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

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Question 1131808: The height in feet of a projectile with an initial velocity of 96 feet per second and an initial height of 256 feet is a function of time in seconds given by
h(t) = −16t2 + 96t + 256.
(a) Find the maximum height of the projectile._______ft
(b) Find the time t when the projectile achieves its maximum height.
t =_____________sec
(c) Find the time t when the projectile has a height of 0 feet.
t =___________sec
Click here to see answer by MathLover1(20849)

Question 1131804: Find the values of a in the domain of f for which
f(a)equals the given number. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)
f(x) = 2 − 5x; f(a) = 7
Click here to see answer by MathLover1(20849)

Question 1131809: Solve the system of equations by the elimination method. (If the system is dependent, let y = c and enter a general solution in terms of c.
{3x−y=14
4x+3y=−3
(x, y) =
Click here to see answer by MathTherapy(10552)

Question 1131890: Quick Copies charges $3.00 to send a fax plus $0.50 per page.
The Copy King charges $0.80 per page with no initial fee.
Make a recommendation of when you would use Quick Copies and Copy King.
1. Define the problem. (What are you trying to figure out?)
2. What is your plan to solve the problem? Be sure to include the techniques that you will be using.
3. Make a hypothesis. (What do you think will happen?)
4. Evaluate/solve the problem. Be sure to include equations, etc. and show all of your work.
5. What is your recommendation? Be very clear with your explanation.
6. Implement your solution
Click here to see answer by joshuajz(12)

Question 1131948: My teacher gave us a homework sheet with this question: The sum of two consecutive integers is less than 55. Find the pair of integers with the greatest sum. I didn�t understand what it meant. Does it mean a +b is less than 55
Click here to see answer by Alan3354(69443)

Question 1132023: A company sells calculators for $35 each. Businesses must order a minimum of 100 calculators, and they must pay a shipping cost of $50.Which amount of money represents a reasonable sum that a business might spend to purchase calculators?
A
$750
B
$1070
C
$2990
D
$3585
Click here to see answer by Boreal(15235)

Question 1131147: A graphing calculator is recommended.
The data in the table below show the distance, in feet, a ball travels for various swing speeds, in miles per hour, of a bat.
Bat speed (mph) Distance (ft)
40 199
45 210
50 246
60 272
70 300
75 326
80 339
(a) Find the linear regression equation for these data. (Round all numerical values to three decimal places.)
y =
(b) Using the regression model, what is the expected distance a ball will travel when the bat speed is 58 miles per hour? Round to the nearest foot.__________ft

Click here to see answer by Boreal(15235)

Question 1130980: The temperature at various times on a summer day at a resort in southern California is given in the following table. The variable t is the number of minutes after 6:00 A.M., and the variable T is the temperature in degrees Fahrenheit.
t (min) T (�F)
20 62
40 61
80 67
120 76
160 81
200 79
240 84
280 87
320 84
360 85
400 78
(a) Find a quadratic model for these data. (Round all numerical values to five decimal places.)
T =
Click here to see answer by Boreal(15235)

Question 1132143: [(x + 1)/(2x + 4)] ≥ 3, x ≠ 2
Click here to see answer by MathLover1(20849)

Question 1130979: A graphing calculator is recommended.
The data in the table below show the distance, in feet, a ball travels for various swing speeds, in miles per hour, of a bat.
Bat speed (mph) Distance (ft)
40 199
45 210
50 246
60 272
70 300
75 326
80 339
(a) Find the linear regression equation for these data. (Round all numerical values to three decimal places.)
y =
(b) Using the regression model, what is the expected distance a ball will travel when the bat speed is 58 miles per hour? Round to the nearest foot.____ft

Click here to see answer by Boreal(15235)

Question 1131009: A graphing calculator is recommended.
The data in the table below show the distance, in feet, a ball travels for various swing speeds, in miles per hour, of a bat.
Bat speed (mph) Distance (ft)
40 199
45 210
50 246
60 272
70 300
75 326
80 339
(a) Find the linear regression equation for these data. (Round all numerical values to three decimal places.)
y =
(b) Using the regression model, what is the expected distance a ball will travel when the bat speed is 58 miles per hour? Round to the nearest foot.

ft

Click here to see answer by Boreal(15235)

Question 1132149: Every day, Katie looks for seashells on the beach. She has 2828 shells in her collection. Katie finds 1212 more shells each day.
Write an inequality to determine the number of days, dd, it will take Katie to collect over 100100 shells.

Click here to see answer by MathLover1(20849)

Question 1132550: Put these integers in order from greatest to least. -1 -3 7 and 10

Click here to see answer by josgarithmetic(39617)

Question 1132550: Put these integers in order from greatest to least. -1 -3 7 and 10

Click here to see answer by ikleyn(52781)

Question 1132772: -(8+x)+4-2x<8
Click here to see answer by greenestamps(13200)

Question 1132772: -(8+x)+4-2x<8
Click here to see answer by MathLover1(20849)

Question 1132789: E and F are sets of real numbers defined as follows.
E={v|v<2}
F={v|v≥7}

Click here to see answer by ikleyn(52781)

Question 1132825: find the sum of consecutive odd numbers such that the sum of the greater number and 5 times of smaller number is 92.
Click here to see answer by josgarithmetic(39617)

Question 1132973:
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Question 1133334: Last year, an orange tree produced 36 oranges. This year, it produced fewer than 10. What are the possible values for how many fewer oranges were produced from the tree this year?

Click here to see answer by MathLover1(20849)

Question 1133398: Solve the inequality and write the solution in interval notation:
3|7a+1|-5≥ 76
Click here to see answer by MathLover1(20849)

Question 1133398: Solve the inequality and write the solution in interval notation:
3|7a+1|-5≥ 76
Click here to see answer by addingup(3677)

Question 1133697: Kwame has a spare time job spraying cars and vans. Vans take 2 hours each and cars take 1 hour each.He has 14hours available per week. He has an agreement with one firm to do 2 of their vans every week. Apart from that he has no fixed work. Kwame's permission to use his back garden contains the clause that he must do atleast twice as many cars as vans.
Click here to see answer by josgarithmetic(39617)

Question 1134019:
Click here to see answer by Alan3354(69443)

Question 1134115:
Click here to see answer by greenestamps(13200)

Question 1134202: Put a positive factor back into the square root:
-2√3
Answer?
Click here to see answer by Theo(13342)

Question 1134203: For what values of the variable does the following expression make sense:
3√a
Click here to see answer by Theo(13342)

Question 1134201: Take a factor out of the square root:
48x^2 , where x≤0
Answer?

Click here to see answer by Theo(13342)

Question 1134201: Take a factor out of the square root:
48x^2 , where x≤0
Answer?

Click here to see answer by ikleyn(52781)

Question 1134201: Take a factor out of the square root:
48x^2 , where x≤0
Answer?

Click here to see answer by josgarithmetic(39617)

Question 1134252: For what values of the variable does the following expression make sense:
a. √8c
b. √−10b
Click here to see answer by Boreal(15235)

Question 1134252: For what values of the variable does the following expression make sense:
a. √8c
b. √−10b
Click here to see answer by MathLover1(20849)

Question 1134346:
Click here to see answer by Alan3354(69443)

Question 1134606:
Click here to see answer by ikleyn(52781)

Question 1134690: Write the verbal sentence as an inequality:A number n minus 8 is no more than -3.
Click here to see answer by josgarithmetic(39617)

Question 1134917: The sets I and H are given below.
I={-2,0,1,7}
H= {-1,0,4,5,6}
Find the intersection of I and H.
Find the union of I and H.
Write your answers using set notation (in roster form).
Click here to see answer by greenestamps(13200)

Question 1135110: Prove that is a > b and c > d, then a + c > b + d.
Click here to see answer by math_helper(2461)

Question 1135301: the quotient of a number and 5 is at most.
write an inequality for the sentence and then solve.
Click here to see answer by josgarithmetic(39617)

Question 1135555: Seven tenths of a number is less than 8.4. Find all possible values of the number.
Click here to see answer by josmiceli(19441)

Question 1135672: Which of the following relations is a function?
A.
(1, 1), (-1, 4), (-4, 1), (1, -5)
B.
(-4, 1), (-1, 4), (1, -5), (-1, 6)
C.
(-4, 1), (-1, -5), (1, 5), (7, 1)
D.
(-4, 4), (-1, 6), (-4, 3), (7, 2)

Click here to see answer by greenestamps(13200)

Question 1135695: (7x^3+4x^5\)
Click here to see answer by ikleyn(52781)

Question 1136177: Paula ran a 15 km race in 1 1/2 hours write an inequality to describe the average speeds s of runners who were faster than Paula graph the inequality
Click here to see answer by josmiceli(19441)

Question 1136616: A student has $500. She buys pencil at $50 each and erasers at $20 each. She gets at least 5 of each and the money spent on pencils is over $100 more that that spend on erasers. Find:
a. How many ways the money can be spent?
b. The greatest number of pencils that can be bought.
c. The greatest number of erasers that can be bought.
Click here to see answer by Edwin McCravy(20055)

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