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Tutors Answer Your Questions about Expressions-with-variables (FREE)
Question 170669: I need a little help with this one. Thanks so much. The question asks to simplify:
(-2a^2b^3)^2 / (2a^2b)^3
i came up with ab^7 but i don't know for sure if it's correct. Any help would be appreciated.: I need a little help with this one. Thanks so much. The question asks to simplify:
(-2a^2b^3)^2 / (2a^2b)^3
i came up with ab^7 but i don't know for sure if it's correct. Any help would be appreciated.
Answer by ankor@dixie-net.com(4538)  (Show Source):
You can put this solution on YOUR website!
:
I'm not sure how you got that answer, but let's just go thru it.
:
You multiply the numerator exponents by 2; (-2^2 = +4)
Multiply the denominator exponents by 3 (2^3=8) and we have
:
Combine the exponents of like terms, in a manner to ensure they are positive:
 = 
:
did this make sense to you?
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Question 170805: Here is one that is confusing me:
Simplify (-2a^2b^3)^2 / (2a^2b)^3
Any help would be appreciated!: Here is one that is confusing me:
Simplify (-2a^2b^3)^2 / (2a^2b)^3
Any help would be appreciated!
Answer by Alan3354(1449) (Show Source): |
Question 170671: This question seemed simple enough but....help is needed!
The Schwarzchild radius describes the critical value to which the radius of a massive body must be reduced for it to become a black hole.
R = 2GM / c^2
where
G = gravitional constant 6.7 x 10^-11
M = mass of the onject
C = speed of light 3 x 10^8
The sun has M = 2 x 10^30. What is the Schwarzchilds radius for the sun? The suns true radius is 700,000.: This question seemed simple enough but....help is needed!
The Schwarzchild radius describes the critical value to which the radius of a massive body must be reduced for it to become a black hole.
R = 2GM / c^2
where
G = gravitional constant 6.7 x 10^-11
M = mass of the onject
C = speed of light 3 x 10^8
The sun has M = 2 x 10^30. What is the Schwarzchilds radius for the sun? The suns true radius is 700,000.
Answer by ankor@dixie-net.com(4538) (Show Source):
You can put this solution on YOUR website!The Schwarzchild radius describes the critical value to which the radius of a massive body must be reduced for it to become a black hole.
R = 2GM / c^2
where
G = gravitional constant 6.7 x 10^-11
M = mass of the onject
C = speed of light 3 x 10^8
The sun has M = 2 x 10^30. What is the Schwarzchilds radius for the sun? The suns true radius is 700,000.
:
Wouldn't just be:
R =  =  =  =  m
Which is about 2.98 km
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Question 170661This question is from textbook Introductory Algebra
: Solve the problem. A cruise boat travels 48 miles downstream in 3 hours and returns upstream in 6 hours. Find the rate of the stream.This question is from textbook Introductory Algebra
: Solve the problem. A cruise boat travels 48 miles downstream in 3 hours and returns upstream in 6 hours. Find the rate of the stream.
Answer by checkley77(3654) (Show Source):
You can put this solution on YOUR website!48/3=16 MPH DOWNSTREAM.
48/6=8 MPH UPSTREAM.
(16-8)/2=8/2=4 MPH IS THE SPEED OF THE STREAM.
PROOF:
16-4=12
8+4=12 SPEED OF THE BOAT IN STILL WATER.
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Question 170736: Evaluation of a polynomial in one variable: Evaluate the expression
b2 - 6b - 2
when b= -5
: Evaluation of a polynomial in one variable: Evaluate the expression
b2 - 6b - 2
when b= -5
Answer by jim_thompson5910(9401) (Show Source):
You can put this solution on YOUR website!When nature calls, don't put her on speaker
 Start with the given expression.
 Plug in  .
 Square  to get  .
 Multiply  and to get  .
 Combine like terms.
So  which means that  when
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Question 170704: Solve: 7x-3y=26
2x+5y=25: Solve: 7x-3y=26
2x+5y=25
Answer by jojo14344(888) (Show Source):
You can put this solution on YOUR website!Line Eqn's:  -----------> A
 -----------------------> B
In A:
 ----------------> C
Subst. C in B:
 ,
Subst. in C:
See the graph:
 -------> Line A (Green) intersect at Line B (RED) at points (5,3) as shown (as computed too)
.
Thank you,
Jojo
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Question 170693: If y varies inversely as x^2, and y = 2 when x = 4, what is the constant of the variation?
Thanks.: If y varies inversely as x^2, and y = 2 when x = 4, what is the constant of the variation?
Thanks.
Answer by Mathtut(570) (Show Source): |
Question 170673: A long distance telephone calling card charges $0.05 per minute, but adds on a $0.75 charge for each call dialed. Using 'C' for the number of calls made and 'I' for the time spent talking, create an expression that will keep track of the cost of using the card.
answer- C=.75 I/.05 ?
Using the expression created calculate the remaining value on a $20.00 phone card after 5 calls that lasted a total of 26 minutes.
answer is $14.95 but don't know how to use an expression to find answer.
I did .75 * 5=3.75 26*.05= 1.30 3.75+1.30=5.05 20.00-5.05= 14.95
Any help would be appreciated as this is my first math course in over 20 years. : A long distance telephone calling card charges $0.05 per minute, but adds on a $0.75 charge for each call dialed. Using 'C' for the number of calls made and 'I' for the time spent talking, create an expression that will keep track of the cost of using the card.
answer- C=.75 I/.05 ?
Using the expression created calculate the remaining value on a $20.00 phone card after 5 calls that lasted a total of 26 minutes.
answer is $14.95 but don't know how to use an expression to find answer.
I did .75 * 5=3.75 26*.05= 1.30 3.75+1.30=5.05 20.00-5.05= 14.95
Any help would be appreciated as this is my first math course in over 20 years.
Answer by nerdybill(1129) (Show Source):
You can put this solution on YOUR website!A long distance telephone calling card charges $0.05 per minute, but adds on a $0.75 charge for each call dialed. Using 'C' for the number of calls made and 'I' for the time spent talking, create an expression that will keep track of the cost of using the card.
"cost of using card" = "total dialing charges" + "total minutes called"
"cost of using card" = .75C + .05I
.
Using the expression created calculate the remaining value on a $20.00 phone card after 5 calls that lasted a total of 26 minutes.
"remaining cost" = "current value" - "cost"
"remaining cost" = 20 - (.75C + .05I)
"remaining cost" = 20 - (.75(5) + .05(26))
"remaining cost" = 20 - (3.75 + .1.3)
"remaining cost" = 20 - 5.05
"remaining cost" = $14.95
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Question 170670: I did all the math for this one, but still having problems writing out the equation:
Suppose a population of initial size 100 grows at the rate of 8% per year forever.
What is the size of the population at the end of year 1? ( 108)
What is the size of the population at the end of year 2? (117)
What is the size of the population at the end of year 3? (126)
(This is where I get lost)
What is the size of the population at the end of year n (for any integer n)?
What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200? : I did all the math for this one, but still having problems writing out the equation:
Suppose a population of initial size 100 grows at the rate of 8% per year forever.
What is the size of the population at the end of year 1? ( 108)
What is the size of the population at the end of year 2? (117)
What is the size of the population at the end of year 3? (126)
(This is where I get lost)
What is the size of the population at the end of year n (for any integer n)?
What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200?
Answer by Alan3354(1449) (Show Source):
You can put this solution on YOUR website! I did all the math for this one, but still having problems writing out the equation:
Suppose a population of initial size 100 grows at the rate of 8% per year forever.
What is the size of the population at the end of year 1? ( 108)
What is the size of the population at the end of year 2? (117)
What is the size of the population at the end of year 3? (126)
(This is where I get lost)
What is the size of the population at the end of year n (for any integer n)?
What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200?
--------------------------
Use PV = SV*(1 + r)^n where PV is Present Value, SV is Start Value, r is rate and n is periods. This is common in interest on money, tho the terms used might be different.
-------------
What is the size of the population at the end of year n (for any integer n)?
That's the eqn, PV = SV*(1 + r)^n
------------------
What algebraic equation would you need to solve to find the number of years x that it would take for our population to reach 200?
The same eqn will do that, PV is 2x SV
200 = 100*(1 + 0.08)^x
2 = (1.08)^x
log(2) = x*log(1.08)
x = log(2)/log(1.08)
x =~ 9.006 years
PS you can use log base 10, or ln, as long as you're consistent.
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Question 170663: need help evaluating x=-4 , y=6, z=-8
2x+3y
5xy-z
-z+2x
_______________________________
p-12= -15
-11= -4+d
-1.6k= -15
not from any textbook that I know of, from a 10 page worksheet: need help evaluating x=-4 , y=6, z=-8
2x+3y
5xy-z
-z+2x
_______________________________
p-12= -15
-11= -4+d
-1.6k= -15
not from any textbook that I know of, from a 10 page worksheet
Answer by midwood_trail(260) (Show Source):
You can put this solution on YOUR website!Evaluate:
x = -4 , y = 6, z = -8
2x+3y
5xy-z
-z+2x
Replace x, y and z with their given values in each expression and simplify.
I will do one of them.
2x + 3y
Let x = -4 and Let y = 6
Then 2(-4) + 3(6) = -8 + 18 = 10
Can you do the rest now?
_______________________________
p-12= -15
-11= -4+d
-1.6k= -15
Here, you need to solve each equation for the given variable.
I will do one of them.
p - 12 = -15
Add 12 to both sides.
p = 12 - 15
p = -3
Can you do the rest now?
I received your e-mail.
Here is the full reply:
Evaluate using: x = -4 , y = 6, z = -8
2x+3y...Replace x with -4 and y with 6
2(-4) + 3(6) = -8 + 18 = 10
==================
5xy-z...5(-4) times (6) -(-8) = 5(-24) + 8 = -120 + 8 = -112
==================
-z+2x...-(-8) + 2(-4) = 8 - 8 = 0
Did you follow?
_______________________________
When crossing the equal sign, change the sign infront of the numbers to the opposite ONLY when adding and subtracting.
p -12 = -15...We add 12 to both sides.
p = +12 - 15
p = -3
========================
-11= -4 + d...Here, we add 4 to both sides.
-11 + 4 = d
-7 = d
====================
-1.6k= -15....Here, we apply the division property or rule of algebra. To find k, divide both sides by the coefficient of k, which is the decimal number -1.6 in this question.
So, k = -15 divided by -1.6
Then, k = 9.375
Did you follow?
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Question 170660This question is from textbook Introductory Algebra
: Solve using the elimination method.
2x - y = 6
5x + y = 22This question is from textbook Introductory Algebra
: Solve using the elimination method.
2x - y = 6
5x + y = 22
Answer by Mathtut(570) (Show Source):
You can put this solution on YOUR website!2x-y=6....eq 1
5x+y=22...eq 2
:
this problem is already set up nicely without having to multiply either equation by anything. Just add eq1 to eq 2 and the y terms will be eliminated.
:
we are left with
the x terms 2x+5x and the constants 6+22
:
2x+5x=6+22
:
7x=28
:
now substitute x's value back into either equation....I will use eq 2
:
5(4)+y=22---->20+y=22--->subtraction 20 frome each side produces
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Question 170660This question is from textbook Introductory Algebra
: Solve using the elimination method.
2x - y = 6
5x + y = 22This question is from textbook Introductory Algebra
: Solve using the elimination method.
2x - y = 6
5x + y = 22
Answer by jim_thompson5910(9401) (Show Source):
You can put this solution on YOUR website!
Start with the given system of equations:
Add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:
 Group like terms.
 Combine like terms. Notice how the y terms cancel out.
 Simplify.
 Divide both sides by  to isolate  .
 Reduce.
------------------------------------------------------------------
 Now go back to the first equation.
 Plug in .
 Multiply.
 Subtract  from both sides.
 Combine like terms on the right side.
 Divide both sides by  to isolate  .
 Reduce.
So our answer is and .
Which form the ordered pair ) .
This means that the system is consistent and independent.
Notice when we graph the equations, we see that they intersect at . So this visually verifies our answer.
 Graph of  (red) and  (green)
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Question 170451: Solve the problem. Roberto invested some money at 7%, and then invested $2,000 more than twice this amount at 11%. His total annual income from the two investments was $3,990. How much was invested at 11%?: Solve the problem. Roberto invested some money at 7%, and then invested $2,000 more than twice this amount at 11%. His total annual income from the two investments was $3,990. How much was invested at 11%?
Answer by jojo14344(888) (Show Source):
You can put this solution on YOUR website!Let ---> money inv. 7%
Therefore,  ---> money inv. @ 11%
It follows,
=$13,000, amount inv @ 7%
Then,
 =$28,000, amount inv at 11% (ANSWER)
Check,
Thank you,
Jojo
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Question 170463This question is from textbook Introductory Algebra
: Solve
12/sqrt(5x+6)=sqrt(2x+5)This question is from textbook Introductory Algebra
: Solve
12/sqrt(5x+6)=sqrt(2x+5)
Answer by stanbon(19020) (Show Source):
You can put this solution on YOUR website!Solve
12/sqrt(5x+6)=sqrt(2x+5)
sqrt[5x+6)(2x+5) = 12
10x^2+37x+30 = 12
10x^2 + 37x +18 = 0
------------
x = [-37 +- sqrt(37^2 - 4*10*18)]/20
x = [-37 +- sqrt(649)]/20
x = [-37 +- 25.4755]/20
x = -3.1238 or x = -0.57623
-------------
Only x= -0.57623 is an acceptable answer as the other makes the
original equation meaningless as it would involve sqrt(negative number)
=================================
Cheers,
Stan H.
===================================
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Question 170480: An eastbound bicyclist enters a tunnel at the same time a westbound bicyclist enters the other end of the tunnel. The eastbound bicyclist travels 10 km/hr and the westbound bicyclist travels 8 km/hr. A fly is flying back and forth between the two bicyclists at 15 km/hr. The fly leaves the eastbound bicyclist just as he enters the tunnel. The tunnel is 9 km long. How far has the fly traveled when the bicyclists meet in the tunnel?: An eastbound bicyclist enters a tunnel at the same time a westbound bicyclist enters the other end of the tunnel. The eastbound bicyclist travels 10 km/hr and the westbound bicyclist travels 8 km/hr. A fly is flying back and forth between the two bicyclists at 15 km/hr. The fly leaves the eastbound bicyclist just as he enters the tunnel. The tunnel is 9 km long. How far has the fly traveled when the bicyclists meet in the tunnel?
Answer by stanbon(19020) (Show Source):
You can put this solution on YOUR website!An eastbound bicyclist enters a tunnel at the same time a westbound bicyclist enters the other end of the tunnel.
The eastbound bicyclist travels 10 km/hr and the westbound bicyclist travels 8 km/hr.
A fly is flying back and forth between the two bicyclists at 15 km/hr.
The fly leaves the eastbound bicyclist just as he enters the tunnel.
The tunnel is 9 km long. How far has the fly traveled when the bicyclists meet in the tunnel?
------------------
Find the time required before the cyclists meet:
Eastbound DATA:
rate = 10 km/h ; distance = x km ; time = x/10 hrs
-----------------
West bound DATA:
rate = 8 km/h ; distance = (9-x) km; time = (9-x)/8 hrs
-------------------
EQUATION:
time = time
x/10 = (9-x)/8
8x = 90-10x
18x = 90
x = 5 km
------------
Time before the two meet = x/10 = 5/10 = 1/2 hr.
---------------
In that time the fly will have flown (1/2)hr * 15/km/hr = 7.5 km
=======================================
Cheers
Stan H.
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Question 170460This question is from textbook Introductory Algebra
: Rationalize the denominator.
(4-√3)/(6+√y)This question is from textbook Introductory Algebra
: Rationalize the denominator.
(4-√3)/(6+√y)
Answer by stanbon(19020) (Show Source):
You can put this solution on YOUR website!Rationalize the denominator.
(4-√3)/(6+√y)
Multiply numerator and denominator by (6-sqrt(y)) to get:
= [(4-sqrt(3))(6-sqrt(y))]/[3y-y^2]
= [24-4sqrt(y)-6sqrt(3)+sqrt(3y)]/[3y-y^2]
==============================================
Cheers,
Stan H.
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Question 170453This question is from textbook Introductory Algebra
: Solve the problem. Karin biked at 13 mph for a time but got a flat tire. She then walked at 5 mph. She traveled a total of 93 miles. Had she biked the whole time, she would have gone 117 miles. How many hours did she walk?This question is from textbook Introductory Algebra
: Solve the problem. Karin biked at 13 mph for a time but got a flat tire. She then walked at 5 mph. She traveled a total of 93 miles. Had she biked the whole time, she would have gone 117 miles. How many hours did she walk?
Answer by ankor@dixie-net.com(4538) (Show Source):
You can put this solution on YOUR website!Karin biked at 13 mph for a time but got a flat tire. She then walked at 5 mph.
She traveled a total of 93 miles. Had she biked the whole time, she would have
gone 117 miles.
:
How many hours did she walk?
:
We know that if she biked the whole way, travel time would be: 117/13 = 9 hrs
:
This is also the travel time of walking and riding a total of 93 mi, implied by
the phrase."Had she biked the whole time"
:
Find the distance she walked, first.
Let d = distance walked
Then
(93-d) = distance she rode
:
Write a time equation: Time = dist/speed:
:
walking time + riding time = 9 hrs
 +  = 9
:
Multiply equation by 65 to get rid of the denominators, results:
13d + 5(93-d) = 65(9)
:
13d + 465 - 5d = 585
:
13d - 5d = 585 - 465
:
8d = 120
d = 
d = 15 miles walked
the
 = 3 hrs walking
:
Check solution, find the distance riding:
 = 6 hr
so we have: 3 + 6 hrs = 9 hrs
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Question 170452This question is from textbook Introductory Algebra
: Solve the problem. Anne and Nancy use a metal alloy that is 24.9% copper to make jewelry. How many ounces of a 20% alloy must be mixed with a 27% alloy to form 100 ounces of the desired alloy?This question is from textbook Introductory Algebra
: Solve the problem. Anne and Nancy use a metal alloy that is 24.9% copper to make jewelry. How many ounces of a 20% alloy must be mixed with a 27% alloy to form 100 ounces of the desired alloy?
Answer by Alan3354(1449) (Show Source):
You can put this solution on YOUR website!Solve the problem. Anne and Nancy use a metal alloy that is 24.9% copper to make jewelry. How many ounces of a 20% alloy must be mixed with a 27% alloy to form 100 ounces of the desired alloy?
--------------------
They want to make 100 oz that's 24.9% Cu. That 100 oz will contain 24.9 oz of Cu.
They have 20% and 27% available.
If they use x oz of the 20%, then they'll need 100-x ounces of the 27%.
The copper in x ounces of 20% is x/5.
The remaining will have 0.27*(100-x) ounces of copper in it.
So,
0.2x + 0.27*(100-x) = 24.9
0.2x + 27 - 0.27x = 24.9
-0.07x = -2.1
x = 30 ounces (of the 20%)
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Question 170465This question is from textbook Introductory Algebra
: Virginia's AT&T 9002 cordless phone has a range of 1000 ft. Her apartment is a corner unit, located as shown in the figure below. Will Virginia be able to use the phone at the community pool?
picture shows the distance from the apartment to the ground is 180 ft., the distance from the ground on the outside of the building to the far side of the grounds is 600 ft., and the distance from the far side of the grounds to the far side of the pool is 400 ft. (looks like a U shape)This question is from textbook Introductory Algebra
: Virginia's AT&T 9002 cordless phone has a range of 1000 ft. Her apartment is a corner unit, located as shown in the figure below. Will Virginia be able to use the phone at the community pool?
picture shows the distance from the apartment to the ground is 180 ft., the distance from the ground on the outside of the building to the far side of the grounds is 600 ft., and the distance from the far side of the grounds to the far side of the pool is 400 ft. (looks like a U shape)
Answer by maali40(13) (Show Source): |
Question 170464This question is from textbook Introductory Algebra
: A 10-m ladder is leaning against a building. The bottom of the ladder is 5 m from the building. How high is the top of the ladder?This question is from textbook Introductory Algebra
: A 10-m ladder is leaning against a building. The bottom of the ladder is 5 m from the building. How high is the top of the ladder?
Answer by nerdybill(1129) (Show Source):
You can put this solution on YOUR website!A 10-m ladder is leaning against a building. The bottom of the ladder is 5 m from the building. How high is the top of the ladder?
.
Apply Pythagorean's theorem:
Let H = height of top of ladder
.
H^2 + 5^2 = 10^2
H^2 + 25 = 100
H^2 = 75
H = sqrt(75)
H = 8.66 m
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Question 170455This question is from textbook Introductory Algebra
: Solve the problem. Marty leaves the airport in his private plane and flies due east at 186 mph. Two hours later, a jet leaves the same airport and flies due east at 434 mph. When will the jet overtake Marty's plane?This question is from textbook Introductory Algebra
: Solve the problem. Marty leaves the airport in his private plane and flies due east at 186 mph. Two hours later, a jet leaves the same airport and flies due east at 434 mph. When will the jet overtake Marty's plane?
Answer by maali40(13) (Show Source):
You can put this solution on YOUR website!186*x=(x-2)*434 868=(434-186)*x x=868/248 hours answer is x hrs after marty left airport.Is the airport moving?? anyway we are saying in3.5hrs marty went 186*3.5 miles in1.5 hrs the other jet go's 186*3.5 MILES =1.5*434 MILES JA DAT'S WHAT SAYING.tHESE ARE INTERESTING 186 mph relative to what? Must be saying 186 miles ,in straight line , away from airport in 1 hour. So in 2 hrs 392 miles away.in 1.5 hrs more (392 +1.5*186) miles away.In 1.5 hrs the other jet is 1.5* 434 miles away if on same straight line he gets hit in rear?? dONT'T FORGET YOUR WATCH!
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Question 170423This question is from textbook
: Evaluate the expression. Write answer without exponents.
(1/27)^2/3This question is from textbook
: Evaluate the expression. Write answer without exponents.
(1/27)^2/3
Answer by jim_thompson5910(9401) (Show Source): |
Question 170350: Need help writing algebraic expressions for
half the weight of a standard laptop computer
the weight of my dog increased my 8 pounds
$20. less than the cost of two airline tickets
the value of a home shared equally by four people
questions are not from a textbook: Need help writing algebraic expressions for
half the weight of a standard laptop computer
the weight of my dog increased my 8 pounds
$20. less than the cost of two airline tickets
the value of a home shared equally by four people
questions are not from a textbook
Answer by checkley77(3654) (Show Source):
You can put this solution on YOUR website!half the weight of a standard laptop computer
(COMPUTER WEIGHT)/2
the weight of my dog increased my 8 pounds
(WEIGHT OF DOG)+8LB.
$20. less than the cost of two airline tickets
(2 TICKETS-$20
the value of a home shared equally by four people
($ OF HOME)/4
|
Question 170288This question is from textbook
: We have to solve using the eliminaiton or substitution method. I am really struggling with this class so I'm not sure where to start.
2(x-y)=3+x which is 2x - 2y =3+x
x = 3y + 4This question is from textbook
: We have to solve using the eliminaiton or substitution method. I am really struggling with this class so I'm not sure where to start.
2(x-y)=3+x which is 2x - 2y =3+x
x = 3y + 4
Answer by Earlsdon(3748) (Show Source):
You can put this solution on YOUR website!Solve the system:
1)  and
2) 
The idea behind the "elimination" or "substitution" method is to reduce the problem from two equations with two unknowns (variables) to one equation with one unknown. This is accomplished by "eliminating" one of the unknowns.
In this problem, you can conveniently substitute the x in the first equation with the x in the second equation, thus eliminating the x-variable.
It would be simpler to first simplify the first equation as you have started to do.
1)
 Subtract x from both sides.
 Now substitute the x from equation 2)
 Simplfy and solve for y. Combine like-terms.
 Subtract 4 from both sides.
 Now substitute this value of y into equation 2) and solve for x.
Substitute y = -1
 So the solution is: (1, -1) and the solution shows the point of intersection of the two lines represented by the two linear equations.
|
Question 170288This question is from textbook
: We have to solve using the eliminaiton or substitution method. I am really struggling with this class so I'm not sure where to start.
2(x-y)=3+x which is 2x - 2y =3+x
x = 3y + 4This question is from textbook
: We have to solve using the eliminaiton or substitution method. I am really struggling with this class so I'm not sure where to start.
2(x-y)=3+x which is 2x - 2y =3+x
x = 3y + 4
Answer by nerdybill(1129) (Show Source):
You can put this solution on YOUR website!First order of business, put all the x's and y's to one side:
2x - 2y =3+x
x = 3y + 4
.
Rearranging then, we have:
x - 2y =3
x - 3y =4
.
Now, using the "elimination method", subtract the second equation from the first:
x - 2y = 3
-x + 3y = -4
---------------
y = -1
.
Now, use the above definition of 'y' and substitute it into equation 2:
x = 3y + 4
x = 3(-1) + 4
x = -3 + 4
x = 1
.
Solution:
(x,y) = (1, -1)
|
Question 170289This question is from textbook
: This problem has to be solved algebraically. I am quite confused by this.
y=1.2x - 32.7
y=-0.7x + 46.15This question is from textbook
: This problem has to be solved algebraically. I am quite confused by this.
y=1.2x - 32.7
y=-0.7x + 46.15
Answer by Alan3354(1449) (Show Source):
You can put this solution on YOUR website! This problem has to be solved algebraically. I am quite confused by this.
y=1.2x - 32.7
y=-0.7x + 46.15
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Since both expressions in x are equal to y, set them equal to each other.
y= 1.2x - 32.7 = -0.7x + 46.15
1.2x - 32.7 = -0.7x + 46.15
1.9x = 78.85
x = 41.5
------------
Sub x into an eqn to find y
y = 1.2x - 32.7
y = 1.2*41.5 -32.7
y = 17.1
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Question 170289This question is from textbook
: This problem has to be solved algebraically. I am quite confused by this.
y=1.2x - 32.7
y=-0.7x + 46.15This question is from textbook
: This problem has to be solved algebraically. I am quite confused by this.
y=1.2x - 32.7
y=-0.7x + 46.15
Answer by stanbon(19020) (Show Source):
You can put this solution on YOUR website!y=1.2x - 32.7
y=-0.7x + 46.15
-----------------
Since they both equal "y" they must equal each other:
1.2x - 32.7 = -0.7x + 46.15
1.9x = 78.85
x = 41.5
==============
Cheers,
Stan H.
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Question 170005: Could you help me solve this problem?
if y varies inversely as x^2, and y=2 when x=4, what is the constant of the variation? 2?
Thank you.: Could you help me solve this problem?
if y varies inversely as x^2, and y=2 when x=4, what is the constant of the variation? 2?
Thank you.
Answer by ankor@dixie-net.com(4538) (Show Source):
You can put this solution on YOUR website!If y varies inversely as x^2," equation for this is:
y  ; inversely means, when x increases, y decrease
:
y=2 when x=4, what is the constant of the variation?
:
Substituting for y and x we have:
2 = 
2 = 
Multiply both sides by 16
2*16 = k
:
k = 32; (the constant of variation)
:
:
Check this: using k=32 and x=4
y = 
y = 
y = 2
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Question 169534: :
Answer by maali40(13) (Show Source):
You can put this solution on YOUR website!x=-2 y=5 z=-3
1. x+y-z (-2 +5 -(-3) )=(2*(-1+1)+3-(-3))=(2(-1+1)+3(1+(-)^2))for all intents here =(3(1+1))=6 no 'division by (1-1)' so arithmetic suffices.
2. 2y-2
----------=(2*5-2)/(-2)=(5-1)/(-1)=(4+(1-1))/(-1) 'here' =-4
x
3. x + 31
---- ----- =-2/5/(-3)+31/30=2/15+31/30=4/30+31/30=35/30=7/6
y*z 30
4. z - y - 12.7=(-3)-(5)-(12.7)=-20.7=-20-7/10=-207/10
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Question 169402: Lin Hisa plans to invest $1,400 in two stocks: Consolidated Industries (CI) and Amalgamated Manufacturing (AM). Suppose that after 5 years Lin's CI stock does not change in value, but her AM stock triples, making her stocks worth $3,300. Write an equation that expresses this fact.: Lin Hisa plans to invest $1,400 in two stocks: Consolidated Industries (CI) and Amalgamated Manufacturing (AM). Suppose that after 5 years Lin's CI stock does not change in value, but her AM stock triples, making her stocks worth $3,300. Write an equation that expresses this fact.
Answer by gonzo(474) (Show Source):
You can put this solution on YOUR website!let x = amount of money invested in CI today
let y = amount of money invested in AM today.
-----
total invested in both equals $1400.
x + y = $1400
-----
5 years from now CI stock doesn't change in value.
5 years from now AM stock triples.
total value of both stocks in 5 years is $3300.
x + 3y = $3300
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you have two equations that you want to solve simultaneously.
x + y = 1400
x + 3y = 3300
-----
if you subtract the second equation from the firsts equation, the unknown variable of x will disappear.
you get:
(x - x) + (3y - y) = (3300 - 1400)
this becomes:
2y = 1900
y = 950
-----
substituting 950 for y in the first equation gets:
x + 950 = 1400
subtract 950 from both sides of the equation to get:
x = 1400 - 950
which becomes:
x = 450.
-----
you now have a value for x and y that should be able to satisfy both equations.
-----
first equation has already been satisfied since that is the equation where we solved for x.
-----
second equation is:
x + 3y = 3300
substituting 450 for x and 950 for y, we get:
450 + (3*950) = 3300
simplifying:
450 + 2850 = 3300
3300 = 3300
equation is satisfied.
-----
answer is:
x = amount invested in CI stock = $450
y = amount invested in AM stock = $950
-----
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Question 169443: Express .46 as a fraction in simplest form.: Express .46 as a fraction in simplest form.
Answer by Mathtut(570) (Show Source): |
Question 169229: I know this is a very simple type of equation, but I've forgotten which ones can cancel out and which have to stay.
This is the problem:
(6a)(-4b)
_________
(-2ab)(-3b)
It's multiple choice, so the possible answers are:
A. 4b
B. 4/b
C. -4a
D. -4/a
E. -4/b
Please help!: I know this is a very simple type of equation, but I've forgotten which ones can cancel out and which have to stay.
This is the problem:
(6a)(-4b)
_________
(-2ab)(-3b)
It's multiple choice, so the possible answers are:
A. 4b
B. 4/b
C. -4a
D. -4/a
E. -4/b
Please help!
Answer by checkley77(3654) (Show Source):
You can put this solution on YOUR website!(6a)(-4b)
_________ multiply these terms.
(-2ab)(-3b)
-24ab/6ab^2 now divide -24 by 6=-4, cancel out the (a) terms one of the (b) terms.
-4/b ans. E)
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Question 169229: I know this is a very simple type of equation, but I've forgotten which ones can cancel out and which have to stay.
This is the problem:
(6a)(-4b)
_________
(-2ab)(-3b)
It's multiple choice, so the possible answers are:
A. 4b
B. 4/b
C. -4a
D. -4/a
E. -4/b
Please help!: I know this is a very simple type of equation, but I've forgotten which ones can cancel out and which have to stay.
This is the problem:
(6a)(-4b)
_________
(-2ab)(-3b)
It's multiple choice, so the possible answers are:
A. 4b
B. 4/b
C. -4a
D. -4/a
E. -4/b
Please help!
Answer by Mathtut(570) (Show Source):
You can put this solution on YOUR website!just seperate all the terms in there own parentheis and start cancelling
 a's canel 1 b cancels and you end with -4 constant in the numerator and a b in the denominator.
:
you end up with -4/b
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Question 169234: The problem is this:
(1-2x)(3x+1)-(x-1)^2
What I have done is this:
(x-1)^2 = x^2 -2x +1
And using FOIL, (1-2x)(3x+1) =
3x +1 -6x^2 -2x
So, simplified, the equation reads: -x -7x^2 +2 or -7x^2 -x +2
But the multiple choice answers are:
a. x(3-7x)
b. -7x^2 -x
c. -7x2 -5x
d. -7x^2 +x
e. None of these
Am I right? Is it e. none of these? Please help!: The problem is this:
(1-2x)(3x+1)-(x-1)^2
What I have done is this:
(x-1)^2 = x^2 -2x +1
And using FOIL, (1-2x)(3x+1) =
3x +1 -6x^2 -2x
So, simplified, the equation reads: -x -7x^2 +2 or -7x^2 -x +2
But the multiple choice answers are:
a. x(3-7x)
b. -7x^2 -x
c. -7x2 -5x
d. -7x^2 +x
e. None of these
Am I right? Is it e. none of these? Please help!
Answer by nerdybill(1129) (Show Source):
You can put this solution on YOUR website!(1-2x)(3x+1)-(x-1)^2
What I have done is this:
(x-1)^2 = x^2 -2x +1
And using FOIL, (1-2x)(3x+1) =
3x +1 -6x^2 -2x
So far, so good!!
.
Now, rewriting:
(1-2x)(3x+1)-(x-1)^2
We get:
(3x +1 -6x^2 -2x) - (x^2 -2x +1)
3x +1 -6x^2 -2x - x^2 + 2x - 1
3x -6x^2 -2x - x^2 + 2x
3x -6x^2- x^2
3x -7x^2
factoring out an 'x':
x(3-7x) (Which is answer 'a')
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Question 169141: How do you solve?
x=1/5 y
3x+2y=26: How do you solve?
x=1/5 y
3x+2y=26
Answer by Alan3354(1449) (Show Source):
You can put this solution on YOUR website!How do you solve?
x=1/5 y
3x+2y=26
--------------
There are a number of ways, but since x is already shown as a function of y, substitution is probably the simplest.
x=1/5 y
3x+2y=26
Sub for x in the 2nd eqn
3*(y/5) + 2y = 26
Multiply by 5
3y + 10y = 130
13y = 130
y = 10
--------
x = y/5
x = 2
Avoid using 1/5 y, it could mean either (1/5)y or 1/(5y). Use y/5 instead, or add parentheses. Parentheses are free.
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Question 168978: 15x-10y=-5
15y=4+5x: 15x-10y=-5
15y=4+5x
Answer by checkley77(3654) (Show Source):
You can put this solution on YOUR website!15y=4+5x or -5x+15y=4 now multiply this equation by 3 & add them
15x-10y=-5
-15x+45y=12
---------------------
35y=7
y=7/35
y=1/5 ans.
15x+45*1/5=12
15x+9=12
15x=12-9
15x=3
x=3/15
x=1/5 ans.
Proof:
15*1/5=4-5*1/5
15/5=4-5/5
3=4-1
3=3
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Question 168931: The weight of an object varies inversely with the square of the distance from earth's center (3,960 miles). A man weighs 250 lbs on the surface of the earth. How much would he weigh in an airplane flying at 30,000 ft?: The weight of an object varies inversely with the square of the distance from earth's center (3,960 miles). A man weighs 250 lbs on the surface of the earth. How much would he weigh in an airplane flying at 30,000 ft?
Answer by Alan3354(1449) (Show Source):
You can put this solution on YOUR website!The weight of an object varies inversely with the square of the distance from earth's center (3,960 miles). A man weighs 250 lbs on the surface of the earth. How much would he weigh in an airplane flying at 30,000 ft?
------------------------------
3960 miles = 3960*5280 feet = 20908800 feet
His weight at 30000 feet above that is
= 
= 249.284 pounds
That's a difference of 0.716 pounds, or 11.45 ounces.
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Question 168843: 5x-3=13-3x
im having a hard time understanding when youre suppose to add and when your suppose to subtract, also i dont understand how youre suppose to combine variables: 5x-3=13-3x
im having a hard time understanding when youre suppose to add and when your suppose to subtract, also i dont understand how youre suppose to combine variables
Answer by gonzo(474) (Show Source):
You can put this solution on YOUR website!you want to get all the x variables on one side of the equation and you want to get all the constants on the other side of the equation.
you do this by adding or subtracting from both sides of the equation.
here's how it works:
your equation is:
5x - 3 = 13 - 3x
you want to get the 3x from the right side of the equation to the left side of the equation.
you do it by adding 3x to both sides of the equation.
equation becomes:
5x - 3 + 3x = 13 - 3x + 3x
you can see that the - 3x and + 3x on the right side of the equation cancel out so the equation becomes:
5x - 3 + 3x = 13
when you combine like terms, the equation becomes:
8x - 3 = 13
now you want to move the -3 over to the right side of the equation.
you do it by adding 3 to both sides of the equation.
8x - 3 + 3 = 13 + 3
when you combine like terms, the -3 and + 3 on the left side of the equation cancel out and you get:
8x = 13 + 3
which becomes:
8x = 16
you divide both sides of the equation by 8 to get
x = 16/8 = 2
-----
you substitute 2 for x in your original equation:
5x - 3 = 13 - 3x
becomes:
5*2 - 3 = 13 - 3*2
which becomes:
10 - 3 = 13 - 6
which becomes:
7 = 7
since this is true, the value of x = 2 is good.
-----
when you combine like terms, you are adding together all the terms that have the same variable.
5x + 6x + 3x = 14x
they are like terms because they are all multiples of x.
-----
similarly, if you have:
5x^2 - 3x + 2x^3 + 15x - 20x^2
you would combine like terms as follows:
5x^2 - 20x^2 = -15x^2
-3x + 15x = 12x
2x^3 doesn't have anything to combine with.
your final combined terms are:
2x^3 - 15x^2 + 12x
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Question 168843: 5x-3=13-3x
im having a hard time understanding when youre suppose to add and when your suppose to subtract, also i dont understand how youre suppose to combine variables: 5x-3=13-3x
im having a hard time understanding when youre suppose to add and when your suppose to subtract, also i dont understand how youre suppose to combine variables
Answer by Mathtut(570) (Show Source):
You can put this solution on YOUR website!what you do to one side you must do to the other side of the equals sign. Combine all like terms where you want them trying to move the variables in such a way as to end up with a positve number in front of the variable.
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;
::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
so you would take the -3x term on the right and add 3x to it thus eliminating it from the right side.......but you must also add 3x to the left so we end up with 5x+3x= 8x on the left.....now lets take care of the constant...to eliminate the -3 on the left we must add 3 to it......and we must add that same amount 3 to the right side making 13+3=16
so we end up with 8x=16 after that process.....now to get x by itself we must divide both sides by 8.....which gives us 
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