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

Tutors Answer Your Questions about Inequalities (FREE)

Question 1130868: Use the method of completing the square to find the standard form of the quadratic function.
f(x) = x^2 − 10x + 4
y =___
State the vertex and axis of symmetry of the graph of the function.
axis of symmetry x=____
vertex (x, y) =

Click here to see answer by josgarithmetic(39613)

Question 1130982: The exponential function
A(t) = 200e−0.014t
gives the amount of medication, in milligrams, in a patient's bloodstream t minutes after the medication has been injected into the patient's bloodstream.
(a) Find the amount of medication, to the nearest milligram, in the patient's bloodstream after 35 minutes._______mg
(b) Use a graphing utility to determine how long it will take, to the nearest minute, for the amount of medication in the patient's bloodstream to reach 50 milligrams._________min
Click here to see answer by ankor@dixie-net.com(22740)

Question 1130981: Solve the system of equations. (If the system is dependent, enter a general solution in terms of c. If there is no solution
{x+ 2y− 4z =21
4x− y+ z=16
2x+ 4y− 2z = 18
(x, y, z) =
Click here to see answer by Edwin McCravy(20054)

Question 1130984: The population P of a city grows exponentially according to the function
P(t) = 5500(1.1)^t, 0 ≤ t ≤ 8
where t is measured in years.
(a) Find the population at time
t = 0
and at time
t = 4.
P(0) =
P(4) =
(b) When, to the nearest year, will the population reach 11,000? ________yr
Click here to see answer by MathLover1(20849)

Question 1130985: During surgery, a patient's circulatory system requires at least 50 milligrams of an anesthetic. The amount of anesthetic present t hours after 70 milligrams of anesthetic is administered is given by the following.
T(t) = 70(0.727)t
(a) How much, to the nearest milligram, of the anesthetic is present in the patient's circulatory system 20 minutes after the anesthetic is administered?_____mg
b) How long, to the nearest minute, can the operation last if the patient does not receive additional anesthetic?_____min
Click here to see answer by josgarithmetic(39613)

Question 1131011: Solve the systems of equations by using the substitution method. (If the system is dependent, enter a general solution in terms of c
{6x+ 7y = −9
2x+ 5y =5
(x, y) =
Click here to see answer by MathLover1(20849)

Question 1131010: Solve the system of equations by the substitution method. (If the system is dependent, let y = c and enter a general solution in terms of c
{6x + 5y= 2
x − 3y= 8
(x, y) =

Click here to see answer by MathLover1(20849)

Question 1130983: A cup of coffee is heated to 180�F and placed in a room that maintains a temperature of 60�F. The temperature of the coffee after t minutes is given by
T(t) = 60 + 115e−0.042t.
(a) Find the temperature, to the nearest degree, of the coffee 20 minutes after it is placed in the room._________�F
(b) Determine when, to the nearest tenth of a minute, the temperature of the coffee will reach 145�F.______________min
Click here to see answer by ankor@dixie-net.com(22740)

Question 1131148: The exponential function
A(t) = 200e−0.014t
gives the amount of medication, in milligrams, in a patient's bloodstream t minutes after the medication has been injected into the patient's bloodstream.
(a) Find the amount of medication, to the nearest milligram, in the patient's bloodstream after 35 minutes._____mg
Click here to see answer by MathLover1(20849)

Question 1131149: During surgery, a patient's circulatory system requires at least 50 milligrams of an anesthetic. The amount of anesthetic present t hours after 70 milligrams of anesthetic is administered is given by the following.
T(t) = 70(0.727)t
(a) How much, to the nearest milligram, of the anesthetic is present in the patient's circulatory system 20 minutes after the anesthetic is administered_______mg
b) How long, to the nearest minute, can the operation last if the patient does not receive additional anesthetic?_______min
Click here to see answer by MathLover1(20849)

Question 1131249: The ninth grade class at Pi High is having a fundraiser. They need to raise at least $1500 . They are selling magazines for $7 each. How many subscriptions does that class need to sell to meet their fundraising goals
Click here to see answer by ikleyn(52754)

Question 1131361: Use the method of completing the square to find the standard form of the quadratic function.
f(x) = x^2 − 8x + 2
y =
State the vertex and axis of symmetry of the graph of the function.
axis of symmetry
x =
axis of symmetry
x =

vertex (x, y) =

Click here to see answer by MathLover1(20849)

Question 1131360: f(x) = −x^2 + 7x + 8
x =
Find the x-intercepts of the graph of f.
(x, y) = ____________(smaller x-value)
(x, y) = ______________(larger x-value)

Click here to see answer by josgarithmetic(39613)

Question 1131359: Find the maximum or minimum value of the function.
f(x) = 3x^2 − 37
State whether this value is a maximum or a minimum
Click here to see answer by MathLover1(20849)

Question 1131358: 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) = -16t^2 + 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 ikleyn(52754)

Question 1131362: A piece of pottery is removed from a kiln and allowed to cool in a controlled environment. The temperature (in degrees Fahrenheit) of the pottery after it is removed from the kiln for various times (in minutes) is shown in the following table.
Time (min) Temperature (�F)
15 2000
20 1950
30 1850
60 1550
(a) Find a linear model for the temperature of the pottery after t minutes.
T(t) =__________?
(b) Explain the meaning of the slope of this line in the context of the problem.
The value of the slope means that the temperature is decreasing at a rate of
_________�F per minute.?
(c) Assuming the temperature continues to decrease at the same rate, what will be the temperature of the pottery in 3 hours?_______�F?
Click here to see answer by Boreal(15235)

Question 1131516: 5-2x/-3 -4<-x
Click here to see answer by greenestamps(13195)

Question 1131539: Use interval notation to express the solution set of the inequality.
|2x − 5| ≥ 1
Click here to see answer by ikleyn(52754)

Question 1131536: Simplify and write the complex number in standard form.
(9 + 6i)(4 − 6i)
Click here to see answer by ikleyn(52754)

Question 1131535: Solve by using the strategies for solving application problems.
A triangle has a perimeter of 105 centimeters. Each of the two longer sides of the triangle is three times as long as the shortest side. Find the length of each side of the triangle.
shortest side___cm
longer side____cm
longer side___cm
Click here to see answer by ankor@dixie-net.com(22740)

Question 1131537: Solve the rational equation. (Enter your answers as a comma-separated list
5/x − 1+7/x+7=6/x-1
x=___
Click here to see answer by MathLover1(20849)

Question 1131537: Solve the rational equation. (Enter your answers as a comma-separated list
5/x − 1+7/x+7=6/x-1
x=___
Click here to see answer by greenestamps(13195)

Question 1131538: Use the properties of inequalities to solve the inequality. Write the solution set using set-builder notation.
−3(x + 2) ≤ 5x + 7
{x| }

Click here to see answer by jim_thompson5910(35256)

Question 1131603: Write the equation in slope-intercept form.
2x − 5y = −15

Check the graph by finding the x- and y- intercepts.
x-intercept (x, y) =
y-intercept (x, y) =
Click here to see answer by MathLover1(20849)

Question 1131604: Find the equation of the line satisfying the given conditions. Write the equation in the form
y = mx + b.
Through (−5, 1), slope −4
Click here to see answer by MathLover1(20849)

Question 1131601: Find the values of a in the domain of f for which
f(a) equals the given number.
f(x) = 2 − 5x; f(a) = 7
a =

Click here to see answer by josgarithmetic(39613)

Question 1131602: Find the zeros of f.
f(x) = 10 + 5x
Click here to see answer by MathLover1(20849)

Question 1131739: 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 ikleyn(52754)

Question 1131737: A bus was purchased for $90,000. Assuming that the bus depreciates at a rate of $5,000 per year (straight-line depreciation) for the first 10 years, write the value v of the bus as a function of the time t (measured in years) for
0 ≤ t ≤ 10.

v(t) =______, 0 ≤ t ≤ 10
Click here to see answer by josgarithmetic(39613)

Question 1131735: Given
g(x) = 3x^2 + 10,
find the following.
(a) g(3) =_____
(b) g(−1) =____
(c) g(0) =____
(d) g 1/2=____
(e) g(c)= _____
(f) g(c + 5)=____
Click here to see answer by josgarithmetic(39613)

Question 1131738: A piece of pottery is removed from a kiln and allowed to cool in a controlled environment. The temperature (in degrees Fahrenheit) of the pottery after it is removed from the kiln for various times (in minutes) is shown in the following table.
Time (min) Temperature (�F)
15 2000
20 1950
30 1850
60 1550
(a) Find a linear model for the temperature of the pottery after t minutes.
T(t) =_______
(b) Explain the meaning of the slope of this line in the context of the problem.
The value of the slope means that the temperature is decreasing at a rate of______�F per minute.
(c) Assuming the temperature continues to decrease at the same rate, what will be the temperature of the pottery in 3 hours?____________�F
Click here to see answer by josgarithmetic(39613)

Question 1131745: A number decreased by 9 is at most-5
Click here to see answer by MathLover1(20849)

Question 1131736: 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.
a =____
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 MathLover1(20849)

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 Boreal(15235)

Question 1131806: A piece of pottery is removed from a kiln and allowed to cool in a controlled environment. The temperature (in degrees Fahrenheit) of the pottery after it is removed from the kiln for various times (in minutes) is shown in the following table.
Time (min) Temperature (�F)
15 2000
20 1950
30 1850
60 1550
(c) Assuming the temperature continues to decrease at the same rate, what will be the temperature of the pottery in 3 hours?______�F
Click here to see answer by Boreal(15235)

Question 1131805: A bus was purchased for $90,000. Assuming that the bus depreciates at a rate of $5,000 per year (straight-line depreciation) for the first 10 years, write the value v of the bus as a function of the time t (measured in years) for
0 ≤ t ≤ 10.
v(t) =____, 0 ≤ t ≤ 10
Click here to see answer by Boreal(15235)

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