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Quadratic-relations-and-conic-sections/161959: What is the standard equation of the circle with radius 4, and center (0,0)?
A (x+4)^2 + y^2 = 16
B (x+4)^2 + (y+4)^2 = 16
C (x+4)^2 + (y+4)^2 = 0
D x^2 + y^2 = 0
E ^2 + y^2 = 4
F x^2 + y^2 = 16

I have no idea where to start on this. Id apperciate seeing the steps and the correct answer. Thank you so much for all your help!
1 solutions

Answer 119342 by jim_thompson5910(28598) About Me  on 2008-10-13 23:27:37 (Show Source):
You can put this solution on YOUR website!
The formula for any circle is %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 where the center is at (h,k) and the radius is "r"


So in this case, the center is (0,0) which means that h=0 and k=0. Also, the radius is 4 which means that r=4


So the equation goes from %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2 to %28x-0%29%5E2%2B%28y-0%29%5E2=4%5E2 after plugging in the given data

Now simplify to get x%5E2%2By%5E2=16


So the answer is F


Linear-systems/161952: please help: y<-5x+6 Graph the linear inequality
1 solutions

Answer 119341 by jim_thompson5910(28598) About Me  on 2008-10-13 23:02:25 (Show Source):
You can put this solution on YOUR website!
1) Graph the line of y=-5x%2B6 to get



note: the line should be a dotted or dashed line
2)

Because the sign is a "<" sign, this means that we must shade the entire region below the line


Linear-equations/161951: please help: y≥-9/5x+7 Graph each linear inequality.
1 solutions

Answer 119340 by jim_thompson5910(28598) About Me  on 2008-10-13 23:00:10 (Show Source):
You can put this solution on YOUR website!
1) First graph the equation y=-%289%2F5%29x%2B7. The graph of y=-%289%2F5%29x%2B7 is:




2)

Now since the inequality sign is a "greater than or equal to sign", this tells us to shade everything above the line (since EVERY "y" value in this region is greater than or equal to every "y" on the line)




real-numbers/161949: 50(3A-B) - 20(B-2A)
1 solutions

Answer 119339 by jim_thompson5910(28598) About Me  on 2008-10-13 22:54:59 (Show Source):
You can put this solution on YOUR website!

50(3A-B) - 20(B-2A) = 50(3A)-50(B) - 20(B)-(-20)(2A)
                    = 150A - 50B - 20B + 40A
                    = 190A - 70B



Equations/161945: (a) (4x+2)(2x) = 32
(b) (3x+2)(9x+3) = 81
(c) log (x-3) + log (x) = 1
(d) log2 (x2 – 6x) = 3 + log2 (1-x)

1 solutions

Answer 119335 by jim_thompson5910(28598) About Me  on 2008-10-13 22:22:33 (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started

1)

%284x%2B2%29%282x%29+=+32+ Start with the given equation


8x%5E2%2B4x+=+32+ Distribute


8x%5E2%2B4x-32=0 Subtract 32 from both sides


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=8, b=4, and c=-32


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-%284%29+%2B-+sqrt%28+%284%29%5E2-4%288%29%28-32%29+%29%29%2F%282%288%29%29 Plug in a=8, b=4, and c=-32


x+=+%28-4+%2B-+sqrt%28+16-4%288%29%28-32%29+%29%29%2F%282%288%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16--1024+%29%29%2F%282%288%29%29 Multiply 4%288%29%28-32%29 to get -1024


x+=+%28-4+%2B-+sqrt%28+16%2B1024+%29%29%2F%282%288%29%29 Rewrite sqrt%2816--1024%29 as sqrt%2816%2B1024%29


x+=+%28-4+%2B-+sqrt%28+1040+%29%29%2F%282%288%29%29 Add 16 to 1024 to get 1040


x+=+%28-4+%2B-+sqrt%28+1040+%29%29%2F%2816%29 Multiply 2 and 8 to get 16.


x+=+%28-4+%2B-+4%2Asqrt%2865%29%29%2F%2816%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-4%2B4%2Asqrt%2865%29%29%2F%2816%29 or x+=+%28-4-4%2Asqrt%2865%29%29%2F%2816%29 Break up the expression.


x+=+%28-1%2Bsqrt%2865%29%29%2F%284%29 or x+=+%28-1-sqrt%2865%29%29%2F%284%29 Reduce


So the answers are x+=+%28-1%2Bsqrt%2865%29%29%2F%284%29 or x+=+%28-1-sqrt%2865%29%29%2F%284%29


which approximate to x=1.766 or x=-2.266








2)

%283x%2B2%29%289x%2B3%29+=+81+ Start with the given equation


27x%5E2%2B27x%2B6+=+81+ FOIL


27x%5E2%2B27x%2B6-81=0 Subtract 81 from both sides


27x%5E2%2B27x-75=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=27, b=27, and c=-75


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-%2827%29+%2B-+sqrt%28+%2827%29%5E2-4%2827%29%28-75%29+%29%29%2F%282%2827%29%29 Plug in a=27, b=27, and c=-75


x+=+%28-27+%2B-+sqrt%28+729-4%2827%29%28-75%29+%29%29%2F%282%2827%29%29 Square 27 to get 729.


x+=+%28-27+%2B-+sqrt%28+729--8100+%29%29%2F%282%2827%29%29 Multiply 4%2827%29%28-75%29 to get -8100


x+=+%28-27+%2B-+sqrt%28+729%2B8100+%29%29%2F%282%2827%29%29 Rewrite sqrt%28729--8100%29 as sqrt%28729%2B8100%29


x+=+%28-27+%2B-+sqrt%28+8829+%29%29%2F%282%2827%29%29 Add 729 to 8100 to get 8829


x+=+%28-27+%2B-+sqrt%28+8829+%29%29%2F%2854%29 Multiply 2 and 27 to get 54.


x+=+%28-27+%2B-+9%2Asqrt%28109%29%29%2F%2854%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-27%2B9%2Asqrt%28109%29%29%2F%2854%29 or x+=+%28-27-9%2Asqrt%28109%29%29%2F%2854%29 Break up the expression.


So the answers are x+=+%28-27%2B9%2Asqrt%28109%29%29%2F%2854%29 or x+=+%28-27-9%2Asqrt%28109%29%29%2F%2854%29


which approximate to x=1.24 or x=-2.24


Graphs/161944: Find the slope and y-intercept of -9x + 6y = 54
Here is what I did:
-9x + 6y = 54
+9x +9x
--------------
6y = 9x + 54
6y/6 (6y over 6) = 9x/6 (9x over 6) + 54/6 (54 over 6)
y = 9/6 (9 over 6) + 9
Simplified : y = 3/2x (3 over 2) + 9
So the answer I came up with is 9 is the slope, and the y-intercept is 3/2 (3 over 2).
Correct??
1 solutions

Answer 119334 by jim_thompson5910(28598) About Me  on 2008-10-13 22:18:07 (Show Source):
You can put this solution on YOUR website!
You work is perfect, but your conclusion is backwards. The slope is m=3%2F2 and the y-intercept is (0,9)

Remember, for any slope-intercept equation y=mx%2Bb the slope is "m" and the y-intercept is (0,b)


Linear-equations/161943: find the gradient of the line 2y - 3x = 5, and draw the line on a graph paper
1 solutions

Answer 119332 by jim_thompson5910(28598) About Me  on 2008-10-13 22:15:30 (Show Source):
You can put this solution on YOUR website!

2y-3x=5 Start with the given equation.


2y=5%2B3x Add 3x to both sides.


2y=3x%2B5 Rearrange the terms.


y=%283x%2B5%29%2F%282%29 Divide both sides by 2 to isolate y.


y=%283%2F2%29x%2B%285%29%2F%282%29 Break up the fraction.


y=%283%2F2%29x%2B5%2F2 Reduce.


So the equation y=%283%2F2%29x%2B5%2F2 is now in slope intercept form y=mx%2Bb where the slope (ie gradient) is m=3%2F2 and the y-intercept is b=5%2F2




Since b=5%2F2 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 which is (0,2.5)




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

Also, because the slope is 3%2F2, this means:

rise%2Frun=3%2F2


which shows us that the rise is 3 and the run is 2. This means that to go from point to point, we can go up 3 and over 2



So starting at , go up 3 units


and to the right 2 units to get to the next point



Now draw a line through these points to graph y=%283%2F2%29x%2B5%2F2

So this is the graph of y=%283%2F2%29x%2B5%2F2 through the points and


Expressions-with-variables/161920: This question is from textbook
6-(-5)=5r-3
1 solutions

Answer 119328 by jim_thompson5910(28598) About Me  on 2008-10-13 21:53:03 (Show Source):
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6-%28-5%29=5r-3 Start with the given equation.


6%2B5=5r-3 Rewrite 6-%28-5%29 as 6%2B5.


11=5r-3 Combine like terms on the left side.


11%2B3=5r Add 3 to both sides


14=5r Combine like terms on the left side



14%2F5=r Divide both sides by 5 to isolate r.


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

Answer:

So the answer is r=14%2F5 which in decimal form is r=2.8.


Linear-systems/161930: the difference between two complementary angles is 50 degrees. what is the measure of the larger angle?
1 solutions

Answer 119324 by jim_thompson5910(28598) About Me  on 2008-10-13 21:45:25 (Show Source):
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Complementary angles ALWAYS add to 90 degrees. So this means that x%2By=90. Since "difference between two complementary angles is 50 degrees", this means that x-y=50


So we have the system of equations:
system%28x%2By=90%2Cx-y=50%29


Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%28x%2By%29%2B%28x-y%29=%2890%29%2B%2850%29


%28x%2Bx%29%2B%28y-y%29=90%2B50 Group like terms.


2x%2B0y=140 Combine like terms. Notice how the y terms cancel out.


2x=140 Simplify.


x=%28140%29%2F%282%29 Divide both sides by 2 to isolate x.


x=70 Reduce. So the first angle is 70 degrees.


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


x%2By=90 Now go back to the first equation.


70%2By=90 Plug in x=70.


70%2By=90 Multiply.


y=90-70 Subtract 70 from both sides.


y=20 Combine like terms on the right side. So the second angle is 20 degrees


So our answer is x=70 and y=20. So the larger angle is 70 degrees.


Exponents/161863: This question is from textbook McDougal Littell

I'm working on expression using only positive exponents . I have 7p-6
I think the answer is 1
_________
7p6 does this look correct? Also Y12. Y12

I think that answer is Y24 Am I right in my thinking?
1 solutions

Answer 119321 by jim_thompson5910(28598) About Me  on 2008-10-13 21:40:37 (Show Source):
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I'm assuming that the expression is %287p%29%5E%28-6%29 right? If it is, then %287p%29%5E%28-6%29=1%2F%287p%29%5E6 where p%3C%3E0

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

Or...

If the expression is 7p%5E%28-6%29, then 7p%5E%28-6%29=7%2Fp%5E6 where p%3C%3E0


Note: the only difference between the two expressions is a change of parenthesis


logarithm/161683: solve 1.6 = logx
1 solutions

Answer 119179 by jim_thompson5910(28598) About Me  on 2008-10-13 00:09:22 (Show Source):
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1.6=log%2810%2C%28x%29%29 Start with the given equation


10%5E1.6=x Rewrite the equation using the property: y=log%28b%2C%28x%29%29 ====> b%5Ey=x


39.81=x Raise 10 to the 1.6th power to get 39.81 (this is approximate)


So the solution is approximately x=39.81


Numeric_Fractions/161694: How do you solve 50 divided by x equals .96?
1 solutions

Answer 119177 by jim_thompson5910(28598) About Me  on 2008-10-13 00:06:49 (Show Source):
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50%2Fx=0.96 Start with the given equation


50=0.96x Multiply both sides by "x"


50%2F0.96=x Divide both sides by 0.96


52.0833=x Divide


So the solution is approximately x=52.0833


Equations/161695: 2(3+7x) - (1+15x)=2
2(4+3r) = 3(r +1) + 11
1/4x - 4 = 3/2x+3/4x
3/4(a-2)-1/3(5-2a)=-2

1 solutions

Answer 119176 by jim_thompson5910(28598) About Me  on 2008-10-13 00:05:20 (Show Source):
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I'll do the first one to get you started




2%283%2B7x%29-%281%2B15x%29=2 Start with the given equation.


6%2B14x-1-15x=2 Distribute.


-x%2B5=2 Combine like terms on the left side.


-x=2-5 Subtract 5 from both sides.


-x=-3 Combine like terms on the right side.


x=%28-3%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=3 Reduce.


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

Answer:

So the answer is x=3


Exponents-negative-and-fractional/161685: (1/16)^-(1/4) =
1 solutions

Answer 119175 by jim_thompson5910(28598) About Me  on 2008-10-13 00:02:57 (Show Source):


Linear-systems/161680: This question is from textbook intermediate algebra
this is an elimination problem i can not get it.
3x+2y=3
9x-8y=-2
1 solutions

Answer 119158 by jim_thompson5910(28598) About Me  on 2008-10-12 20:44:42 (Show Source):
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Start with the given system of equations:
system%283x%2B2y=3%2C9x-8y=-2%29


4%283x%2B2y%29=4%283%29 Multiply the both sides of the first equation by 4.


12x%2B8y=12 Distribute and multiply.


So we have the new system of equations:
system%2812x%2B8y=12%2C9x-8y=-2%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%2812x%2B8y%29%2B%289x-8y%29=%2812%29%2B%28-2%29


%2812x%2B9x%29%2B%288y%2B-8y%29=12%2B-2 Group like terms.


21x%2B0y=10 Combine like terms. Notice how the y terms cancel out.


21x=10 Simplify.


x=%2810%29%2F%2821%29 Divide both sides by 21 to isolate x.


So the first part of the answer is x=%2810%29%2F%2821%29


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


12x%2B8y=12 Now go back to the first equation.


12%2810%2F21%29%2B8y=12 Plug in x=10%2F21.


40%2F7%2B8y=12 Multiply.


7%2840%2Fcross%287%29%2B8y%29=7%2812%29 Multiply both sides by the LCD 7 to clear any fractions.


40%2B56y=84 Distribute and multiply.


56y=84-40 Subtract 40 from both sides.


56y=44 Combine like terms on the right side.


y=%2844%29%2F%2856%29 Divide both sides by 56 to isolate y.


y=11%2F14 Reduce.


So the second part of the answer is y=11%2F14


=========================

Answer:


So the solutions are x=%2810%29%2F%2821%29 and y=11%2F14 which forms the ordered pair


Radicals/161678: i don't understand how to do this problem. 4sqrt%282%29(2+2sqrt%283%29)
1 solutions

Answer 119157 by jim_thompson5910(28598) About Me  on 2008-10-12 20:15:40 (Show Source):


Radicals/161677: 10sqrt%284%29-sqrt%284%29
1 solutions

Answer 119155 by jim_thompson5910(28598) About Me  on 2008-10-12 19:58:50 (Show Source):


Vectors/161537: If // v // = 2, what is //-4v//?
1 solutions

Answer 119144 by jim_thompson5910(28598) About Me  on 2008-10-12 19:16:09 (Show Source):
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Let v=ai%2Bbj. Since ||v||=2, this means that sqrt%28a%5E2%2Bb%5E2%29=2


Now let's compute -4v:


v=ai%2Bbj Start with the given vector


-4v=-4%28ai%2Bbj%29 Multiply both sides by -4


-4v=-4ai-4bj%29 Distribute


So this means:

||-4v||==4||v||


So this shows us that the length of ||-4v|| is simply 4 times that of ||v||. So the length of ||-4v|| is 8 units


In other words, ||-4v||=8



Equations/161663: ((8x^(3/2)/y^3))^4/3
1 solutions

Answer 119141 by jim_thompson5910(28598) About Me  on 2008-10-12 19:04:07 (Show Source):
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%28%288x%5E%283%2F2%29%29%2F%28y%5E3%29%29%5E%284%2F3%29 Start with the given expression


%28%282%5E3x%5E%283%2F2%29%29%2F%28y%5E3%29%29%5E%284%2F3%29 Rewrite 8 as 2%5E3


%282%5E3x%5E%283%2F2%29%29%5E%284%2F3%29%2F%28y%5E3%29%5E%284%2F3%29 Rewrite the fraction



Distribute the outer exponent to each of the inner exponents.


%282%5E4x%5E%2812%2F6%29%29%2F%28y%5E%2812%2F3%29%29 Multiply


%2816x%5E2%29%2F%28y%5E4%29 Reduce



So %28%288x%5E%283%2F2%29%29%2F%28y%5E3%29%29%5E%284%2F3%29 simplifies to %2816x%5E2%29%2F%28y%5E4%29


Exponents/161664: I haven't done a problem like this for several years and I don't remember how to solve it! It's driving me crazy! Here is the problem:
1024=2^n-1. Solve for n.
I don't remember how to bring the exponent (n-1) down so that I can solve for n.
1 solutions

Answer 119138 by jim_thompson5910(28598) About Me  on 2008-10-12 18:40:30 (Show Source):
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There are at least two ways to solve this

Method #1:

1024=2%5E%28n-1%29 Start with the given equation


2%5E10=2%5E%28n-1%29 Rewrite 1,024 as 2%5E10. This is possible since 2%5E10=1024


Since the bases are equal (they are both 2), this means that the exponents are equal. So


10=n-1 Set the exponents equal to one another.


10%2B1=n%2Bcross%28-1%2B1%29 Add 1 to both sides.


11=n Add.


So the answer is n=11



=================================================


Method #2

1024=2%5E%28n-1%29 Start with the given equation


log%2810%2C%281024%29%29=log%2810%2C%282%5E%28n-1%29%29%29 Take the log of both sides.


log%2810%2C%281024%29%29=%28n-1%29log%2810%2C%282%29%29 Rewrite the right side using the identity log%28b%2C%28x%5Ey%29%29=y%2Alog%28b%2C%28x%29%29


log%2810%2C%281024%29%29%2Flog%2810%2C%282%29%29=n-1 Divide both sides by log%2810%2C%282%29%29


10=n-1 Evaluate log%2810%2C%281024%29%29%2Flog%2810%2C%282%29%29 to get 10


10%2B1=n%2Bcross%28-1%2B1%29 Add 1 to both sides.


11=n Add.


So the answer is n=11


Polynomials-and-rational-expressions/161613: This question is from textbook College Algebra
What does it mean when a number is a "zero" of a polynomial, and what the zeros have to do with the graph.
Thanks!
1 solutions

Answer 119090 by jim_thompson5910(28598) About Me  on 2008-10-12 12:47:56 (Show Source):
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A "zero" is a value of x that will make "y" equal to zero. For instance, the equation y=x%2B2 has the zero x=-2 since y=-2%2B2=0. Graphically, the zeros are the same as the x-intercepts (since the x-intercepts occur when y=0).


Systems-of-equations/161600: My worksheet says:
Solve the system of equations:
3X+2Y=17
2X-Y=9
Please help
thanks
1 solutions

Answer 119081 by jim_thompson5910(28598) About Me  on 2008-10-12 11:18:49 (Show Source):
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Start with the given system of equations:
system%283x%2B2y=17%2C2x-y=9%29


2%282x-y%29=2%289%29 Multiply the both sides of the second equation by 2.


4x-2y=18 Distribute and multiply.


So we have the new system of equations:
system%283x%2B2y=17%2C4x-2y=18%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%283x%2B2y%29%2B%284x-2y%29=%2817%29%2B%2818%29


%283x%2B4x%29%2B%282y%2B-2y%29=17%2B18 Group like terms.


7x%2B0y=35 Combine like terms. Notice how the y terms cancel out.


7x=35 Simplify.


x=%2835%29%2F%287%29 Divide both sides by 7 to isolate x.


x=5 Reduce.


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


3x%2B2y=17 Now go back to the first equation.


3%285%29%2B2y=17 Plug in x=5.


15%2B2y=17 Multiply.


2y=17-15 Subtract 15 from both sides.


2y=2 Combine like terms on the right side.


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


y=1 Reduce.


So our answer is x=5 and y=1.


Which form the ordered pair .


This means that the system is consistent and independent.


Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.


Graph of 3x%2B2y=17 (red) and 2x-y=9 (green)


Linear-equations/161509: 3/4x-5=2/3x
1 solutions

Answer 118970 by jim_thompson5910(28598) About Me  on 2008-10-11 14:23:15 (Show Source):
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%283%2F4%29x-5=%282%2F3%29x Start with the given equation.


12%28%283%2Fcross%284%29%29x-5%29=12%28%282%2Fcross%283%29%29x%29 Multiply both sides by the LCD 12 to clear any fractions.


9x-60=8x Distribute and multiply.


9x=8x%2B60 Add 60 to both sides.


9x-8x=60 Subtract 8x from both sides.


x=60 Combine like terms on the left side.


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

Answer:

So the answer is x=60


Equations/161510: solve for x***
(1/10) - (x-4/x) = (1/x) + (3/20)

1 solutions

Answer 118969 by jim_thompson5910(28598) About Me  on 2008-10-11 14:22:29 (Show Source):
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1%2F10+-+%28x-4%29%2Fx+=+1%2Fx+%2B+3%2F20 Start with the given equation.


Multiply every term by the LCD 20x to clear the fractions.



2x+-+20%28x-4%29+=+20+%2B+3x Multiply and simplify


2x-20x%2B80=20%2B3x Distribute.


-18x%2B80=20%2B3x Combine like terms on the left side.


-18x=20%2B3x-80 Subtract 80 from both sides.


-18x-3x=20-80 Subtract 3x from both sides.


-21x=20-80 Combine like terms on the left side.


-21x=-60 Combine like terms on the right side.


x=%28-60%29%2F%28-21%29 Divide both sides by -21 to isolate x.


x=20%2F7 Reduce.


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

Answer:

So the answer is x=20%2F7 which approximates to x=2.857.


Equations/161508: solve for x
(1/x) - (x-4/x) = (1/x) + (3/20)
1 solutions

Answer 118967 by jim_thompson5910(28598) About Me  on 2008-10-11 14:12:39 (Show Source):
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1%2Fx+-+%28x-4%29%2Fx+=+1%2Fx+%2B+3%2F20 Start with the given equation.


Multiply every term by the LCD 20x to clear the fractions.



20+-+20%28x-4%29+=+20+%2B+3x Multiply and simplify


20-20x%2B80=20%2B3x Distribute.


-20x%2B100=20%2B3x Combine like terms on the left side.


-20x=20%2B3x-100 Subtract 100 from both sides.


-20x-3x=20-100 Subtract 3x from both sides.


-23x=20-100 Combine like terms on the left side.


-23x=-80 Combine like terms on the right side.


x=%28-80%29%2F%28-23%29 Divide both sides by -23 to isolate x.


x=80%2F23 Reduce.


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

Answer:

So the answer is x=80%2F23 which approximates to x=3.478.


Graphs/161506: explain the basic method for graphing a linear equation. Please gie me an exmple and show how it would be graphed.
1 solutions

Answer 118961 by jim_thompson5910(28598) About Me  on 2008-10-11 13:27:45 (Show Source):
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Let's say that you have the equation y=%281%2F2%29x%2B3 and you want to graph it.




Looking at y=%281%2F2%29x%2B3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=1%2F2 and the y-intercept is b=3


Since b=3 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%2F2, this means:

rise%2Frun=1%2F2


which shows us that the rise is 1 and the run is 2. This means that to go from point to point, we can go up 1 and over 2



So starting at , go up 1 unit


and to the right 2 units to get to the next point



Now draw a line through these points to graph y=%281%2F2%29x%2B3

So this is the graph of y=%281%2F2%29x%2B3 through the points and


Square-cubic-other-roots/161504: 1) The Path of a falling object is given by the function s=-16t^2+v^o t+s^o where v^o represents the initial velocity in ft/sec and s^o represents the initial height in feet.
A) If a rock is thrown upward what an initial velocity of 64 feet per second from the top of a 25-foot building, write the height (S) equation using this information.
I got s=-16t^2+64t+25
B) How high is the rock after 1 second?
I got s=-16*1^2+64*1+25 so s=73
The questions I need the help on is C)& D)
C) After how many seconds will the graph reach maximum height?
D) What is the maximim height?

1 solutions

Answer 118960 by jim_thompson5910(28598) About Me  on 2008-10-11 13:25:41 (Show Source):
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Note: I'm replacing "s" with "y" and "t" with "x" to get the equation y=-16x%5E2%2B64x%2B25

To answers questions C and D, we need to find the vertex. Remember, the vertex represents the highest/lowest point.



In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From y=-16x%5E2%2B64x%2B25, we can see that a=-16, b=64, and c=25.


x=%28-%2864%29%29%2F%282%28-16%29%29 Plug in a=-16 and b=64.


x=%28-64%29%2F%28-32%29 Multiply 2 and -16 to get -32.


x=2 Divide.


So the x-coordinate of the vertex is x=2. Note: this means that the axis of symmetry is also x=2.


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.


y=-16x%5E2%2B64x%2B25 Start with the given equation.


y=-16%282%29%5E2%2B64%282%29%2B25 Plug in x=2.


y=-16%284%29%2B64%282%29%2B25 Square 2 to get 4.


y=-64%2B64%282%29%2B25 Multiply -16 and 4 to get -64.


y=-64%2B128%2B25 Multiply 64 and 2 to get 128.


y=89 Combine like terms.


So the y-coordinate of the vertex is y=89.


So the vertex is .


Since the vertex is , this means that x=2 and y=89.


So at 2 seconds, the object is at the highest point of 89 feet.


Graphs/161493: How can I solve the inequality 8x<-24 and then graph the solutions?
1 solutions

Answer 118955 by jim_thompson5910(28598) About Me  on 2008-10-11 12:07:29 (Show Source):
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8x%3C-24 Start with the given inequality.


x%3C%28-24%29%2F%288%29 Divide both sides by 8 to isolate x.


x%3C-3 Reduce.


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

Answer:

So the answer is x%3C-3



So the answer in interval notation is





Also, the answer in set-builder notation is



Here's the graph of the solution set



Expressions-with-variables/161481: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM PLEASE:
Find functions f and g so that h(x) = (f o g)(x).
h(x) = cube root (59x^2 + 78)
1 solutions

Answer 118924 by jim_thompson5910(28598) About Me  on 2008-10-11 00:18:35 (Show Source):
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There are so many possible answers (actually there are an infinite number of possible answers), but here's one simple answer


Let f%28x%29=root%283%2Cx%2B78%29 and g%28x%29=59x%5E2


So %28fog%29%28x%29=root%283%2C%2859x%5E2%29%2B78%29=root%283%2C59x%5E2%2B78%29


Notice how I simply replaced the "x" in f(x) with 59x%5E2 to get %28fog%29%28x%29


Distributive-associative-commutative-properties/161473: (5x-6)(5x_6)
I tried to answer this but it made no sice in the end I has -25-60x24
1 solutions

Answer 118923 by jim_thompson5910(28598) About Me  on 2008-10-11 00:15:16 (Show Source):
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%285x-6%29%285x-6%29 Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


%28highlight%285x%29-6%29%28highlight%285x%29-6%29 Multiply the First terms:%285%2Ax%29%2A%285%2Ax%29=25%2Ax%5E2.


%28highlight%285x%29-6%29%285x%2Bhighlight%28-6%29%29 Multiply the Outer terms:%285%2Ax%29%2A%28-6%29=-30%2Ax.


%285x%2Bhighlight%28-6%29%29%28highlight%285x%29-6%29 Multiply the Inner terms:%28-6%29%2A%285%2Ax%29=-30%2Ax.


%285x%2Bhighlight%28-6%29%29%285x%2Bhighlight%28-6%29%29 Multiply the Last terms:%28-6%29%2A%28-6%29=36.


25%2Ax%5E2-30%2Ax-30%2Ax%2B36 Now collect every term to make a single expression.


25%2Ax%5E2-60%2Ax%2B36 Now combine like terms.


So %285x-6%29%285x-6%29 FOILs to 25%2Ax%5E2-60%2Ax%2B36.


In other words, %285x-6%29%285x-6%29=25%2Ax%5E2-60%2Ax%2B36.


test/161474: (11x+3y)(x+4y) I tried to do the foil method
11x^2+44xy+3yx+12y^2
1 solutions

Answer 118922 by jim_thompson5910(28598) About Me  on 2008-10-11 00:14:09 (Show Source):
You can put this solution on YOUR website!
You're doing great. Now you just need to combine like terms.


The terms that have "xy" and "yx" are the same terms (since you can switch the terms), which that means that 3yx is the same as 3xy. So the expression also looks like this:


11x%5E2%2B44xy%2B3xy%2B12y%5E2


11x%5E2%2B47xy%2B12y%5E2 Now combine like terms.


So %2811x%2B3y%29%28x%2B4y%29+ FOILs to 11x%5E2%2B47xy%2B12y%5E2