4x2 + 20x + 19 19 + x 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Use transformations to graph the given function. Select one: a. b. c. f(x) = −(x + 3)2 + 2 8/21/24, 6:11 PM Midterm Exam: Attempt review 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Find and identify the graph of . and Select one: a. b. c. (f + g)(x) f + g f(x) = |x| g(x) = −3 (f + g)(x) = |x − 3| (f + g)(x) = |x| − 3 (f + g)(x) = |x − 3| 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 d. Write the given equation in the form . Identify the center and radius. Select one: a. Center: b. Center: c. Center: d. Center: (f + g)(x) = |x| − 3 (x − h)2 + (y − k)2 = r2 x2 + y2 + 16x + 8y − 20 = 0 (x + 8)2 + (y + 4)2 = 100 (−8, −4); r = 10 (x + 8)2 + (y + 4)2 = 100 (8, 4); r = 10 (x + 16)2 + (y + 8)2 = 20 (16, 8); r = 20 (x + 16)2 + (y + 8)2 = 20 (−16, −8); r = 20 8/21/24, 6:11 PM Midterm Exam: Attempt review Incorrect 0.00 points out of 5.00 Solve the problem. a. Identify the power function of the form that is the parent function to the given graph. b. In order, outline the transformations that would be required on the graph of to make the graph of the given function. c. Match the function with the graph. i. ii iii p(x) = 3(x + 3)3 − 3 y = xn y = xn 8/21/24, 6:11 PM Midterm Exam: Attempt review Select one: a. a. b. Shift to the left 3 units. Stretch vertically by a factor of 3. Shift downward 3 units. c. Graph ii. b. a. b. Shift to the left units. Shrink vertically by a factor of . Shift downward units. c. Graph iv. c. a. b. Shift to the left units. Stretch vertically by a factor of . Shift downward units. c. Graph i. d. a. b. Shift to the left units. Stretch vertically by a factor of . Shift downward units. c. Graph iii. y = x3 y = x3 y = x3 y = x3 3 1 3 3 y = x3 y = x3 3 3 3 y = x3 y = x3 3 3 3 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Question 16 Correct 5.00 points out of 5.00 Write the domain and range of the function in interval notation. Select one: a. Domain: Range: b. Domain: Range: c. Domain: Range: d. Domain: Range: Write a polynomial that meets the given conditions. Answers may vary. Degree polynomial with zeros and Select one: a. b. c. d. f(x) = x2 − 45 f(x) = x2 + 10x + 6 (0, ∞) (−∞, −19] (−∞, ∞) [6, ∞) (−∞, ∞) (−∞, 6] (−∞, ∞) [−19, ∞) f(x) 2 3√5 – −3√5 – f(x) = x2 + 6√5 –x + 45 f(x) = x2 − 6√5 –x + 45 f(x) = x2 + 45 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Question 18 Correct 5.00 points out of 5.00 Question 19 Correct 5.00 points out of 5.00 Solve the problem. Determine if the lower bound theorem identifies ( -4 ) as a lower bound for the real zeros of ( f(x) ). ( f(x)=3x^3+2x^2-9x+4 ) Select one: a. No b. Yes Find all the rational zeros. ( f (x) = 4x^ 4 + 9x ^3 - 34x^ 2 - 25x - 4 ) Select one: a. ( - displaystylefrac{1}{4}, -4 ) b. ( displaystylefrac{1}{4}, 4 , pm1 ) c. ( - displaystylefrac{1}{4}, -4, 1 ) d. ( displaystylefrac{1}{4}, 4 ) Solve the problem. A power company burns coal to generate electricity. The cost ( C(x) ) (in ( $1000 )) to remove ( x% ) of the air pollutants is given by: ( C(x)=displaystylefrac{500x}{140-x} ) ( a. ) Compute the cost to remove ( 25% ) of the air pollutants. ( b. ) If the power company budgets ( $1.4 ) million for pollution control, what percentage of the air pollutants can be removed? Select one: a. ( a.,, displaystylefrac{2500}{23}b.,,135.17% ) b. ( a.,, displaystylefrac{2500000}{23}b.,,103.16% ) c. ( a.,, displaystylefrac{2500000}{23}b.,,135.17% ) d. ( a.,, displaystylefrac{2500}{23}b.,,103.16% ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Find the constant of variation ( k ). ( N ) varies jointly as ( t ) and ( p ). When ( t ) is ( 6 ) and ( p ) is ( 3 ), ( N ) is ( 36 ). Select one: a. ( k=2 ) b. ( k=72 ) c. ( k=18 ) d. ( k=648 ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Incorrect 0.00 points out of 5.00 Use the graph of ( y= bigg( dfrac{1}{3}bigg) ^x ) to graph the function. Write the domain and range in interval notation. ( f(x)=-bigg(dfrac{1}{3}bigg )^x +2 ) Select one: a. Domain: ( (- infty, infty) ) Range: ( (2, infty) ) b. Domain: ( (- infty, infty) ) Range: ( (- infty, 2) ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 c. Domain: ( (- infty, infty) ) Range: ( (- infty,-2) ) d. Domain: ( (- infty, infty) ) Range: ( (-2, infty) ) Determine whether the two functions are inverses. ( f(x)= dfrac{2}{x,+,3} ) and ( g(x)= dfrac{2,+,3x}{x} ) Select one: a. Yes b. No 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Question 24 Correct 5.00 points out of 5.00 Question 25 Correct 5.00 points out of 5.00 Provide the missing information. Given the function ( f:= lbrace{} (1,2), (2,3),(3,4) rbrace ) write the set of ordered pairs representing ( f^{-1} ). Select one: a. ( lbrace{} (2,1),(3,2),(4,3) rbrace ) b. ( lbrace{} (2,4),(1,2),(2,3) rbrace ) c. ( lbrace{} (4,3),(1,2),(3,3) rbrace ) d. ( lbrace{} (2,1),(1,2),(2,3) rbrace ) Evaluate the function at the given value of ( x ) . Round to ( 4 ) decimal places if necessary. ( hleft(xright)=displaystyleleft(frac{1}{3}right)^x; h(-3) ) Select one: a. ( 27 ) b. ( 9 ) c. ( displaystyle frac{1}{9} ) d. ( displaystylefrac{1}{27} ) Solve the problem. Bethany needs to borrow ( $8000 ). She can borrow money at ( 6.9% ) simple interest for ( 3 ,yr ) or she can borrow at ( 6.5% ) with interest compounded continuously for ( 3, yr ). Which option results in less total interest? Select one: a. ( 6.9% ) simple interest results in less total interest b. ( 6.5% ) compounded continuously results in less total interest 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Question 27 Incorrect 0.00 points out of 5.00 Question 28 Correct 5.00 points out of 5.00 Approximate ( f(x) = ln x ) for the given value of (x). Round to four decimal places. ( f(460) ) Select one: a. ( 4.6000 ) b. ( 6.6000 ) c. ( 6.1312 ) d. ( 2.6628 ) Simplify the expression without using a calculator. ( log_{1/2} bigg( displaystyle frac{1}{16} bigg) ) Select one: a. ( - displaystyle frac{1}{4} ) b. ( displaystyle frac{1}{4} ) c. (4) d. (-4) Solve the equation. ( (ln x)^2 - ln x^5 = -6 ) Select one: a. ( {, } ) b. ( {2,, 3} ) c. ( {e^2,, e^3};,, x approx 7.3891, ,,x approx 20.0855 ) d. ( {e^{-2},, e^{-3}};,, x approx 0.1353, ,,x approx 0.0498 ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Write the equation in exponential form. ( log_8 displaystyle frac{1}{512} = -3 ) Select one: a. ( 8^{-3} = displaystyle frac{1}{512} ) b. ( bigg( displaystyle frac{1}{512} bigg)^{-3} = 8 ) c. ( displaystyle frac{1}{512} = 3^{-8} ) d. ( displaystyle frac{1}{512} = -3^8 ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Sketch the angle in standard position. ( -315° ) Select one: a. b. c. 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Question 32 Correct 5.00 points out of 5.00 d. Find a positive angle and a negative angle that is coterminal to the given angle. ( -124^circ ) Select one: a. ( 236^circ , , -484^circ ) b. ( 56^circ, , -304^circ ) c. ( 484^circ, , -236^circ ) d. ( 276^circ, , -524^circ ) Evaluate the function if possible. ( displaystyle tan , , frac{pi}{2} ) Select one: a. ( Undefined ) b. ( 0 ) c. ( 1 ) d. ( -1 ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Identify the ordered pair on the unit circle corresponding to the real number ( t ) . ( t = displaystyle frac{2pi}{3} ) Select one: a. ( displaystyle left ( -frac{1}{2}, , frac{sqrt{3}}{2} right) ) b. ( displaystyle left (- frac{sqrt{2}}{2}, , frac{sqrt{2}}{2} right) ) c. ( displaystyle left (- frac {1}{2}, , -frac{sqrt{3}}{2} right) ) d. ( displaystyle left (- frac{sqrt3}{2}, , frac{1}{2} right) ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Identify the amplitude, period, phase shift, and vertical shift, and graph the function. ( displaystyle y = cos , left( -frac{pi}{4}x - frac{pi}{5}right) - 1 ) Select one: a. Amplitude: ( 1 ) Period: ( 8 ) Phase shift: ( displaystyle frac{4}{5} ) Vertical shift: ( -1 ) b. Amplitude: ( 1 ) Period: ( 8 ) Phase shift: ( displaystyle -frac{4}{5} ) Vertical shift: ( -1 ) c. Amplitude: ( 1 ) Period: ( 8 ) Phase shift: ( displaystyle -frac{4}{5} ) Vertical shift: ( 1 ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 d. Amplitude: ( 0 ) Period: ( 8 ) Phase shift: ( displaystyle -frac{4}{5} ) Vertical shift: ( -1 ) Given the stated conditions, identify the quadrant in which ( θ ) lies. ( sin , , 0 ) and ( cot , , 0 ) Select one: a. ( II ) b. ( I ) c. ( III ) d. ( IV ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Solve the problem. A video camera located at ground level follows the liftoff of a rocket. Suppose the camera is ( 1,100 m ) from the launch pad. a. Write the angle of elevation ( theta ) from the camera to the rocket as a function of the rocket's height, ( h ). b. Use a calculator to find ( theta ) to the nearest tenth of a degree when the rocket's height is ( 500 m ). Select one: a. a. ( theta = sin^{-1} bigg( displaystyle frac{h}{1,100} bigg) ) b. ( theta = 27.0^{circ} ) b. a. ( theta = tan^{-1} bigg( displaystyle frac{h}{1,100} bigg) ) b. ( theta = 24.4^{circ} ) c. a. ( theta = cot^{-1} bigg( displaystyle frac{h}{1,100} bigg) ) b. ( theta = 65.6^{circ} ) d. a. ( theta = tan^{-1} bigg( displaystyle frac{1,100}{h} bigg) ) b. ( theta = 65.6^{circ} ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Question 38 Correct 5.00 points out of 5.00 Use a calculator to approximate the function value in both radians and degrees. Round to ( 4 ) decimal places. ( arctan( -2.36) ) Select one: a. ( -0.0236 radians ) or ( -1.3522^{circ} ) b. ( 0.9924 radians ) or ( 56.8614^{circ} ) c. ( -0.5850 radians ) or ( -33.5181^{circ} ) d. ( -1.1700 radians ) or ( -67.0362^{circ} ) Use an appropriate Pythangorean identity to find the indicated value. Given ( sec t = displaystyle frac{25}{7} ) for ( displaystyle frac{3pi}{2} t 2pi ), find the value of ( tan t ). Select one: a. ( - displaystyle frac{7}{24} ) b. ( displaystyle frac{7}{24} ) c. ( - displaystyle frac{24}{7} ) d. ( displaystyle frac{24}{7} ) 8/21/24, 6:11 PM Midterm Exam: Attempt review Correct 5.00 points out of 5.00 Question 40 Correct 5.00 points out of 5.00 Use the periodic properties of the trigonometric functions to simplify the expression to a single function of ( t ). ( sin (t + 2pi) cdot sec (t + 2pi) ) Select one: a. ( tan t ) b. ( sec t ) c. ( csc t ) d. ( sin t ) Find two angles between ( 0^circ ) and ( 360^circ ) for the given condition. ( cot (theta) = -1 ) Select one: a. ( 225 ) and ( 45 ) b. ( 225 ) and ( 315 ) c. ( 135 ) and ( 45 ) d. ( 135 ) and ( 315 ) Quiz navigation Show one page at a time Finish review 26 27 38 39 40 8/21/24, 6:11 PM Midterm Exam: Attempt review 8/21/24, 6:11 PM Midterm Exam: Attempt review