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Equations/551876: I'm doing the following problem out of a book: ax-b=cx+d. The answer in the back of the book is x=(d+b)/(a+c). I don't get the /(a+c) part. Can you explain in more detail?
1 solutions

Answer 359983 by jim_thompson5910(28595) About Me  on 2012-01-02 16:01:15 (Show Source):
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ax-b=cx%2Bd

ax=cx%2Bd%2Bb

ax-cx=d%2Bb

x%28a-c%29=d%2Bb

x=%28d%2Bb%29%2F%28a-c%29


So there must be a typo somewhere.


test/551864:
1 solutions

Answer 359981 by jim_thompson5910(28595) About Me  on 2012-01-02 15:59:27 (Show Source):
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Please post the full problem along with the full instructions.


Money_Word_Problems/551865: explain how to find the intrest rate when the simple interest is $360,the principal is $1600 and the time is 6 years.
1 solutions

Answer 359979 by jim_thompson5910(28595) About Me  on 2012-01-02 15:58:35 (Show Source):
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I=Prt

360=1600r(6)

360=9600r

360/9600=r

0.0375=r

r = 0.0375

So the interest rate is 3.75% (3 and 3 quarters percent)


Linear-equations/551869: Find the x and y intercepts and graph the equation plotting the intercepts.
-3x-5y=15
1 solutions

Answer 359978 by jim_thompson5910(28595) About Me  on 2012-01-02 15:56:32 (Show Source):
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x-intercept


To find the x-intercept, plug in y=0 and solve for x


-3x-5y=15 Start with the given equation.


-3x-5%280%29=15 Plug in y=0.


-3x-0=15 Multiply -5 and 0 to get 0.


-3x=15 Simplify.


x=%2815%29%2F%28-3%29 Divide both sides by -3 to isolate x.


x=-5 Reduce.


So the x-intercept is .


------------------------------------------


y-intercept


To find the y-intercept, plug in x=0 and solve for y


-3x-5y=15 Start with the given equation.


-3%280%29-5y=15 Plug in x=0.


-0-5y=15 Multiply -3 and 0 to get 0.


-5y=15 Simplify.


y=%2815%29%2F%28-5%29 Divide both sides by -5 to isolate y.


y=-3 Reduce.


So the y-intercept is .


Now let's plot the points and which are the x and y intercepts respectively.





Now draw a straight line through the plotted points to graph -3x-5y=15.


Graph of -3x-5y=15


Linear-equations/551872: Write the slope-intercept for the line with slope= (-1/2) and y-intercept=(0,3) and graph line.
1 solutions

Answer 359977 by jim_thompson5910(28595) About Me  on 2012-01-02 15:55:47 (Show Source):
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y = mx+b

y = -1/2x + 3

which graphs to

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+%28-1%2F2%29x+%2B+3%29+


Travel_Word_Problems/551863: How far can a car travel in 40 minutes if it is traveling at an average speed of 50 miles per hour?
1 solutions

Answer 359976 by jim_thompson5910(28595) About Me  on 2012-01-02 15:50:58 (Show Source):
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40 min = 40/60 = 2/3 hr


d = rt

d =50(2/3)

d =100/3

d = 33.333 miles.


Polygons/551859: find the measure of each interior angle of a regular 15-sided poygon
1 solutions

Answer 359973 by jim_thompson5910(28595) About Me  on 2012-01-02 15:38:52 (Show Source):
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I = (180(n-2))/n

I = (180(15-2))/(15)

I = (180(13))/(15)

I = 2340/(15)

I = 156

So the measure of each interior angle of a 15-sided polygon is 156 degrees.


Equations/551853: -5/9 / 15/7
1 solutions

Answer 359971 by jim_thompson5910(28595) About Me  on 2012-01-02 15:23:44 (Show Source):


Triangles/551852: in triangle xyz, xy=5, yz=8, and xz=7. which angle is largest?

1 solutions

Answer 359970 by jim_thompson5910(28595) About Me  on 2012-01-02 15:22:25 (Show Source):
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The largest angle is opposite the largest side. So the largest angle is angle x since it is opposite side yz = 8 (a drawing may help see this)


Geometry_Word_Problems/551844: A trapezoid with a height of 8ft has bases of legths 14ft and 12ft. Find the area of the trapezoid.
1 solutions

Answer 359969 by jim_thompson5910(28595) About Me  on 2012-01-02 15:14:09 (Show Source):
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A=%28h%28b%5B1%5D%2Bb%5B2%5D%29%29%2F2 Start with the area of a trapezoid formula.


A=%288%2814%2B12%29%29%2F2 Plug in h=8, b%5B1%5D=14, b%5B2%5D=12.


A=%288%2826%29%29%2F2 Add 14 to 12 to get 26.


A=%28208%29%2F2 Multiply 8 and 26 to get 208.


A=104 Divide 208 by 2 to get 104.


So the area of the trapezoid is 104 square feet


Exponents-negative-and-fractional/551846: explain why 2 to the negative third power equals 1 over 2 to the third power

1 solutions

Answer 359968 by jim_thompson5910(28595) About Me  on 2012-01-02 15:10:53 (Show Source):
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This is because x%5E%28-k%29=1%2F%28x%5Ek%29 where k is some positive number.


Geometry_Word_Problems/551842: find the area of a triangle with a base of 16 meters and an altitude of 7 meters.
1 solutions

Answer 359966 by jim_thompson5910(28595) About Me  on 2012-01-02 15:05:39 (Show Source):
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A = (bh)/2

A = (16*7)/2

A = 112/2

A = 56

So the area is 56 square meters.


expressions/551840: Express the ratio of 6:14 as a percent.
1 solutions

Answer 359965 by jim_thompson5910(28595) About Me  on 2012-01-02 15:04:36 (Show Source):
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6:14 is the same as 6/14 = 0.42857 which is 42.857%


test/551835:
1 solutions

Answer 359964 by jim_thompson5910(28595) About Me  on 2012-01-02 15:03:50 (Show Source):
You can put this solution on YOUR website!
Please post the full problem along with the full instructions. Thank you.


Numbers_Word_Problems/551834: The sum of three time a number and 7 more than the number is the difference between -11 and twice the number. What is the number?
1 solutions

Answer 359963 by jim_thompson5910(28595) About Me  on 2012-01-02 14:56:39 (Show Source):
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"The sum of three time a number and 7 more than the number is the difference between -11 and twice the number" translates to 3n+%2B+n+%2B+7=-11-2n


3n%2Bn%2B7=-11-2n Start with the given equation.


4n%2B7=-11-2n Combine like terms on the left side.


4n=-11-2n-7 Subtract 7 from both sides.


4n%2B2n=-11-7 Add 2n to both sides.


6n=-11-7 Combine like terms on the left side.


6n=-18 Combine like terms on the right side.


n=%28-18%29%2F%286%29 Divide both sides by 6 to isolate n.


n=-3 Reduce.


----------------------------------------------------------------------

Answer:

So the solution is n=-3


Functions/551833: Express the doamin of the function graph f(x)=square root X-3 plus two

1 solutions

Answer 359962 by jim_thompson5910(28595) About Me  on 2012-01-02 14:55:29 (Show Source):
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You cannot take the square root of a negative number. So x-3%3E=0 which means that the domain is x%3E=3


Rational-functions/551714: For each pair of functions, find f(g(x)) and g(f(x)).
f(x)= 3x+5, g(x)= x^2+1
1 solutions

Answer 359961 by jim_thompson5910(28595) About Me  on 2012-01-02 14:50:47 (Show Source):
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f(x)= 3x+5

f(g(x))= 3g(x)+5

f(g(x))= 3(x^2+1)+5

f(g(x))= 3x^2+3+5

-------------------------------------------------------
g(x)= x^2+1

g(f(x))= (f(x))^2+1

g(f(x))= (x^2+1)^2+1

g(f(x))= x^4+2x^2+1+1

g(f(x))= x^4+2x^2+2


Equations/551831: about 2/3 of an orchestra is made up of string instruments. If 1/5 of the string instruments are violins, what fraction of the orchestra if made up of violins?
1 solutions

Answer 359958 by jim_thompson5910(28595) About Me  on 2012-01-02 14:47:27 (Show Source):
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(2/3)*(1/5) = 2/15 of the instruments are violins


Sequences-and-series/551829: Please help me solve this problem. and how it would be broken down.
simplify.
26-3*2/4^4+3^4=
1 solutions

Answer 359957 by jim_thompson5910(28595) About Me  on 2012-01-02 14:46:55 (Show Source):
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(26-3*2)/(4^4+3^4)

(26-3*2)/(256+81)

(26-6)/(256+81)

20/337


So (26-3*2)/(4^4+3^4) = 20/337



Quadratic_Equations/551828: Solve: 5x^2 -4x -33 = 0

1 solutions

Answer 359956 by jim_thompson5910(28595) About Me  on 2012-01-02 14:45:31 (Show Source):
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5x%5E2-4x-33=0 Start with the given equation.


Notice that the quadratic 5x%5E2-4x-33 is in the form of Ax%5E2%2BBx%2BC where A=5, B=-4, and C=-33


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%285%29%28-33%29+%29%29%2F%282%285%29%29 Plug in A=5, B=-4, and C=-33


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%285%29%28-33%29+%29%29%2F%282%285%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%285%29%28-33%29+%29%29%2F%282%285%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16--660+%29%29%2F%282%285%29%29 Multiply 4%285%29%28-33%29 to get -660


x+=+%284+%2B-+sqrt%28+16%2B660+%29%29%2F%282%285%29%29 Rewrite sqrt%2816--660%29 as sqrt%2816%2B660%29


x+=+%284+%2B-+sqrt%28+676+%29%29%2F%282%285%29%29 Add 16 to 660 to get 676


x+=+%284+%2B-+sqrt%28+676+%29%29%2F%2810%29 Multiply 2 and 5 to get 10.


x+=+%284+%2B-+26%29%2F%2810%29 Take the square root of 676 to get 26.


x+=+%284+%2B+26%29%2F%2810%29 or x+=+%284+-+26%29%2F%2810%29 Break up the expression.


x+=+%2830%29%2F%2810%29 or x+=++%28-22%29%2F%2810%29 Combine like terms.


x+=+3 or x+=+-11%2F5 Simplify.


So the solutions are x+=+3 or x+=+-11%2F5



Triangles/551827: How do you find the area and perimeter of a square when you are only given the diaganol length of 18meters? Thanks:]
1 solutions

Answer 359955 by jim_thompson5910(28595) About Me  on 2012-01-02 14:44:43 (Show Source):
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Hint: If the side length of the square is x, then 2x%5E2=d%5E2 where d is the diagonal. So because the diagonal is 18 m, we know that d = 18 and 2x%5E2=18%5E2


Once you have the side length, you can plug it into the formulas


Area: A=s%5E2


Perimeter: P=4s


where 's' is the side length


Problems-with-consecutive-odd-even-integers/551826: the sum of 4 consecutive integers of 114
1 solutions

Answer 359954 by jim_thompson5910(28595) About Me  on 2012-01-02 14:39:16 (Show Source):
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n + n+1 + n+2 + n+3 = 114

4n+6=114

4n=114-6

4n=108

n=(108)/(4)

n=27


So the first number is 27 and the four numbers are: 27, 28, 29, 30


Inequalities/551824: What is the solution of this inequality : -3+2<-x+10
1 solutions

Answer 359953 by jim_thompson5910(28595) About Me  on 2012-01-02 14:36:50 (Show Source):
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-3%2B2%3C-x%2B10 Start with the given inequality.


-1%3C-x%2B10 Combine like terms on the left side.


0%3C-x%2B10%2B1 Add 1 to both sides.


x%3C10%2B1 Add x to both sides.


x%3C11 Combine like terms on the right side.


----------------------------------------------------------------------

Answer:

So the solution is x%3C11


Matrices-and-determiminant/551600: I am stuck on how I'm suppose to find the determinant and use the determinant to write an expression. Can you please explain how to find the determinant. Thank you.
Matrix: 4 x
10 15
Question: Write an expression for the value of the determinant of the above matrix.

1 solutions

Answer 359952 by jim_thompson5910(28595) About Me  on 2012-01-02 14:36:17 (Show Source):


Equations/551823: find the value of x when you have these equations 2x+5 5x-3 3x+2 4x-2
1 solutions

Answer 359951 by jim_thompson5910(28595) About Me  on 2012-01-02 14:32:31 (Show Source):
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Where is the equal sign? Please repost. Thanks.


Linear-systems/551778: Solve x^2 + x - 42=0
x= Is the answer 6?
1 solutions

Answer 359948 by jim_thompson5910(28595) About Me  on 2012-01-02 14:28:08 (Show Source):
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x%5E2%2Bx-42=0 Start with the given equation.


Notice that the quadratic x%5E2%2Bx-42 is in the form of Ax%5E2%2BBx%2BC where A=1, B=1, and C=-42


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%281%29%28-42%29+%29%29%2F%282%281%29%29 Plug in A=1, B=1, and C=-42


x+=+%28-1+%2B-+sqrt%28+1-4%281%29%28-42%29+%29%29%2F%282%281%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--168+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-42%29 to get -168


x+=+%28-1+%2B-+sqrt%28+1%2B168+%29%29%2F%282%281%29%29 Rewrite sqrt%281--168%29 as sqrt%281%2B168%29


x+=+%28-1+%2B-+sqrt%28+169+%29%29%2F%282%281%29%29 Add 1 to 168 to get 169


x+=+%28-1+%2B-+sqrt%28+169+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-1+%2B-+13%29%2F%282%29 Take the square root of 169 to get 13.


x+=+%28-1+%2B+13%29%2F%282%29 or x+=+%28-1+-+13%29%2F%282%29 Break up the expression.


x+=+%2812%29%2F%282%29 or x+=++%28-14%29%2F%282%29 Combine like terms.


x+=+6 or x+=+-7 Simplify.


So the solutions are x+=+6 or x+=+-7



Inequalities/550214: solve.
-6< x+5<6
{x| < x< }
1 solutions

Answer 359947 by jim_thompson5910(28595) About Me  on 2012-01-02 14:27:28 (Show Source):
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-6< x+5<6

-6-5< x+5-5<6-5

-11 < x <1


Inequalities/551552: Give an example of an open sentence. Explain why an open sentence is neither true nor false.
1 solutions

Answer 359945 by jim_thompson5910(28595) About Me  on 2012-01-02 14:26:13 (Show Source):
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Ex: x+5 = 10 is an open sentence because it is neither completely true or completely false (it all depends on the value of x)


Inequalities/551820: What is the solution of this inequality : -2(n+1) -3<1
1 solutions

Answer 359944 by jim_thompson5910(28595) About Me  on 2012-01-02 14:24:17 (Show Source):
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-2%28n%2B1%29-3%3C1 Start with the given inequality.


-2n-2-3%3C1 Distribute.


-2n-5%3C1 Combine like terms on the left side.


-2n%3C1%2B5 Add 5 to both sides.


-2n%3C6 Combine like terms on the right side.


n%3E%286%29%2F%28-2%29 Divide both sides by -2 to isolate n. note: Remember, the inequality sign flips when we divide both sides by a negative number.


n%3E-3 Reduce.


----------------------------------------------------------------------

Answer:

So the solution is n%3E-3


Equations/551819: 2n2-3b,if n =3 and b= 1
1 solutions

Answer 359943 by jim_thompson5910(28595) About Me  on 2012-01-02 14:23:51 (Show Source):
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2n^2-3b

2(3)^2-3(1)

2(9)-3(1)

18-3

15


So 2n^2-3b = 15 when n=3 and b= 1


Probability-and-statistics/551818: How many ways can five women and two men can be seated on a chair if only three seats?

1 solutions

Answer 359942 by jim_thompson5910(28595) About Me  on 2012-01-02 14:22:48 (Show Source):
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There are 5+2 = 7 people total and P(7,3) = (7!)/(7-3)! = (7!)/(4!) = 5040/24 = 210 ways to seat all of them in 3 seats (assuming order matters).


If order doesn't matter, then there are C(7,3) = (P(7,3))/(3!) = 210/6 = 35 different ways to seat them.