Questions on Algebra: Evaluation of expressions, parentheses answered by real tutors!

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Question 751351: I don't know how to solve (5/3)+(3/2x)=(1/6).
Answer by stanbon(57307)

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solve (5/3)+(3/2)x = (1/6)
-------
Multiply thru by 6 to get:
2*5 + 3*3x = 1
------------
9x = -9
x = -1
============
Cheers,
Stan H.
-----

Question 751043: Please help me solve this equation
Evaluate each expression:
(5/3)^0
32^2/5
Simplify each expression:
(3y^2)(4y^5)
(5a^4a^2)^3
Simplyify the expression and eliminate any negative exponent:
(4x^2y^4)(2x^5y^-2)
(2u^3v^2)(3uy^-3)^2
Found 2 solutions by lwsshak3, dkppathak:
Answer by lwsshak3(6491)   (Show Source):
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Evaluate each expression:
(5/3)^0=1(any expression raised to zero power=1
32^2/5=fifth root of 32=2 squared=4
Simplify each expression:
(3y^2)(4y^5)=12y^7
(5a^4a^2)^3=5^3a^12a^2=125a^12a^2
Simplyify the expression and eliminate any negative exponent:
(4x^2y^4)(2x^5y^-2)=8x^7y^2
(2u^3v^2)(3uy^-3)^2=(2u^3v^2)(9u^2y^-6)=18u^5v^2/y^6

Answer by dkppathak(29)   (Show Source):
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(5/3)^0=0 as zero power on any number is 0
32^2/5 =(2^5) ^2/5= 2^2=4
Simplify each expression:
(3y^2)(4y^5)=12 y^2+5 =12y^7
(5a^4a^2)^3=5a^4+2 =5a^6
Simplyify the expression and eliminate any negative exponent:
(4x^2y^4)(2x^5y^-2)=8x^2+5 y4-2 =8x^7 y2
(2u^3v^2)(3uy^-3)^2 = (6u^3v^2)(9u^2y^-6) =54u^5v^2y^-6

Question 750911: Wendy bought 7 bags. Each bag costs the same amount. She paid the cashier $90 and received g dollars as change. What was the cost of each bag in terms of g?
Found 2 solutions by JoeTaxpayer, jim_thompson5910:
Answer by JoeTaxpayer(112)   (Show Source):
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7 bags cost (90-g)
1 bag cost (90-g)/7

Answer by jim_thompson5910(28579)   (Show Source):
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let b = cost of each bag

Since she bought 7 bags, this means the total cost of them is 7b dollars.

Since she received g dollars in change after paying $90, this implies that 7b < 90 and

g = 90 - 7b

since that's how you compute change (change = amount paid - cost)

Now solve for b

So the cost of each bag, in terms of g, is

Question 750332: what is the answer of (6^1/4)^2/3 could you explain to me please ? and (8/125)^-4/3, thank you

Answer by ankor@dixie-net.com(15649)   (Show Source):
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what is the answer of
(6^1/4)^2/3 = 6^(2/12) (multiply the exponents here
6^(1/6) (reduce the fraction)
:
(8/125)^-4/3,
inverting the fraction gets rid of the negative
(125/8)^(4/3)
find the cube root
(5/2)^4
Find the 4th power
625/16

Question 750478: 4/3-6=-8
Answer by jim_thompson5910(28579)   (Show Source):
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4/3-6=-8

4/(-3)=-8

-1.333=-8 ... FALSE

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

4/3-6=-8

1.333-6=-8

-4.667=-8 ... FALSE

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

So 4/3-6=-8 is never true

My guess is that a variable is missing.

Question 750428: 6xy from -12xy
Answer by tommyt3rd(514)   (Show Source):
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if you mean subtract then

-12xy-6xy=-18xy

:)

Question 750053: factorise completely: 27xy + 9x
Answer by Cromlix(307)   (Show Source):
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27 xy + 9x
9x(3y + 1)

Question 750052: A butcher buys xkg of beef daily,he takes 2% of the beefhome and sells the rest.Find x if the butcher takes home 15kg of beef in 6 days.
Answer by josgarithmetic(1507)   (Show Source):
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Six days... Bought 6x kg of beef. 2% of 6x kg was taken home. That was 15 kg.

kg.

Question 750050: Alli was born in 1983.How old is he now? Give the answer in Roman numerals.
Answer by Edwin McCravy(8908)   (Show Source):
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2013 -1983 ----- 30 years old. 30 is three 10s, and X is 10 in Roman numerals. So three tens in Roman numerals is three X's or XXX. Edwin

Question 734148: (3-4i)(1+4i)

Answer by tommyt3rd(514)   (Show Source):
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Using distribution we can write

:)

Question 741011: (5n-2)3n-(5n-2)(n-1) Is equivalent to ?
Answer by tommyt3rd(514)   (Show Source):
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Using grouping w can write:

(5n-2)3n-(5n-2)(n-1)=(5n-2)(3n-(n-1))=(5n-2)(2n+1)

Question 741012: Simplify 5(x-2)+2(3x^2-12x+12
Answer by tommyt3rd(514)   (Show Source):
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Use distribution then combine like terms:

:)

Question 744206: How do you solve (x-4)(x+8)=0
Answer by tommyt3rd(514)   (Show Source):
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We can use the zero product property:

(x-4)(x+8)=0 means
x-4=0 or x+8=0

so that x=4 or x=-8

:)

Question 741131: find all pair of integers factors with number 23
Answer by tommyt3rd(514)   (Show Source):
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please repost - this question is not clear :)

Question 748921: solve 4-(-6)6
Answer by tommyt3rd(514)   (Show Source):
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Evaluation....
4-(-6)6=4-((-6)(6))=4-(-36)=4+36=40

:)

Question 749591: Multiply (-5/6)(1/8)(-3/7)(-1/7)
Answer by Alan3354(30993)   (Show Source):
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Multiply (-5/6)(1/8)(-3/7)(-1/7)
--------
Multiply the NUMs
5*1*3*1 = 15
---
Multiply the DENs
6*8*7*7 = 2352
--> 15/2352 = 5/784
----
There are 3 minus signs, and odd number --> negative
====================
= -5/784

Question 749518: which of the following statements is equivalent to the expression -2s-5(6t-7s)
Answer by rfer(12657)   (Show Source):
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-2s-30t+35s=
33s-30t

Question 749527: A woman's age added thrice her daughter's age amounts to 80years. Five years ago,she was nine times as old as her daughter. How old is each now?
Answer by lwsshak3(6491)   (Show Source):
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A woman's age added thrice her daughter's age amounts to 80years. Five years ago,she was nine times as old as her daughter. How old is each now?
***
Now:
let x=daughter's age
let y=woman's age
y+3x=80
..
5 yrs ago:
x-5=daughter's age
y-5=woman's age
woman nine times as old as her daughter
y-5=9(x-5)
..
y+3x=80
y-5=9(x-5)=9x-45
..
y+3x=80
y-9x=-40
subtract
12x=120
x=10
y=80-3x=50
daughter's age=10
woman's age=50

Question 748847: Insert Parentheses to make the following statement true:
7+3*5-6-2*4=6
Thank you
Answer by MathTherapy(1423)   (Show Source):
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Insert Parentheses to make the following statement true:
7+3*5-6-2*4=6
Thank you

======
Check
======

Question 748750: (6^-7)^3
Answer by stanbon(57307)   (Show Source):
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(6^-7)^3
------
= 6^(-21)
----
= 1/[6^21]
===============
Cheers,
Stan H.
=====================

Question 748509: 3a+b+5a+2b
Answer by lenny460(764)   (Show Source):
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3a + b + 5a + 2b
Combine like terms:
3a + 5a = 8a
b + 2b = 3b

Answer:
8a + 3b

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 746234: solve the inequality
-5/7> 1/4- v/2
Answer by kekegeter (57)   (Show Source):
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-5/7>1/4-v/2
-5/7>-2v+1/2^2
-20>-7*2v+7
v>27/14
v Є [27/14,∞]

Question 747007: how to solve the square root of x over 5 plus 4 equals 14
Answer by Cromlix(307)   (Show Source):
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square root of x over 5 plus 4 equals 14
square root of x/5 = 14 - 4
square root of x/5 = 10
square root of x = 50
x = 50^2
x = 2500

Question 747633: -7/12+3/4-(-5/8)-13/24
Answer by checkley79(3050)   (Show Source):
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-7/12+3/4-(-5/8)-13/24
-7/12+3/4+5/8-13/24 FIND THE LOWEST COMMON DENOMINATOR.
12=1*2*2*3
4=1*2*2
8=1*2*2*2
24=1*2*2*2*3
LCD=1*2*2*2*3=24
(-7*2+3*6+5*3-13*1)/24
(-14+18+15-13)/24
6/24=1/4 ANS.

Question 747410: 3{[6(x-4)+5]-2[5(x+8)-3]} The directions says to simplify the problem. I have tried everything but nothing I do allows me to come up with the right.
Answer by stanbon(57307)   (Show Source):
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3{[6(x-4)+5]-2[5(x+8)-3]}
-------------
= 3{[6x-24+5]-2[5x+40-3]}
-------------
= 3{6x-19-10x+74}
-----
= 3{-4x+55}
-----
= -12x+165
======================
Cheers,
Stan H.
======================

Question 747378: what is the excluded value of -s over 3s +4
Answer by Alan3354(30993)   (Show Source):
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what is the excluded value of -s over 3s +4
----------
It's the value of s that makes the denominator = 0.

Question 747366: what is the excluded value p when -3 over 2p to the second power - p
Answer by stanbon(57307)   (Show Source):
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what is the excluded value p when -3 over 2p to the second power - p
------
-3/(2p^2-p)
-----
The denominator cannot be zero.
----
Solve:
2p^2-p = 0
p(2p-1) = 0
---
p = 0 or 2p-1 = 0
---
p = 0 or 2p = 1
----
p = 0 or p = 1/2
--------------------
p = 0 or p = 1/2
Those are the excluded values.
Cheers,
Stan H.
==============

Question 747262: 4xsquared + 9x + 7 = 0
Answer by jim_thompson5910(28579)   (Show Source):
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Use the quadratic formula to solve for x

Plug in , ,

or

or

So the two solutions are or

Question 742672: reduce the expression(factor separately the numerator and the denominator, and then simplify; 5-x/x-5
Answer by tommyt3rd(514)   (Show Source):
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If you mean to write:
5-x/x-5
then its
5-1-5=-1 as long as x is not 0
But if you mean:

then we notice that 5-x and x-5 are opposite in value. therefore their quotient is -1:

(as long as x does not equal -5)

Also notice that is just a coincidence that both expressions have the same value
:)

Question 738846: 30-5 (3+1)
Answer by tommyt3rd(514)   (Show Source):
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by following the order of operations we write:
30-5 (3+1)=30-5(4)=30-20=10

Question 743061: Divide: 6+i
-----
5-i
Write the expression in standard form.
Answer by tommyt3rd(514)   (Show Source):
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Question 746493: evaluate 5a when a = 4

Answer by Cromlix(307)   (Show Source):
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When a = 4
5a = 5 x 4 = 20

Question 745884: I know the answer to the problem but not sure how they got it. 30-5(4-2)
Answer by nerdybill(6958)   (Show Source):
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Apply the "order of operations" (PEMDAS)
30-5(4-2)
parentheses first:
30-5(2)
multiplication next:
30-10
finally, subtraction
20

Question 745814: Evaluate ((7pi)/6) to the nearest hundredth. The angle is given in radians.
Answer by stanbon(57307)   (Show Source):
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Evaluate ((7pi)/6) to the nearest hundredth. The angle is given in radians.
---------
Assuming you are convert to degrees:
= [(7/6)pi]
=====
= (7/6)*180
-----
= 7*30
-----
= 210 degrees
======================
Cheers,
Stan H.

Question 745720: The problem says: "A car is traveling at the speed of 55 mph.You want to write an algebraic expression to show how far the car will travel in a certain number of hours. What will the constant? The Variable?" i know the constant is a number that stays the same and doesnt change, so im assuming that it would be the speed, right?
I think that the variable would be the number of hours. But im not sure if i need to multiply or divide. Would it be 55x? x= the time traveled... Am I correct?
Answer by ankor@dixie-net.com(15649)   (Show Source):
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"A car is traveling at the speed of 55 mph.You want to write an algebraic expression to show how far the car will travel in a certain number of hours. What will the constant? The Variable?"
:
I think you're right
:
The equation will be
d(x) = 55x
where
d(x) = the distance as a function of time
x = the variable, time in hours
55 = the slope
there is no constant

Question 745320: what is (x+7)-(x-5)?

Answer by tommyt3rd(514)   (Show Source):
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(x+7)-(x-5)=x+7-x-(-5)=7+5=12

Question 745198: I am trying to help my son with some algebra. I am wanting to confirm the following problems. Can someone answer the following and please show your work if possible??? I have 3 different problems below as I read somewhere you were limited to 3 questions. I wasn't sure if I could send one question w/3 different math problems or do I need to send 3 different questions. If one at a time please answer any below and I will send two more questions. If you can answer all 3 BLESS YOU! Also note problem #3, I did not know how to say 4square on here you know like 4(With the little 2 up high beside it meaning 4x4 =16
#1) 17 + 3(8-5)???
Is this the way to solve it:
8-5 = 3 & 17+3 = 20 So the last step would be 20 - 3 = 17 OR 20x3 =60???

#2) 5*6-3*8???
Is this the way to solve it:
5*6=30 & 3*8=24 So the last step would be 30 - 24 = 6

#1) 28+ 4(Square) /2???
Is this the way to solve it:
4square (Same as 4x4) = 16 THEN 16/2 = 8 So the last step would be 28+8=36

Answer by ankor@dixie-net.com(15649)   (Show Source):
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#1) 17 + 3(8-5)???
First do the math inside the bracket
17 + 3(3) =
multiply by what's inside the bracket by 3
17 + 9 = 26
:
#2) 5*6-3*8???
Using the order of operations; Exponent, mult, divide, add, subtract
Unless brackets are used, then do the math inside the bracket first
Is this the way to solve it: So you are right on this one
5*6=30 & 3*8=24 So the last step would be 30 - 24 = 6

#1) Assuming the problem is: =
You solved it correctly

Question 745162: Simplify (1-(3/x^3))/(4+(1/X^2))
Answer by stanbon(57307)   (Show Source):
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Simplify (1-(3/x^3))/(4+(1/X^2))
-----
[(x^2-3)/x^3] / [(4x^2 +1)/x^2]
------
Invert the denominator and multiply:
-------
[(x^2-3)/x^3] * [x^2/(4x^2 +1)]
------------
= [(x^2-3)/x]
------
= [(x^2-3)/x(4x^2+1)]
=======================
Cheers,
Stan H.
========================

Question 744747: Evaluate
37
∑ (2K-10)
K=7
Answer by tommyt3rd(514)   (Show Source):
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The sums are a little tricky because we are not summing from 1 to a number...

or 1054

Question 744663: s(r-4) r=4 s=6
Answer by erika514(38)   (Show Source):
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Hi,
For this problem we are going to plug in our values for r and s into the given expression. In this problem r=4 and s=6, so when we insert them in for their variables we get 6(4-4). When we simplify, we subtract what is inside the parentheses first (4-4) to get 0 and the we multiply the 6 in front of the parentheses to get 6*0=0 Our final answer to our problem is 0. Hope this helps you and let me know if you have any more questions.

Question 744202: How do you factor 4x³+108
Answer by lenny460(764)   (Show Source):
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How do you factor 4x^3 + 108
Factor:
4(x^3 + 27)
We can now factor (x^3 + 27) using the sum of cubes formula:
a^3 + b^3 = (a + b)(a^2 - ab + b^2)

Answer:
4(x + 3)(x^2 - 3x + 9)

Lennox Obuong
Algebra Tutor
Nairobi, Kenya
Email: obuong3@aol.com

Question 743957: How to evaluate the expression, if possible (-32^1/5)
Answer by Alan3354(30993)   (Show Source):
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How to evaluate the expression, if possible (-32^1/5)
--------------
There are 5 5th roots of -32
The principal root is -2.

Question 741508: Do you now two numbers that are multipled to get -96, and added to get -46?
Answer by ankor@dixie-net.com(15649)   (Show Source):
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two numbers that are multiplied to get -96, and added to get -46?
Two numbers x & y, two equations
xy = -96
x+y= -46
y = (-46-x)
replace y in the 1st equation
x(-46-x) = -96
-46x - x^2 = -96
x^2 + 46x = 96; multiplied by -1
A quadratic equation
x^2 + 46x - 96 = 0
Factors to
(x+48)(x-2) = 0
two solutions
x = -48 then y = 2
and
x = +2 then y = -48