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Graphs/365336: How do you graph 3x - y = 3
1 solutions

Answer 260437 by jim_thompson5910(28595) About Me  on 2010-11-02 21:06:43 (Show Source):
You can put this solution on YOUR website!
3x-y=3 Start with the given equation.


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


-y=-3x%2B3 Rearrange the terms.


y=%28-3x%2B3%29%2F%28-1%29 Divide both sides by -1 to isolate y.


y=%28%28-3%29%2F%28-1%29%29x%2B%283%29%2F%28-1%29 Break up the fraction.


y=3x-3 Reduce.


Looking at y=3x-3 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=3 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 3, this means:

rise%2Frun=3%2F1


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



So starting at , go up 3 units


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=3x-3

So this is the graph of y=3x-3 through the points and


Trigonometry-basics/365339: I have a homework problem for trigonometry that is stumping me. it is to verify the identity:
cot^2x-cos^2x= cot^2xcos^2x.
I have to make both sides of the equation equal. I have tried using identities such as cot^2x=csc^2x-1, but nothing seems to be working. Thanks for your help!
1 solutions

Answer 260436 by jim_thompson5910(28595) About Me  on 2010-11-02 21:05:34 (Show Source):
You can put this solution on YOUR website!
cot^2x-cos^2x= cot^2xcos^2x .... Start with the given equation.


I'm only going to manipulate the right side.


cot^2x-cos^2x= (csc^2x-1)cos^2x ... Plug in cot^2x=csc^2x-1


cot^2x-cos^2x= csc^2xcos^2x-cos^2x ... Distribute.


cot^2x-cos^2x= ( 1/(sin^2x) )cos^2x-cos^2x ... Use the identity csc(x)=1/sin(x).


cot^2x-cos^2x= (cos^2x)/(sin^2x)-cos^2x ... Multiply


cot^2x-cos^2x= cot^2x-cos^2x ... Use the identity (cos(x))/(sin(x))=cot(x).


So this verifies the identity.


test/363911: Hi, Could someone please show me how to get the correct answer from the problem below. I am required to show all the steps I used to get the final answer, but I have no idea to do this.
Directions: approximate each number using a calculator. Round your answer to three decimal places.
e3.9 (should read e to the 3.9 power e^3.9)

The answer is: 49.402
1 solutions

Answer 259598 by jim_thompson5910(28595) About Me  on 2010-10-30 19:43:03 (Show Source):
You can put this solution on YOUR website!
Type either e^3.9 or exp(3.9) into your calculator to get e%5E3.9=49.402. On most calculators, there's an 'e' button along with a '^' button.


Note: there aren't many steps (if there are any steps at all) since a calculator is involved.


Quadratic_Equations/363908: 3x^2+12x+5=p(x+q)^2+r
Find the values of p,q and r
1 solutions

Answer 259597 by jim_thompson5910(28595) About Me  on 2010-10-30 19:40:24 (Show Source):
You can put this solution on YOUR website!
3x%5E2%2B12x%2B5=p%28x%2Bq%29%5E2%2Br Start with the given equation.


3x%5E2%2B12x%2B5=p%28x%5E2%2B2qx%2Bq%5E2%29%2Br FOIL



3x%5E2%2B12x%2B5=px%5E2%2B2pqx%2Bpq%5E2%2Br Distribute.


Notice that the coefficients for the x%5E2 terms are 3 (on the left) and p (on the right). So p=3


So the equation becomes 3x%5E2%2B12x%2B5=3x%5E2%2B2%2A3qx%2B3q%5E2%2Br


3x%5E2%2B12x%2B5=3x%5E2%2B6qx%2B3q%5E2%2Br Multiply


Now notice that the coefficients for the x terms are 12 and 6q. So 6q=12, which means that q=2


So the equation then becomes 3x%5E2%2B12x%2B5=3x%5E2%2B6%2A2x%2B3%282%29%5E2%2Br and simplifies to 3x%5E2%2B12x%2B5=3x%5E2%2B12x%2B12%2Br


Finally, we see that 12+r=5, which means that r=-7




test/363907: Hi,
Can someone plese show me what steps I would take to obtain my answer.
I appreciate it!
Section 12.1, #1
The answer shown in the book is: 9.190 but I have no idea how to get the correct answer, like what steps to use. I appreciate your help!


Approximate each number using a calculator. Round your answer to three decimal places.
2^32 (should read 2 to the 32nd power)


1 solutions

Answer 259595 by jim_thompson5910(28595) About Me  on 2010-10-30 19:35:53 (Show Source):
You can put this solution on YOUR website!
2%5E32=4294967296, so there must be a typo somewhere.


Inequalities/363640: Please help me solve: +7-y%3E5-y+
1 solutions

Answer 259306 by jim_thompson5910(28595) About Me  on 2010-10-29 15:41:48 (Show Source):
You can put this solution on YOUR website!

7-y%3E5-y Start with the given inequality.


-y%3E5-y-7 Subtract 7 from both sides.


-y%2By%3E5-7 Add y to both sides.


0y%3E5-7 Combine like terms on the left side.


0y%3E-2 Combine like terms on the right side.


0%3E-2 Simplify.


Since the inequality above is ALWAYS true, this means that there are an infinite number of solutions.


Expressions-with-variables/363396: (4a+2b-6c)+(3a+2c)=
1 solutions

Answer 259103 by jim_thompson5910(28595) About Me  on 2010-10-28 21:38:36 (Show Source):


Rate-of-work-word-problems/363386: Write an equation of the line passing through (-3,13),(8,9), and (-8,23).
I wasn't sure how to do this because they have different slopes.
The slope of (-3,13) and (8,9) is 4/-11
The slope of (8,9) and (-8,23) is 7/-8
How would I write an equation for that?
1 solutions

Answer 259099 by jim_thompson5910(28595) About Me  on 2010-10-28 21:30:59 (Show Source):
You can put this solution on YOUR website!
You can't draw a straight line through all of those points since the slope of the line through (-3,13) and (8,9) is -4%2F11 and the slope through (8,9) and (-8,23) is -7%2F8. The slopes need to be equal.


Rectangles/363379: a rectangular piece of cardboard is 30 inches by 20 inches. a square with a side of 2 inches is cut out of each corner and the carboard is folded up to form a box. what is the volume of the box
1 solutions

Answer 259090 by jim_thompson5910(28595) About Me  on 2010-10-28 21:13:18 (Show Source):
You can put this solution on YOUR website!
Since 2 inches is cut from each dimension, the new length is now 30-2*2 = 30-4 = 26 inches and the new width is 20-2*2 = 20-4 = 16 inches.


So the volume is 26%2A16%2A2+=+832 cubic inches.


Signed-numbers/363376: how do you get 3000 using order of operation?
1 solutions

Answer 259086 by jim_thompson5910(28595) About Me  on 2010-10-28 21:04:52 (Show Source):
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You're going to have to be more specific and post the entire problem.


Miscellaneous_Word_Problems/363374: in a factory, one inspector checks every 8th item coming off the assembly like. another inspector checks every 12th item. if 1500 items are produced each day, how many items are inspected two times
1 solutions

Answer 259083 by jim_thompson5910(28595) About Me  on 2010-10-28 21:03:24 (Show Source):
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Hint: The LCM of 12 and 8 is 24. So simply count off every 24th item until you reach 1500. A shortcut is to divide 1500 into 24.


Equations/363313: __ + ( __ / __) x __ = 24
Where do the numbers 2, 8, 4 and 16 go in this equation to make it correct?
I have tried every possible way and can't figure it out.
Thanks for your help.
1 solutions

Answer 259081 by jim_thompson5910(28595) About Me  on 2010-10-28 20:59:56 (Show Source):
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Here are ALL of the possible ways to plug in the 4 given numbers into the 4 given slots above. You'll notice that none of these ways generates 24. So either there's a typo or there's actually no solution.


16+8/4*2 = 20
8+16/4*2 = 16
16+4/8*2 = 17
4+16/8*2 = 8
8+4/16*2 = 8.5
4+8/16*2 = 5
16+8/2*4 = 32
8+16/2*4 = 40
16+2/8*4 = 17
2+16/8*4 = 10
8+2/16*4 = 8.5
2+8/16*4 = 4
16+4/2*8 = 32
4+16/2*8 = 68
16+2/4*8 = 20
2+16/4*8 = 34
4+2/16*8 = 5
2+4/16*8 = 4
8+4/2*16 = 40
4+8/2*16 = 68
8+2/4*16 = 16
2+8/4*16 = 34
4+2/8*16 = 8
2+4/8*16 = 10


test/363361: 3 over 4 equals C over 24 ? I need to find the answer for the variable c
1 solutions

Answer 259068 by jim_thompson5910(28595) About Me  on 2010-10-28 20:42:09 (Show Source):
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3%2F4=c%2F24 Start with the given ratio


%283%2F4%29%2A24=c Multiply both sides by 24


72%2F4=c Multiply


18=c Simplify


So our answer is c=18


Inverses/363363: (1-3/4) (1+3/4) can you please help me solve this problem. thank you
1 solutions

Answer 259067 by jim_thompson5910(28595) About Me  on 2010-10-28 20:41:24 (Show Source):
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Use the difference of squares formula %28A-B%29%28A%2BB%29=A%5E2-B%5E2 to get:





So %281-3%2F4%29%281%2B3%2F4%29=7%2F16


Equations/358952: 3-4d=13
-22=11-6a
21=-10m-3

4-2y-y=12
-15=6p+15-10p
4e-3e-2e=1-o
1 solutions

Answer 259066 by jim_thompson5910(28595) About Me  on 2010-10-28 20:39:32 (Show Source):
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I'll do the first one to get you started.

3-4d=13 Start with the given equation.


-4d=13-3 Subtract 3 from both sides.


-4d=10 Combine like terms on the right side.


d=%2810%29%2F%28-4%29 Divide both sides by -4 to isolate d.


d=-5%2F2 Reduce.


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

Answer:

So the solution is d=-5%2F2


Equations/360341: 4x2+5x+6=0
كيف تم حساب نقطة الإنعطاف في الرسم البياني
1 solutions

Answer 259064 by jim_thompson5910(28595) About Me  on 2010-10-28 20:38:45 (Show Source):
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4x%5E2%2B5x%2B6=0 Start with the given equation.


Notice that the quadratic 4x%5E2%2B5x%2B6 is in the form of Ax%5E2%2BBx%2BC where A=4, B=5, and C=6


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-%285%29+%2B-+sqrt%28+%285%29%5E2-4%284%29%286%29+%29%29%2F%282%284%29%29 Plug in A=4, B=5, and C=6


x+=+%28-5+%2B-+sqrt%28+25-4%284%29%286%29+%29%29%2F%282%284%29%29 Square 5 to get 25.


x+=+%28-5+%2B-+sqrt%28+25-96+%29%29%2F%282%284%29%29 Multiply 4%284%29%286%29 to get 96


x+=+%28-5+%2B-+sqrt%28+-71+%29%29%2F%282%284%29%29 Subtract 96 from 25 to get -71


x+=+%28-5+%2B-+sqrt%28+-71+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-5+%2B-+i%2Asqrt%2871%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-5%2Bi%2Asqrt%2871%29%29%2F%288%29 or x+=+%28-5-i%2Asqrt%2871%29%29%2F%288%29 Break up the expression.


So the solutions are x+=+%28-5%2Bi%2Asqrt%2871%29%29%2F%288%29 or x+=+%28-5-i%2Asqrt%2871%29%29%2F%288%29


Equations/361650: -3(b-8)-5+9(b+2)=1

1 solutions

Answer 259063 by jim_thompson5910(28595) About Me  on 2010-10-28 20:38:11 (Show Source):
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-3%28b-8%29-5%2B9%28b%2B2%29=1 Start with the given equation.


-3b%2B24-5%2B9b%2B18=1 Distribute.


6b%2B37=1 Combine like terms on the left side.


6b=1-37 Subtract 37 from both sides.


6b=-36 Combine like terms on the right side.


b=%28-36%29%2F%286%29 Divide both sides by 6 to isolate b.


b=-6 Reduce.


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

Answer:

So the solution is b=-6


Equations/360819: 5d=9d-18
1 solutions

Answer 259062 by jim_thompson5910(28595) About Me  on 2010-10-28 20:37:26 (Show Source):
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5d=9d-18 Start with the given equation.


5d-9d=-18 Subtract 9d from both sides.


-4d=-18 Combine like terms on the left side.


d=%28-18%29%2F%28-4%29 Divide both sides by -4 to isolate d.


d=9%2F2 Reduce.


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

Answer:

So the solution is d=9%2F2


Equations/361821: How do you solve a/6-5=9?
1 solutions

Answer 259060 by jim_thompson5910(28595) About Me  on 2010-10-28 20:36:25 (Show Source):
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a%2F6-5=9 Start with the given equation.


6%28a%2Fcross%286%29-5%29=6%289%29 Multiply both sides by the LCD 6 to clear any fractions.


a-30=54 Distribute and multiply.


a=54%2B30 Add 30 to both sides.


a=84 Combine like terms on the right side.


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

Answer:

So the solution is a=84


Equations/362158: (6+5)-x=6
1 solutions

Answer 259059 by jim_thompson5910(28595) About Me  on 2010-10-28 20:35:51 (Show Source):
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6%2B5-x=6 Start with the given equation.


-x%2B11=6 Combine like terms on the left side.


-x=6-11 Subtract 11 from both sides.


-x=-5 Combine like terms on the right side.


x=%28-5%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=5 Reduce.


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

Answer:

So the solution is x=5


Equations/362157: 5/8(p-4)=2
1 solutions

Answer 259058 by jim_thompson5910(28595) About Me  on 2010-10-28 20:35:09 (Show Source):
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%285%2F8%29%28p-4%29=2 Start with the given equation.


%285%2F8%29p-5%2F2=2 Distribute.


8%28%285%2Fcross%288%29%29p-5%2Fcross%282%29%29=8%282%29 Multiply both sides by the LCD 8 to clear any fractions.


5p-20=16 Distribute and multiply.


5p=16%2B20 Add 20 to both sides.


5p=36 Combine like terms on the right side.


p=%2836%29%2F%285%29 Divide both sides by 5 to isolate p.


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

Answer:

So the solution is p=36%2F5


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Equations/363359: 10x+4=9x
1 solutions

Answer 259057 by jim_thompson5910(28595) About Me  on 2010-10-28 20:34:31 (Show Source):
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10x%2B4=9x Start with the given equation.


10x=9x-4 Subtract 4 from both sides.


10x-9x=-4 Subtract 9x from both sides.


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


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

Answer:

So the solution is x=-4


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Circles/363356: if the area in the form of a circle is to be roped off by a rope 10m long what will be the radious of this area
1 solutions

Answer 259056 by jim_thompson5910(28595) About Me  on 2010-10-28 20:32:20 (Show Source):
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C=2pi%2Ar Start with the circumference of a circle formula.


C%2F%282pi%29=r Divide both sides by 2pi to isolate "r".


r=C%2F%282pi%29 Flip the equation.


r=10%2F%282pi%29 Plug in C=10 (the given distance of the rope).


r=10%2F%282%2A3.14159265%29 Replace pi with 3.14159265 (note: Use more digits of pi to get better accuracy).


r=10%2F%286.2831853%29 Multiply 2 and 3.14159265 to get 6.2831853.


r=1.59154943273756 Divide 10 into 6.2831853 to get 1.59154943273756 (this figure is approximate).


So the radius of a circle which has a circumference of 10 meters is about 1.59154943273756 meters.


Numeric_Fractions/363302: Please could someone kindly Help me!!!
This is my Question:
Mr Jeffries is twice as old as his daughter. In six years Mr Jeffries age will be three times what his daughter's age was six years ago. How old is each person now?
This is how I'm doing it not sure if right???
Mr.Jeffries x years-----> x+6
Daughter 2x years-----> 2x+6
(Jeffries)(Daughter)
3(x+6)= (2x+6)
3x+18 = 2x+6
3x-2x = 18-6
1x = 12
1x 1x
x = 12
I don't think this answer is right
Please Help!!!
Thanks:)
1 solutions

Answer 259053 by jim_thompson5910(28595) About Me  on 2010-10-28 20:26:53 (Show Source):
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Let x = daughters age

Since "Mr Jeffries is twice as old as his daughter", this means that his age is 2x (eg if she is x=10, then he is 2x=20)


So "In six years Mr Jeffries age will be three times what his daughter's age was six years ago" means that 2x%2B6=3%28x-6%29


2x%2B6=3%28x-6%29 Start with the given equation.


2x%2B6=3x-18 Distribute.


2x=3x-18-6 Subtract 6 from both sides.


2x-3x=-18-6 Subtract 3x from both sides.


-x=-18-6 Combine like terms on the left side.


-x=-24 Combine like terms on the right side.


x=%28-24%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=24 Reduce.


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

Answer:

So the solution is x=24 which means that the daughter is 24 years old. So Mr Jeffries is 2*24=48 years old


Notice that in 6 years he will be 48+6=54 and 6 years ago his daughter was 24-6=18. Finally, notice that 18*3=54. So this verifies the answer.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Equations/363319: How do you transform this equation to isolate x ?
x / (x +y) = c
If I multiply each side by (x +y), I get:
x = cx + cy
then I can subtract cx from both sides:
x - cx = cy
But I still can't get x by itself. ???
1 solutions

Answer 259048 by jim_thompson5910(28595) About Me  on 2010-10-28 20:14:16 (Show Source):
You can put this solution on YOUR website!
You're doing great, I'll start where you left off.


x+-+cx+=+cy Start with the given equation.


x%281+-+c%29+=+cy Factor out the GCF 'x'.


x+=+%28cy%29%2F%281-c%29 Divide both sides by 1-c to isolate x.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Expressions-with-variables/363347: Solve for C: P = R-C/n
I'm stuck. I can get as far as this:
Pn = R-C
Pn-R = -C
I'm stuck getting rid of the negative to solve for C.
Please help!
1 solutions

Answer 259046 by jim_thompson5910(28595) About Me  on 2010-10-28 20:11:48 (Show Source):
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Is the equation P=%28R-C%29%2Fn or is it P=R-C%2Fn ?


Numeric_Fractions/363348: simplify the expression: -18+6-4x+10-11x+2
1 solutions

Answer 259044 by jim_thompson5910(28595) About Me  on 2010-10-28 20:11:05 (Show Source):
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-18%2B6-4x%2B10-11x%2B2=%28-4x-11x%29%2B%28-18%2B6%2B10%2B2%29=-15x


So -18%2B6-4x%2B10-11x%2B2=-15x


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Graphs/363342: my question is how do you graph y=2/3x-5
1 solutions

Answer 259043 by jim_thompson5910(28595) About Me  on 2010-10-28 20:09:51 (Show Source):
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Looking at y=%282%2F3%29x-5 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=2%2F3 and the y-intercept is b=-5


Since b=-5 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 2%2F3, this means:

rise%2Frun=2%2F3


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



So starting at , go up 2 units


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



Now draw a line through these points to graph y=%282%2F3%29x-5

So this is the graph of y=%282%2F3%29x-5 through the points and


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim


Rate-of-work-word-problems/363280: i paint a house in 4 hours and my wife paints the same house in 6 hours how long does it take for us to paint the house together?
i have not been in scholl for over 20 yrs and need a reminder of the equations
1 solutions

Answer 259015 by jim_thompson5910(28595) About Me  on 2010-10-28 18:17:53 (Show Source):


Graphs/363121: -x+5y=10 use the intercepts to graph the equation
1 solutions

Answer 258876 by jim_thompson5910(28595) About Me  on 2010-10-28 13:29:41 (Show Source):
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x-intercept


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


-x%2B5y=10 Start with the given equation.


-x%2B5%280%29=10 Plug in y=0.


-x%2B0=10 Multiply 5 and 0 to get 0.


-x=10 Simplify.


x=%2810%29%2F%28-1%29 Divide both sides by -1 to isolate x.


x=-10 Reduce.


So the x-intercept is .


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


y-intercept


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


-x%2B5y=10 Start with the given equation.


-0%2B5y=10 Plug in x=0.


5y=10 Simplify.


y=%2810%29%2F%285%29 Divide both sides by 5 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%2B5y=10.


Graph of -x%2B5y=10


Equations/363127: how to solve 2(n+5)=-2
1 solutions

Answer 258874 by jim_thompson5910(28595) About Me  on 2010-10-28 13:27:27 (Show Source):
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2%28n%2B5%29=-2 Start with the given equation.


2n%2B10=-2 Distribute.


2n=-2-10 Subtract 10 from both sides.


2n=-12 Combine like terms on the right side.


n=%28-12%29%2F%282%29 Divide both sides by 2 to isolate n.


n=-6 Reduce.


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

Answer:

So the answer is n=-6