Questions on Algebra: Radicals -- complicated equations involving roots answered by real tutors!

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Question 1065509: If (a - b)² = 5 and ab = 1, find the positive value of a + b.
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I've successfully solved similar problems with addition of squares, but not a difference of squares.

Click here to see answer by rothauserc(4718) About Me 
Question 1065509: If (a - b)² = 5 and ab = 1, find the positive value of a + b.
---
I've successfully solved similar problems with addition of squares, but not a difference of squares.

Click here to see answer by ikleyn(52776) About Me 

Question 1065850: what is 3-√t=- 2
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Question 1065891: Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not solve the equation.
3x^2-20x-1=0
The number is ____

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Question 1065890: If an object is propelled upward from ground level on Mars with an initial velocity of 130 feet per​ second, its​ height, s,​ (in feet) in t seconds is given by the formula s=−13t^2+130t.
How long will it take for the object to be at a height of 208 ​feet?
The object will be at a height of 208 feet in ____ seconds.

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Question 1065985: f(x) = 3x - 7 and g(x) = -2x - 6 Find ( f o g) (4)
please show work

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Question 1066075: Determine the number that will complete the square to solve the equation after the constant term has been written on the right side. Do not solve the equation.
3x^2-20x-1=0
The number is ____.

Click here to see answer by rothauserc(4718) About Me 

Question 1066870: If each side of a square is increased by 2 cm, the total area of both the new square and the original square will be 200 cm2. Approximate to the nearest tenth of a centimeter the length of each side of the original square.
Click here to see answer by josgarithmetic(39616) About Me 

Question 1066869: I try to figure out this one but still don't get it. My answer still not match from the textbook. Please help!
If each side of a square is increased by 5 cm, the total area of both the new square and the original square will be 200 cm2. Approximate to the nearest tenth of a centimeter the length of each side of the original square.

Click here to see answer by josgarithmetic(39616) About Me 

Question 1067151: Evaluate the following expression.
7^0

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Question 1067428: write 15 as a radical

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Question 1067437: Hello . I am a high school student and we just learned about radical and radical notation.
Our teacher says index of radical must be integer and greater than 2 by definition. But I can’t understand why we can’t have radical with negative or rational numbers? For example why we can’t have this? http://imgur.com/a/qWZqG
Our teacher says it’s because negative and rational indexes are not defined for radical notations but why they are not defined? They certainly has answers. any help is greatly appreciated

Click here to see answer by Boreal(15235) About Me 

Question 1067862: square root of (3x+1) +1= x
Click here to see answer by josgarithmetic(39616) About Me 

Question 1068001: Can someone explain to me how to Simplify sqrt 72a^3b^4? Thank you.

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Question 1068033: Minerva starts a savings account with $50. The interest on the account balance is compounded annually. The graph below shows the account balance in terms of x ,the number of years since the account was opened.
Graph: https://vallejocity.owschools.com/media/g_alg01_ccss_2016/8/img_alg1u08l08_01.gif
After 12 years, Minerva's account balance should be about $100, assuming that she does not add or withdraw any money from the account.
A.) True
B.) False
C.) Cannot be determined from the information given.

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

Question 1068066: The function f(x) = 200 × (1.098)^x represents a village's population while it is growing at the rate of 9.8% per year.
1.) Create a table to show the village's population at 0, 2, 4, 6, 8, and 10 years from now.
2.) Use your table to create a graph that represents the village's population growth.
3.) When the population doubles from its current size, the village will need to dig a new water well. To the nearest half of a year, about how long before it is time for the village to dig the new well?

Click here to see answer by ikleyn(52776) About Me 

Question 1068084: Radical-Square Roots: Simplify expressions with square roots. Please show work.
-8√32m^2p^4q

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Question 1068110: Multiply and Divide Radicals: Show work
(-2+√3)(-5+2√3)

Click here to see answer by Fombitz(32388) About Me 

Question 1068028: You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money from the account. Which equation below gives the amount of money you will have in the account after t years?
A.) A(t) = 2,000e^5t
B.) A(t) = 2,000e^0.05t
C.) A(t) = 2,000(1.5)^t
D.) A(t) = 2,000(1.05)^t

Click here to see answer by ikleyn(52776) About Me 

Question 1068029: You invest $2,000 in an account that is compounded continuously at an interest rate of 5%. You never withdraw money from the account. Which equation below gives the amount of money you will have in the account after t years?
A.) A(t) = 2,000e^5t
B.) A(t) = 2,000e^0.05t
C.) A(t) = 2,000(1.5)^t
D.) A(t) = 2,000(1.05)^t

Click here to see answer by ikleyn(52776) About Me 

Question 1068031: You invest $2,000 in an account that is compounded annually at an interest rate of 5%. You never withdraw money from the account. How much money will be in the account after 4 years?

Click here to see answer by josgarithmetic(39616) About Me 

Question 1068183: The bacteria in an old piece of cheese is growing at a rate that can be modeled by y = 280 • 2^x. Determine which number represents the growth rate.
A.) 0.5
B.) 1
C.) 2
D.) 280

Click here to see answer by Lightning_Fast(78) About Me 

Question 1068508: I'm having difficulty solving this quadratic equation. Please help me!
1/5x - 1/10x = 1
My answer came to x=1. I know its wrong. Please help me

Click here to see answer by rothauserc(4718) About Me 
Question 1068508: I'm having difficulty solving this quadratic equation. Please help me!
1/5x - 1/10x = 1
My answer came to x=1. I know its wrong. Please help me

Click here to see answer by MathTherapy(10551) About Me 

Question 1068538: I am having a bit of an issue solving sqrt(3x+1)-sqrt(x-1)=2 or √3x+1-√x-1 = 2
This is what I have done so far:
√3x+1 = √x-1+2
=> (√3x+1)2 = (√x-1+2)2
=> 3x+1 = x-1+4+4√x-1
=> -4√x-1 = -3x-1+x-1+4 or is it 4 √x+1 = -3x-1+x-1+4?
=> 4√x-1 = 2x-2 *This is where I get lost. I have seen this as -2x+2 as well. I am really confused at this point and need to get to the next steps.
Thank you for your help in advance.

Click here to see answer by Fombitz(32388) About Me 
Question 1068538: I am having a bit of an issue solving sqrt(3x+1)-sqrt(x-1)=2 or √3x+1-√x-1 = 2
This is what I have done so far:
√3x+1 = √x-1+2
=> (√3x+1)2 = (√x-1+2)2
=> 3x+1 = x-1+4+4√x-1
=> -4√x-1 = -3x-1+x-1+4 or is it 4 √x+1 = -3x-1+x-1+4?
=> 4√x-1 = 2x-2 *This is where I get lost. I have seen this as -2x+2 as well. I am really confused at this point and need to get to the next steps.
Thank you for your help in advance.

Click here to see answer by Boreal(15235) About Me 
Question 1068538: I am having a bit of an issue solving sqrt(3x+1)-sqrt(x-1)=2 or √3x+1-√x-1 = 2
This is what I have done so far:
√3x+1 = √x-1+2
=> (√3x+1)2 = (√x-1+2)2
=> 3x+1 = x-1+4+4√x-1
=> -4√x-1 = -3x-1+x-1+4 or is it 4 √x+1 = -3x-1+x-1+4?
=> 4√x-1 = 2x-2 *This is where I get lost. I have seen this as -2x+2 as well. I am really confused at this point and need to get to the next steps.
Thank you for your help in advance.

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

Question 1068698: Rationalize the denominator and simplify 5 divided by 4-√3

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Question 1068732: What's the common ratio and next term of this sequence?
333 1/3, 250, 187 1/2

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Question 1068805: What terms are missing from the geometric sequence below?
A) ____, -11 , 22,____ , 88 , -176

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Question 1068922: A population of butterflies grow in such a way that each generation is simply 1.5 times the previous generation. There were 350 butterflies in the first generation, how many will there be by the 19th generation?

Click here to see answer by ankor@dixie-net.com(22740) About Me 

Question 1068939: a total of 242 mosquitoes filled the room, but only females bite. If the ratio of males to females is four to five, how many of the mosquitoes could bite?
Click here to see answer by addingup(3677) About Me 

Question 1068920: Given the following geometric sequence, find the common ratio: {225, 45, 9, ...}.
A.) 5
B.)-5
C.) 1/5
D.) -1/5

Click here to see answer by ikleyn(52776) About Me 

Question 1068936: the ratio of average snowfall in the two towns is four to five. If the first town usally gets 22 inches a year, what is the average snowfall in the second town?
Click here to see answer by ikleyn(52776) About Me 

Question 1068938: mike mussinas's won/lost record is 13-5. what percentage of the game did he lose?
Click here to see answer by trsomas23@gmail.com(17) About Me 

Question 1068935: 540 people visited the gift shop. if two visitors bought something for every three who only looked, how many people only looked?
Click here to see answer by trsomas23@gmail.com(17) About Me 

Question 1068919: For the following geometric sequence find the recursive formula: {-1, 3, -9, ...}.

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Question 1068899: A scientist begins an experiment with a culture of 5 bacteria cells. Every hour, the number of bacteria cells triples. Which equation can be used to represent the number of bacteria cells, y, as it relates to time in hours, x?
A.) y = 5 x
B.) y = 3(5) x
C.) y = 3 x
D.) y = 5(3) x

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Question 1068937: mike mussinas's won/lost record is 13-5. what percentage of the game did he win?
Click here to see answer by rfer(16322) About Me 

Question 1068918: For the following geometric sequence find the recursive formula and the 5th term in the sequence. In your final answer, include all of your work.
{-4, 12, -36, ...}

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Question 1069137: Please explain how to solve
Sqrt 5x+1-4 = 0.
I get the following;
sqrt 5x+1-4=0
sqrt 5x-3=0
5x-3=0^2
5x-3=0
5x-3+3=0+3
5x=3
5x/5 = 3/5
x=3/5
Thank you.

Click here to see answer by ikleyn(52776) About Me 
Question 1069137: Please explain how to solve
Sqrt 5x+1-4 = 0.
I get the following;
sqrt 5x+1-4=0
sqrt 5x-3=0
5x-3=0^2
5x-3=0
5x-3+3=0+3
5x=3
5x/5 = 3/5
x=3/5
Thank you.

Click here to see answer by MathTherapy(10551) About Me 

Question 1069316: I have to solve this factoring problem :
6x^4-10x^3-6x^2
the # after the ^ is the exponents
I found a GCF of 2x^2 and left off at:
2x^2(3x^2-5x-3)
I did x+x=b which is -5
and x*x=ac which is -9
so what two numbers would added give me -5 but multiplied give me -9?
Thats as far as i got. Please help me
Thanks

Click here to see answer by josgarithmetic(39616) About Me 
Question 1069316: I have to solve this factoring problem :
6x^4-10x^3-6x^2
the # after the ^ is the exponents
I found a GCF of 2x^2 and left off at:
2x^2(3x^2-5x-3)
I did x+x=b which is -5
and x*x=ac which is -9
so what two numbers would added give me -5 but multiplied give me -9?
Thats as far as i got. Please help me
Thanks

Click here to see answer by MathTherapy(10551) About Me 

Question 1069545: what type of problem is this?: -3(2x+3)^2-6=-33
Click here to see answer by addingup(3677) About Me 

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