Question

MA-119 Review for Final Exam: Fall 2019 Simplify completely and express in terms of positive exponents 2. Find the slope interest form of the equation of the line that is perpendicular toy passes through the point. 51 ) 3. Find the slope-intercept form of the equation of the line through the points (-2) and (2 4. Solve for x and check the solution 3x+2 -1 -6 5. Factor completely: a) 12 -10-1815 b)x+ 5x-16x - 30 Based on the graph on the right a) For what values of xis y positive Express your answer in interval notation b) Find the domain of the function c) Find the range of the function d) Determine the value of a e) Determine the coordinates of the neces 1) Determine the coordinates of the intercept 8) For what values of x is 0-39 7. Solve for x and express your answer in interval notation, se builder notation, and graphi 4-55x+2) 8. Factor completely 'y-Sy 9. Solve for x and check State the restrictions on the variable s 10. Find the domain of f(x) - - 4 - 2x Express your answer in interval and set builder notation 11. Calculate using radicals: (-27) 12. Assuming that x and y are positive, express in radical form and simplify: (-8x*y 13. Solve and check: 9 - 2x + 4 = 9 14. Simplify and express in a+bi form: (3 47) 15. Solve using the Square Root Property and express the solution in a +bi form: (x-7)= -16 16. A painting measuring 12 inches by 8 inches is surrounded by a frame of uniform width Ir the combined area of the painting and the frame is 192 square inches, determine the width of the frame. 17. The sum of a positive number and twice its square is 11.88. Find the number.

Answer 1

(2) 44-2x+7=0 (2,-5) solve for y in order to pind the slope Of the line in the earuation given 44-2x +7 =0 4y=2x-7 4y m= slope Therefore the slope is and the Slo pe of the perpendicalao line is the Flipped and negative of this : -a → -2

use the point slope for to obtain the eayuation for the perpendicalar lin y-yı = m Ca -x1) y--5 = -2 Cx-2) C2)-5) %3D %3D m:-2 y +5 -2x+4-5 %3D (3) (-2,4) (2,6). The slope-iotercept forM OF the eqvuation cohere m is the slope of the line and b is the y-intercept. the line is4= Mx+6, y2-Y1 6-4 %3D 2. 2+2 using the point (-2,4) %3D 4= )x-2+b. 4 =-1 +b b=5

y 3 ()x+5 on the ofther hand iF Tuse the point (2,6) 6 )x2 +b 6 = 1+6 b = 6-1 %3D %3D %3D samef both are Sar X +5 (4) 13x +21+1 = 6 %3D 13x+2/+1= 6 %3D { l2/= +2} 3x +2 +1 =6 30 +3 = 6 3C = 6-3 %3D

18x +2/+ 6 -(3x+2) += 6 |x/ = -x -3x-2+1 = 6 -3x- = 6 -32 6+ (S@) 12xy-1oy-18x +15 12xy-10y and -18x +15 pall out from each binomial separately Ry (6x -5) taking zy = -3(6x-5) 12xy-10y %3D common 18x +15 %3D taking -3 common desined factorization 12xy-10y-18x + IS = (2y-3) C6x-5) %3D (6) x°+ 5x -16x-80 x3+5x° and - 16x - 80 -1600-8O Pull out from each group separately x° (x+5) -16 (x+5) ( taking x² common Ctaking -16 comroom °+52²-166 - 80 = (x +5)· Cx²-16) Cx +5). (x²-16

4oc -5< 3(x+2) 4X-5< 3x +6 4x-3x <6+5 set builder form: {x/ xER; -0Ln< ||} (8) x°y - 3y x°y - sy = y (x³- 8) Try to factor as a difference of cubes. 3-8 2-63 = a-b) Ca?+abt b?) 23= 8 %3D . x3-8 = x3_29 2-23 = (∞-2)Coc*+2 + 4) *x°y-8y = g Cx3-8) yCx3-8) = y Cc-2). Coc@+ 20c+4) %3D %3D

2/3 (-27) %3D 27=3 %3D 3* = 9 (14) 6+4i) a binomial , rewoite the TO Sayuare pooblem as the binomial oultipled by the binoroial. C3+4i) (3+4i) - 6 9+12i+12i+l16 {i* --1} 9+24i-16 7+241