New! Get regular updates about newly solved problems via algebra.com's RSS system.

Recent problems solved by 'Nate'

Nate answered: 3498 problems
Jump to solutions: 0..29 , 30..59 , 60..89 , 90..119 , 120..149 , 150..179 , 180..209 , 210..239 , 240..269 , 270..299 , 300..329 , 330..359 , 360..389 , 390..419 , 420..449 , 450..479 , 480..509 , 510..539 , 540..569 , 570..599 , 600..629 , 630..659 , 660..689 , 690..719 , 720..749 , 750..779 , 780..809 , 810..839 , 840..869 , 870..899 , 900..929 , 930..959 , 960..989 , 990..1019 , 1020..1049 , 1050..1079 , 1080..1109 , 1110..1139 , 1140..1169 , 1170..1199 , 1200..1229 , 1230..1259 , 1260..1289 , 1290..1319 , 1320..1349 , 1350..1379 , 1380..1409 , 1410..1439 , 1440..1469 , 1470..1499 , 1500..1529 , 1530..1559 , 1560..1589 , 1590..1619 , 1620..1649 , 1650..1679 , 1680..1709 , 1710..1739 , 1740..1769 , 1770..1799 , 1800..1829 , 1830..1859 , 1860..1889 , 1890..1919 , 1920..1949 , 1950..1979 , 1980..2009 , 2010..2039 , 2040..2069 , 2070..2099 , 2100..2129 , 2130..2159 , 2160..2189 , 2190..2219 , 2220..2249 , 2250..2279 , 2280..2309 , 2310..2339 , 2340..2369 , 2370..2399 , 2400..2429 , 2430..2459 , 2460..2489 , 2490..2519 , 2520..2549 , 2550..2579 , 2580..2609 , 2610..2639 , 2640..2669 , 2670..2699 , 2700..2729 , 2730..2759 , 2760..2789 , 2790..2819 , 2820..2849 , 2850..2879 , 2880..2909 , 2910..2939 , 2940..2969 , 2970..2999 , 3000..3029 , 3030..3059 , 3060..3089 , 3090..3119 , 3120..3149 , 3150..3179 , 3180..3209 , 3210..3239 , 3240..3269 , 3270..3299 , 3300..3329 , 3330..3359 , 3360..3389 , 3390..3419 , 3420..3449 , 3450..3479 , 3480..3509, >>Next

Trigonometry-basics/74587: Find the number of distinguisable permutations of the letters in the word PEPPERY.
1 solutions

Answer 53556 by Nate(3500) on 2007-03-15 18:44:00 (Show Source):

You can put this solution on YOUR website!
PEPPERY
Letters = 7
Repeating = 3 p's and 2 e's
7!/(3!2!) or 420

Money_Word_Problems/74277: Emma Knutt has $10,000 to invest. She would like to earn $980 per year in interest. How much should she invest at 9% if the rest is to be invested at 11%?
1 solutions

Answer 53315 by Nate(3500) on 2007-03-13 15:31:58 (Show Source):

You can put this solution on YOUR website!
$x is 09% or 0.09
$10,000 - x in 11% or 0.11
0.09x + 0.11(10,000 - x) = 980
0.09x + 1,100 - 0.11x = 980
-0.02x = -120
x = 6,000
$6,000 in 9% and $4,000 in 11%

Exponents-negative-and-fractional/73997: How can you do two thirds to the 4th power?
1 solutions

Answer 53009 by Nate(3500) on 2007-03-11 01:11:31 (Show Source):

You can put this solution on YOUR website!
(2/3)^4
2^4 / 3^4
16 / 81

Percentage-and-ratio-word-problems/74003: you borrow 18000 for nine months. what interest will you be charged if the simple interest rate is 8% per year
1 solutions

Answer 53008 by Nate(3500) on 2007-03-11 01:09:14 (Show Source):

You can put this solution on YOUR website!
I = PRT
I = (18000)(0.08)(9/12)
I = 1080

Inequalities/72716: I saw this question asked but it was incorrectly written.
Solve the inequality 21/15-3x <0 and express the solution as an interval. Could be written: 21 divided by 15-3x <0
1 solutions

Answer 51981 by Nate(3500) on 2007-02-28 18:50:41 (Show Source):

You can put this solution on YOUR website!
21 / (15 - 3x) = f(x)
Horizontal asymptope is at zero ... so all values are less than or greater than zero.
15 - 3x can't be zero
15 - 3x = 0
15 = 3x
5 = x
Values left or right of this asymptope are either greater than or less than zero.
Right of 5 ~> f(6) = 21 / (15 - 18) = 21 / (-3) = -7
x > 5
graph%28300%2C300%2C-1%2C9%2C-10%2C10%2C21%2F%2815+-+3x%29%29

graph%28300%2C300%2C-1%2C9%2C-10%2C10%2C21%2F%2815+-+3x%29%29

Exponential-and-logarithmic-functions/72007: This question is from textbook Study Guide and Practice Workbook
I need to figure out what "compounded annually" means. Ex: $500 paying 4% interest compounded annually. What does this mean?
1 solutions

Answer 51481 by Nate(3500) on 2007-02-24 17:04:27 (Show Source):

You can put this solution on YOUR website!
compounded means that you take the interest of per time
annually means per year
I = Prt
I = 500*0.04*t
I = 20t
where t is in years

Polynomials-and-rational-expressions/71797: Find the roots of the polynomial x3 -x2 +16x -16
Please explain also.
Thank you
1 solutions

Answer 51333 by Nate(3500) on 2007-02-22 20:40:21 (Show Source):

You can put this solution on YOUR website!
x3 - x2 + 16x - 16
(x3 - x2) + (16x - 16)
x2(x - 1) + 16(x - 1)
(x2 + 16)(x - 1)

Linear-equations/71800: Find the center and radius of the circle: (x-5)^2+(y+2)^2=7
a)center
b)radius
1 solutions

Answer 51332 by Nate(3500) on 2007-02-22 20:38:14 (Show Source):

You can put this solution on YOUR website!
(x - h)^2 + (y - k)^2 = r^2
C(5,-2) and radius = sqrt(7)

Inverses/71358: My daughter is having trouble with the following problem, and I can't remember how to do it, let alone explain it... Please help!
(x-5)/6 = (x-11)/2
1 solutions

Answer 51036 by Nate(3500) on 2007-02-19 19:59:55 (Show Source):

You can put this solution on YOUR website!
(x - 5)/6 = (x - 11)/2 mult. each side by the lowest number each one goes into
6(x - 5)/6 = 6(x - 11)/2
x - 5 = 3(x - 11)
x - 5 = 3x - 33
28 = 2x
14 = x

Trigonometry-basics/70835: Hi! I was wondering, I know this may be kind of elementary and seem like a stupid question, but I was wondering if you could possibly help me with a problem dealing with logarithms?
8logt-4logs+7logv
Thank you so much!!
1 solutions

Answer 50613 by Nate(3500) on 2007-02-15 19:14:22 (Show Source):

You can put this solution on YOUR website!
8log(t) - 4log(s) + 7log(v) coefficients become exponents
log(t^8) - log(s^4) + log(v^7) subtraction becomes division
log(t^8/s^4) + log(v^7) addition becomes multiplication
log(t^8v^7/s^4)

logarithm/70846: i do not know how to solve
6e^-1.4x=21
1 solutions

Answer 50612 by Nate(3500) on 2007-02-15 19:05:04 (Show Source):

You can put this solution on YOUR website!
6e^-1.4x = 21
e^-1.4x = 3.5
ln(e^-1.4x) = ln(3.5)
-1.4x = ln(3.5)
x = -ln(3.5)/1.4

Systems-of-equations/70060: given: f(x)=x^2+3 and g(x) = (sqrt)2-x find f o g(x)
1 solutions

Answer 50581 by Nate(3500) on 2007-02-15 15:14:53 (Show Source):

You can put this solution on YOUR website!
f(g(x)) means that the g(x) is placed in the f(x) function
f(sqrt(2 - x)) = (sqrt(2 - x))^2 + 3
f(g(x)) = 2 - x + 3 = -x + 5

Miscellaneous_Word_Problems/70782: Please help me with this problem:
If the numerator of a fraction is randomly selected from the set {1,3,5,7,9} and the denominator is randomly selected from the set {1,2,3,4,5}, what is the probability that the decimal representation of the fraction is a terminating decimal? Express your answer as a common fraction.
1 solutions

Answer 50580 by Nate(3500) on 2007-02-15 15:12:18 (Show Source):

You can put this solution on YOUR website!
We know that all the fractions with 1,2,4, and 5 and terminating.
1/3 is not terminating
5/3 is not
7/3 is not
So 3 are not terminating
Total = 5*5 = 25
3/25

Linear_Equations_And_Systems_Word_Problems/70735: Martina leaves home at 9 A.M., bicycling at a rate of
24 mi/h. Two hours later, John leaves, driving at the rate of 48 mi/h. At what time will John catch up with Martina?
1 solutions

Answer 50578 by Nate(3500) on 2007-02-15 15:09:22 (Show Source):

You can put this solution on YOUR website!
Martina leaves home at 9 A.M., bicycling at a rate of
24 mi/h.
Martina has been cycling for two hours going 24 mi/h so she has already traveled 48 miles.
rate = 24
time = x
distance = 24x
already traveled 48 miles ~> 24x + 48 = distance
Two hours later, John leaves, driving at the rate of 48 mi/h. At what time will John catch up with Martina?
rate = 48
time = x
distance = 48x
When the distances are the same, they will meet.
48x = 24x + 48
24x = 48
x = 2 hours after John left
so ... 4 hours after 9:00 A.M.
1:00 P.M.

Miscellaneous_Word_Problems/70784: The faces of a weighted cube are numbered 1,2,3,4,5, and 6, with one digit per face. When tossed, the cube is twice as likely to land with an even digit showing on its top face as an odd. Each odd number is as likely to appear as any other odd number, and each even number is as likely as any other even number. what is the probability that the cube, when tossed, shows a 5 on its top face? Express your answer as a common fraction.
1 solutions

Answer 50575 by Nate(3500) on 2007-02-15 15:01:10 (Show Source):

You can put this solution on YOUR website!
even = e
odd = o
2o = e
e + o = 100% = 1
2o + o = 1
o = 1/3
Chances of getting an odd = 1/3
Chances of getting an even = 2/3
5 is odd ~> (1/3)
1,3,5 odd numbers ... 3 odds ~> 1/3 of getting a 5
(1/3)(1/3) = 1/9 or about 11.11%

Distributive-associative-commutative-properties/70788: Factor:

4b^2-15b+9
1 solutions

Answer 50571 by Nate(3500) on 2007-02-15 14:51:54 (Show Source):

You can put this solution on YOUR website!
4b^2 - 15b + 9
You take the product of the leading coefficient with the constant.
4 * 9 = 36
Consider all factors of 36:
1,36 or -1,-36
2,18 or -2,-18
3,12 or -3,-12
4,9 or -4,-9
6,6 or -6,-6
Does any of the pairs sum to the linear term (-15)?
-3 and -12 does!
4b^2 - 3b - 12b + 9
Now, we group (doesn't matter if you group 4b^2 and -3b or 4b^2 and -12b):
(4b^2 - 3b) + (-12b + 9)
b(4b - 3) - 3(4b - 3)
(b - 3)(4b - 3)

Exponents-negative-and-fractional/69735: how do you write 31.3 x 10^6 in standard notation?
1 solutions

Answer 49682 by Nate(3500) on 2007-02-07 16:40:09 (Show Source):

You can put this solution on YOUR website!
3.13 x 10^7 because ~> 3.13 x 10 x 10^6 = 31.3 x 10^6

Exponential-and-logarithmic-functions/69727: This question is from textbook Algebra & Trigonometry with Geometry
Exam around the corner last few problems from Chapter quiz's:
Given that log(a)(x)=3.58 and log(a)(y)=4.79, find log(a)(y/x).
Write the expression log(a)(y+5)+2log(a)(x+1) as one logarithm.
Solve the equation 1n(x+5)-1n(3)=1n(x-3).
The population P of a certain culture is expected to be given by a model P=100e^rt where r is a constant to be determined and t is a number of days since the original population of 100 was established. Find the value of r if the population is expected to reach 200 in 3 days.
Find the exact solution to the equation 3^x+5=9^x.
The amount A in an account after t years from an initial principle P invested at an annual rate r compounded continuously is given by A=Pe^rt where r is expressed as a decimal. How many years will it take an initial investment of $1,000 to grow to $1,700 at the rate of 4.42% compounded continously?
The amount of a radioactive tracer remaining after t days is given by A=A0 e^-0.058t. where A0 is the starting amount at the beginning of the time period. How many days will it take for one half of the original amount to decay?
Thanks for helping me prep for my exam. Respectfully, John
1 solutions

Answer 49681 by Nate(3500) on 2007-02-07 16:39:11 (Show Source):

You can put this solution on YOUR website!
Exam around the corner last few problems from Chapter quiz's:
Given that log(a)(x)=3.58 and log(a)(y)=4.79, find log(a)(y/x).
log(a)(x) = 3.58 and log(a)(y) = 4.79
x = a^3.58 and y = a^4.79
log(a)(a^4.79/a^3.58)
log(a)(a^1.21)
1.21
Write the expression log(a)(y+5) + 2log(a)(x+1) as one logarithm.
log(a)(y+5) + log(a)(x+1)^2
log(a)(y+5)(x+1)^2
Solve the equation ln(x + 5) - ln(3) = ln(x - 3).
ln(x + 5) - ln(3) = ln(x - 3)
ln((x + 5)/3) = ln(x - 3)
(x + 5)/3 = x - 3
x + 5 = 3x - 9
14 = 2x
7 = x
The population P of a certain culture is expected to be given by a model P=100e^rt where r is a constant to be determined and t is a number of days since the original population of 100 was established. Find the value of r if the population is expected to reach 200 in 3 days
P = 100e^(rt)
200 = 100e^(3r)
2 = e^(3r)
ln(2) = 3r
ln(2)/3 = r
Find the exact solution to the equation 3^x+5=9^x.
3^(x + 5) = 9^x
3^(x + 5) = 3^2x
x + 5 = 2x
5 = x
The other story problems are just like the first.

Exponents-negative-and-fractional/69730: how do you write 7 x 10^-7, 6 x 10^-8, 5 x 10^-6, 4 x 10^-10 in order from least to greatest?
1 solutions

Answer 49680 by Nate(3500) on 2007-02-07 16:32:12 (Show Source):

You can put this solution on YOUR website!
7 x 10^-7, 6 x 10^-8, 5 x 10^-6, 4 x 10^-10
0.0000007
0.00000006
0.000005
0.0000000004
(4 x 10^-10), (6 x 10^-8), (7 x 10^-7), and (5 x 10^-6)

Equations/69731: In a town election, the winning candidate had 220 more votes
than the loser. If 810 votes were cast in all, how many votes did each candidate
receive?
1 solutions

Answer 49679 by Nate(3500) on 2007-02-07 16:30:01 (Show Source):

You can put this solution on YOUR website!
winning candidate's votes = w
losing candidate's votes = l
l + w = 810 or l = 810 - w
and
220 + l = w
plug:
220 + 810 - w = w
1030 = 2w
515 = w
295 = l

Exponents-negative-and-fractional/69732: how do you simplify 4(3 x 10^5) then write it in scientific notation?
1 solutions

Answer 49678 by Nate(3500) on 2007-02-07 16:27:43 (Show Source):

You can put this solution on YOUR website!
4(3 x 10^5)
12 x 10^5
1.2 x 10^6

Quadratic_Equations/69502: *Find the zero's for the ff quadratic equation:
2x^2-x+8=0

1 solutions

Answer 49495 by Nate(3500) on 2007-02-05 20:00:27 (Show Source):

You can put this solution on YOUR website!
2x^2 - x + 8 = 0
x^2 - x/2 + 4 = 0
x^2 - x/2 = -4
(x - 1/4)^2 = -4 + 1/16 = -64/16 + 1/16 = -63/16
x - 1/4 = +- i*sqrt(63)/4
x = (1 +- i*sqrt(63))/4

Equations/69503: Find the constant term that should be added to make the following a perfect square trinomial:
x^2 + 7x
Multiple choice:
a)49
b)49/2
c)7/2
d)49/4
Thank you for your help
1 solutions

Answer 49493 by Nate(3500) on 2007-02-05 19:56:17 (Show Source):

You can put this solution on YOUR website!
(x + k)^2 = x^2 + 2k*x + k^2
2k = 7
k = 3.5
k^2 = 3.5^2 = 12.25 = 49/4
x^2 + 7x + 49/4

Linear-systems/69504: i have to find the midpoint of the line between the two given points....
1. (10,4)and(2,6) 2. (-2,-1)and (-8,6)
1 solutions

Answer 49490 by Nate(3500) on 2007-02-05 19:49:19 (Show Source):

You can put this solution on YOUR website!
1. (10,4)and(2,6)
You sum the two and divide by 2.
(10 + 2)/2 = 12/2 = 6
(4 + 6)/2 = 10/2 = 5
(6,5)
It is finding the average. I'll let you solve the next.

Radicals/69505: what is the answer to radical 12
1 solutions

Answer 49488 by Nate(3500) on 2007-02-05 19:47:20 (Show Source):

You can put this solution on YOUR website!
like square root? radical numbers can be different
sqrt(12) = sqrt(4*3) = 2*sqrt(3)

Square-cubic-other-roots/69508: (2+3√12) /2
1 solutions

Answer 49486 by Nate(3500) on 2007-02-05 19:45:39 (Show Source):

You can put this solution on YOUR website!
(2 + 3*sqrt(12))/2
2/2 + 3*sqrt(4*3)/2
1 + 3*2*sqrt(3)/2
1 + 3*sqrt(3)

Equations/69510: This question is from textbook Beginning Algebra
How do I solve -7x = -26+6x ?
1 solutions

Answer 49485 by Nate(3500) on 2007-02-05 19:44:28 (Show Source):

You can put this solution on YOUR website!
-7x = -26 + 6x
-13x = -26
x = 2

Linear-equations/69506: how is using one ,two or three variables to equations different from each other and how are they the same?
1 solutions

Answer 49484 by Nate(3500) on 2007-02-05 19:43:25 (Show Source):

You can put this solution on YOUR website!
Equations using one variable only need one equation to solve.
x + 1 = 2
x = 1
Equations using two variables generally needs two equations to solve.
x + y = 2
x - y = 0
x = 1
y = 1
Equations using three variables generally needs three equations to solve.
x + z + 2y = 4
x + z - y = 1
2x + 2z - 4y = 0
x = 1
z = 1
y = 1
You can obviously find many reasons to described how they are the same.

Polynomials-and-rational-expressions/69509: Factor 6x^2 + 25x + 4. Please disregard first question as it was typed incorrectly.
1 solutions

Answer 49481 by Nate(3500) on 2007-02-05 19:39:30 (Show Source):

You can put this solution on YOUR website!
Just did it: (6x + 1)(x + 4)

Polynomials-and-rational-expressions/69507: Factor 6x^2 + 25 + 4
1 solutions

Answer 49480 by Nate(3500) on 2007-02-05 19:38:35 (Show Source):

You can put this solution on YOUR website!
leading coefficient * constant = 6 * 4 = 24
Factors that sum to 25 ~> 24,1
6x^2 + 24x + x + 4
(6x^2 + 24x) + (x + 4)
6x(x + 4) + 1(x + 4)
(6x + 1)(x + 4)

Equations/69500: Solve: 9x^2 = 14
Can someone please give me hand in this? Thank you
1 solutions

Answer 49479 by Nate(3500) on 2007-02-05 19:36:21 (Show Source):

You can put this solution on YOUR website!
x^2 = 14/9
sqrt(x^2) = +- sqrt(14)/3
x = +- sqrt(14)/3

See tutors' answers!

Recent problems solved by 'Nate'