# Questions on Algebra: Inverse operations for addition and multiplication, reciprocals answered by real tutors!

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Question 994469: 3/4n-11/15=3/5

Answer by Fombitz(25151)   (Show Source):
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Multiply both sides by to eliminate fractions.

Question 993416: Bob is training for a race. Bob ran 14.6 miles away from his home. Then, Bob ran 9.8 miles toward his home. Finally, Bob ran 5.3 miles away from his home. How far is Bob from his home?
Answer by davidrolf(2)   (Show Source):
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Miles away from home are positive.
14.6-9.8+5.3=10.1 miles away from home

Question 992900: Given the function f(x)=5x+4 , find its inverse.
Found 2 solutions by MathTherapy, ikleyn:
Answer by MathTherapy(4047)   (Show Source):
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Given the function f(x)=5x+4 , find its inverse.




Answer by ikleyn(988)   (Show Source):
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.
Given the function f(x)=5x+4 , find its inverse.
--------------------------------------------------

y = 5x + 4.

x = .

Answer.  The inverse to   y = 5x +4   is   x = .

Question 992656: what is 18 multiplied by the quantity of 11 plus r
Answer by ikleyn(988)   (Show Source):
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.
what is 18 multiplied by the quantity of 11 plus r?
------------------------------------------------------

18*(11 + r).

Question 992509: inverse for 3x squared -5
Answer by Timnewman(249)   (Show Source):
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The inverse of 3x²-5
Is the same as it's reciprocal.
Then the inverse= or

Question 992132: Find the sum of 5 and 2 in 4654128
Found 2 solutions by Alan3354, MathLover1:
Answer by Alan3354(47455)   (Show Source):
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Find the sum of 5 and 2 in 4654128
================
What?
The sum of 5 and 2 is 7 everywhere.

Answer by MathLover1(11324)   (Show Source):
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Find the sum of and in :
The is in the ten thousands place. It tells you there is sets
of ten thousand in the thousand place.
so, you have
The is in the tens place.
so, you have
and their sum is:

Question 991982: Given the function f(x) = 4(x+3) − 5, solve for the inverse function when x = 3.
Answer by josgarithmetic(13975)   (Show Source):
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Solve for y and simplify, and then say , and now forget about the assignment of y and just use .

Question 990566: A varies jointly as B and C,and A=9 when B=5,C=7,find B and A=54,C=10
Answer by Timnewman(249)   (Show Source):
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Hi dear,
If A varies jointly as B and C,
A=kBC----(1)
Where K is proportionality Constant.
From equ 1,
k=A/BC
When A=9,B=5,C=7
k=9/5*7
k=9/35
Put k=9/35 in equ 1
A=9BC/35(this is the relationship between A,B,C.
when A=54,C=10
Then,
54=(9B*10)/35
54=90B/35
90B=1890
B=21
HOPE THIS HELPS?
Cheers,
Tim.

Question 990353: Order the following numbers from least to greatest: -1/2, 0.8, 2, 10%, 1 1/4
Found 2 solutions by Lilly0, stanbon:
Answer by Lilly0(1)   (Show Source):
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For these problems, it's easiest to convert everything to a decimal. So:
- = -0.5; 0.8; 2; 10% = 0.10; 1 = 1.25
Now you have:
-0.5; 0.8; 2; 0.10; 1.25
Least will always be the negative with the greatest number (-8 < -4), so our first number would be -0.5. Then comes 0.10 because it is closest to 0. After that is 0.8. Then, you have your numbers greater than one, so you have 1.25, then 2. Here's the order:
-, 10%, 0.8, 1 , 2
Hope I helped :)

Answer by stanbon(69061)   (Show Source):
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Order the following numbers from least to greatest: -1/2, 0.8, 2, 10%, 1 1/4
----
Ans: -1/2, 10% = 0.10, 0.80, 1 1/4, 2
------------------
Cheers,
Stan H.
---------

Question 990352: what is the domain of h(x)=1/x+9
Answer by Boreal(1464)   (Show Source):
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domain of 1/(x+9) are all reals except -9, which would make the denominator 0.
domain of (1/x)+9 are all reals except 0.

Question 988528: Jack is thinking number of a number. Eight more than the product of 5 and the number is 93. Find Jack's number
Answer by macston(4006)   (Show Source):
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.
N=the number
.
5N+8=93
5N=85
N=17
ANSWER: Jack's number was 17.

Question 987756: will a sequence of reciprocals ever have 0 term?
Answer by ikleyn(988)   (Show Source):

Question 987661: Find the inverse Olof each function. Then graph the function and its inverse.
A. Y=-3
B. f(x) = x-5

Answer by josgarithmetic(13975)   (Show Source):
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Inverse for y=-3 is not a function, but would still be a relation. y=-3 will include ALL values of x but just ONE value for y. When you switch roles of x and y, you would have x=-3 for ALL values of y. This is x=-3.

f^-1 from your definition of f(x) gives .
.
Graphically like these:

f is the red line, and its inverse is the green line.

Question 987241: I really don't understabd this question.
Find the inverse function f-1(x) for the given function f(x)
f(x)=x+1/6

Answer by macston(4006)   (Show Source):
You can put this solution on YOUR website!
.
Solve for x.
.
Swap x and y.
.
This is the inverse.
.
.
-OR-
.
Solve for x
.

.
Swap x and y
.
This is the inverse.
.

Question 986801: I think this has something to do with reciprocals? Please help me solve this equation: 2 1/4 divided by (-5 1/3) . I am so confused because i cant remember what to do with the whole numbers?
Answer by Alan3354(47455)   (Show Source):
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I think this has something to do with reciprocals? Please help me solve this equation: 2 1/4 divided by (-5 1/3) . I am so confused because i cant remember what to do with the whole numbers?
====================
Step 1, change the mixed numbers to "improper fractions."

Question 986799: What Is the answer for
-2.5
0.75
-2^3
1^20

Found 2 solutions by Alan3354, solver91311:
Answer by Alan3354(47455)   (Show Source):
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I'm gonna guess cattle.
----
It might be sheep, but I have a feeling it's cattle.

Answer by solver91311(20879)   (Show Source):
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In order for there to be an answer, there must be a question. You listed four numbers, but did not indicate what the question is. Repost and make it clear what you want.

John

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

Question 986790: -|-2-(-3)|-2|-5+8|
Answer by josgarithmetic(13975)   (Show Source):
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Much easier and safer to work INSIDE grouping symbols first; and absolute value function serves as a grouping symbol.

Question 985609: How to solve -3k - 18 = -5 - k - 13

Answer by jim_thompson5910(33401)   (Show Source):
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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.

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

So the solution is

Question 984822: how to find the inverse and domain of f(x) = (3x)/(sqrt(6x^2-12))
Answer by josgarithmetic(13975)   (Show Source):
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The INVERSE relation,

, two parts. Upper part and a lower part.

, still this inverse relation is two parts.
Domain is . Each branch depends on which one of the branches of the original function is used.

Question 984671: What is the inverse of y= 4-7x all over 3

Answer by Fombitz(25151)   (Show Source):
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Interchange x and y and solve for y.
This new y is the inverse of the old y.

Question 984210: Inverse of f(x)=2x+7
Answer by MathLover1(11324)   (Show Source):
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to find an inverse of , first recall that

now swap and
....solve for

so, inverse is:

Question 982542: The time it takes to double the balance in an account varies inversely with the intrest rate. If you invest $1000 at 6% it will take 12 years to double your money. Find the time it will take to double your money at 4%. Answer by ankor@dixie-net.com(18980) (Show Source): You can put this solution on YOUR website! The time it takes to double the balance in an account varies inversely with the interest rate. If you invest$1000 at 6% it will take 12 years to double your money.
Find the time it will take to double your money at 4%.
:
let t = time to double at 4%
:
An inverse relationship equation between the interest and the time to double
=
cross multiply
4t = 12 * 6
4t = 72
t = 72/4
t = 18 yrs to double at 4%

Question 981728: solve x/5 -4=2

Answer by Alan3354(47455)   (Show Source):
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Multiply by 5

Question 980424: the sum of 6 and x
Answer by MathLover1(11324)   (Show Source):
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the sum of and :

Question 980010: The sum of two digits of a two digit number is 14.The difference between the first digit and the second digit of the two digit number is 12.What is the product of the two digit of the two digit number?
A 56
B 48
C 45
D cannot be determined
E none of the above

Answer by Edwin McCravy(13211)   (Show Source):
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The difference between the first digit and the second digit of the two digit number is 12.
That alone tells you that there is no such number because the most any
two digits can differ by is 9 when you subtract the smallest digit 0 from
the largest digit 9 and get 9-0 = 9.  There is no way to subtract two
digits and get 12.  So this makes the problem ridiculous.

Edwin

Question 979428: Please help me solve this if 24.3-x+17.03=31.62 find the value of x.
Answer by rothauserc(2272)   (Show Source):
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24.3 -x +17.03 = 31.62
41.33 - x = 31.62
-x = -9.71
x = 9.71
*************************************
24.3 - 9.71 + 17.03 = 31.62
14.59 + 17.03 = 31.62
31.62 = 31.62

Question 977819: Problem: Find the odd number pair in the given question.
A) 24-81
B) 33-91
C) 28-44
D) 20-11
I think answer is D but doubt about that please solve the question with explanation.

Answer by Edwin McCravy(13211)   (Show Source):
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An EVEN number of pieces of candy CAN be divided evenly between two people.
An ODD number of pieces of candy CANNOT be divided evenly between two people.

Numbers that end in 0,2,4,6 or 8 are EVEN numbers.
Numbers that end in 1,3,5,7 or 9 are ODD numbers.

A) 24-81, 24 ends with a 4, it's EVEN, 81 ends with a 1, it's ODD, that's not it.
B) 33-91, 33 ends with a 3, it's ODD, 91 ends with a 1, it's ODD, that's it!
C) 28-44, 28 ends with a 8, it's EVEN, 44 ends with a 4, it's EVEN, that's not it.
D) 20-11, 20 ends with a 0, it's EVEN, 11 ends with a 1, it's ODD, that's not it.

Only B) has 2 ODD numbers.

Edwin

Question 977706: find the inverse function. a.) f(x)=6-3x, b.)f(x)= 3 square root of x c.)f(x)= x^2+2
Answer by Cromlix(3061)   (Show Source):
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Hi there,
Inverse function.
This is how I do them:-
a) f(x) = 6 - 3x
y = 6 - 3x
Change the x for the y and the y for the x:-
x = 6 - 3y
Subtract 6 from both sides
x - 6 = 6 - 6 - 3y
x - 6 = -3y
Multiply both sides by -1
6 - x = 3y
Divide both sides by 3
(6 - x)/3 = 3y/3
y = (6 - x)/3
...................
b) f(x) = 3 square root x
y = 3 square root x
Change x for y and y for x
x = 3 square root y
Divide both sides by 3
x/3 = 3 square root y/3
x/3 = square root y
Square both sides
(x/3)^2 = (square root y)^2
(x/3)^2 = y
y = (x/3)^2
....................
c)f(x) = x^2 + 2
y = x^2 + 2
Change x for y and y for x
x = y^2 + 2
Take 2 off both sides
x - 2 = y^2 + 2 - 2
x - 2 = y^2
Square root both sides
Square root(x - 2) = Square root (y^2)
Square root (x - 2) = y
y = Square root (x - 2)
...........................
Hope this helps:-)

Question 976520: Find the matrix product, if possible 3 -1 0 -1
6 0 3 6
I'm not sure how it reads on your end, but there are 2 rows, 4 columns, with eight set of numbers. Please solve and thank you.

Answer by Fombitz(25151)   (Show Source):
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I'll assume they're 2x2 matrices,

Question 976521: Add the matrices below, where possible. 3 -5
-5 + 1
-4 6
Not sure how it shows on your side, but there are 2 columns, 3 rows, 6 set of numbers. Please solve, Thank you.

Answer by Fombitz(25151)   (Show Source):
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-2
-4
2
Those are the answers.
Arrange them how you want them.

Question 976113: Please solve and show work.
Add the 2 matrices below, where possible.
3 -5
-5 + 1
-4 6
Thanks.

Answer by Fombitz(25151)   (Show Source):
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(3,-5,-4)+(-5,1,6)=(3-5,-5+1,-4+6)=(-2,-4,2)

Question 976235: Please solve and show work. Find the inverse for the matrix, if it exists.
5 5
0 -4
Thank you.

Answer by rothauserc(2272)   (Show Source):
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A =
| 5 5 |
| 0 -4 |
now A^-1 exists iff
A x A^-1 = A^-1 x A = I where I is the identity matrix
determinant of A is written det A
det A = (5*-4) - (5*0) = -20
A^-1 = (1/-20) *
| -4 -5 |
| 0 5 |
the above matrix is formed using the following algorithm
| a11 a12 |
| a21 a22 |
the resulting matrix is formed as
| a22 -a12 |
| -a21 a11 |
then multiply this matrix by 1 / det A
A^-1 =
| 1/5 1/4 |
| 0 -1/4 |
A x A-1 =
|5 5|
|0 -4| x
|1/5 1/4|
| 0 -1/4|
A x A^-1 =
| 1 0 |
| 0 1 |
note matrix multiplication is each element in result is row elements times column elements added
A^-1 x A =
|1/5 1/4|
| 0 -1/4| x
|5 5|
|0 -4| =
| 1 0 |
| 0 1 |
our answer checks since I2 =
| 1 0 |
| 0 1 |
A^-1 =
| 1/5 1/4 |
| 0 -1/4 |

Question 976112: Please solve and show work. Thank you.
Find the inverse for the matrix, it if exists.
-2 0
-6 -3
Thank you.

Answer by Boreal(1464)   (Show Source):
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=1/6
inverse is
-3 === 0 * 1/6
6 === -2
-1/2== 0 INVERSE
-1 ===-1/3
A ;; B ;;; D ;; -B
C ;; D ;;; -C ;; A , EACH OF THESE LATTER IS MULTIPLIED BY THE DETERMINANT 1/AD-BC IN THE ORIGINAL MATRIX.

Question 974904: Inverse of f(x)=5x+10
Answer by solver91311(20879)   (Show Source):
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Replace with

Solve for in terms of

Swap the variables and

Replace with

John

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

Question 974128: find the product (5x-4)(x^2-6x+5)
Answer by josgarithmetic(13975)   (Show Source):
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Use Distributive Property and then combine like-terms. You can extend Distributive Property as this way:

Once in this form, you would apply distributive property again on each of the products.

Question 974008: An experiment consists of randomly selecting a card from seven cards numbered from 1 to 7. One card is selected at random and replaced.
What is the probability of selecting two odd numbers? Express your answer as a fraction in simplest form.

Answer by stanbon(69061)   (Show Source):
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An experiment consists of randomly selecting a card from seven cards numbered from 1 to 7. One card is selected at random and replaced.
What is the probability of selecting two odd numbers? Express your answer as a fraction in simplest form.
-------
Number set:: 1,2,3,4,5,6,7
----
number of odd digits:: 4
-----
P(select an odd number) = 4/7
----
P(select odd number twice) = (4/7)^2 = 16/49
===============
Cheers,
Stan H.
----------

Question 973988: An integer is divided by 7 giving a remainder of 5. The resulting quotient when divided by 5 gives a remainder of 3. The resulting quotient is then divided by 9 giving a quotient of 1 and a remainder of 1.
What will the finale remainder be if the order of the divisors is reversed?

Answer by josmiceli(13716)   (Show Source):
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(1)
(2)
(3)
---------------------
(3)
(3)
and
(2)
(2)
(2)
and
(1)
(1)
(1)
----------------------
Reverse the order of the divisors

---------------------
I get a remainder of with order of
divisors reversed. You should get a 2nd
opinion on this. I may be wrong.

Question 973822: 18 more than the product of 0.5 and the difference of 16 and 7
Answer by Boreal(1464)   (Show Source):
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x is the number
x-18=0.5*9
x=22.5
22.5 is 18 more than (1/2)(16-7), which is 4.5

Question 973270: If f(x) = 8x-4 find
f(5)

Answer by MathLover1(11324)   (Show Source):

Question 973273: If f(x) = 8x-4 Find
f(c)

Answer by Alan3354(47455)   (Show Source):
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If f(x) = 8x-4 Find
f(c)
=================
Wherever there's an x, sub c
---
f(c) = 8c-4
=======================
Was that hard?

Question 973269: If f(x) = 7x-3/2
find f(15)

Answer by Boreal(1464)   (Show Source):
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f(15)=7*15 - (3/2)
=105-1 (1/2)
=103.5
If it is (7x-3)/2
f(15)= (102/2) =51. The parentheses make a big difference.