Questions on Algebra: Operations with Signed Numbers answered by real tutors!

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Tutors Answer Your Questions about Signed-numbers (FREE)


Question 748333: Slove:
12x^2-6x=0

Answer by tommyt3rd(482) About Me  (Show Source):
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12x%5E2-6x=0
6x%282x-1%29=0

so x=0 or 2x-1=0 (i.e. x=1/2)


:)



Question 613432: -3(-2 - 6 x 2) - [4(2 - 4) - 2]
Answer by tommyt3rd(482) About Me  (Show Source):

Question 651087: If somebody could please help me on a college algebra problem. I need to simplify this problem :
5/6*(2/3-1/6)+7/18
I started out by reducting it to
(4/6 - 1/6)
5/6*3/6+7/8 than somehow got
15/6+7/8
but than i got stuck.
So could somebody please help me and show me how to do this?
That'd be great. Thank you! :)

Answer by tommyt3rd(482) About Me  (Show Source):

Question 680402: D=36+5.8x
Answer by tommyt3rd(482) About Me  (Show Source):
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The question seems to be incomplete, please check :)


Question 713565: How do i factorise the below
(a+2)(2a)+7a+14
and
64x^2+80xy+25y^2
Thanks.

Answer by tommyt3rd(482) About Me  (Show Source):
You can put this solution on YOUR website!
First one:


second:


:)


Question 716100: 3+3 x 3-3+3= ?

Answer by tommyt3rd(482) About Me  (Show Source):
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Order of operations tells us to multiply first, then we do all additions and subtractions:
3+3 x 3-3+3=3+9-3+3=12-3+3=9+3=12
:)


Question 689586: 4x + 5y = ?
x=6,y=17

Answer by tommyt3rd(482) About Me  (Show Source):
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4x + 5y = 4(6)+5(17)=24+85=109
:)


Question 719079: 91,92,93,94,880,960,975,977, ----,----.???

Answer by tommyt3rd(482) About Me  (Show Source):
You can put this solution on YOUR website!
I see no discernable pattern, recheck your numbers there may be an error :)


Question 639963: mr. bailey purchased some groceries that cost d dollars. he paid with a $50 bill. write an expression for the amount of the change he will receive
Answer by tommyt3rd(482) About Me  (Show Source):
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Mr. Bailey will receive d-50 dollars in change


Question 746310: If 2x+3y=24 and 2x-3y=12 then value of xy is_____________
Found 2 solutions by mananth, Cromlix:
Answer by mananth(12270) About Me  (Show Source):
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2.00 x + 3.00 y = 24.00 .............1
Total value
2.00 x -3.00 y = 12.00 .............2
Eliminate y
multiply (1)by 1.00
Multiply (2) by 1.00
2.00 x 3.00 y = 24.00
2.00 x -3.00 y = 12.00
Add the two equations
4.00 x = 36.00
/ 4.00
x = 9.00
plug value of x in (1)
2.00 x + 3.00 y = 24.00
18.00 + 3.00 y = 24.00
3.00 y = 24.00 -18.00
3.00 y = 6.00
y = 2.00
xy=9*2=18

Answer by Cromlix(294) About Me  (Show Source):
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2x + 3y = 24.....1
2x - 3y = 12.....2
Add 1 to 2
4x = 36
x = 9
Substitute x = 9
into 1
2(9) + 3y = 24
18 + 3y = 24
3y = 24 - 18
3y = 6
y = 2
Therefore value of xy = 9 x 2 = 18


Question 617695: Solve for b:
(1/b) - (b/(b-1)) = 2

Answer by tommyt3rd(482) About Me  (Show Source):
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%281%2Fb%29+-+%28b%2F%28b-1%29%29+=+2


%28-3b%5E2%2B3b-1%29%2F%28b%2A%28b-1%29%29=0
Only the numerator contributes solutions so...

b+=+%28-3+%2B-+sqrt%28+%283%29%5E2-4%2A%28-3%29%2A%28-1%29%29%29%2F%282%2A%28-1%29%29+

which simplifies to...

b+=+%281+%2B-+sqrt%28+-3%29%29%2F2+


Question 730564: If tan θ= -3 and cos θ<0, then tan θ/2=?
Answer by tommyt3rd(482) About Me  (Show Source):
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tan%28theta%29=opp%2Fadj=-3%2F1
so
hyp=sqrt%281%5E2%2B%28-3%29%5E2%29=sqrt%2810%29
so
sin%28theta%29=%283%2Asqrt%2810%29%29%2F10
cos%28theta%29=-sqrt%2810%29%2F10 (we take the negative case because cosine is negative for this example)
now
tan%28theta%2F2%29=sin%28theta%29%2F%281%2Bcos%28theta%29%29
Therefore...

tan%28theta%2F2%29=%28%283%2Asqrt%2810%29%29%2F10%29%2F%281-sqrt%2810%29%2F10%29
which simplifies to
%28sqrt%2810%29%2B1%29%2F3


Question 675803: How I write a second inequality with the same meaning: x<5
Answer by tommyt3rd(482) About Me  (Show Source):
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The inequality x<5 is a statement about the size of x compared to 5

adding/subtracting...
x+1<5+1
x+2<5+2
x+a<5+a
multiples of both sides...
2x<10
2x<15
bx<5b
In fact many reversible things we do to the left (as well as the right side) are possible :)


Question 653590: How is (-2) squared different from -2 squared
Answer by tommyt3rd(482) About Me  (Show Source):

Question 704940: Evaluate each express for x=16 and y=4
3x-3y

Answer by tommyt3rd(482) About Me  (Show Source):
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3x-3y=3(x-y)=3(16-4)=3(12)=36


Question 715693: (-25) - (-21) = ?

Answer by tommyt3rd(482) About Me  (Show Source):
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(-25) - (-21) =
-25 + [-(-21)]=
-25+21=
21+(-25)=
21 +(-21)+(-4)=
-4


Question 740688: what is the answer to 53-[3(8+2)+5(9-5)]

Answer by tommyt3rd(482) About Me  (Show Source):
You can put this solution on YOUR website!
53-[3(8+2)+5(9-5)]=
53-[3(10)+5(4)]=
53-[30+20]=
53-50=3
:)


Question 744711: I am calculating angles and must figure out cosine to the power of -1.
I know what square root is etc., but how do you calculate to a minus power?

Answer by josgarithmetic(1495) About Me  (Show Source):
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According to context you are referring to inverse function of cosine. Let me use different notation than the "exponent negative 1".

let x be some angle or angle measurement.
cos(x) is some number between -1 and +1.

The inverse function of cosine, is "arcos()", read as "the arc whose cosine is...". The input is NOT an angle measurement, but is a cosine value.

Common value: 30 degrees is a commonly known or used angle value. DRAW a unit circle to visualize this. cos%2830%29=%281%2F2%29sqrt%283%29.

Now, it may be asked, what is the arc which has a cosine of %281%2F2%29sqrt%283%29 ?
This is equivalent to asking, what is arcos%28sqrt%283%29%2F2%29 ?
arcos%28sqrt%283%29%2F2%29=30.


Question 743682: I need to make the following equation true by adding 2 pairs of brackets
5+7*3-2*9=72

Answer by pfongk(1) About Me  (Show Source):
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I wasn't sure how to edit my question. The bulletin board for Uni has stated that it should be 108 not 72 for the answer, I had worked out that answer so I don't need this question answered anymore. Sorry.


Question 742454: Hello
I am just starting back to school and it has been a long time since I've had to do any math problems, let alone Pre-Algebra. I am learning to perform the Order of Operations. I am using the P,E,M,D,A,S method. My problem is...
(-36 / 6) - (4 / 4) so far I have this

-36 4____ But should'nt 4/4=1, -36/6=6 or = to 1
6 4

Answer by Alan3354(30993) About Me  (Show Source):
You can put this solution on YOUR website!

(-36 / 6) - (4 / 4)
4/4 = 1
-36/6 = -6
-----------
= -6 - 1
= -7


Question 741501: -1+9(-7g-9)
Answer by jim_thompson5910(28536) About Me  (Show Source):
You can put this solution on YOUR website!
-1+9(-7g-9)

-1+9(-7g)+9(-9)

-1-63g-81

-63g-82


Question 736330: 2[3 - 5(3 - 1)²]
Answer by rfer(12654) About Me  (Show Source):
You can put this solution on YOUR website!
2[3-5(2)^2]
2[3-5(4)]
2[3-20]
2(-17)=-34


Question 736300: I am dealing with adding signed number. for example: -10+(-7) can u help me.
Answer by jim_thompson5910(28536) About Me  (Show Source):
You can put this solution on YOUR website!
Both numbers are negative, so you add the numbers (ignore the negative signs) to get 10+7 = 17

Then you make the result negative since both numbers are negative to get the final answer to be -17

Real World Example: you are 10 dollars in debt (represented by the integer -10) and you go 7 more dollars in debt (-7). In total, you are 17 dollars in debt (-17)


Question 735915: (-4+6)[(-8)+(-7)-(-10)] I am not sure how to solve this problem.
Answer by rfer(12654) About Me  (Show Source):

Question 731341: help me perform indicated operations
-8[4+(-2+7)]
_______________
-3[4-(-9)]-3(-9)
thank you, Debbie
Espimom1@aol.com

Answer by josgarithmetic(1495) About Me  (Show Source):
You can put this solution on YOUR website!
The rational expression contains no exponents.

Parentheses:
-8[4+(-2+7)]
_______________
-3[4-(-9)]-3(-9)


=%28-8%284%2B%285%29%29%29%2F%28-3%284%2B9%29-3-9%29

Parentheses:
%28-8%284%2B%285%29%29%29%2F%28-3%284%2B9%29-3-9%29=%28-8%2A9%29%2F%28-3%2A13-3-9%29

Multiplications:
%28-8%2A9%29%2F%28-3%2A13-3-9%29=-72%2F%28-39-3-9%29

Divisions? Not ready.

Additions? None as written.

Subtractions:
-72%2F%28-39-3-9%29=-72%2F%28-52%29

Divisions:
=1%264%2F13


Question 730116: find how long it takes a person to drive 135 miles if she drives on cruise control set at 60 mph.
Answer by Alan3354(30993) About Me  (Show Source):
You can put this solution on YOUR website!
find how long it takes a person to drive 135 miles if she drives on cruise control set at 60 mph.
-----------
d = r*t
t = d/r


Question 730029: i need to solve for X: x/a+x/b=1 it's x over a plus x over b = 1, someone just provided the answer and that does not help. i need to see how you actually arrived at the answer.
Answer by lynnlo(4155) About Me  (Show Source):
You can put this solution on YOUR website!
OK,THIS ONE IS SIMPLE
PROBLEM:
X/A+X/B
X/A+X/B=0
1/A-1/B=0
X=AB/A+B


Question 730021: i need to solve for X: x/a+x/b=1 it's x over a plus x over b = 1
Answer by lynnlo(4155) About Me  (Show Source):

Question 728633: 1/14+18/x=? I need to know how to do a problem like this
Answer by josmiceli(9667) About Me  (Show Source):
You can put this solution on YOUR website!
+1%2F14+%2B+18%2Fx+
This is an expression, not an equation, so
the most you can do with it is express it
as a single fraction.
Multiply the 1st fraction by +x%2Fx+
Multiply the 2nd fraction by +14%2F14+
This changes nothing, since you're multiplying
by +1+ in both cases
+%281%2F14%29%2A%28x%2Fx%29+%2B+%2818%2Fx%29%2A%2814%2F14%29+
+x%2F%2814x%29+%2B+252%2F%2814x%29+
+%28+x+%2B+252+%29+%2F+%28+14x+%29+
Hope this helps


Question 726475: 21<6u

Answer by lenny460(764) About Me  (Show Source):
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21<6u
21 < 6u
Divide each side of the inequality by 3.
21/3 = 7
6u/3 = 2u
Therefore:
Answer:
7 < 2u or
2u > 7


Question 725766: How do I explain to my student: Michelle has 47 dollars, 11 more than Susan.
Is it 47 = s + 11

Answer by Alan3354(30993) About Me  (Show Source):
You can put this solution on YOUR website!
How do I explain to my student: Michelle has 47 dollars, 11 more than Susan.
Is it 47 = s + 11
----------------
Just saying Michelle has 47 dollars, and it's 11 more than Susan explains that.
What else is there to know?
No other question was asked.


Question 722929: Is (8, -1) a solution of the system, 2x + 3y = 13 and x - y = 9?
Found 2 solutions by DrBeeee, jim_thompson5910:
Answer by DrBeeee(378) About Me  (Show Source):
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Put (x,y) = (8,-1) into the two equations and check.
Is (2*8+3*(-1) = 13)?
Is (16 - 3 = 13)?
Is (13 = 13)? Yes
Is (8 -(-1) = 9)?
Is (9 = 9)? Yes
Answer: Yes, (8,-1) is the solution (and only solution) to the given system of equations.

Answer by jim_thompson5910(28536) About Me  (Show Source):
You can put this solution on YOUR website!
2x + 3y = 13

2(8) + 3(-1) = 13 ... plug in (8,1)

16 - 3 = 13

13 = 13

so (8,1) satisfies the first equation

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

x - y = 9

8 - (-1) = 9 ... plug in (8,1)

8 + 1 = 9

9 = 9

and (8,1) satisfies the second equation

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

(8,1) satisfies BOTH equations at the same time, so it is the solution to the system of equations


Question 709560: 16x+6+20x-14
Answer by jerryguo41(162) About Me  (Show Source):
You can put this solution on YOUR website!
16x%2B6%2B20x-14
Simplify by adding/subtracting common terms
-4x-8
or by factoring
-4%28x%2B2%29


Question 709270: y=-3x^2-9x-12 need help finding the vertex and axis
Answer by josgarithmetic(1495) About Me  (Show Source):
You can put this solution on YOUR website!
EDIT: Fixed the sign mistake.

First, factor. Then complete the square.
y=-3%28x%5E2%2B3x%2B4%29
The square to add and subtract is %283%2F2%29%5E2.
y=-3%28x%5E2%2B3x%2B%283%2F2%29%5E2+%2B4-%283%2F2%29%5E2%29
y=-3%28%28x%2B%283%2F2%29%29%5E2%2B%287%2F4%29%29
y=-3%28x%2B3%2F2%29%5E2%2B7%2F4
y=-3%28x%2B3%2F2%29%5E2-21%2F4
y=-3%28x%2B3%2F2%29%5E2-5%261%2F4%29


The value of "h" is -%283%2F2%29 and the value of "k" is -%2821%2F4%29 or -%285%261%2F4%29.
The vertex is (-%283%2F2%29,-5%261%2F4)


Question 709004: y=mx+b, for m
Answer by rfer(12654) About Me  (Show Source):
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y-b=mx
(y-b)/x=m


Question 708707: There exist pairs of integers, x and n, for which xn = (25)(4 to the 4th power)(8 to the 8/3 power )(16 to the 3/4 power). What is the greatest
possible value of n among these pairs?

Answer by KMST(1868) About Me  (Show Source):
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Of all the pairs (x,n) whose product is the same xn=N number, the greatest n will be paired with the least positive x.
Since N=1%2AN, the greatest integer that could be n is N
So we have to find N=%2825%29%2A%284%5E4%29%2A%288%5E%288%2F3%29%29%2A%2816%5E%283%2F4%29%29%5Eor N =(25)*(4^4)*(8^(8/3))*(16^(3/4))
Either way, that expression is hard to type.
Luckily, it can be simplified, because
16=2%5E4 --> 16^(3/4)=%28root%284%2C16%29%29%5E3=%28root%284%2C2%5E4%29%29%5E3=2%5E3
8=2%5E3 --> 8^(8/3)=%28root%283%2C8%29%29%5E8=%28root%283%2C2%5E3%29%29%5E8=2%5E8
and, while we are at it,
4=2%5E2 --> 4%5E4=%282%5E2%29%5E4=2%5E%282%2A4%29=2%5E8
So substituting all that, we get a large number that can be calculated with a calculator,
N=%2825%29%2A%282%5E8%29%2A%282%5E8%29%2A%282%5E3%29=highlight%2825%2A2%5E19%29 or with pencil and paper:


NOTE 1:
If it was specified that x, and n could not be 1,
then the least possible positive x would be 2,
and that would make 25%5E2%5E18 the greatest possible n.

NOTE 2:
Since xn=25%2A2%5E19=2%5E19%2A5%5E2 the positive factors are all of the form 2%5Ea%2A5%5Eb
with a being any of the 20 integers from 0 to 19 including 0 and 19,
and b being 0, 1, or 2 (just 3 choices).
That makes the total number of positive factors 3%2A20=60.
That makes 60 (x,n) ordered pairs, or 30 {x,n} sets of factors (if order does not matter).
Considering the negative factors doubles the possibilities.


Question 706063: there are 7 children with 1 set of twins. The youngest is 6 and the oldest is 16. the mean is 11, the median is 10 and the mode is 15. What are their ages?


Answer by stanbon(57285) About Me  (Show Source):
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there are 7 children with 1 set of twins. The youngest is 6 and the oldest is 16. the mean is 11, the median is 10 and the mode is 15. What are their ages?
---------
Ages from youngest to oldest: 6........10..........16
1st: 6
2nd: x
3rd: y
4th: 10
5th: 15
6th: 15
7th: 16
----
Equation:
Mean = (6+x+y+10+15+15+16)/7 = 11
-----
x+y + 52 = 77
----
x+y = 25
-----
Comment: x+y cannot be 25 if 10 is the median.
=============================
Cheers,
Stan H.


Question 704922: 3a+2=17
Answer by jim_thompson5910(28536) About Me  (Show Source):
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3a%2B2=17 Start with the given equation.


3a=17-2 Subtract 2 from both sides.


3a=15 Combine like terms on the right side.


a=%2815%29%2F%283%29 Divide both sides by 3 to isolate a.


a=5 Reduce.


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

Answer:

So the solution is a=5


Question 702926: Can you explain this to me?

1/(x^2+x-2)- 2/(x+2)

Answer by checkley79(3050) About Me  (Show Source):
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1/(x^2+x-2)- 2/(x+2) FIND THE COMMON DENOMINATOR.
[(X+2)-2(X^2+X-2)]/(X^2+X-2)(X+2)
[X+2-2X^2-2X+4]/(X^2+X-2)(X+2)
[(-2X^2-X+6]/(X^2+X-2)(X+2)
[(-2X+3)(X+2)]/(X^2+X-2)(X+2) CANCEL OUT THE (X+2) TERMS.
(-2X+3)/(X^2+X-2) ANS.


Question 701696: Hi my name is Gabrielle McGlothen I am in the 6th grade and I was wondering if you could help me with Subtraction of signed numbers please could you i really need help with this i cant not solve wall these numbers and i really need a tutor

Answer by jim_thompson5910(28536) About Me  (Show Source):
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Go ahead and post the problem so we can help you out. Thanks.


Question 699139: 5+6+10=
4+9+8=
1+7+3=
9+9+10=
6+5+4=

Answer by checkley79(3050) About Me  (Show Source):
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5+6+10=21
4+9+8=21
1+7+3=11
9+9+10=28
6+5+4=15


Question 698784: solve by using subsitution
4x+4y=-20
x-4y=15

Answer by Simnepi(204) About Me  (Show Source):
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4x+4y=-20 Equation (1)
x-4y=15 Equation (2)
Rearranging (2) gives
x=15+4y Equation (3)
We can now substitute the value of x from (3) into (1)
4*(15+4y)+4y = -20
Multiplying out and simplifying we get
60+20y = -20
therefore 20y = -80
which gives y = -4
Now we can substitute this value of y into either (1), (2) or (3) to find the value of x
lets use (3)
x=15+4y
x=15+4*-4
so x= -1


Question 698785: solve the system algebraically.
Find the number of solutions for the system
-5x+3y=-15
-10x+6y=-30
A)No solution
B)one solution
C)infinite number of solutions
D)None of these

Answer by unlockmath(1599) About Me  (Show Source):
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Hello,
With these:
-5x+3y=-15
-10x+6y=-30
Multiply the first equation by 2 to get:
-10x+6y=-30
Notice this equation is exactly like the second equation:
Therefore, they both lie on each other giving us:
Infinite solutions.
Make sense?
RJ
www.math-unlock.com


Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125