Questions on Algebra: Equations answered by real tutors!

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Question 1200140: Find the range of m for which the line y = 2x + 1 intersects the curve y = x^2+ 6x + m.
Click here to see answer by math_tutor2020(3816)

Question 1200146: Evaluate using limit laws:
Limit (as x approaches negative infinity) (x/sqrt(x^2-1))
Limit (as x approaches positive infinity) (x/sqrt(x^2-1))
Click here to see answer by math_tutor2020(3816)

Question 1200186: The equation of a curve xy = 12 and the equation of a line L is 2x + y = k, where k is
a constant.
i) In the case where k = 11, find the coordinates of the points of intersction of L
and the curve.
ii) Find the set of values of & for which I does not intersect the curve.
Click here to see answer by math_tutor2020(3816)

Question 1200218: How do you solve:
[(3d^2 - 9d + 6) / (2d^2 - 10d + 12)][(6-2d) / (3-3d)]
Click here to see answer by Alan3354(69443)

Question 1200291: Find the area below f(x)= -x^2+ 4x + 3 and above g(x) = -x^3 + 7x^2 - 10x + 5 over the interval 1 ≤ x ≤ 2.
Click here to see answer by htmentor(1343)

Question 1200313: The one-to-one functions g and h are defined as follows.
g={(-8,-4), (-2,-7), (3,7), (7,3)}
h(x)=-x+13/5
Find the following.
g^-1(7)
h^-1(7)
(h*h^-1(3)
Click here to see answer by ikleyn(52776)

Question 1200312: Assume that f(x) is continuous everywhere and
lim (as x approaches to 4) (f(x)+2)/(x-4) = 11
What is the equation of the tangent line to y=f(x) and at what point (x,y) does it occur?
Click here to see answer by Edwin McCravy(20054)

Question 1200440: 5 less than the square of a number.

Click here to see answer by ikleyn(52776)

Question 1200438: Harry invested $4,000.00 in two investments: one investment was a CD that paid 3.4% annual
interest, and the other investment was a bond that paid 2.5% annual interest. If he received a check in
the mail at the end of the year for $114.40 for both investments, how much did he invest in the CD?
Click here to see answer by josgarithmetic(39616)

Question 1200496: Find d^2y/dx^2 for y=csc(x)
Click here to see answer by Alan3354(69443)

Question 1200494: Consider the functions f(x) and g(x), for which f(0)=6, g(0)=4, f'(0)=12 and g'(0)=-8. Find h'(0) for the function h(x) = f(x)/g(x).
Click here to see answer by ikleyn(52776)

Question 1200500: Factor
Click here to see answer by Theo(13342)

Question 1200500: Factor
Click here to see answer by ikleyn(52776)

Question 1200549: At the circus, two adult tickets and five child tickets cost $48, and five adult tickets and three child tickets cost $63. Which system of linear equations below can be used to determine the price of each ticket?
Let x represent the cost of an adult ticket, and let y represent the cost of a child ticket.
Click here to see answer by josgarithmetic(39616)

Question 1200545: Consider the equation and the following ordered pairs: (−4,y)
and (x,−3)
3x-3y=6
Click here to see answer by josgarithmetic(39616)

Question 1200555: Given that and find the value of

Click here to see answer by josgarithmetic(39616)

Question 1200563: Find d^93/dx^93 (cos(3x))
Click here to see answer by Solver92311(821)

Question 1200554: Solve for x: https://ibb.co/rdHHZVM

Click here to see answer by ikleyn(52776)

Question 1200571: Question: If a = 2b+c and b=3c+d , find a in terms of c and d .
How is this worked out please ? how do you do subject of the formula with 2 equations ?
Click here to see answer by ankor@dixie-net.com(22740)

Question 1200575: A camera has a listed price of $767.95 before tax. If the sales tax rate is 7.25%, find the total cost of the camera with sales tax included.

Click here to see answer by josgarithmetic(39616)

Question 1200537: Find an equation of the line containing the centers of the 2 circles
x^2 + y^2 - 4x + 6y + 4 = 0 and x^2 + y^2 + 6x + 4y + 9 = 0.

Click here to see answer by josgarithmetic(39616)

Question 1200591: If p=6q-r and t=3q+r , find p in terms of r and t .
What I did :
I first did r subject of formula:
3q+r=t
r=t-3q
Then I substituted the r in the other equation :
p=6q-(t-3q)
p=6q-t+3q
p=9q-t
But the correct answer is :p=2t-3r, how is this supposed to be worked out please?
Click here to see answer by ikleyn(52776)

Question 1200606: The one-to-one function f is defined below.
f(x)=9-x^3
Find f^-1(x), where f^-1 is the inverse of f.
Click here to see answer by ikleyn(52776)

Question 1200702: John bought a .60 donut and .35 cup of coffee. How much did John leave for a tip and taxes if he spent 1.25? Assign a variable and write an equation for the situation then solve.
Click here to see answer by ikleyn(52776)

Question 1200740: The Young family and the Kim family each used their sprinklers last summer. The Young family's sprinkler was used for 40 hours. The Kim family's sprinkler was used for 25 hours. There was a combined total output of 2075L of water. What was the water output rate for each sprinkler if the sum of the two rates was 65L per hour?
Click here to see answer by ikleyn(52776)

Question 1200749: Find dy/dx of (3y^2/(1-3xy)) and find the point on the curve where dy/dx = 0.
Click here to see answer by Edwin McCravy(20054)

Question 1200748: If f(x) = 10x^(ln(x)), find f'(2)
Click here to see answer by Edwin McCravy(20054)

Question 1200794: what is (-6, -3) Reflection across x-axis

Click here to see answer by ikleyn(52776)

Question 1200825: If y(x) = ln(secx + tanx), determine the third derivative of y(x), i.e., find d^3y/dx^3.
Click here to see answer by Edwin McCravy(20054)

Question 1200824: Using the chain rule, show that the following statements are always true:
a) If f(x) is an odd function then f'(x) is an even function
b) If f(x) is an even function then f'(x) is an odd function
Click here to see answer by Edwin McCravy(20054)

Question 1200823: Determine all the pairs of real numbers a and b so that the following function, f(x) is differentiable at all real values, x.
f(x) = https://ibb.co/7SrG6KP
Click here to see answer by Edwin McCravy(20054)

Question 1200942: This is from my derivatives of exponents lesson. I seem to be confused :(
Question =
If f(x)=10^3x-5 times e^2x^2, determine the values of x so that f'(x)=0.
Thank you so much :)
Click here to see answer by Edwin McCravy(20054)

Question 1200940: Hi there,
Hope you're doing well. Here is a question from my unit 1 (derivatives) calculus review package that I can't figure out :)
Find the coordinates of the point on the curve 𝑦 = (𝑥 − 2)^2 at which the tangent line is perpendicular to the line 2𝑥 − 𝑦 + 2 = 0.
Thank you so much <3
Click here to see answer by math_helper(2461)

Question 1200978: This is from my derivatives of exponents lesson.
If f(x)=10^(3x-5) times e^[(2x)^2], determine the values of x so that f'(x)=0.
Thank you!
Click here to see answer by psbhowmick(878)

Question 1201007: Find the equations for each line that passes through the point (4,-1) and is tangent to the curve y=x^2+4x+3.
Click here to see answer by mccravyedwin(406)

Question 1201007: Find the equations for each line that passes through the point (4,-1) and is tangent to the curve y=x^2+4x+3.
Click here to see answer by Edwin McCravy(20054)

Question 1201003: A rectangle is inscribed in a circle: x^2 + y^2 = 9.
Find the dimensions of the rectangle with the maximum area.
Click here to see answer by Alan3354(69443)

Question 1201003: A rectangle is inscribed in a circle: x^2 + y^2 = 9.
Find the dimensions of the rectangle with the maximum area.
Click here to see answer by greenestamps(13198)

Question 1201010: Evaluate the following limit:
https://ibb.co/5skKTSb
Click here to see answer by Theo(13342)

Question 1201010: Evaluate the following limit:
https://ibb.co/5skKTSb
Click here to see answer by greenestamps(13198)

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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, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 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20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 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30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105, 39106..39150, 39151..39195, 39196..39240, 39241..39285, 39286..39330, 39331..39375, 39376..39420, 39421..39465, 39466..39510, 39511..39555, 39556..39600, 39601..39645, 39646..39690, 39691..39735, 39736..39780, 39781..39825, 39826..39870, 39871..39915, 39916..39960, 39961..40005, 40006..40050, 40051..40095, 40096..40140, 40141..40185, 40186..40230, 40231..40275, 40276..40320, 40321..40365, 40366..40410, 40411..40455, 40456..40500, 40501..40545, 40546..40590, 40591..40635, 40636..40680, 40681..40725, 40726..40770, 40771..40815, 40816..40860, 40861..40905, 40906..40950, 40951..40995, 40996..41040, 41041..41085, 41086..41130, 41131..41175, 41176..41220, 41221..41265, 41266..41310, 41311..41355, 41356..41400, 41401..41445, 41446..41490, 41491..41535, 41536..41580