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Percentage-and-ratio-word-problems/494855: at a run festival, 3/5 of the runners are women. if there are 550 runners, how many are women?
1 solutions
Answer 335823 by Gogonati(809) About Me  on 2011-09-10 09:50:45 (Show Source):
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The women are 3*550/5=330.

Trigonometry-basics/494838: Please help me with this problem. I need to solve the equation for solutions over the interval [0 degrees,360 degrees):
+cos%5E2%28x%29=sin%5E2%28x%29%2B1+
1 solutions
Answer 335822 by Gogonati(809) About Me  on 2011-09-10 09:48:13 (Show Source):
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Substitute in our equation %28sinx%29%5E2=1-%28cosx%29%5E2
%28cosx%29%5E2=%281-%28cox%29%5E2%29%2B1 => 2%28cosx%29%5E2=2 => %28cosx%29%5E2=1
From the final equation we get: cosx=1 and cosx=-1. Solving this two equations we
get:1) cosx=1 => x=2n%2Api, and 2)cosx=-1 => x=%282n-1%29%2Api, where
n=0, +-1, +-2, ...

Functions/493099: How do you solve f(x)=8?
With f(x)=x^2-x-12
1 solutions
Answer 335283 by Gogonati(809) About Me  on 2011-09-07 17:23:23 (Show Source):
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8=x%5E2-x-12 Set the equation equal to zero
x%5E2-x-20=0 Solve this quadratic equation
x%5E2-x-20=%28x%2B4%29%28x-5%29=0 The roots are x=-4 and x=5.

Percentage-and-ratio-word-problems/493083: $1800 is invested at 6% per year compounded quarterly. The amount obtained after 2 years is
A) 222.72.46
B) $1910.45
C) $2027.69
D) 2868.93
Please show how you got it I don't understand what "compounded quarterly" means and also explain what "Semi-annually" is :s
1 solutions
Answer 335282 by Gogonati(809) About Me  on 2011-09-07 17:18:32 (Show Source):
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A%28t%29=P%281%2Br%2Fm%29%5E%28m%2At%29, substituting we get:
A%28t%29=1800%281%2B0.06%2F4%29%5E%284%2A2%29
A(t)=$2027.69
The correct answer is C.

Equations/493076: please help me solve this equation for y:
y(y-4)(7y+2)=0
1 solutions
Answer 335279 by Gogonati(809) About Me  on 2011-09-07 17:03:57 (Show Source):
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Set each factor on the left side to zero:
y=0; y-4=0 => y=4; 7y+12=0 => y=-12/7
Answer:The solution set is {-12/7, 0, 4}

logarithm/493072: Alright, the question is log base 3 2x+log base 3 7= log base 3 28.

I know that the answer is 2, but i have no clue how to get to it. I tried canceling out the log base 3 part since they are all the same, and then it came out to 2x+7=28 and solved that, but then x would equal 10.5z please help!
1 solutions
Answer 335278 by Gogonati(809) About Me  on 2011-09-07 16:59:44 (Show Source):

Quadratic_Equations/492989: Can someone help?
51p=2p^2+72
1 solutions
Answer 335273 by Gogonati(809) About Me  on 2011-09-07 16:52:38 (Show Source):
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Set the equation equal to zero and use the quadratic formula to find the solution
2p%5E2-51p%2B72=0
p=%2851%2B-sqrt%282025%29%29%2F4
p=24 and p=2/3.

Rational-functions/493036: Suppose f(x)=2x+5. Find the value if -2f(x+1)
It doesn't make any sense on how to solve.
1 solutions
Answer 335266 by Gogonati(809) About Me  on 2011-09-07 16:36:21 (Show Source):
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-2f(x+1)=-2[2(x+1)+5]=-2(2x+7)=-4x-14

Quadratic_Equations/491547: Find a quadratic equation with the given roots r1 and r2. Write the answer in the form
ax2 + bx + c = 0,
where a, b, and c are integers and a > 0.
r1 = 4 and r2 = 11
1 solutions
Answer 334682 by Gogonati(809) About Me  on 2011-09-05 15:28:37 (Show Source):
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Since the roots are r1=4 and r2=11 the quadratic equation will be:
ax%5E2%2Bbx%2Bc=a%28x-r1%29%28x-r2%29=0, assuming a=1, substituting the roots we get:
%28x-4%29%28x-11%29=x%5E2-15x%2B44=0
Answer:An quadratic equation with the given roots 4 and 11 is x%5E2-15x%2B44=0.

absolute-value/491488: how to solve |4x+5|=2x+4
1 solutions
Answer 334677 by Gogonati(809) About Me  on 2011-09-05 15:18:42 (Show Source):
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By the definition of absolute value:abs%284x%2B5%29=4x%2B5 if 4x+5>=0, and
abs%284x%2B5%29=-4x-5, if4x+5<0 Thus we will solve two equations:
1)If x>=-5/4 we get :4x+5=2x+4 <=>2x=-1 <=>x=-1/2.
2)If x<-5/4 we get:-4x-5=2x+4 <=>6x=-9 <=>x=-3/2.

Equations/491534: Can someone help?
Factor the following expression into a product of two binomials:
64x^2-64x+16
1 solutions
Answer 334668 by Gogonati(809) About Me  on 2011-09-05 15:01:35 (Show Source):

test/491535: Hello everyone, I need help please?
Completely factor the following expression:
49x2 – 28xy + 4y2
1 solutions
Answer 334665 by Gogonati(809) About Me  on 2011-09-05 14:57:51 (Show Source):

Equations/491536: Completely factor the following expression:
9y2 – 16z2
1 solutions
Answer 334661 by Gogonati(809) About Me  on 2011-09-05 14:53:47 (Show Source):

Linear-systems/490647: Solve. <(is less than or equal to)
-11 < 3x-4 < -3 =
1 solutions
Answer 334227 by Gogonati(809) About Me  on 2011-09-03 17:03:12 (Show Source):
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-11<3x-4<-3
-11+4<3x-4+4<-3+4
-7<3x<1
-7/3<3x/3<1/3
-7/3< x <1/3
The solution set is:{ x: -7/3< x < 1/3 }.

Numbers_Word_Problems/490659: the sum of four consecutive odd integers if the first integer is x. write as an algebraic expression.
1 solutions
Answer 334225 by Gogonati(809) About Me  on 2011-09-03 16:55:07 (Show Source):
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x+(x+2)+(x+4)+(x+6)=4x+12.

Equations/490662: Need help..
Factor out the greatest common factor from the expression
27x^6-18x
1 solutions
Answer 334223 by Gogonati(809) About Me  on 2011-09-03 16:51:57 (Show Source):

Equations/490666: Factor the expression 16a^2-72ab+81b^2 into a product of binomials.
1 solutions
Answer 334222 by Gogonati(809) About Me  on 2011-09-03 16:49:49 (Show Source):

Graphs/490702: if m = -2/3, and passes through (5,-4)
write linear equation.

1 solutions
Answer 334219 by Gogonati(809) About Me  on 2011-09-03 16:44:57 (Show Source):
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The equation will be:y%2B4=%28-2%2F3%29%28x-5%29. Converting in the standard form we get:
3y%2B12=-2x%2B10 <=> 2x%2B3y=-2.

Miscellaneous_Word_Problems/490671: Factor the following expression completely:
-6x3 – 20x2 + 16x
1 solutions
Answer 334217 by Gogonati(809) About Me  on 2011-09-03 16:36:33 (Show Source):

test/490679: A line through the point (4,7) and parallel to the line y=2
1 solutions
Answer 334212 by Gogonati(809) About Me  on 2011-09-03 16:20:13 (Show Source):
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A line through the point (4, 7) and parallel to the line y=2 is the line y=7.

Divisibility_and_Prime_Numbers/489708: Simplify to get a single fraction:
c.(x^2+6x+8)/(x^2-4)
don't really get this bc i got 1 remainder 6x+4, but that's not a single fraction. help please!
1 solutions
Answer 333752 by Gogonati(809) About Me  on 2011-09-01 12:53:43 (Show Source):

Numbers_Word_Problems/489758: nine less than twice a number is 14
1 solutions
Answer 333749 by Gogonati(809) About Me  on 2011-09-01 12:48:44 (Show Source):
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The equation will be:14=9-2x <=>5=-2x <=>x=-5/2 or x=-2.5

Rate-of-work-word-problems/489756: If 3 people can do a job in 20 hours how long would it take 4 people to do the same job.
I tried a ratio: 3 is to 4 as 20 is to x (3/4 =20/x) = 60/4x divide each side by 4 and x is 15. Am I on the right track?
1 solutions
Answer 333747 by Gogonati(809) About Me  on 2011-09-01 12:45:24 (Show Source):
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You are on the right track because the quantities in this problem are into inverse proportion.
x*y=k<=>k=20*3=60, and 4*x=60<=> x=15.

Linear-equations/489739: I need help with this problem:
Find y if the line through (3,1) and (7,y) has a slope of 2. Thanks for your response.
1 solutions
Answer 333744 by Gogonati(809) About Me  on 2011-09-01 12:38:03 (Show Source):
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The equation of the line is:y-y%5B0%5D=m%28x-x%5B0%5D%29, where (x, y)=(3, 1), and
(xo, yo)=(7, y)substituting into above equation we get:
1-y=2%283-7%29<=>y=1%2B8<=>y=9.

Proportions/488460: solve for porportions 2/x-3=5/x-2
1 solutions
Answer 333384 by Gogonati(809) About Me  on 2011-08-30 16:52:42 (Show Source):
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To solve the proportion 2%2F%28x-3%29=5%2F%28x-2%29, we cross multiply:
2(x-2)=5(x-3), distribute both sides of equation 2x-4=5x-15<=>3x=11<=>x=11/3.

Numbers_Word_Problems/488409: Two different numbers are made up of the same two digits. The sum of the digits is 8 and the difference between the numbers is 36. Find the numbers.
1 solutions
Answer 333383 by Gogonati(809) About Me  on 2011-08-30 16:46:22 (Show Source):
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Let the first digit be x and the second digit be y. Since the sum of the digits is 8, we write the first equation of the system: x+y=8.
Since the difference between the numbers is 36 we write the second equation:
10x+y-(10y+x)=36, simplifying this equation we get:
10(x-y)-(x-y)=36
(x-y)(10-1)=36
9(x-y)=36
x-y=4, is the second equation of the system:system%28x%2By=8%2C+x-y=4%29
Solving this system we get: x=6, and y=2
Answer: The numbers are 62 and 26.

Numeric_Fractions/488445: Find the slope of the line passing through the points (-3,7) and (-3,-5)
1 solutions
Answer 333378 by Gogonati(809) About Me  on 2011-08-30 16:29:30 (Show Source):
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The slope of this line is undefined because is perpendicular to the x-axis.

Miscellaneous_Word_Problems/488420: The cost to purchase and install carpet in a 15 ft. by 16 ft. rectangular room was more than $6000. What was the price per sq. ft. to buy and install the carpet?
1 solutions
Answer 333376 by Gogonati(809) About Me  on 2011-08-30 16:25:11 (Show Source):
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The area of the rectangular room is 15*16=240 sq. ft.
The price per sq. ft will be:6000/240=25.
Answer:The price per sq. ft. to buy and install the carpet is more than $25.

Equations/488438: Gevin borrowed money from his parent to purchase a game system for $150. Write an equation to represent y, the amount he still owes, after x monthly payments of $5 each.
1 solutions
Answer 333373 by Gogonati(809) About Me  on 2011-08-30 16:18:16 (Show Source):
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The amount he still owes represented from the equation: y=150-5x, where x represent the number of months.

Age_Word_Problems/488434: Craig is 24 years younger than his mother. Together their ages total 56 years. How is each person? Explain how you found your answer. I need help why this question i have been trying for one hour to do it.
1 solutions
Answer 333370 by Gogonati(809) About Me  on 2011-08-30 16:13:48 (Show Source):
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Let mother's age be x years , then Craig's age is x-24 years. Since together their ages total is 56 years, we write the equation:
x+x-24=56, solving this equation we get mother's age.
2x-24=56
2x-24+24=56+24
2x=80 divide both sides by 2, and get x=40.
Answer:Mother's age is 40, and Craig's age is 40-24= 16.

Linear-equations/486515: Write the slope-intercept equation for the line that passes through (-7, 6) and is perpendicular to -7x + 9y = -2
1 solutions
Answer 332562 by Gogonati(809) About Me  on 2011-08-26 16:39:10 (Show Source):
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We write the equation -7x+9y=-2 in the slope intercept form y=%287%2F9%29%2Ax-2%2F9
As we know perpendicular lines have reciprocal negatives slopes.
Therefore we must find the equation of a line with slope -9/7 through the point
(-7, 6). This equation is given by the formula y-y%5B0%5D=m%28x-x%5B0%5D%29,
substituting we get: y-6=%28-9%2F7%29%28x%2B7%29. Simplifying this equation we get:
y=%28-9%2F7%29x-3, what is the required equation.