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Linear-equations/537432: Given the function g described by g(x)=2x find the following
g(-10)=
g(18)=
g(33)=
1 solutions

Answer 352980 by jim_thompson5910(28548) About Me  on 2011-11-28 13:10:23 (Show Source):
You can put this solution on YOUR website!
g(-10)=2(-10) = -20
g(18)=2(18) = 36
g(33)=2(33) = 66


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Jim


Linear-equations/537629: Write the equation of the line in slope-intercept form with a slope of 2 and a y-intercept of –3.
1 solutions

Answer 352979 by jim_thompson5910(28548) About Me  on 2011-11-28 13:09:22 (Show Source):
You can put this solution on YOUR website!
y = mx+b

y = 2x-3

Note: m = 2 and b = -3


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Distributive-associative-commutative-properties/534235: how do i solve 6-6(3x-4)=-60
1 solutions

Answer 352977 by jim_thompson5910(28548) About Me  on 2011-11-28 13:08:19 (Show Source):
You can put this solution on YOUR website!
6-6%283x-4%29=-60 Start with the given equation.


6-18x%2B24=-60 Distribute.


-18x%2B30=-60 Combine like terms on the left side.


-18x=-60-30 Subtract 30 from both sides.


-18x=-90 Combine like terms on the right side.


x=%28-90%29%2F%28-18%29 Divide both sides by -18 to isolate x.


x=5 Reduce.


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

Answer:

So the solution is x=5


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Jim


Distributive-associative-commutative-properties/536288: Use the intercepts to grapg the equation. x + 4y = 8
1 solutions

Answer 352976 by jim_thompson5910(28548) About Me  on 2011-11-28 13:07:37 (Show Source):
You can put this solution on YOUR website!

x-intercept


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


x%2B4y=8 Start with the given equation.


x%2B4%280%29=8 Plug in y=0.


x%2B0=8 Multiply 4 and 0 to get 0.


x=8 Simplify.


So the x-intercept is .


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


y-intercept


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


x%2B4y=8 Start with the given equation.


0%2B4y=8 Plug in x=0.


4y=8 Simplify.


y=%288%29%2F%284%29 Divide both sides by 4 to isolate y.


y=2 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 x%2B4y=8.


Graph of x%2B4y=8


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Equations/537570: I can't find the answer for 2/5h -7 = 12/5h - 2h + 3
1 solutions

Answer 352975 by jim_thompson5910(28548) About Me  on 2011-11-28 13:06:16 (Show Source):
You can put this solution on YOUR website!
%282%2F5%29h-7=%2812%2F5%29h-2h%2B3 Start with the given equation.


5%28%282%2Fcross%285%29%29h-7%29=5%28%2812%2Fcross%285%29%29h-2h%2B3%29 Multiply both sides by the LCD 5 to clear any fractions.


2h-35=12h-10h%2B15 Distribute and multiply.


2h-35=2h%2B15 Combine like terms on the right side.


2h=2h%2B15%2B35 Add 35 to both sides.


2h-2h=15%2B35 Subtract 2h from both sides.


0h=15%2B35 Combine like terms on the left side.


0h=50 Combine like terms on the right side.


0=50 Simplify.


Since this equation is NEVER true for any h value, this means that there are no solutions.


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Equations/537625: What is the solution of the equation 7(x – 2) + 8 = 3(2x + 3)?

1 solutions

Answer 352974 by jim_thompson5910(28548) About Me  on 2011-11-28 13:05:15 (Show Source):
You can put this solution on YOUR website!
7%28x-2%29%2B8=3%282x%2B3%29 Start with the given equation.


7x-14%2B8=6x%2B9 Distribute.


7x-6=6x%2B9 Combine like terms on the left side.


7x=6x%2B9%2B6 Add 6 to both sides.


7x-6x=9%2B6 Subtract 6x from both sides.


x=9%2B6 Combine like terms on the left side.


x=15 Combine like terms on the right side.


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

Answer:

So the solution is x=15


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Equations/537730: what is teh slope of 2x+y=3
1 solutions

Answer 352973 by jim_thompson5910(28548) About Me  on 2011-11-28 13:04:44 (Show Source):
You can put this solution on YOUR website!
Solve for y:


2x+y=3


y=3-2x


y = -2x+3


The equation is now in y = mx+b form where m is the slope. Since m = -2, the slope is -2.


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Jim


Equations/537728: solve -8x - 45 = 2 - 15x
1 solutions

Answer 352972 by jim_thompson5910(28548) About Me  on 2011-11-28 13:02:36 (Show Source):
You can put this solution on YOUR website!
-8x-45=2-15x Start with the given equation.


-8x=2-15x%2B45 Add 45 to both sides.


-8x%2B15x=2%2B45 Add 15x to both sides.


7x=2%2B45 Combine like terms on the left side.


7x=47 Combine like terms on the right side.


x=%2847%29%2F%287%29 Divide both sides by 7 to isolate x.


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

Answer:

So the solution is x=47%2F7


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percentage/537727: 10% off £28
1 solutions

Answer 352971 by jim_thompson5910(28548) About Me  on 2011-11-28 13:00:10 (Show Source):
You can put this solution on YOUR website!
10% of 28 is 0.1*28 = 2.8


So 10% off of 28 is 28 - 2.8 = 25.2


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Linear-equations/537672: what is the slope intercept equation of the line passing through the points (1,7) and (3,3)
1 solutions

Answer 352969 by jim_thompson5910(28548) About Me  on 2011-11-28 12:57:04 (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=1 and y%5B1%5D=7.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=3.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%283-7%29%2F%283-1%29 Plug in y%5B2%5D=3, y%5B1%5D=7, x%5B2%5D=3, and x%5B1%5D=1


m=%28-4%29%2F%283-1%29 Subtract 7 from 3 to get -4


m=%28-4%29%2F%282%29 Subtract 1 from 3 to get 2


m=-2 Reduce


So the slope of the line that goes through the points and is m=-2


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-7=-2%28x-1%29 Plug in m=-2, x%5B1%5D=1, and y%5B1%5D=7


y-7=-2x%2B-2%28-1%29 Distribute


y-7=-2x%2B2 Multiply


y=-2x%2B2%2B7 Add 7 to both sides.


y=-2x%2B9 Combine like terms.


So the equation that goes through the points and is y=-2x%2B9


Notice how the graph of y=-2x%2B9 goes through the points and . So this visually verifies our answer.
Graph of y=-2x%2B9 through the points and


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Equations/537718: Write equations for the horizontal and vertical lines passing through the point (-6,3)
1 solutions

Answer 352968 by jim_thompson5910(28548) About Me  on 2011-11-28 12:54:40 (Show Source):
You can put this solution on YOUR website!
Horizontal lines are of the form y = y1, where y1 is some number. Since the y coordinate here is 3, this means that y1 = 3


So the equation of the horizontal line is y = 3


Using the same logic, you'll find that the equation of the vertical line is x = -6


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Square-cubic-other-roots/537709: what is the square root of 172.8?

1 solutions

Answer 352967 by jim_thompson5910(28548) About Me  on 2011-11-28 12:52:56 (Show Source):
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Using a calculator,


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Equations/537722: The value of x is 6,what is the value of m?
7x-12= 5x+m
1 solutions

Answer 352965 by jim_thompson5910(28548) About Me  on 2011-11-28 12:51:46 (Show Source):
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7x-12= 5x+m


7(6)-12= 5(6)+m


42-12 = 30+m


30 = 30+m


30-30 = m


0 = m


m = 0


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Equations/537714: solve please
-36x/24x=

1 solutions

Answer 352964 by jim_thompson5910(28548) About Me  on 2011-11-28 12:50:49 (Show Source):
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-36x/24x = (-36/24)(x/x) = (-3/2)(1) = -3/2


So -36x/24x = -3/2


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Equations/537721: Please solve.
4(x+2)=
1 solutions

Answer 352963 by jim_thompson5910(28548) About Me  on 2011-11-28 12:49:33 (Show Source):
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Use the distributive property to get


4(x+2) = 4(x)+4(2) = 4x+8


So 4(x+2) = 4x+8


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Radicals/537720: how to solve: .1=1/sqr root of n
1 solutions

Answer 352962 by jim_thompson5910(28548) About Me  on 2011-11-28 12:48:46 (Show Source):
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1=1%2Fsqrt%28n%29


sqrt%28n%29=1


%28sqrt%28n%29%29=1%5E2


n=1


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Equations/537719: 1/5n + 4/5n + -1/5n=

1 solutions

Answer 352961 by jim_thompson5910(28548) About Me  on 2011-11-28 12:47:48 (Show Source):
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1/5n + 4/5n + -1/5n


1/5n + 4/5n - 1/5n


(1/5+4/5-1/5)n


4/5n


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logarithm/537712: I want to factorise this polynom
x^3 - 8

The answer should be (x - 2 )(x^2 + 2x + 4)
I want to know the method please
Thank you
1 solutions

Answer 352960 by jim_thompson5910(28548) About Me  on 2011-11-28 12:46:23 (Show Source):
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x%5E3-8 Start with the given expression.


%28x%29%5E3-%282%29%5E3 Rewrite x%5E3 as %28x%29%5E3. Rewrite 8 as %282%29%5E3.


%28x-2%29%28%28x%29%5E2%2B%28x%29%282%29%2B%282%29%5E2%29 Now factor by using the difference of cubes formula. Remember the difference of cubes formula is A%5E3-B%5E3=%28A-B%29%28A%5E2%2BAB%2BB%5E2%29


%28x-2%29%28x%5E2%2B2x%2B4%29 Multiply

-----------------------------------
Answer:
So x%5E3-8 factors to %28x-2%29%28x%5E2%2B2x%2B4%29.

In other words, x%5E3-8=%28x-2%29%28x%5E2%2B2x%2B4%29


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test/537386: PLease Help Me Solve this problem:A formula from anthropology says that C=100b/L. Find L if c =100 and b=9
1 solutions

Answer 352846 by jim_thompson5910(28548) About Me  on 2011-11-27 18:58:34 (Show Source):
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C=100b/L


LC=100b


L = 100b/C


L = 100(9)/100


L = 900/100


L = 9


So the answer is L = 9


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Polynomials-and-rational-expressions/537375: Use the quadratic formula to solve the equation x^2+6x+25=0
1 solutions

Answer 352844 by jim_thompson5910(28548) About Me  on 2011-11-27 18:50:57 (Show Source):
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x%5E2%2B6x%2B25=0 Start with the given equation.


Notice that the quadratic x%5E2%2B6x%2B25 is in the form of Ax%5E2%2BBx%2BC where A=1, B=6, and C=25


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-%286%29+%2B-+sqrt%28+%286%29%5E2-4%281%29%2825%29+%29%29%2F%282%281%29%29 Plug in A=1, B=6, and C=25


x+=+%28-6+%2B-+sqrt%28+36-4%281%29%2825%29+%29%29%2F%282%281%29%29 Square 6 to get 36.


x+=+%28-6+%2B-+sqrt%28+36-100+%29%29%2F%282%281%29%29 Multiply 4%281%29%2825%29 to get 100


x+=+%28-6+%2B-+sqrt%28+-64+%29%29%2F%282%281%29%29 Subtract 100 from 36 to get -64


x+=+%28-6+%2B-+sqrt%28+-64+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-6+%2B-+8%2Ai%29%2F%282%29 Take the square root of -64 to get 8%2Ai.


x+=+%28-6+%2B+8%2Ai%29%2F%282%29 or x+=+%28-6+-+8%2Ai%29%2F%282%29 Break up the expression.


x+=+%28-6%29%2F%282%29+%2B+%288%2Ai%29%2F%282%29 or x+=++%28-6%29%2F%282%29+-+%288%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+-3%2B4%2Ai or x+=++-3-4%2Ai Reduce.


So the solutions are x+=+-3%2B4%2Ai or x+=+-3-4%2Ai


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Functions/537382: -8
___ find the decimal notation for the fraction
7
1 solutions

Answer 352843 by jim_thompson5910(28548) About Me  on 2011-11-27 18:50:05 (Show Source):
You can put this solution on YOUR website!
Using a calculator, -8%2F7=-1.14285714285714


Coordinate-system/537362: how would you graph y=1/3x+1?
1 solutions

Answer 352830 by jim_thompson5910(28548) About Me  on 2011-11-27 18:26:14 (Show Source):
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Looking at y=%281%2F3%29x%2B1 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=1%2F3 and the y-intercept is b=1


Since b=1 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is 1%2F3, this means:

rise%2Frun=1%2F3


which shows us that the rise is 1 and the run is 3. This means that to go from point to point, we can go up 1 and over 3



So starting at , go up 1 unit


and to the right 3 units to get to the next point



Now draw a line through these points to graph y=%281%2F3%29x%2B1

So this is the graph of y=%281%2F3%29x%2B1 through the points and


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Linear-equations/537345: how do i write y+1=1/3(x-4)in slope intercept form
1 solutions

Answer 352829 by jim_thompson5910(28548) About Me  on 2011-11-27 18:24:14 (Show Source):
You can put this solution on YOUR website!













The equation is now in y = mx+b form where m+=+1%2F3 and b+=+-7%2F3

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Polynomials-and-rational-expressions/537304: Hello,
I need to find the domain to this equation
x^2+18/x^2-4x-5
1 solutions

Answer 352792 by jim_thompson5910(28548) About Me  on 2011-11-27 17:11:03 (Show Source):
You can put this solution on YOUR website!
Hint: you CANNOT divide by zero. So to avoid dividing by zero, you must take out or exclude the values of x which make the denominator x%5E2-4x-5 equal to zero.


Linear-equations/537288: what is the equation of a line that contains the points (1,1) and (3, 9)
1 solutions

Answer 352790 by jim_thompson5910(28548) About Me  on 2011-11-27 16:58:56 (Show Source):
You can put this solution on YOUR website!

First let's find the slope of the line through the points and


Note: is the first point . So this means that x%5B1%5D=1 and y%5B1%5D=1.
Also, is the second point . So this means that x%5B2%5D=3 and y%5B2%5D=9.


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula.


m=%289-1%29%2F%283-1%29 Plug in y%5B2%5D=9, y%5B1%5D=1, x%5B2%5D=3, and x%5B1%5D=1


m=%288%29%2F%283-1%29 Subtract 1 from 9 to get 8


m=%288%29%2F%282%29 Subtract 1 from 3 to get 2


m=4 Reduce


So the slope of the line that goes through the points and is m=4


Now let's use the point slope formula:


y-y%5B1%5D=m%28x-x%5B1%5D%29 Start with the point slope formula


y-1=4%28x-1%29 Plug in m=4, x%5B1%5D=1, and y%5B1%5D=1


y-1=4x%2B4%28-1%29 Distribute


y-1=4x-4 Multiply


y=4x-4%2B1 Add 1 to both sides.


y=4x-3 Combine like terms.


y=4x-3 Simplify


So the equation that goes through the points and is y=4x-3


Notice how the graph of y=4x-3 goes through the points and . So this visually verifies our answer.
Graph of y=4x-3 through the points and


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Equations/537294: m^2-m=6 =m^2-m-6=0 I need details on the solution please
1 solutions

Answer 352789 by jim_thompson5910(28548) About Me  on 2011-11-27 16:58:28 (Show Source):
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m%5E2-m-6=0 Start with the given equation.


Notice that the quadratic m%5E2-m-6 is in the form of Am%5E2%2BBm%2BC where A=1, B=-1, and C=-6


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


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


m+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-1, and C=-6


m+=+%281+%2B-+sqrt%28+%28-1%29%5E2-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Negate -1 to get 1.


m+=+%281+%2B-+sqrt%28+1-4%281%29%28-6%29+%29%29%2F%282%281%29%29 Square -1 to get 1.


m+=+%281+%2B-+sqrt%28+1--24+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-6%29 to get -24


m+=+%281+%2B-+sqrt%28+1%2B24+%29%29%2F%282%281%29%29 Rewrite sqrt%281--24%29 as sqrt%281%2B24%29


m+=+%281+%2B-+sqrt%28+25+%29%29%2F%282%281%29%29 Add 1 to 24 to get 25


m+=+%281+%2B-+sqrt%28+25+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


m+=+%281+%2B-+5%29%2F%282%29 Take the square root of 25 to get 5.


m+=+%281+%2B+5%29%2F%282%29 or m+=+%281+-+5%29%2F%282%29 Break up the expression.


m+=+%286%29%2F%282%29 or m+=++%28-4%29%2F%282%29 Combine like terms.


m+=+3 or m+=+-2 Simplify.


So the solutions are m+=+3 or m+=+-2


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Quadratic_Equations/537287: Write a quadratic equation that has integer coefficients and has as solutions the given pair of numbers. (Use x as the variable.)
9 and 1
1 solutions

Answer 352785 by jim_thompson5910(28548) About Me  on 2011-11-27 16:49:23 (Show Source):
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x=9 or x=1 Start with the given solutions.


x-9=0 or x-1=0 Get everything to one side so that only 0 remains on the right side (for both equations).


%28x-9%29%28x-1%29=0 Use the zero product property to combine the equations.


x%5E2-10x%2B9=0 FOIL out the left side.


So the answer is x%5E2-10x%2B9=0


To check your work, simply solve x%5E2-10x%2B9=0 for x. Doing so will show you that the solutions are x=9 or x=1, which confirm the answer.


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Polynomials-and-rational-expressions/537284: 3/4x = 5x/12 - 1
1 solutions

Answer 352784 by jim_thompson5910(28548) About Me  on 2011-11-27 16:40:36 (Show Source):
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%283%2F4%29x=5x%2F12-1 Start with the given equation.


12%28%283%2Fcross%284%29%29x%29=12%285x%2Fcross%2812%29-1%29 Multiply both sides by the LCD 12 to clear any fractions.


9x=5x-12 Distribute and multiply.


9x-5x=-12 Subtract 5x from both sides.


4x=-12 Combine like terms on the left side.


x=%28-12%29%2F%284%29 Divide both sides by 4 to isolate x.


x=-3 Reduce.


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

Answer:

So the solution is x=-3


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Linear-equations/537271: What is the slope of the equation:
2y-x=37
1 solutions

Answer 352777 by jim_thompson5910(28548) About Me  on 2011-11-27 16:17:29 (Show Source):
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Solve for y


2y-x=37


2y=x+37


y = 1/2x+37/2


So after solving for y, we get


and we can see the equation is in y = mx+b form where m is the slope. Since m = 1/2, the slope is 1/2 (one-half)


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Linear-equations/537259: an equation that goes through the point (1, 5) and has a slope of 2/3
1 solutions

Answer 352767 by jim_thompson5910(28548) About Me  on 2011-11-27 15:57:22 (Show Source):
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y-y1 = m(x-x1)


y-5=(2/3)(x-1)


y-5=(2/3)x-(2/3)(1)


y-5=(2/3)x-2/3


y=(2/3)x-2/3+5


y=(2/3)x+13/3


So the answer is


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Equations/537171: Help solve equation 3x + 3=x+9
1 solutions

Answer 352744 by jim_thompson5910(28548) About Me  on 2011-11-27 13:17:49 (Show Source):
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3x%2B3=x%2B9 Start with the given equation.


3x=x%2B9-3 Subtract 3 from both sides.


3x-x=9-3 Subtract x from both sides.


2x=9-3 Combine like terms on the left side.


2x=6 Combine like terms on the right side.


x=%286%29%2F%282%29 Divide both sides by 2 to isolate x.


x=3 Reduce.


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

Answer:

So the solution is x=3


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