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Nate answered: 3498 problems
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PLEASE HELP ME WITH THIS PROBLEM:
Let f(x)=x^3-8x^2+17x-9. Use the factor theorem to find other solutions to f(x)-f(1)=0, besides x=1.
1 solutions
Answer 36667 by Nate(3500)   on 2006-10-02 21:51:54 (Show Source):
You can put this solution on YOUR website!f(x) = x^3 - 8x^2 + 17x - 9
f(1) = 1 - 8 + 17 - 9 = -7 + 8 = 1
f(x) - f(1) = 0
x^3 - 8x^2 + 17x - 9 - 1 = 0
x^3 - 8x^2 + 17x - 10 = 0
(x - 1)(x^2 - 7x + 10) = 0 use Descarte's Rule of Signs and all that stuff
(x - 1)(x - 5)(x - 2) = 0
x = 1 and x = 5 and x = 2
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absolute-value/54409: This question is from textbook ALGEBRA AND TRIGONOMETRY
SOMEONE PLEASE HELP ME WITH THIS PROBLEM:
IF f(x)=x(x+3)(x-1), use interval notation to give all values of x where f(x)>0.
1 solutions
Answer 36657 by Nate(3500) on 2006-10-02 21:42:43 (Show Source):
You can put this solution on YOUR website!f(x) must be greater than the value of zero
0 < x(x + 3)(x - 1)
The zeros for x(x + 3)(x - 1) is at x=0, x=-3, and x=1.
Pick Points:
<```(-3)```(0)```(1)```>
x = -4
0 < (-4)(-4 + 3)(-4 - 1)
0 < (-4)(-1)(-5)
0 < -20 Not True
<---(-3)```(0)```(1)```>
x = -1
0 < (-1)(-1 + 3)(-1 - 1)
0 < (-1)(2)(-2)
0 < 4 True
<---(-3)====(0)```(1)```>
x = 0.5
0 < (0.5)(0.5 + 3)(0.5 - 1) We already know we will get a negative number, so this is false.
<---(-3)====(0)----(1)```>
x = 2
0 < (2)(2 + 3)(2 - 1)
0 < (2)(5)(1)
0 < 10 This is true.
<---(-3)====(0)----(1)====>
(-3,0)U(1,+  )
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Expressions-with-variables/54382: A passenger train leaves traveling 60 mph. A freight train leaves at the same time traveling 40 mph and travels the same distance. The passenger train arrives at its destination 1.5 hours earlier than the freight train. How long does each train take to make the trip?
1 solutions
Answer 36656 by Nate(3500) on 2006-10-02 21:37:08 (Show Source):
You can put this solution on YOUR website!1st train's rate: 40
1st train's time: h
Distance = rate * time
Distance = 40h
2nd train's rate: 60
2nd train's time: h - 1.5
Distance = rate * time
Distance = 60h - 90
They both travel the same distance.
40h = 60h - 90
90 = 20h
4.5 = h
Freight Train's Time ~> 4.5 hours
Passenger Train's Time ~> 3 hours
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Functions/54383: I have two questions I'm stumped on. One is Suppose the rectangular TV screen measures 50" on the diagonal and 30" in height. What is its width?
The other is The speed of light is approx 3 x 10^5 km/sec. Write an equation which is a function of distance y and time x.
1 solutions
Answer 36653 by Nate(3500) on 2006-10-02 21:31:35 (Show Source):
You can put this solution on YOUR website!Hypotenuse ~> 50 inches
Leg ~> a
Leg ~> 30 inches
a^2 + 30^2 = 50^2
a^2 + 900 = 2500
a^2 = 1600
a = 40
The width is 40 inches exactly.
Distance (y) = Rate (3 x 10^5) * Time (x)
y = 300,000x
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Expressions-with-variables/54281: Sue worked 7 hours more than twice the number of hours worked by Jim. The total number of hours worked by both of the is 49. Find the number of hours worked by each.
How many ounces of a 15% alcohol solution must be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution?
How much candy costing $2.50 per pound must be mixed with candy costing $3.50 per pound to create 100 pounds of mixed candy selling at $2.90?
You inherit $16,000 and invest in two stocks that pay 6% and 8% annual interest. If the total interest is $1180, how much is invested at each rate?
The sum of two consecutive odd integers is 40 Find the integers
Train A leaves Station A traveling at 40 mph at the same time that Train B leaves Station B at 60 mph. If Station A and Station B are 325 miles apart and the trains are traveling toward each other, how many hours is it before the two trains meet? How far are they from Station B when they meet?
Please, If you could show me how to identify the variables, write an equation and solve the equation
1 solutions
Answer 36536 by Nate(3500) on 2006-10-01 20:56:25 (Show Source):
You can put this solution on YOUR website!Sue worked 7 hours more than twice the number of hours worked by Jim. The total number of hours worked by both of the is 49. Find the number of hours worked by each.
Jim's hours = h
Sue's hours = 2h + 7
h + 2h + 7 = 49
3h = 42
h = 14
Jim's hours = h = 14 hours
Sue's hours = 2(14) + 7 = 35 hours
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How many ounces of a 15% alcohol solution must be mixed with 4 ounces of a 20% alcohol solution to make a 17% alcohol solution?
 You should add 6 ounces of 15% alcohol solution.
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How much candy costing $2.50 per pound must be mixed with candy costing $3.50 per pound to create 100 pounds of mixed candy selling at $2.90?
 60 pounds should be $2.50 and 40 pounds should be $3.50
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You inherit $16,000 and invest in two stocks that pay 6% and 8% annual interest. If the total interest is $1180, how much is invested at each rate?
.06(x) + .08(16000 - x) = 1180
.06x + 1280 - .08x = 1180
-.02x = -100
x = 5000
$5000 should be in 6% and $11,000 should be in 8%
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The sum of two consecutive odd integers is 40 Find the integers.
first integer = i
second integer = i + 2
i + i + 2 = 40
2i = 38
i = 19
i + 2 = 21
19 and 21
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Train A leaves Station A traveling at 40 mph at the same time that Train B leaves Station B at 60 mph. If Station A and Station B are 325 miles apart and the trains are traveling toward each other, how many hours is it before the two trains meet? How far are they from Station B when they meet?
Where  is the time.
Distance = Rate * Time
Distance of Train A + Distance of Train B = 325
40t + 60t = 325
100t = 325
t = 3.25 hours
Train B's Distance = 3.25(60) = 195 miles from Stations B
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Money_Word_Problems/54283: The second angle of a triangle is 18 degrees more than twice the first. The third angle is three times as large as the second. How large are the angles?
1 solutions
Answer 36534 by Nate(3500) on 2006-10-01 20:42:07 (Show Source):
You can put this solution on YOUR website!First angle = x
Second angle = 2x + 18
Third angle = 3(2x + 18) = 6x + 54
x + 2x + 18 + 6x + 54 = 180
9x + 72 = 180
9x = 108
x = 12
First angle = 12 degrees
Second angle = 42 degrees
Third angle = 126 degrees
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Coordinate-system/54271: find the vertex, focus, directrix of the parabola by x^2 -4x -6y -16 = 0
1 solutions
Answer 36523 by Nate(3500) on 2006-10-01 19:56:46 (Show Source):
You can put this solution on YOUR website!x^2 - 4x - 16 = 6y
x^2 - 4x = 6y + 16
(x - 2)^2 = 6y + 20
(x - 2)^2 - 20 = 6y
(1/6)(x - 2)^2 - 10/3 = y
vertex: (2,-10/3)
p = 1/(4a) = 1/(4/6) = 3/2 = 1.5
foci: (2,-10/3 + 1.5)
directrix: y = -10/3 - 1.5
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Systems-of-equations/54262: Helping my daughter and need your help. Need help solving this problem. I need to solve each system using the elimination method. Write no solution or infinitely many solutions where appropriate.
1. 2x + 5y = -1
x + 2y = 0
Thanks
1 solutions
Answer 36520 by Nate(3500) on 2006-10-01 19:45:21 (Show Source):
You can put this solution on YOUR website!To use the elimination method, you need to get an opposite of a coefficient with the same coefficient.
x + 2y = 0
2x + 4y = 0
-2x - 4y = 0
Now, combine that with the other equation:
2x + 5y = -1
-2x - 4y = 0
0x + 1y = -1
y = -1
Plug:
x + 2y = 0
x - 2 = 0
x = 2
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Sequences-and-series/54265: 3, 6, 11, 18 ...
The first four terms of a sequence are shown above. Which of the following could be the formula that gives the nth term of this sequence for all positive integers n?
A. 2n
B. 2n + 1
C. 3n
D. n^2 + 1
E. n^2 + 2
1 solutions
Answer 36518 by Nate(3500) on 2006-10-01 19:40:03 (Show Source):
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Inequalities/54266: This question is from textbook Algebra for College Students
To solve for this equation,  or  I would have to do the same to both sides correct? if I (-5) to the 11 side I must do the same to the 8 side right? From there I would solve for x normally and that gives me the 2 answers? I think I have the logic down, just need to make sure my steps are correct.
Thank you
1 solutions
Answer 36516 by Nate(3500) on 2006-10-01 19:37:22 (Show Source):
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Circles/54267: find the center and radius of the circle given by x(squared)- 4x + y(squared) -6y + 12 = 0
1 solutions
Answer 36515 by Nate(3500) on 2006-10-01 19:31:21 (Show Source):
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Linear_Equations_And_Systems_Word_Problems/54268: Stephanie drove at an average rate of 50 miles per hour for 2 hours and then increased her average rate by 50% for the next 3 hours. Her average rate of speed for the 5 hours was t miles per hour. What is the value of t?
1 solutions
Answer 36514 by Nate(3500) on 2006-10-01 19:29:56 (Show Source):
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Graphs/54196: Please help me with this problem. I missed this problem on a test:
Graph the equation y = 3x - 7 for -1 < x ≤ 3. What is the domain of the function? What is the range of the function?
Thank you.
welljesse
1 solutions
Answer 36481 by Nate(3500) on 2006-10-01 13:52:16 (Show Source):
You can put this solution on YOUR website!The domain is already stated.
Domain: 
The range is a little harder to determine.
The lowest  can be is close to -1, but not equal to.
y = 3(-1) - 7
y = -3 - 7 = -10
The range is greater than -10. 
Also, the greatest can be is 3, and it can be equal to.
y = 3(3) - 7
y = 9 - 7 = 2
The range is less than or equal to two. 
Range: 
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Miscellaneous_Word_Problems/54197: If a piece of real estate purchased for $50,000 in 1998 appreciates at the rate of 5% per year, then its value t years after the purchase will be
f(t)=50000(1.05^t). According to this model, by how much will the value of this piece of property increase between the years 2007 and 2008?
1 solutions
Answer 36480 by Nate(3500) on 2006-10-01 13:48:09 (Show Source):
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Travel_Word_Problems/54201: Two cars leave from a town at the same time traveling in opposite directions. One travels 5 mph faster than the other. In 3 hours, they are 267 miles apart. How many mph is each car traveling? I know Distance = rate * time.
1 solutions
Answer 36478 by Nate(3500) on 2006-10-01 13:44:01 (Show Source):
You can put this solution on YOUR website!Rate of 1st car: r
Time of 1st car: 3
Distance = Rate * Time
Distance = 3r
Rate of 2nd car: r + 5
Time of 2nd car: 3
Distance = Rate * Time
Distance = 3r + 15
Distance of 1st car + Distance of 2nd car = 267
3r + 3r + 15 = 267
6r + 15 = 267
6r = 252
r = 42
One car went 42mph, but the other went 47mph.
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Complex_Numbers/54202: It's been a long time since I've done algebra....I'm a 43 yr old Dad...trying to help my 15 yr old daughter with homework (she's gone right now) explain to me if you please how to solve this equation:
2x - 5y =9
y = 3X - 7
Thanks for your help in advance.....Don Gillis
1 solutions
Answer 36477 by Nate(3500) on 2006-10-01 13:40:23 (Show Source):
You can put this solution on YOUR website!There are two main ways of easily solving these, but you would simply use substitution.
Remember, the  value is equal to  . You would just put that value in for the second equation.
2x - 5y = 9
2x - 5(3x - 7) = 9
2x - 15x + 35 = 9
-13x = -26
x = 2
Remember: 
Answer: x = 2 and y = -1
You can also solve this by graphing each line:
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Permutations/54143: Anyone interested to help me out? Given two six sided dice compute the probability of getting two 11's in a row. My answer is 1/21 multiplied by 1/21=441. Please check my work. Thank you.
1 solutions
Answer 36437 by Nate(3500) on 2006-09-30 17:25:01 (Show Source):
You can put this solution on YOUR website!There are only two ways to get eleven. ~> 6 and 5 ~or~ 5 and 6
6^2 = 36 There are a total of 36 different outcomes.
2/36 = 1/18 Is the probability of getting an 11
(1/18)(1/18) = 1/324
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