Questions on Algebra: Equations answered by real tutors!

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Tutors Answer Your Questions about Equations (FREE)


Question 570957: b+8
_____=7
3

Answer by JBarnum(1826) About Me  (Show Source):

Question 570920: How do I find an equation of the line containging the given pair of points. (-2,-3) and (-7,-9)
Answer by josmiceli(6766) About Me  (Show Source):
You can put this solution on YOUR website!
Use the point-slope formula
+%28+y+-%28-3%29+%29+%2F+%28+x+-%28-2%29+%29+=+%28+-9+-%28-3%29+%29+%2F+%28+-7+-%28-2%29+%29+
+%28+y+%2B+3+%29+%2F+%28+x+%2B+2+%29+=+%28+-9+%2B+3+%29+%2F+%28+-7+%2B+2+%29+
+%28+y+%2B+3+%29+%2F+%28+x+%2B+2+%29+=+%28-6%29+%2F+%28-5%29+
+%28+y+%2B+3+%29+%2F+%28+x+%2B+2+%29+=+6%2F5+
Multiply both sides by +5%2A%28+x+%2B+2+%29+
+5%2A%28+y+%2B+3+%29+=+6%2A%28+x+%2B+2+%29+
+5y+%2B+15+=+6x+%2B+12+
+5y+=+6x+-+3+
+y+=+%286%2F5%29%2Ax+-+3%2F5+
------------------
Does the line go through (-2,-3) and (-7,-9) ?
+y+=+%286%2F5%29%2Ax+-+3%2F5+
+-3+=+%286%2F5%29%2A%28-2%29+-+3%2F5+
+-3+=+-%2812%2F5%29+-+3%2F5+
+-3+=+-%2815%2F5%29+
+-3+=+-3+
and
+-9+=+%286%2F5%29%2A%28-7%29+-+3%2F5+
+-9+=+-%2842%2F5%29+-+3%2F5+
+-9+=+-%2845%2F5%29+
+-9+=+-9+
OK


Question 570826: solve the following:
1. 6x4-11x3-35x2+34x+24
2. log(7x+2)-log(x-1)=1

Answer by Theo(2960) About Me  (Show Source):
You can put this solution on YOUR website!
1. 6x4-11x3-35x2+34x+24
i graphed your first problem to see what the graph of the equation looked like.
if you're allowed to do this, it's a perfectly legitimate way of narrowing the problem down to possible solutions.
here's the graph that i created.
$$$
the graph shows that there are real solutions around the following points>
x = -2.0
x = -0.5
x = somewhere between 1.3 and 1.4
x = 3.0
these can be confirmed through solving of the equation by other than graphical means, or using the graphing software to find the zero points of the equation.
using the graphing software to find the zero points of the equations involves finding the intersection of the graph with the x-axis which is equivalent to the equation of y = 0.
this provides you with the value of x when the value of y = 0.
the graphing software i used indicates the zero points of the equation are at the following points on the graph.
x = -2.0
x = -0.5
x = 1.3333333 which can also be shown as x = 1 and 1/3 or x = 4/3.
x = 3.0
in this case, the graph showed the zero points fairly clearly.
in other cases, the graph will show the approximate point which can then be found exactly either through the graphing software or through algebraic calculations.
the graph itself took the grunt work out of finding where the possible real solutions were.
if we wished to find the solutions through calculations, we would do the following:
we know that -2.0 and 3.0 are roots of the equation, so we can use synthetic division to simplify the original equation.
if -2.0 and 3.0 are solutions, this means that (x+2) and (x-3) are factors.
we can reduce the equation using synthetic division by first dividing by (x+2) and then dividing the reduced equation by (x-3).
the result of that will be a quadratic equation that can then be solved using quadratic equation solving methods.
the attached diagram shows the synthetic division.
$$$
the original equation is:
6x^4 - 11x^3 - 35x^2 + 34x + 24
after dividing by (x+2), the first reduced equation becomes:
6x^3 - 23x^2 + 11x + 12
after dividing that by (x-3), the second reduced equation becomes:
6x^2 - 5x - 4
it appears that this equation won't factor easily, so we use the quadratic formula of:
x = (-b +/- sqrt(b^2-4ac))/(2a)
we set the quadratic expression equal to 0 to get:
6x^2 - 5x - 4 = 0
this puts it in standard form.
since the standard form of a quadratic equation is:
ax^2 + bx + c = 0, this means that:
a = 6
b = -5
c = -4
replacing a, b, and c in the quadratic formula with their respective values gets us:
x = (-(-5) +/- sqrt((-5)^2 - (4*(6)*(-4))) / (2*6) which simplifies to:
x = (5 +/- sqrt(25+96))/12 which simplifies further to:
x = (5 +/- sqrt(121)/12 which simplifies further to:
x = (5 +/- 11)/12
this leads to 2 solutions of x which are:
x = 16/12
x = -6/12
these solutions simplify to:
x = 4/3
x = -1/2
the decimal equivalent of these solutions is:
x = 1.333333333
x = -.5
our 4 solutions are:
x = -2.0
x = -.5
x = 1.33333333
x = 3.0
these are the same solutions as found using the graphical software.
if you have the graphing software to do it, the graphing solution is the way to go.
if you don't have graphing solutions available, you would have have to do trial and error to determine that (x+2) and (x-3) were factors and then use the quadratic formula to find the roots of the quadratic equation that was left.
it's a laborious process that is significantly simplified through the use of the graphing software.
the calculator i used was the TI-84.
it takes a little getting used to but, once you know how to use it, it works just fine.
there are others.
The TI-83 is similar but a little cheaper and still does the job adequately.
the graphical sofwtare solution won't find the complex roots of the equation.
it will only find the real roots.
if there are complex roots (a combination of real and imaginary parts), they would have to be found by other means or by graphing software that enables you to find complex roots.
i haven't seen such software nor have had occasion to use it as most problems in high school level algebra and elementary college level algebra don't require anything so sophisticated.

2. log(7x+2)-log(x-1)=1
your second equation is solved as follows:
since, in general, log(a*b) = log(a) + log(b), your first equation can be rewritten as shown below:
log((7x+2)/(x-1)) = 1
note that instead of using the general equation as log(a*b) = log(a) + log(b), we went in the reverse direction and used the general equation as log(a) + log(b) = log(a*b).
this is perfectly legitimate and is the proper way to back track from a log equation that has already been parceled out into its purest log form back to its original form.
you now have the equation:
log ((7x+2)/(x-1)) = 1
if you take the anti-log of both sides of this equation, you will get:
anti-log (log((7x+2)/(x-1)) = anti-log (1)
this can be simplified to:
(7x+2)/(x-1) = 10
the anti-log of the log of anything is anything.
in mathematical terms this would look like:
anti-log(log(a)) = a.
the anti-log of 1 is equal to 10 because the log of 10 is equal to 1.
you now have a simple equation that can be solved through normal algebraic means.
multiply both sides of that equation by (x-1) to get:
(7x + 2) = 10 * (x-1)
simplify to get:
7x + 2 = 10x - 10
subtract 7x from both sides of this equation and add 10 to both sides of this equation to get:
12 = 3x
commute this equation to get:
commute this equation means to flip each side of the equation using the general properties of algebraic equations that state if a = b then b = a. this is the law of commutation you should already know about.
the equation of 12 = 3x becomes:
3x = 12
divide both sides of this equation by 3 to get:
x = 4
the solution to this equation should be x = 4 if we did everything correctly.
to confirm, we go back to the original equation and replace x with 4 to see if the equation is true.
the original equation is:
log(7x+2)-log(x-1)=1
replace x with 4 to get:
log(7*4)+2) - log((4-1) = 1
simplify to get:
log(30) - log(3) = 1
use your calculator to get:
1 = 1
this confirms the solution of x = 4 is good.

note that when you deal with logs, the log of anything implies the base of 10 is being used, unless you specifically state what the base is.
this is what allowed us to find that the anti-log of 1 is equal to 10.
the basic property of logarithms states that:
log(b,x) = y if and only if b^y = x.
in our equation, we had log(x)) = 1 and we wanted to find the anti-log of 1 in order to find x.
by the basic property of logarithms, and using x as the variable that we are taking the log of, our equation of:
log(x) = 1 becomes:
log(10,x) = 1 because the implied base of 10 is now shown.
log(10,x) = 1 means log of x to the base of 10 equals 1.
by the basic properties of logarithms, this equation is true if and only if
10^1 = x
this simplifies to x = 10
the equation becomes:
log(10,10) = 1 which can also be shown as:
log(10) = 1 since the base of 10 is implied.
since log(10) = 1, then the anti-log of 1 is equal to 10.









Question 570823: 1/x-8/21=3/7x
Answer by mananth(10539) About Me  (Show Source):
You can put this solution on YOUR website!
%281%2Fx%29-%288%2F21%29=%283%2F7x%29
Add 8/21 to both sides of the equation
%281%2Fx%29=%283%2F7x%29%2B%288%2F21%29
add -(3/7x) to both sides
%281%2Fx%29-%283%2F7x%29=8%2F21
LCD = 7x
7-3=7x*8/21
4=56x/21
multiply by 21
84= 56x
/56
x=3/2
m.ananth@hotmail.ca


Question 570744: Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 147 miles in the same time that Dana travels 129 miles. If Chuck's rate of travel is 6 mph more that Dana's, and they travel the same length of time, at what speed does chuck travel?
Answer by mananth(10539) About Me  (Show Source):
You can put this solution on YOUR website!
Dana x 129 miles
Chuck x+ 8 147 miles
The time taken by them is the same
t=d/r
129 / x = 147 /(x+ 8 )
Cross multiply
129 (x + 8 ) = 147 * x
129 x + 1032 = 147 x
147 x -129 x = 1032
18 x = 1032
/ 18
x = 57.33 Dana mph
65.33 Chuck mph


Question 570727: How do I write this as an equation?
A student took a test composed of 20 questions, with correct answers worth 3 points. If the student received 48 points for his grade, how many questions were correct? My answer is 16 because 16*3=48

Answer by mananth(10539) About Me  (Show Source):
You can put this solution on YOUR website!
correct questions answered = x
3 points each
3x is what he got
3x=48
x=48/3
x= 16


Question 570721: For what values of K does the equation have equal solutions? 2x^2-Kx+8=0
Answer by josmiceli(6766) About Me  (Show Source):
You can put this solution on YOUR website!
When the equation has the form +f%28x%29+=+ax%5E2+%2B+bx+%2B+c+,
The quadratic formula to find the roots is
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
For real solutions, +b%5E2+-+4a%2Ac+ must be +0+ or positive
given:
+2x%5E2+-+K%2Ax+%2B+8+=+0+
+b%5E2+-+4a%2Ac+=+%28-K%29%5E2+-+4%2A2%2A8+
+b%5E2+-+4a%2Ac+=+K%5E2+-+64+
To be positive or zero,
+K%5E2+-+64+%3E=+0+
+K%5E2+%3E=+64+
+K+%3E=+8+
and, also, using (-) root
+K+%3C=+-8+
so,
+8+%3C=+K+%3C=+-8+


Question 570432: Is 3 ft equal to 30 in?
Answer by Alan3354(21541) About Me  (Show Source):

Question 570382: the sum of the measure of two complementary angles is 90. if on angle measures 15 more than twice the measure of the complement, find the measure of each angle.
Answer by solver91311(12114) About Me  (Show Source):
You can put this solution on YOUR website!

Let represent the measure of the complement of the angle. Then twice the measure of the complement is and 15 more than that is . Since the sum of the measures of complementary angles is 90, if is the measure of the complement, then must be the measure of the angle. So:



Solve for then calculate

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism



Question 570116: -10(x)+6-4x=-4x+8
I keep getting -1/5 but when I try to check it that does not equal out. Not sure if I am checking it wrong or doing it wrong! Thanks

Answer by Maths68(1140) About Me  (Show Source):
You can put this solution on YOUR website!
-10x%2B6-4x=-4x%2B8
-10x%2B6-cross%284x%29=-cross%284x%29%2B8
-10x%2B6=8
-10x=8-6
-10x=2
-10x%2F-10=2%2F-10
cross%28-10%29x%2Fcross%28-10%29=cross%282%29%2Fcross%28-10%29
x=-1%2F5

Check
=====
-10x%2B6-4x=-4x%2B8
-10%28-1%2F5%29%2B6-4%28-1%2F5%29=-4%28-1%2F5%29%2B8
10%2F5%2B6%2B4%2F5=4%2F5%2B8
Take LCD both sides of the equation
%2810%2B30%2B4%29%2F5=%284%2B40%29%2F5
44%2F5=44%2F5







Question 570087: how do you solve 3x-6=x
Answer by rfer(10417) About Me  (Show Source):
You can put this solution on YOUR website!
3x-x=6
2x=6
x=6/2
x=3


Question 570094: The distance from Cleveland to Pittsburgh is about 2/5 of the distance from Cleveland to Chicago. About how far is Cleveland from Chicago? (It is 120 miles from Cleveland to Pittsburgh.) How do I set up an equation for this problem?
Answer by rfer(10417) About Me  (Show Source):
You can put this solution on YOUR website!
120/(2/5)=x
120*5/2=x
600/2=x
x=300


Question 570078: 1/4r + 9 = 10 - 3/4r
Answer by stanbon(48502) About Me  (Show Source):
You can put this solution on YOUR website!
1/4r + 9 = 10 - 3/4r
-----
Add (3/4)r to both sides:
r + 9 = 10
r = 1
---------------
Cheers,
Stan H.


Question 570069: 2a+6=-a-8
Show work please, and try to
explain it as best as possible
thx :)

Found 3 solutions by mananth, stanbon, jim_thompson5910:
Answer by mananth(10539) About Me  (Show Source):
You can put this solution on YOUR website!
2a+6=-a-8
You find that the variable a is on both sides of the = sign.
to find the value of a you have to have the a's on one side and the numbers on the other side.
Fisrt lets bring the a on the right side to the left of the = sign
add a to both sides of the equation
2a+a+6 =-a+a-8
2a+a=3a, +a & -a= 0 on the right side. You have -8 left
3a+6 =-8
we remove the number from the left side of the = sign
add -6 to both sides of the equation
3a+6-6 = -8-6
+6 & -6 =0
3a= -14
Now the 3 has to be eliminated to find the value of a
you divide both sides of the equation by 3
%28cross%283%29%29a%2F%28cross%283%29%29 =+-14%2F3
a=-14%2F3

Answer by stanbon(48502) About Me  (Show Source):
You can put this solution on YOUR website!
2a+6=-a-8
-----
Add a to both sides to get:
3a + 6 = -8
Subtract 6 from both sides to get:
3a = -14
----
Divide both sides by 3 to get:
a = -14/3
================
cheers,
Stan H.

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
2a%2B6=-a-8 Start with the given equation.


2a=-a-8-6 Subtract 6 from both sides.


2a%2Ba=-8-6 Add a to both sides.


3a=-8-6 Combine like terms on the left side.


3a=-14 Combine like terms on the right side.


a=%28-14%29%2F%283%29 Divide both sides by 3 to isolate a.


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

Answer:

So the solution is a=-14%2F3


Question 570035: 6r+2r=7r solve.
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
6r%2B2r=7r Start with the given equation.


8r=7r Combine like terms on the left side.


8r-7r=0 Subtract 7r from both sides.


r=0 Combine like terms on the left side.


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

Answer:

So the solution is r=0


Question 570028: x2-2x=48....i have to solve for x by completing the square..how do you do this?
^(squared)

Answer by solver91311(12114) About Me  (Show Source):
You can put this solution on YOUR website!


Step 1. Move the constant term to the right hand side. This step is already done.

Step 2. Divide through by the lead coefficient. The lead coefficient in this problem is 1, so you can skip this step.

Step 3. Divide the coefficient on the first degree term by 2. In this case, 2 divided by 2 is 1.

Step 4. Square the result of Step 3. 1 squared is 1.

Step 5. Add the result of Step 4 to both sides of the equation.



Step 6. Factor the perfect square trinomial in the LHS:



Step 7. Take the square root of both sides, considering both the positive and negative root:



So



or



Step 8. Solve the two linear equations to get your two roots.

John

My calculator said it, I believe it, that settles it
The Out Campaign: Scarlet Letter of Atheism



Question 569627: Three more than six times some number
Answer by nyc_function(2626) About Me  (Show Source):
You can put this solution on YOUR website!
The given statement can be written:
6x + 3


Question 569716: A boat on a river travels downstream between two points, 60 mi apart, in one hour. The return trip against the current takes 2.5 hours. What is the boat's speed?
___mph
How fast does the current in the river flow?
___ mph


Answer by scott8148(5869) About Me  (Show Source):
You can put this solution on YOUR website!
b + c = 60 mi / 1 hr = 60 mph

b - c = 60 mi / 2.5 hr = 24 mph

adding equations ___ b + c + b - c = 60 + 24 ___ 2b = 84 ___ b = 42

substituting ___ (42) + c = 60 ___ c = 18


Question 569640: %286%2F7y%29-%281%2F3%29=%281%2F5%29 can you show the solution please?
Found 2 solutions by JBarnum, Alan3354:
Answer by JBarnum(1826) About Me  (Show Source):
You can put this solution on YOUR website!
i dont like fractions so first thing i do is multiply the denominators together
7y * 3 * 5 = 105y
now multiply everything by 105y
%28105y%29%286%2F7y%29-%28105y%29%281%2F3%29=%28105y%29%281%2F5%29
%2815%2Across%287y%29%29%286%2Fcross%287y%29%29-%2835y%2Across%283%29%29%281%2Fcross%283%29%29=%2821y%2Across%285%29%29%281%2Fcross%285%29%29
%2815%2A6%29-%2835y%29=21y
90-35y=21yadd 35y to both sides
90=56y divide by 56
90%2F56=y reduce by 2
45%2F28=y

Answer by Alan3354(21541) About Me  (Show Source):
You can put this solution on YOUR website!
6/7y-1/3=1/5
Multiply by 7*3*5 to eliminate fractions.
90y - 35 = 21
Add 35
90y = 56
Divide by 90
y = 56/90
y = 28/45


Question 569626: The length of the top of a computer is 2 1/5 feet longer than its width. If its width measures m feet, express its length as an algebraic expression in m.
Answer by JBarnum(1826) About Me  (Show Source):

Question 569585: p/2-2=-6
Answer by TutorDelphia(189) About Me  (Show Source):
You can put this solution on YOUR website!
p/2-2=-6
add 2 to both sides
p/2=-4
multiply both sides by 2
p=-8


Question 569408: x+3/10=-3/5
Answer by domo816(3) About Me  (Show Source):
You can put this solution on YOUR website!
x+3/10=-3/5
x=-3/5-3/10
-3/5*2/2=-6/10
x=-6/10-3/10
x=-9/10


Question 569248: 4(2b-6)+11=8b-13
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!

4%282b-6%29%2B11=8b-13 Start with the given equation.


8b-24%2B11=8b-13 Distribute.


8b-13=8b-13 Combine like terms on the left side.


8b=8b-13%2B13 Add 13 to both sides.


8b-8b=-13%2B13 Subtract 8b from both sides.


0b=-13%2B13 Combine like terms on the left side.


0b=0 Combine like terms on the right side.


0=0 Simplify.


Since this equation is always true for any b value, this means b can equal any number.

So there are an infinite number of solutions.

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

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

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


Question 569222: bob bought a boat,he recieved .06 discount and 200 dollars off and paid 600 dollars for the boat,what is the original price for the boat
Answer by stanbon(48502) About Me  (Show Source):
You can put this solution on YOUR website!
bob bought a boat,he recieved .06 discount and 200 dollars off and paid 600 dollars for the boat,what is the original price for the boat
-----------------------
Let original price be "x":
x - 0.06x - 200 = 600
0.94x = 800
x = 800/0.94
x = $851.06
================
Cheers,
Stan H.
================


Question 568794: I need to solve the varible problem

1. p=s-c?
(s) being the variable

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
p=s-c Start with the given equation


p%2Bc=s-c%2Bc Add 'c' to both sides


p%2Bc=s Combine like terms


s=p%2Bc Flip the equation


So the solution is s=p%2Bc

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

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

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


Question 568877: 2(x-3)+5=-10
Answer by stanbon(48502) About Me  (Show Source):
You can put this solution on YOUR website!
2(x-3)+5=-10
----
Subtract 5 from both sides:
2(x-3) = -15
---
2x-6 = -15
---
Add 6 to both sides:
2x = -9
---
Divide by 2:
x = -4.5
==============
Cheers,
Stan H.
=============


Question 568759: 12z=4z-56
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
12z=4z-56 Start with the given equation.


12z-4z=-56 Subtract 4z from both sides.


8z=-56 Combine like terms on the left side.


z=%28-56%29%2F%288%29 Divide both sides by 8 to isolate z.


z=-7 Reduce.


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

Answer:

So the solution is z=-7

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

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

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


Question 568758: 10(y-1)=y+4
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
10%28y-1%29=y%2B4 Start with the given equation.


10y-10=y%2B4 Distribute.


10y=y%2B4%2B10 Add 10 to both sides.


10y-y=4%2B10 Subtract y from both sides.


9y=4%2B10 Combine like terms on the left side.


9y=14 Combine like terms on the right side.


y=%2814%29%2F%289%29 Divide both sides by 9 to isolate y.


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

Answer:

So the solution is y=14%2F9
-------------------------------------------------------------------------------------------------
If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

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


Question 568716: 3x-2(5-4x)=12
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
3x-2%285-4x%29=12 Start with the given equation.


3x-10%2B8x=12 Distribute.


11x-10=12 Combine like terms on the left side.


11x=12%2B10 Add 10 to both sides.


11x=22 Combine like terms on the right side.


x=%2822%29%2F%2811%29 Divide both sides by 11 to isolate x.


x=2 Reduce.


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

Answer:

So the solution is x=2

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Question 568646: what would be the answer for y+7=9
Answer by nyc_function(2626) About Me  (Show Source):
You can put this solution on YOUR website!
y + 7 = 9

To find the value of y, subtract 7 from 9.

y = 9 - 7

y = 2



Question 568618: For the equation 3x^2+xy+2y^2=0, which of the following is true?
(a) x=y+√y^2-4(3)(2y^2) (over/divided)2(3)
(b) x=-y+√y^2-4(3)(2y^2) (over/divided)2(3)
(c) x=-y+√x^2-4(3)(2y^2) (over/divided)2(3)
(d) x=-y+√y^2-4(3)(3x^2) (over/divided)2(3)
Thank you so much in advance!

Answer by AnlytcPhil(1116) About Me  (Show Source):
You can put this solution on YOUR website!
3x² + xy + 2y² = 0

(3)x² + (y)x + (2y²) = 0

a=3, b=y, c = 2y²

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

x+=+%28-y+%2B-+sqrt%28+y%5E2-4%2A3%2A2y%5E2+%29%29%2F%282%2A3%29+

The 2 solutions are 

x+=+%28-y+%2B+sqrt%28+y%5E2-4%2A3%2A2y%5E2+%29%29%2F%282%2A3%29+ and x+=+%28-y+-+sqrt%28+y%5E2-4%2A3%2A2y%5E2+%29%29%2F%282%2A3%29+

The first one is the same as choice (b)

Edwin


Question 568584: 9b+42=-12
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
9b%2B42=-12 Start with the given equation.


9b=-12-42 Subtract 42 from both sides.


9b=-54 Combine like terms on the right side.


b=%28-54%29%2F%289%29 Divide both sides by 9 to isolate b.


b=-6 Reduce.


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

Answer:

So the solution is b=-6

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Question 568582: 2c+6+7c=8
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
2c%2B6%2B7c=8 Start with the given equation.


9c%2B6=8 Combine like terms on the left side.


9c=8-6 Subtract 6 from both sides.


9c=2 Combine like terms on the right side.


c=%282%29%2F%289%29 Divide both sides by 9 to isolate c.


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

Answer:

So the solution is c=2%2F9
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Question 568579: 18y=12y+24
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
18y=12y%2B24 Start with the given equation.


18y-12y=24 Subtract 12y from both sides.


6y=24 Combine like terms on the left side.


y=%2824%29%2F%286%29 Divide both sides by 6 to isolate y.


y=4 Reduce.


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

Answer:

So the solution is y=4

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Question 568549: 9a+2=4a-18
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
9a%2B2=4a-18 Start with the given equation.


9a=4a-18-2 Subtract 2 from both sides.


9a-4a=-18-2 Subtract 4a from both sides.


5a=-18-2 Combine like terms on the left side.


5a=-20 Combine like terms on the right side.


a=%28-20%29%2F%285%29 Divide both sides by 5 to isolate a.


a=-4 Reduce.


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

Answer:

So the solution is a=-4

-------------------------------------------------------------------------------------------------
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Question 568546: 12(m – 4) = 3m - 3
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
12%28m-4%29=3m-3 Start with the given equation.


12m-48=3m-3 Distribute.


12m=3m-3%2B48 Add 48 to both sides.


12m-3m=-3%2B48 Subtract 3m from both sides.


9m=-3%2B48 Combine like terms on the left side.


9m=45 Combine like terms on the right side.


m=%2845%29%2F%289%29 Divide both sides by 9 to isolate m.


m=5 Reduce.


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Answer:

So the solution is m=5

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Question 568542: 2x+5=9x-16
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
2x%2B5=9x-16 Start with the given equation.


2x=9x-16-5 Subtract 5 from both sides.


2x-9x=-16-5 Subtract 9x from both sides.


-7x=-16-5 Combine like terms on the left side.


-7x=-21 Combine like terms on the right side.


x=%28-21%29%2F%28-7%29 Divide both sides by -7 to isolate x.


x=3 Reduce.


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Answer:

So the solution is x=3

-------------------------------------------------------------------------------------------------
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Question 568525: -10(x+3)+28=-16-16
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
-10%28x%2B3%29%2B28=-16-16 Start with the given equation.


-10x-30%2B28=-16-16 Distribute.


-10x-2=-16-16 Combine like terms on the left side.


-10x-2=-32 Combine like terms on the right side.


-10x=-32%2B2 Add 2 to both sides.


-10x=-30 Combine like terms on the right side.


x=%28-30%29%2F%28-10%29 Divide both sides by -10 to isolate x.


x=3 Reduce.


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Answer:

So the solution is x=3


-------------------------------------------------------------------------------------------------
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Question 567412: If 4p-2=-3(p-4), then p=?
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
4p-2=-3%28p-4%29 Start with the given equation.


4p-2=-3p%2B12 Distribute.


4p=-3p%2B12%2B2 Add 2 to both sides.


4p%2B3p=12%2B2 Add 3p to both sides.


7p=12%2B2 Combine like terms on the left side.


7p=14 Combine like terms on the right side.


p=%2814%29%2F%287%29 Divide both sides by 7 to isolate p.


p=2 Reduce.


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Answer:

So the solution is p=2


Question 568491: What is the answer to 5(w-3)+4(2w+1), please
could you do step to step how to wrk it out, please?

Answer by stanbon(48502) About Me  (Show Source):
You can put this solution on YOUR website!
5(w-3)+4(2w+1)
----
5w-15+8w+4
---
= 13w-11
=================
Cheers,
Stan H.


Question 568472: Find the smallest positive number t such that
e^(sin(t))=5/7

Answer by stanbon(48502) About Me  (Show Source):
You can put this solution on YOUR website!
Find the smallest positive number t such that
e^(sin(t))=5/7
-----
Take the natural log of both sides to get:
sin(t) = ln(5/7)
---
sin(t) = -0.3365
---
Take the inverse sin of both sides to get:
t = 200.07 degrees or 3.4848 radians
==================
Cheers,
Stan H.
==================


Question 568236: 2[x-5(x+2)+3]
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
2[x-5(x+2)+3]


2[x-5x-10+3]


2[-4x-7]


-8x-14


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