Questions on Algebra: Expressions involving variables, substitution answered by real tutors!

Tutors Answer Your Questions about Expressions-with-variables (FREE)

Question 571246: how do you solve
-8x2+22x-5
Found 2 solutions by Alan3354, scott8148:
Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
how do you solve
-8x2+22x-5
--------------
Equations are solved.
This is not an equation, there's no equal sign.

Answer by scott8148(5879)   (Show Source):
You can put this solution on YOUR website!
factoring ___ (-4x + 1)(2x - 5)

Question 570120: 4x+3x+2=7 What does "x" equal?

Answer by Maths68(1140)   (Show Source):
You can put this solution on YOUR website!

Check
=====

Question 569999: I got the problem:
5r-s=5
-4r+5s=17
on my homework and every time I try solving it I get really long decimals for my coordinates. I don't know if I'm substituting the wrong numbers in or if I'm my error is just in the math.
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
You have an error in your math as the answers are actually whole numbers. Post your work here or email me at jim_thompson5910@hotmail.com to send me what you have so far so I can see where you went wrong. Thanks.

Question 569886: 5x - 4 - x = -3x - 6 - x
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Start with the given equation.

Combine like terms on the left side.

Combine like terms on the right side.

Add to both sides.

Add to both sides.

Combine like terms on the left side.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

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

Answer:

So the solution is

Question 569896: I have an assignment for solving inequalities. I had to write an expression that would represent the cost of any amount of ceramic tile given that ceramic tile costs $2.00 per square ft. (use variable c to represent a square foot of ceramic tile). Do not write an equation. My answer to this was $2.00 per square ft=2c.
Write an expression that would represent the cost of any given amount of the decorative tile given that decorative tile costs $5.00 per square ft. (use variable d to represent a square ft of decorative tile). I wrote $5.00 per square ft=5d
Would you please let me know if this is correct because there still are 10 more parts to this and I have to write them as inequality equations.
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
write an expression that would represent the cost of any amount of ceramic tile given that ceramic tile costs $2.00 per square ft. (use variable c to represent a square foot of ceramic tile).
Do not write an equation. My answer to this was $2.00 per square ft=2c.
Ans: 2c where c is the amount of ceramic tile in square feet.
-----------------------------------
Write an expression that would represent the cost of any given amount of the decorative tile given that decorative tile costs $5.00 per square ft. (use variable d to represent a square ft of decorative tile). I wrote $5.00 per square ft=5d
Ans: 5d
================
Cheers,
Stan H.

Question 569597: so is there an easier way to do this problem 14y+10=23y-17
Found 2 solutions by Alan3354, TutorDelphia:
Answer by Alan3354(21550)   (Show Source):
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so is there an easier way to do this problem 14y+10=23y-17
--------
Easier than what?

Answer by TutorDelphia(189)   (Show Source):
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14y+10=23y-17
add 17 to both sides
14y+27=23y
subtract 14y from both sides
27=9y
divide both sides by 9
3=y
y=3

Question 569241: Let a, b,c be positive integers with a>=b>=c such that
a^2 - b^2 - c^2 +ab=2011
and
a^2 + 3b^2 + 3c^2 -3ab -2ac-2bc=-1997
what is a?
Answer by richard1234(4789)   (Show Source):
You can put this solution on YOUR website!
It is generally best to avoid posting this question until the day after the AMC10/12A exams (yes, I took this exam as well). But since it's pretty late in the day, I'll show the solution. Make sure not to publicize it to anyone else.

Adding both equations (I should have done this myself during the exam...I tried adding three times the first equation to the second equation and got nowhere).

This factors to

Essentially we have three square numbers adding to 14, so the only possibility is {9,4,1}. Since a and c are the furthest apart, we have

So our three numbers are either {c,c+1,c+3} or {c,c+2,c+3}. Suppose the numbers are {c,c+1,c+3}. Plugging into the first equation we have

(this is actually a linear equation)

If c = 250, then a = 253 and we are done. For sake of completeness we can try the other case:

, however if you solved this, c would not be an integer. Therefore a = 253.

Question 569044: -2x+5y=13;solve for x
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Start with the given equation

Subtract 5y from both sides.

Multiply every term by -1

Rearrange the terms

Divide both sides by 2 to isolate x

So the solution is
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Jim
-------------------------------------------------------------------------------------------------

Question 568531: You have 8 bags of grass seed. Each bag covers 1200 ft squared of ground. The function A(b)= 1200b represents the are A(b), in square feet, that b bags cover. What domain and range are reasonable for the function? Explain.
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Domain: Set of all nonnegative integers (ie integers that are not negative)

Range: The set {0, 1200, 2400, 3600, 4800, ...}

The reason why negative numbers are excluded is because negative bag counts or negative area doesn't make much sense. Integers are stressed here because you cannot buy half a bag (you must buy whole bags)

The range is simply the set of all multiples of 1200

Question 568528: 1/3(x-2)=4
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!

-------------------------------------------------------------------------------------------------
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Jim
-------------------------------------------------------------------------------------------------

Question 568501: I need help for this question:
Define variables and write an equation to model the relationship in each table.
Number of hours. Total Pay
4 $32
6. $48
8. $64
10. $80
Any help would be appreciated! Thank you!
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
I need help for this question:
Define variables and write an equation to model the relationship in each table.
Number of hours. Total Pay
4 $32
6. $48
8. $64
10. $80
------
Total Pay = 8*(Number of hours)
---
P = 8n
=======================
Cheers,
Stan H.
===========

Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Let x = # of hours and y = total pay

Notice how as x increases by 2, y increases by 16. So the change is 16/2 = 8, which means that the slope is 8. So

Now when x = 4, y = 32. So use this info to find b in

So the equation is or simply
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Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
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Question 568018: Write the fraction in terms of the LCM of the denominators.
9 over (x-1)^2 , 6 over x(x-1)
I thought I was supposed to find the LCD. How do you solve this?
I know the answer is 9x over x(x-1)^2 , 6x-6 over x(x-1)^2
but I don't understand how to get to that.
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
Write the fraction in terms of the LCM of the denominators.
9 over (x-1)^2 , 6 over x(x-1)
-------
LCM = x(x-1)^2
---
Rewrite each fraction with the LCM as its denominator
---
[9/(x-1)^2] = [9x/LCM]
----
[6/(x(x-1))] = [6(x+1)/LCM]
----
Cheers,
Stan H.
----

Question 567916: What is M-2?

Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
It's a binomial.

Question 567770: 3a-b=5
a=3/4b
the answer is (3,4) and i don't understand why
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Start with the first equation

Plug in . In other words, replace 'a' with

Multiply

Combine like terms

Multiply both sides by 4.

Multiply

Divide both sides by 5 to isolate b.

Divide

Now that we know that b = 4, we can use this to find 'a'

Move onto the second equation

Plug in b = 4 (ie replace b with 4)

Multiply

Reduce

So the solutions are a = 3 and b = 4 giving us the ordered pair (3, 4)

Question 567537: help me solve this
2/3m - 2(1/6m + 4)= -m + 12
Answer by unlockmath(1120)   (Show Source):
You can put this solution on YOUR website!
Hello, Let's expand this out first.
2/3m - 2(1/6m + 4)= -m + 12 to:
2/3m - 1/3m - 8= -m + 12
Add 8 to both sides:
2/3m - 1/3m = -m + 20
Multiply both sides by 3 to get:
2m-m=-3m+60
This can be rewritten as:
5m=60
m=12
Make sense?
RJ
www.math-unlock.com

Question 567358: w=s/f solve for f
can you show the steps? Thanks!
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
w=s/f solve for f
can you show the steps? Thanks!
---
Multiply both sides by f to get:
fw = s
Divide both sides by w to get:
f = s/w
-----
OR
w = s/f
Invert both sides to get:
f/s = 1/w
Multiply both sides by s to get:
f = s/w
==============================
Cheers,
Stan H.
================

Question 567028: What is the ordered pair(x,y) form
3x + 5y = 21
-9x + 4y = -6
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
3 x + 5 y = 21 .............1
-9 x + 4 y = -6 .............2
Eliminate y
multiply (1)by -4
Multiply (2) by 5
-12 x -20 y = -84
-45 x 20 y = -30
Add the two equations
-57 x = -114
/ -57
x = 2
plug value of x in (1)
3 x + 5 y = 21
6 + 5 y = 21
5 y = 21 -6
5 y = 15
y = 3
(2,3)

Question 567019: 2x+3y=29
5y-4x=19
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
2 x + 3 y = 29 .............1
-4 x + 5 y = 19 .............2
Eliminate y
multiply (1)by -5
Multiply (2) by 3
-10 x -15 y = -145
-12 x 15 y = 57
Add the two equations
-22 x = -88
/ -22
x = 4
plug value of x in (1)
2 x + 3 y = 29
8 + 3 y = 29
3 y = 29 -8
3 y = 21
y = 7

Question 566840: The value of an uncircumcised "Mint State-65' 1950 Jefferson nickel minted in Denver is 7/5 the value a nickel minted in Philadelphia in similar condition. Together the total value of the two coins is $36. what is the value if each coin?
Answer by solver91311(12118)   (Show Source):
You can put this solution on YOUR website!

Sorry it took so long to answer this one, but I had to pick myself up off of the floor. "uncircumcised" ??? I wasn't aware they did that to coins. Exactly what part of a coin is cut off when they circumcise one? You know those lists of "Dumb things people say"? You just made the list. This one may go viral. I can just imagine the floor of the US Mint littered with little foreskins from nickels, dimes, and quarters. I wonder who holds the position of Head Mohel for the US Treasury Department?

Let represent the value of the Philadelphia mint coin. Then is the value of the Denver mint coin. The sum of the two values is $36, so:

Solve for , then calculate

John

My calculator said it, I believe it, that settles it

Question 566816: Solve: (for y) M - 3N = Y+ N
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
M - 3N = Y+ N

M - 3N-N = Y+ N -N

M - 4N = Y

Y = M - 4N

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Jim
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Question 566793: Evaluate: f (-(2)/(3)) if f (x) = (x)/(2)
Answer by solver91311(12118)   (Show Source):
You can put this solution on YOUR website!

Replace the with and then do the arithmetic.

John

My calculator said it, I believe it, that settles it

Question 566566: Solve this question using substitution y=5x+5 y=15x-1
Answer by Maths68(1140)   (Show Source):
You can put this solution on YOUR website!
........(1)
.......(2)
Substitute the value of y from (2) to (1)

Put the value of x in (1)
........(1)

x,y = 3/5, 8

Check
=====
Put the value of x and y in (1)
........(1)

Put the value of x and y in (2)

Question 565855: Add the equations, then solve for the variable.

5e+7f=6
2e-7f=22
Answer by ad_alta(170)   (Show Source):
You can put this solution on YOUR website!
Adding, we get 7e=28, so e=4. That means f=-2.

Question 565524: Solve by the substitution method.
4m + n = 33
m - 7n = 30
Answer by stanbon(48510)   (Show Source):
You can put this solution on YOUR website!
Solve by the substitution method.
4m + n = 33
m - 7n = 30
----------------
m = 7n+30
---
Substitute for "m" and solve for "n":
4(7n+30) + n = 33
28n + 120 + n = 33
29n + 120 = 33
29n = -87
n = -3
--------
Solve for "m":
m = 7n+30
m = 7(-3)+30
m = 9
----------------
Cheers,
Stan H.

Question 565392: How do you write an equation for this table?
X=1, 2, 3, 4, 5, 6, 7
Y=1, 3, 7, 15, 31, 63, 127
Answer by Edwin McCravy(6931)   (Show Source):
You can put this solution on YOUR website!
X=1, 2, 3, 4, 5, 6, 7
Y=1, 3, 7, 15, 31, 63, 127

If you look at the Y-values, you will discover that each one is one less than the corresponding term of this sequence: 2, 4, 8, 16, 32, 64, 128 which are the 1st, 2nd, 3rd, 4th, etc. powers of 2. So the X-th term of the given sequence is 1 less than 2^X. So the equation you're looking for is: Y = 2^X - 1 You just have to be observant and familiar with the various powers of small numbers to do problems like these. Edwin

Question 565195: what is 12y+21=9y? i know the answer is -7 but i dont know how to find the answer or how to do the promblem please help!!!
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Start with the given equation.

Subtract from both sides.

Subtract from both sides.

Combine like terms on the left side.

Divide both sides by to isolate .

Reduce.

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

Answer:

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

Jim
-------------------------------------------------------------------------------------------------

Question 565136: what would m equal if it was in the problem m+3n=7?
Answer by jim_thompson5910(21667)   (Show Source):
You can put this solution on YOUR website!
Start with the given equation

Subtract 3n from both sides to isolate 'm'

So after solving for 'm', the solution is
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Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
-------------------------------------------------------------------------------------------------

Question 419123: Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). The perimeter of some traffic sign must be 122 inches. Also, its length is 32 inches longer than its width. Find the dimensions of this sign.
Fill in the blank.
The width of the sign is _ inches?
The length of the sign is _ inches?

Answer by luckystar65(1)   (Show Source):
You can put this solution on YOUR website!

Question 564692: How do you solve y=4x and y=-x-15 by substitution?
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
y=4x

y=-x-15
substitute y
4x=-x-15
+x
5x=-15
/5
x=-3
y=4x
y=4*-3
y=-12

Question 564290: Translate to an algebraic expression 16 increased by b
Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
Translate to an algebraic expression 16 increased by b
---
16 + b

Question 564110: I need help on Expressions involving variables, substitution.
"John paid $34 for two algebra and three geometry books. He paid $36 for three algebra and two geometry books. What is the cost of each book?"
Thank You!

Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
Algebra book cost x
geometry book cost y
2x+3y=34
3y=-2x+34
y=(-2/3)x+34/3
3x+2y=36
substitute y in the equation
3x+2((-2/3)x+34/3)=36
3x-(4/3) x +68/3=36
multiply equation by 3
9x-4x+68=108
5x=40
x=8 , algebra book cost
plug x in equation 2x+3y=34 to get y=6

Question 564114: I need help with elimination.
x+2y=-1
2x-3y=12
Thank you!
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
1 x + 2 y = -1 .............1
2 x -3 y = 12 .............2
Eliminate y
multiply (1)by 3
Multiply (2) by 2
3 x 6 y = -3
4 x -6 y = 24
Add the two equations
7 x = 21
/ 7
x = 3
plug value of x in (1)
1 x + 2 y = -1
3 + 2 y = -1
2 y = -1 -3
2 y = -4
y = -2

Question 564117: I need help with substitution.
y=4x+5
y=3x+4
Thank you!
Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
y=4x+5
y=3x+4
Substitute y in the second equation
4x+5=y=3x+4
4x-3x=-1
x=-1
when x=-1
y=1

Question 563695: A collection of 52 dimes and nickels is worth $4.50. How many nickels and dimes are there?
Answer by scott8148(5879)   (Show Source):
You can put this solution on YOUR website!
"A collection of 52 dimes and nickels" ___ n + d = 52

"worth $4.50" ___ 5n + 10d = 450

Question 563622: Simplify the expression

2ln(e^A)+3lnB^e
Answer by Alan3354(21550)   (Show Source):
You can put this solution on YOUR website!
Simplify the expression

2ln(e^A)+3lnB^e
-------------
=

Question 562852: x^4+3x^3-x^2+2x-6 for x=3
im really confuse with this problem
Answer by Maths68(1140)   (Show Source):
You can put this solution on YOUR website!
=
for
=
=
=
=
=

Question 562781: To buy both a new car and a new house, Tina sought two loans totalling $321,929. The simple interest rate on the first loan was 1.0%, while the simple interest rate on the second loan was 8.8%. At the end of the first year, Tina paid a combined interest payment of $25,677.83. What were the amounts of the two loans?
I think i know the answer but could someone please help me work out this problem?
Answer by KMST(578)   (Show Source):
You can put this solution on YOUR website!
Let x be the price of the house and y be the price of the car

The interest on the house is .
The interest on the car is
The total interest for the first year is

Multiplying times 100 to get rid of some decimals

The equations
and
form a system of linear equations.
It could be solved several different ways.
For example, subtracting the second equation from the first one we get
which simplifies to
and dividing both sides by 7.8, we get

Substituting that into we get
-->
Tina bought a house for $33,999 and a car for $287,930.
Very strange.

Question 562776: Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.
10x + 11y = -26.5
20x + 5y = -27.5

Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
10 x + 11 y = -26.5 .............1
20 x + 5 y = -27.5 .............2
Eliminate y
multiply (1)by -5
Multiply (2) by 11
-50 x -55 y = 132.5
220 x 55 y = -302.5
Add the two equations
170 x = -170
/ 170
x = -1
plug value of x in (1)
10 x + 11 y = -26.5
-10 + 11 y = -26.5
11 y = -26.5 + 10
11 y = -16.5
y = -1.50

Question 562761: To buy both a new car and a new house, Tina sought two loans totalling $321,929. The simple interest rate on the first loan was 1.0%, while the simple interest rate on the second loan was 8.8%. At the end of the first year, Tina paid a combined interest payment of $25,677.83. What were the amounts of the two loans?
I think i know the expression and answer but not sure how to work it out
.01x + .088(321929-x) = 25677.83
x=33,999
(321929-x)=287,930
Answer: first loan (x)=$33,999 .....second loan (321929-x)=287,930

Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
Yes you are correct

Question 562757: solve by substitution and show work
10x + 11y = -26.5,
20x + 5y = -27.5

Answer by mananth(10541)   (Show Source):
You can put this solution on YOUR website!
10x+11y =-26.5 .............1
5y=-27.5-20x ---------2
/ 5 =
y=-5.5-4x
Substitute y in (1)
10x+11( -5.5-4x)=-26.5
10 x -60.5 + -44 x = -26.5
10 x -44 x = -26.5 60.5
-34 x = 34
/ -34
x= -1
Plug the value of x in (1)
10 x + 11 y = -26.5
10 * -1 + 11 y = -26.5
-10 + 11 y = -26.5
11 y = -16.5
/ 11
y= -1.5
m.ananth@hotmail.ca

Question 562738: ugg help me please I am so lost

7^m/7^n=
Answer by issacodegard(60)   (Show Source):
You can put this solution on YOUR website!
Hi, with the same base, we add/subtract exponents when multiplying/dividing.

Question 562638: This is the only ones on my homework I am having an issue with please help me out.

Product rule
9^4*9^9=
quotient rule
7^m/7^n=
Power rule
(3^3) ^2=

Answer by solver91311(12118)   (Show Source):
You can put this solution on YOUR website!

John

My calculator said it, I believe it, that settles it