University:
Felician University
Course:
MATH-160 | College Algebra
Academic year:

2024
Views:

475

Pages:

8
Author:

Clint W.

1. 2. Solve the following inequality. Solve the following inequality. 1зх+41 < s 24<-2(х-3) < 36 А. 4 х<3 в. -4 <х<·4 : А. ,/... -16,< х < -15 � \ в. -21 <х< -9 С. -21 <х<-15 {ji) 4 -4<х<- -15 <х<-9 4. -8 <х< - D. Which ofthe following graphs shows the solution set for the inequality below? 3. 12х+4/ > 2 А. в. 4. -8 -7 -6 -5 -4 -3 -2 -6 -5 -4 -3 -2 -] о @ ◄ D. ◄ -8 -6 -7 -5 -6 -4 -5 -З -4 -2 е -3 о -1 о -] 2 -2 о о -] о 3 2 3 4 6 4 о 2 3 2 3 5 4 ► 4 6 ► Тот can spend up to $40 for gasoline and а carwash at а service station. The carwash will cost $6.00, and а gasolirie costs $4.50 per gallon. The inequality_ below can Ье • solved for g, the number of gallons of gasoline Тот can buy. -"' 4.5g + 6 :о 40 Which of the following is а true statement? . . '" А. Tpm can buy ovei@allons of ga�oline. • В. Тот cari buy at most 7 gallons of gasoline С. Тот can buy 6 gallons, but not 7 gallons. .· @тоm can buy!iallons of gasoline, but not 8 gallons. 5. Which ofthe following graphs shows the solution to - 4 < О? ' the inequality _..!.,х 21 Е 1 10 А. G) - ; 6. -8 < 1 1 -12 ф -8 1 1 ) о 1 -41 о 4 IQ о1 4 8 12 4 8 12 � -12 08 -4 D. < 1 -12 -8 -4 1 1 -4 с. 1 1 1 -12 1 IS о 4 1 1 8 1 8 1 12 1 -.SXL 'f х >-g 12 ) 1� · Which graph represents the following system of inequalities? 1 2 J.°'- \__, у> -хSь\"� ys;-2x-l А. у w. у ' 11 • - - ' \ 2 1 1' - "' i , С. W D. Z -х , ,,, l/1, 1 J;, t· ,,, '""';.'11,. 1:/ '''l'i'"� У. z. 7. :::------2..;, А.· у< 2х+ 2 _ у<х 8. D. у< 2х+ 2 • у> --Х At an ice-cream parlor, ice-cream cones cost х dollars each and sundaes cost у dollars . • � � each. The total cost of 4 .cone§-aщ:l З sundae_s is mor� than $20. The total cost of 5 cones _ and I sundae is Iess than $16. This situation can Ье represented Ьу which ofthe following alities: . В. 4х + Зу < 20 , 5х+у>16 4х + Зу> 20 5х +у<, 16 9. ' С. 4х + Зу?. 20 5х+ у< 16 D. 4х +Зу< 20 5х +у< 16 Choose the system ofinequalities that best matches the graph below. 1 )(� А. в. . . . . . jl.-1 у< -1 х :S. 1 :s. у -1 x -1 x>l 1 о. Blade-Z maiшfactures roller 9lades. The production facility has fixed costs of$300 а dax and total production costs of$3,300 per day at an output ofl00 pair ofskates per qay. Which of the following equations represents the daily productюn cost for Blade-ZЪased on the number of skates manufactured? ьо \ {1 DР 3i .; (Let С(-;) represent the daily production co�t and х represent the number of airs ofskates manufactured.) _,__--"'1 ;:. l'h',L..+;Ь А. С(х) �300 )(..� В. С(х) = 30х - 300 С.!'(;х) = 30х + 30� {!__.) .. D . С( � "'-( 1 -j,.:::�(�� -ф--�-- -------'L,,-� � Cl"''-= r-) 1-'v--�+lc::> - З3СЬ ::,f!l(/DO) _+- ;� -:!;>DD ;,bD !;(::ЬD ::. VV'\ • I о D 11. Meghan is com .J?.teting her chemistry and ge�metry homJ/;?rk:=Ea�hemistry assignment ha�roЫems, and each geometry assignment has у proЫems. She must comp\ete а total of 81 proЫems. The equation below describes the relationship between the number of chemistry proЫems and the number of geometry proЫems. Sx+ Зу= 81 The ordered pai�, ffJis а solution ofthe equation. What does the solution (9, 12) represent? Each chemistry assignment contains 9 proЫems and each geometry assignment contains 12 proЫems. в. с. D. Meghan must complete З more geometry assignments than chemistry assignments. Meghan spent 9 minutes оп her chemistry homework and 12 minutes оп her geometry homework. Meghan must complete 9 more chemistry assignments than geometry assignments. А rental car company charges а base fee of $50.4 7 plus $0.50 per mile driven. Ifх represents the number ofmiles drivel!,· which ofthe following equations could Ье used to ·�,.4. findy, the total cost ofthe Ьill? А. у= $0.80х + $50.4 7 в. у = $50.47х + $0.50 с. у = $50.97х у= $0.50х + $50.47 0 Solve for х. с. х==- 18 ;, . ... -t':Г== rox �х=' -- х=-18 ' ,._ ' 14. '1 Х - 5 = (с,Х: + С\ Х. +- l О q. х - 5 ==- I S JL . +- ,о 9х - 5 = бх + 9х + 1О The steps John used to solve an equation are shown below. Solve: О.4х + 5 + О.2х = 17 Step 1: О.4х + О.2х + 5 = 17 Step 2: 0.бх+ 5 = 17 Step 3: О.бх = 12 Step 4: х = 20 Which properties justify Step 1 and Step З? А. perty Step 1: Distributive roperty ofEquality Step 3: Divisi В. Step 1: Distrib • е Property action Property ofEquality Step 3: S с. Step 1: Commurative ,Property of Equality Step 3: Division Property'ofEquality ,/ ' ' _;· '· . ' ' Step 1: Commutative Property 6f Addition Step З: Subtraction Property of Eqtiality з What is а solution to the linear equation -х-5 = 10? 4 А. 16. 15 х=4 В. 20 3 х=- С. 45 4 Х=- Which is а correct step in solving tl'ie foHowing equation for х? К 2(2-х)=-1.75 ��=1.75� @�'i - = 2(2-х)=О 1" е, ,..,в:--· 4-х = 1.75 D. х = -2.25 + 2 Ч -2 Х .::= f.1 '5 -2.х.� /,7S-t ' 17. Use elimination to iiiid the ·solution to •• the system of equations. ID .J--'-} =- io '1 :::.О ',�+у = Use syj,эtitiition to solve for х in the system of equations: 10] /5Х + 3у � 3D 1!х-Е-��3й '"' - tx - � ::;:. - 'f ::: 3 '-1 2х- Зу= 4 . · �)( - � у J lX Х=� 14,у=8 А. х= в. х = 2,у= О с. х = -4,у=4 D. 18. х = -4,у=ЗО А. х=4 В. х = 10 С. х = -4 D. х =8 зх ;: /J., )( :::. ч The equations representing income and expenses for Tom's candy store are shown in the graph below. у $120,000 $110,000 $100,000 $90,000 $80,000 $70,000 income_V • ,_ .,,.�� $60,000 $50,000 $40,000 $30,000 $20,000 $10,000 $0 L.-- ,, ' .., ..,; 'l � ¼xpen ses .v zo о х (D < n Income: 20,ОООх - Зу = О Expenses: 1 О,ОООх - Зу+ 90,000 = О . Let х represent the month and у represent the amount in do llars. In which month were the store's expenses greater than its income? . А.' ,·November • • в. ·september - �. - ---.A-ug_u_s)_t_ � ''• D. October l'б о 20. . ' Written Portion: ! \,, .. х Reid and Sharon work in two different clothing stores. Reid' s store sells shirts for $ 14 each and pants for $39 each. Sharon' s store sells shirts for $12 each and � for $44 each. У ' · \ ' ' One day, Reid sold $145 worth ofshirts and pants, and Sharon sold the same number of shirtiiand pants, but her sales were worth $156. When х is the' шimber of shir!s sold and у is the number ofpants sold, the situation can Ье modeled Ьу а system of Iiiiear • 1 equations. �· ', А. Write the two equations that form the system of equations which models the information above. equations: в. => Use the equations found in Part А to determine how many shirts and pants Reid · sold. J _/� fiчx. -/(.�Х. -ч"'�У 'i:,-('lt40 -1--3°1.у= IЧ.5 Jч·!J 'J..X +- 'fЧ у ==- / 5 <с] J (,/3 Х -1- ь Но� ;� J.-I SЧ JЧ%''/ :�чч,ч. "/ -:::.. 3 -J. shirts: Х, -;::. � pants:Y= 3 -;.)( у =-:J. С. . Оп another day, Reid and Sharon each sold 5 shirts and 2 pants. Who sold the greatest dollar amount of merchandi�e? R�J /Ч Х. +- ��V / '-t3' �tOV' -r ччу /):�. ;Ч� ' ' ,. 1,