Questions on Algebra: Inequalities, trichotomy answered by real tutors!

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Question 985861: tebogo has R420 to spend at the amusement park. it will cost her R35 to enter the park and it will cost her R25 per ride and R15 to play some games. what will the inequality be that represents the correct numbers of possible rides r and games g, that tebogo can play and ride
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Question 985936: Solve the following inequality:
2y^2-y-3>0

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Question 986180: 4k-(2k-5)
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Question 986424: Suppose sin t = 6/7
and cos t < 0. Find each of the following (exact values):

cos t =
tan t =
csc t =
sec t =
cot t =

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Question 986423: Find the exact value of the trigonometric function at the given real number.
A undefined
B − 1/2
C −1/sqrt3
D −sqrt2/2
E −sqrt3/2
F -1
G −2/sqrt3
H -sqrt2
I -sqrt3
J -2
K 0
L 1/2
M 1/sqrt3
N sqrt2/2
P sqrt3/2
Q 1
R 2/sqrt3
S sqrt2
T sqrt3
U 2


(a) sin(-5π /6) =
(b) cos(π ) =
(c) tan(-π /2) =
(d) cot(5π /3) =
(e) sec(π /4) =
(f) csc(11π /6) =

Click here to see answer by Alan3354(69443) About Me 

Question 986421: Let f (x) = 1/x + 3
and g(x) = 3x/x + 3

Find f + g, f − g, f g, f/g and their domains.
NOTE: Enter DNE in any unused blanks.
(f + g)/(x) =
Domain:
(−∞, a] ∪ [b, ∞)

(−∞, a) ∪ (a, ∞)

(−∞, ∞)

(−∞, a) ∪ (b, ∞)

(−∞, a) ∪ (a, b) ∪ (b, ∞)
a =
b =



(f − g)/(x) =
Domain:
(−∞, a) ∪ (b, ∞)

(−∞, a) ∪ (a, b) ∪ (b, ∞)

(−∞, a] ∪ [b, ∞)

(−∞, ∞)

(−∞, a) ∪ (a, ∞)
a =
b =





(fg)/(x) =
Domain:
(−∞, a) ∪ (b, ∞)

(−∞, a) ∪ (a, b) ∪ (b, ∞)

(−∞, a] ∪ [b, ∞)

(−∞, ∞)

(−∞, a) ∪ (a, ∞)
a =
b =





f/g(x) =

(Don't forget to simplify)
Domain: [Remember to find the domain before simplifying the function.]
(−∞, a) ∪ (a, b) ∪ (b, ∞)

(−∞, a] ∪ [b, ∞)

(−∞, a) ∪ (b, ∞)

(−∞, a) ∪ (a, ∞)

(−∞, ∞)
a =
b =

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Question 986774: The defference of three times a number and four is negative nineteen
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Question 986840: how to solve abosolute value a+12=33
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Question 986930: 3x-2
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Question 986959: 2x+y >orequal to 8,x+y> orequalto 12, 3x+2y a.unbounded b.infeasible c.feasible and bounded d.feasible and unbounded
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Question 987018: I2-3xI≥ 8
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Question 987018: I2-3xI≥ 8
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Question 987207: Jan's account Ballenger is $3800. Of this, $750 is for rent. Jan wants to keep a ballence of at least $500. Write and solve an inequality describing how much she can withdrawal and still leave enough for rent and a $500 ballence.

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Question 987252: three times the difference of a number and 12 is at least 105. find all possible values for the number.
Click here to see answer by macston(5194) About Me 

Question 987238: can you show me a number line for the following disjunction
x>10 or x>6

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Question 987466: x<-5 and x<5
solve the compound inequality, graph it and write it in an interval notation.
I have tried to solve it separately and come up with the same exact answer as the question but the interval notation doesn't make sense to me(-infinity sign, -5)

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Question 987503: 8-3/8k=-4
solving equations and inequalities

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Question 987504: A company produces alarm clocks. During the regular workweek, the labor cost to produce one clock is $2.00. However, if a clock produced on overtime, the labor cost to produce it is $3.00. Management has decided to spend no more than $21,000 on labor costs per week. The company must produce 10,000 clocks this week. What is the minimum number of clocks that must be produced during the workweek?
I hope you guys can help me solve a word problem! I've tried to figure out the different equations for the workweek vs. overtime and the 10,000 is the number I think that's throwing me off the most! Hope you can help! Thank you!

Click here to see answer by josmiceli(19441) About Me 

Question 987688: Can you please help me solve this?
+x%5E2%2B4x-5%3C0+
I have an example here in my book but it doesn't show if the problem have different signs. Thank you!

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Question 987725: -9/2 is less than or equal to -1/2-2y is less than or equal to 3/2
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Question 987771: Find B - A if the graph of Ax + By = 7 passes through (2,1) and is parallel to the graph of 2x - 7y = 3.
Click here to see answer by josgarithmetic(39613) About Me 

Question 988807: Solve for x in the inequality:
-1 is less than (x+2)/(x-3)

Any tips, tricks, advice for other inequality problems is greatly appreciated as well as help with this problem! Thank you in advance!

Click here to see answer by MathTherapy(10549) About Me 

Question 989642: Please help me solve this equation: 3/2(3x+5)=-24
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Question 990110: Interval notation of of x _< -5
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Question 990179: hi im trying to help my sister with her algebra and we cant seem to solve the equation properly heres the equation if you can just explain how to do it it would be greatly appreciated 3(-2-3x)=-9x-4
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Question 990338: what is -5<10-x<5
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Question 990338: what is -5<10-x<5
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Question 990264: Show that n <= 1 +sqrt(2)+sqrt(3)+...+sqrt(n) <= n(n+1)/2
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Question 991294: x < -3

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Question 991794: X less than or equal to 2 and x less than or equal to -1 on a number line
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Question 992177: A student who can afford to spend up to $2,200 sees the ad shown in the illustration. If she buys a computer, how many games can she buy?
Image is in the following link..
https://www.webassign.net/gfcolalg/1-7-82.gif

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Question 992220: Solve the nonlinear inequality. Express the solution using interval notation.
x^8 > x^6

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Question 992215: x/
x + 2 > 5

word form: X over x + 2 is less than 5?
How do i write the answer in interval notation?
I do not understand the process to solve this problem.

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Question 992216: 1 + 12/x+1 - 12/x less than or equal to 0

Solve the nonlinear inequality. Express the solution using interval notation.

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Question 992218: 20/x+1 - x/2 +1 is less than or equal to 0

Solve the nonlinear inequality. Express the solution using interval notation.

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Question 992340: 20/x+1 -( x/2) +1 is less than or equal to 0

Can someone help me with this one, please? Once I go into factoring, i lose myself.
Solve the nonlinear inequality. Express the solution using interval notation.

Click here to see answer by stanbon(75887) About Me 

Question 992343: Going to use this symbol as the absolute value symbol: #
# x + 1/
2 # ≥ 3

IN english: the absolute value of x+1 over 2 is greater than or equal to 3

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Question 992342: Determine the values of the variable for which the expression is defined as a real number. (Enter your answer using interval notation.)
square root of x^2 − 16

I squared the entire thing, so that took care of the square root. Then I factored it into (x-4) (x+4) but thats as far as I got...
help, please? :(

Click here to see answer by stanbon(75887) About Me 
Question 992342: Determine the values of the variable for which the expression is defined as a real number. (Enter your answer using interval notation.)
square root of x^2 − 16

I squared the entire thing, so that took care of the square root. Then I factored it into (x-4) (x+4) but thats as far as I got...
help, please? :(

Click here to see answer by ikleyn(52754) About Me 

Question 992341: A determined gardener has 110 ft of deer-resistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area that is enclosed to be at least 700 ft2. What range of values (in ft) is possible for the length of her garden? (Enter your answer using interval notation.)
Click here to see answer by josgarithmetic(39613) About Me 
Question 992341: A determined gardener has 110 ft of deer-resistant fence. She wants to enclose a rectangular vegetable garden in her backyard, and she wants the area that is enclosed to be at least 700 ft2. What range of values (in ft) is possible for the length of her garden? (Enter your answer using interval notation.)
Click here to see answer by solver91311(24713) About Me 

Question 992538: what is solution for complex inequality of 5 <2-3y <14
Click here to see answer by ikleyn(52754) About Me 

Question 992550: Jason earned $42 each of the last two weeks, and $58 this week. In order to maintain an average of at least $50 a week, how much must Jason earn this week?
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Question 992581: Which of the following points satisfies the linear inequality
X-3y>4
_

make sure you put the line underneath the arrow

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Question 992891: you have 12 dollars to buy 5 goldfish. Write and solve an inequality that represents the prices you can pay per fish
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205