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Graphs/109763: Solve and graph.
A small firm produces AM and AM/FM car radios. The AM radios take 15 hours to produce, and the AM/FM radios take 20 hours. The number of production hours is limited to 300 hours per week. The plant’s capacity is limited to a total of 18 radios per week, and existing orders require that at least 4 AM radios and at least 3 AM/FM radios be produced a week. Write a system of inequalities representing this situation. Then draw a graph of the feasible region given these conditions, in which x is the number of AM radios and y the number of AM/FM radios.
1 solutions
Answer 80065 by ankor@dixie-net.com(15622)   on 2007-11-13 10:23:43 (Show Source):
You can put this solution on YOUR website!:
This same problem came up a few weeks ago. This is what I submitted then, perhaps it will help you.
:
A small firm produces both AM and AM/FM car radios. The AM radios take 15 h to produce, and the AM/FM radios take 20 h. The number of production hours is limited to 300 h per week. The plant's capacity is limited to a total of 18 radios per week, and existing orders require that at least 4 AM radios and at least 3 AM/FM radios be produced per week. Write a system of inequalities representing this situation. Then, draw a graph of the feasible region given these conditions, in which X is the number of AM radios and Y is the number of AM/FM radios.
:
Let x = number of AM radios; let y = number of AM/FM radios
The production hour constraint:
15x + 20y =< 300
Arrange in general form to plot the graph
20y =< 300 - 15x
y =< 300/20 - (15/20)x
y =< 15 - .75x, use this to plot the production hr graph (Purple line)
:
Plant's capacity constraint:
x + y =< 18
y =< 18 - x, plot this graph also (Green line)
:
Min AM radio production constraint:
x => 4
This will be a vertical line going thru the x axis at +4, (I can't draw this in)
:
Min AM/FM radio production constraint
y => 3
This will be a horizontal line going thru the y axis at +3, (Dark blue line)
:
Here is the graph as presented by these equations except for x => 4,
:
:
The feasibility region:
1. At or below the purple or green line, whichever is lowest
2. At or above the horizontal line
3. At or to the right of the vertical line which you have to draw in at x = +4
:
How about this, did it all make some sense to you?
|
Quadratic-relations-and-conic-sections/109687: Alright, so I'm supposed to solve this equation algebraically, but I'm not sure what the last step is. Like how to show the answer. So here's the answer I got... 
Is that it?
1 solutions
Answer 80064 by ankor@dixie-net.com(15622) on 2007-11-13 10:17:44 (Show Source):
You can put this solution on YOUR website!algebraically, but I'm not sure what the last step is. Like how to show the answer. So here's the answer I got... -3x^2-2x+1<0 x=(2+or-sqrt(4+12))/(2*-3) = (2+or-sqrt(16))/(-6)
:
x = 
You are right but at this point, I would separate the two solutions:
x = 
x = 
x = + 
and
x = 
x = 
x = -1
x=-1 or =1/3
|
Miscellaneous_Word_Problems/109633: This question is from textbook
The length of a rectangle is three centimeters greater than the width. The area is 108 square centimeters. Find the length and width of the rectangle.
1 solutions
Answer 79994 by ankor@dixie-net.com(15622) on 2007-11-12 21:53:37 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is three centimeters greater than the width. The area is 108 square centimeters. Find the length and width of the rectangle.
:
Let x = the width
:
It says,"The length of a rectangle is three centimeters greater than the width."
Therefore: (x+3) = the length
:
L * W = 108
Same as:
(x+3)*x = 108
x^2 + 3x = 108
x^2 + 3x - 108 = 0
:
Factor this to:
(x + 12)(x - 9) = 0
:
x = +9 cm is the width (it's positive solution we want here)
Then
9 + 3 = 12 cm is the length
;
:
Check: 12 * 9 = 108
:
That wasn't so hard, was it? Any questions?
|
Geometry_Word_Problems/109747: A rectangular lawn is 60 feet by 80 feet. How wide a uniform strip must be cut around the edge when mowing the grass in order that half of the grass be cut?
1 solutions
Answer 79988 by ankor@dixie-net.com(15622) on 2007-11-12 21:08:35 (Show Source):
You can put this solution on YOUR website!A rectangular lawn is 60 feet by 80 feet. How wide a uniform strip must be cut around the edge when mowing the grass in order that half of the grass be cut?
:
Let x = width of the mowed area
then
Un-mowed area = half the total area
(60-2x)* (80-2x) =  (60*80)
:
4800 - 280x + 4x^2 = 2400
:
Arrange as a quadratic equation:
4x^2 - 280x + 4800 - 2400 = 0
:
4x^2 - 280x + 2400 = 0
:
Simplify, divide by 4:
x^2 - 70x + 600 = 0
:
Factor this to:
(x - 60)(x - 10) = 0
:
x = +10 ft uniform strip is the only solution that makes sense.
:
:
Check solution
(60-20) * (80-20) = 2400, half the total area
:
Did this make sense to you? Any questions?
|
Linear_Equations_And_Systems_Word_Problems/109709: tom quig travelled 270 miles east of st louis . for most of the trip he travelled 70mph , byt for one period of thme he was slowed to 20 mph due to major accident . if the total time of travel was 6 hours , how many miles did he drive on the reduced speed?
1 solutions
Answer 79965 by ankor@dixie-net.com(15622) on 2007-11-12 18:54:48 (Show Source):
You can put this solution on YOUR website!tom traveled 270 miles. For most of the trip he traveled 70 mph, but for one period of time he was slowed to 20 mph. if the total time of travel was 6 hours, how many miles did he drive at reduced speed?
:
Let x = no. of miles at 20 mph
Then
(270-x) = no. of miles at 70 mph
:
Write a time equation: Time = Distance/speed
:
20 mph time + 70 mph time = 6
 +  = 6
:
multiply equation by 140, get rid of the denominators:
140* + 140* = 140*6
:
Cancel out the denominators and you have:
7x + 2(270-x) = 840
:
7x - 2x + 540 = 840
:
5x = 840 - 540
:
5x = 300
:
x = 
x = 60 miles at 20 mph
;
:
Check solution by finding the distances:
60/20 + 210/70 =
3 + 3 = 6
|
Pythagorean-theorem/109613: A square and a rectangle have the same area. The length of the rectangle is 8 in. more than a side of the square, and the width of the rectangle is 4 in. less than a side of the square. Find the length of a side of the square.
1 solutions
Answer 79948 by ankor@dixie-net.com(15622) on 2007-11-12 18:02:30 (Show Source):
You can put this solution on YOUR website!A square and a rectangle have the same area. The length of the rectangle is 8 in. more than a side of the square, and the width of the rectangle is 4 in. less than a side of the square. Find the length of a side of the square.
;
Let x = side of the square
then
x^2 = area of the square
:
The rectangle:
It says,"The length of the rectangle is 8 in. more than a side of the square,:
L = (x+8)
and
It says,"the width of the rectangle is 4 in. less than a side of the square."
W = (x-4)
:
(x+8)(x-4) = area of the rectangle
(x^2 + 4x - 32) = area of the rectangles also(FOILed the demensions)
:
It said the area of the rectangle = area of the square; therefore
x^2 + 4x - 32 = x^2
:
x^2 - x^2 + 4x = 32
:
4x = 32
:
x = 8 in is the side of the square
:
:
Check our solution, find out if the square and the rectangle have the same area
(8+8)*8-4) =
16 * 4 = 64
and
8 * 8 = 64
:
Did this make sense to you, any questions?
|
Linear_Equations_And_Systems_Word_Problems/109396: a jet plane travelling at a constant speed goes 1200 mi with the wind , then turns around and travels for 1000 mi against the wind . If the speed of the wind is constant 50 mph , and the total flight took 4 hrs , find the speed of the plane.
1 solutions
Answer 79893 by ankor@dixie-net.com(15622) on 2007-11-12 15:11:41 (Show Source):
You can put this solution on YOUR website!jet plane traveling at a constant speed goes 1200 mi with the wind , then turns around and travels for 1000 mi against the wind . If the speed of the wind is constant 50 mph , and the total flight took 4 hrs , find the speed of the plane.
:
Let s = speed of the plane
then
(s+50) = speed with the wind
and
(s-50) = speed against the wind
:
Write a time equation: Time = dist/speed
:
Time with + time against = 4 hr
 +  = 4
:
Multiply equation by (s+50)(s-50) to eliminate the denominators:
(s+50)(s-50)* + (s+50)(s-50)* = 4(s+50)(s-50)
:
Cancel out the denominators and you have;
1200(s-50) + 1000(s+50) = 4(s^2 - 2500)
:
1200s - 60000 + 1000s + 50000 = 4s^2 - 10000
:
2200s - 10000 = 4s^2 - 10000
:
Arrange as quadratic equation on the left:
4s^2 - 2200s - 10000 + 10000 = 0
:
4s^2 - 2200s = 0
:
Factor this:
4s(s - 550) = 0
:
Solution:
4s = 0
s = 0
and
s = +550 mph is our solution; (speed of the plane in still air)
:
:
Check our solution, find the time total:
speed with the wind: 600 mph
speed against the wind: 500 mph
1200/600 + 1000/500
2 + 2 = 4hrs
|
Complex_Numbers/109206: √8-x+6=4
1 solutions
Answer 79832 by ankor@dixie-net.com(15622) on 2007-11-12 09:49:54 (Show Source):
You can put this solution on YOUR website!:
:
:
Square both sides:
2 - x = 4^2
:
2 - x = 16
:
-x = 16 - 2
:
-x = 14
:
We always want our unknown (x) to be positive, multiply equation by -1
x = -14
:
:
Check solution in original equation:
 ; minus a minus is a plus
:
Did this help you?
:
Next time you can write it Sqrt(8 - x - 6) = 4; brackets make it clear
|
Quadratic_Equations/109323: one positive integer is 7 less than twice another. the sum of their squares is 346. find the integers
i dont understand how to set this up
1 solutions
Answer 79787 by ankor@dixie-net.com(15622) on 2007-11-11 21:25:00 (Show Source):
You can put this solution on YOUR website!You set it up by writing exactly what it says
(think of the word "is" as meaning equal "=")
:
Let x = "one positive integer
Let y = "another positive integer
:
One positive integer is 7 less than twice another
x = 2y - 7
:
the sum of their squares is 346.
x^2 + y^2 = 346
:
Find the integers
:
From the 1st statement, we know that x = (2y-7),
x^2 + y^2 = 346
:
Substitute (2y-7) for x in the above equation
(2y-7)^2 + y^2 = 346
:
FOIL (2y-7)(2y-7)
4y^2 - 28y + 49 + y^2 = 346
:
5y^2 - 28y + 49 - 346 = 0
:
5y^2 - 28y - 297 = 0
:
We probably should use the quadratic formula, however,
we know the positive solution has to be an integer,
let's play around with the factors of 297, we come up with:
(5y + 27) (y - 11) = 0
:
y = +11
:
x = 2(11) - 7
x = 22 - 7
x = 15
:
Check our solutions:
11^2 + 15^2 =
121 + 225 = 346
|
Mixture_Word_Problems/109296: A researcher orders a broth of 0.3% glucose for her lab. However she needs a stronger broth,one that is 26.4% glucose. Fortunately, she has 69.6 liters of 34.8% glucose broth in the stock room. How much 26.4% glucose broth can she make?
I need help with this problem, I believe it is solving for a percent mixture problem. Thanks.
1 solutions
Answer 79779 by ankor@dixie-net.com(15622) on 2007-11-11 20:55:15 (Show Source):
You can put this solution on YOUR website!A researcher orders a broth of 0.3% glucose; needs 26.4% glucose. has 69.6 liters of 34.8% glucose. How much 26.4% glucose broth can she make?
:
Let x = amt (in liters) of .3 % glucose required:
and
69.6 liters of 34.8% available
Therefore
Resulting amt = (69.6 + x) liter
:
.003x + .348(69.6) = .264(69.6+x)
:
.003x + 24.2208 = 18.3744 + .264x
:
.264x - .003x = 24.2208 - 18.3744
:
.261x = 5.8464
:
x = 22.4 liters of .03% glucose
Therefore
Total amt = 69.6 + 22.4 = 92 liters of 26.4% stuff
:
:
Check solution:
.003(22.4) + .348(69.6) = .264(92)
.0672 + 24.2208 = 24.288
e
|
Travel_Word_Problems/109391: This is not in a textbook it's in a Math Student workbook made up by my university.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Jennie drives to her son's house in 5 hours when there is heavy traffic. When there is no traffic, the same trip takes 4 hours. She can drive an average of 12 m.p.h. faster when there is no traffic than when thereis heavy traffic.
What is her average speed when there is no traffic?
What is the distance from her house to her son's house?
1 solutions
Answer 79769 by ankor@dixie-net.com(15622) on 2007-11-11 19:48:49 (Show Source):
You can put this solution on YOUR website!Jennie drives to her son's house in 5 hours when there is heavy traffic. When there is no traffic, the same trip takes 4 hours. She can drive an average of 12 m.p.h. faster when there is no traffic than when there is heavy traffic.
:
What is her average speed when there is no traffic?
:
Let s = Av speed, no traffic
Then
(s-12) = Av speed in traffic
:
The distance for both situations is given as the same:
:
Write a distance equation: Distance = time * speed
:
Dist traffic = Dist no traffic
5(s-12) = 4s
5s - 60 = 4s
5s - 4s = +60
s = 60 mph no traffic
and
60 - 12 = 48 mph in traffic
:
:
What is the distance from her house to her son's house?
5(48) = 240 miles
and
4(60) = 240 miles
|
Miscellaneous_Word_Problems/109329: ron takes two hours more than paul to mow the lawn . working togather they can mow the lawn in 5 hrs . how long does it take each of them working alone
1 solutions
Answer 79739 by ankor@dixie-net.com(15622) on 2007-11-11 18:11:12 (Show Source):
You can put this solution on YOUR website!ron takes two hours more than paul to mow the lawn . working together they can mow the lawn in 5 hrs . how long does it take each of them working alone>
:
x = number of hrs required by Paul working alone:
Then
(x+2) = number of hrs required by Ron working alone
:
Let the completed job = 1
:
A simple equation:
 +  = 1
:
Multiply equation by x(x+2) to get rid of the denominators:
x(x+2)* + x(x+2)* = x(x+2)*1
:
Cancel out the denominators:
5(x+2) + 5x = x(x+2)
:
5x + 10 + 5x = x^2 + 2x
:
combine like terms, arrange as a quadratic equation on the left:
x^2 + 2x- 5x - 5x - 10 = 0
:
x^2 - 8x - 10 = 0
:
This won't readily factor, solve using the quadratic formula:
a = 1; b = -8; c = -10
:
I assume you know how to do that;
You should get:
x = 9.1 hrs (Paul's time)
|
logarithm/109177: For this question I keep coming up with 1/7, but it's marked incorrect. Can you please help me figure out what I'm not doing correctly?
The log base is 4. Find the value of x in the following equation.
log_4 x+7=log_4 50+log_4 x
1 solutions
Answer 79719 by ankor@dixie-net.com(15622) on 2007-11-11 16:15:29 (Show Source):
You can put this solution on YOUR website!he log base is 4. Find the value of x in the following equation.
log_4 x+7=log_4 50+log_4 x
:
I can't see why your answer is incorrect
:
Since you have base 4 in all the terms, it does not matter what base you use:
:
log(x+7) = log(50*x); addition of logs is the same as multiplying
Therefore:
x + 7 = 50x
7 = 50x - x
49x = 7
x = 7/49
x = 1/7
:
Check on a calc:
ln(50/7) = 1.996
:
ln(50) + ln(1/7) = 1.996, equality reigns
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Human-and-algebraic-language/109189: 4. Landscaping- Decorative Moon Rocks cost $92 per cu yd. What will be the cost of a conical pile of this rock 3 1/3 yd in diameter and 2 1/4 yd high? Round to nearest dollar.
1 solutions
Answer 79683 by ankor@dixie-net.com(15622) on 2007-11-11 11:43:16 (Show Source):
You can put this solution on YOUR website!Moon Rocks cost $92 per cu yd. What will be the cost of a conical pile of this rock 3 1/3 yd in diameter
and 2 1/4 yd high? Round to nearest dollar.
:
WE know the volume of a cone: V = 
:
Let the diameter which is given as: 3 1/3 = 
Find the radius: * =  = 
and
Let the height which is given as: 2 1/4 = 
:
V = 
:
V = 
:
Note that in  we can cancel the 9:
V = 
V = 
V = 6.545 cu yd
:
Cost = 6.545 * 92 = 602.13 = $602
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Miscellaneous_Word_Problems/109246: This question is from textbook Introductory Algebra
An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide. The area of the cross-section of the gutter is 50 in.^2. Find the depth of the gutter.
1 solutions
Answer 79674 by ankor@dixie-net.com(15622) on 2007-11-11 11:13:13 (Show Source):
You can put this solution on YOUR website!An open rectangular gutter is made by turning up the sides of a piece of metal 20 in. wide. The area of the cross-section of the gutter is 50 in.^2. Find the depth of the gutter.
:
Let x = depth of gutter
:
The cross section would look sort of like this:
x|__|x
:
The bottom = (20 - 2x)
:
Area:
x(20-2x)= 50
-2x^2 + 20x - 50 = 0
Divide equation by -2 to simplify
x^2 - 10x + 25 = 0
Factors to:
(x-5)(x-5) = 0
x = 5 inches is depth of the gutter
:
:
Check:
Bottom = 20 - 2(5) = 10
5 * 10 = 50 sq/in as given
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Linear_Algebra/109178: I am helping my daughter with her homework and have no idea what I am doing.
Computer diskette problem: A computer store sells 10 floppy diskettes for $15, and 30 for $40. Assume that the number of dollars varies linearly with the number of diskettes.
a) Write the particular equation expressing dollars in terms of diskettes.
b) Predicit the price for a box of 100.
c) State the domain for your variable.
d) Sketch and label the graph.
1 solutions
Answer 79621 by ankor@dixie-net.com(15622) on 2007-11-10 21:54:33 (Show Source):
You can put this solution on YOUR website!A computer store sells 10 floppy diskettes for $15, and 30 for $40. Assume that the number of dollars varies linearly with the number of diskettes.
:
a) Write the particular equation expressing dollars in terms of diskettes.
:
Let x = no. of floppies sold
Let y = cost of the item
:
find the slope of the equation, slope formula: m = 
Using the given data assign as follows:
x1=10, y1=15; x2=30, y2= 40
:
m =  =  = 1.25 is the slope
:
Find equation using the point/slope formula: y - y1 = m(x - x1)
:
y - 15 - 1.25(x - 10)
y - 15 = 1.25x - 12.5
y = 1.25x - 12.5 + 15
y = 1.25x + 2.5; is the equation expressing cost in terms of no. of items
:
:
b) Predict the price for a box of 100.
:
Substitute 100 for x in the equation we just created:
y = 1.25(100) + 2.5
y = 125 + 2.5
y = $127.5 is the cost of 100 items
:
:
c) State the domain for your variable.
:
The domain would be all real integers => 1. You can't include 0 because in our
equation the cost of 0 items is $2.50, hardly reasonable.
:
d) Sketch and label the graph.
You can plot the points given and draw a straight line thru them, it should look like this:
y (vertical is cost) and x (horizontal) is no. of items sold
:
:
How about this, you got a handle this now?
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Travel_Word_Problems/109097: A pair of skydivers jump out of an airplane 5.5 km above the ground. The equation H= 5500-5t2 is an approximate model for the diver's altitude in metres at t seconds after jumping out of a plane.
a.) After 10 seconds, how far have the divers fallen?
b.) They open their chutes at an altitude of 1000 metres. How long did they free-fall?
c.) If a parachute does not open at 1000 metres, how much time is left to use the emergency chute?
1 solutions
Answer 79619 by ankor@dixie-net.com(15622) on 2007-11-10 21:11:49 (Show Source):
You can put this solution on YOUR website!A pair of skydivers jump out of an airplane 5.5 km above the ground. The equation H = 5500-5t^2 is an approximate model for the diver's altitude in metres at t seconds after jumping out of a plane.
:
a.) After 10 seconds, how far have the divers fallen?
:
Substitute 10 for t in 5t^2:
Meters fallen = 5(10^2) = 5(100) = 500 meters after 10 seconds
:
b.) They open their chutes at an altitude of 1000 metres. How long did they free-fall?
5500 - 5t^2 = 1000
-5t^2 = 1000 - 5500
t^2 =  ; divided both sides by -5
t^2 = +900
t = 
t = 30 seconds
:
c.) If a parachute does not open at 1000 metres, how much time is left to use the emergency chute?
Find how long it would take to hit the ground
5500 - 5t^2 = 0
-5t^2 = -5500
t^2 = 
t = 
t = 33.2 seconds
:
It looks like he only has about 3 seconds to trip the emergency chute
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Linear-systems/109163: This question is from textbook
Starting one hour later, Jonathan sets out walking at 8 km/h to overtake his little sister who averages 5 km/h. How long woll it take Jonathan?
1 solutions
Answer 79618 by ankor@dixie-net.com(15622) on 2007-11-10 20:40:35 (Show Source):
You can put this solution on YOUR website!Starting one hour later, Jonathan sets out walking at 8 km/h to overtake his little sister who averages 5 km/h. How long will it take Jonathan?
:
Let t = time it takes J to catch up with his sister
Then
(t+1) = time traveled by the sister
:
When J catches up with his sister, they will have traveled the same distance
Write a distance equation; Distance = speed * time
:
8t = 5(t+1)
8t = 5t + 5
8t - 5t = 5
3t = 5
t = hr = 1  hr = 1 hr 40 sec
:
:
Confirm solution by find the distances:
8 * (5/3) = 40/3
:
5 * (3/3 + 5/3) = 40/3
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Inequalities/109164: This question is from textbook prentice hall
Please help me---I am not sure how to setup this problem in order to solve it.
Problem: Find the greatest possible pair of numbers such that one integer is 5 more than twice the other and the sum is less than 30.
1 solutions
Answer 79611 by ankor@dixie-net.com(15622) on 2007-11-10 19:12:50 (Show Source):
You can put this solution on YOUR website!Find the greatest possible pair of numbers such that one integer is 5 more than twice the other and the sum is less than 30.
Let x = one number
Then
(x+5) = the other number:
:
x + (x+5) < 30
2x < 30 - 5
2x < 25
x < 25/2
x < 12.5
but it has to be an integer
x = 12
:
12 and 17 are the greatest integers less than 30
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Polynomials-and-rational-expressions/109156: This problem is not in the book.
15/x - 15/x+2 =2 Can you help me solve this? Thanks Rhee
1 solutions
Answer 79610 by ankor@dixie-net.com(15622) on 2007-11-10 19:05:48 (Show Source):
You can put this solution on YOUR website!15/x - 15/x+2 = 2
;
 -  = 2
:
The common denominator will be x(x+2)
Multiply equation by that:
x(x+2)* - x(x+2)* = x(x+2) * 2
:
Cancel out the denominators and you have:
15(x+2) - 15x = 2x(x+2)
:
15x + 30 - 15x = 2x^2 + 4x
:
The 15x's cancel; subtract 30 from both sides, you have a quadratic equation
2x^2 + 4x - 30 = 0
:
Factor this to:
(2x - 6)(x + 5) = 0
:
Two solutions:
2x = +6
x = 6/2
x = 3
and
x = - 5
:
Check both solutions in the original equation:
x = 3
 -  = 2
5 - 3 = 2; a good solution
:
 -  = 2
-3 - (-5) = 2; also a good solution
:
Did this help you understand this? Any questions?
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Quadratic_Equations/109166: find length and width of area 204 perimeter 58
1 solutions
Answer 79603 by ankor@dixie-net.com(15622) on 2007-11-10 18:49:37 (Show Source):
You can put this solution on YOUR website!find length and width of area 204 perimeter 58
:
Let x = length, y = width
:
Perimeter:
2x + 2y = 58
Simplify, divide by 2:
x + y = 29
y = (29-x)
:
Area =
x*y = 204
;
Substitute (29-x) for y:
x(29-x) = 204
-x^2 + 29x - 204 = 0; a quadratic equation
:
Multiply by -1, (easier to factor):
x^2 - 29x + 204 = 0
:
Factor:
(x - 12)(x - 17) = 0
:
x = +12; then y = 17
or
x = 17; then y = 12
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Trigonometry-basics/108919: An A-frame cabin has a triangular front with a base of 30 ft and a height of 20 ft. If the front is to be glass that costs $3 per square foot, what will the glass cost?
HELP ME PLEASE!!! I hate word problems.
1 solutions
Answer 79572 by ankor@dixie-net.com(15622) on 2007-11-10 13:20:58 (Show Source):
You can put this solution on YOUR website!n A-frame cabin has a triangular front with a base of 30 ft and a height of 20 ft. If the front is to be glass that costs $3 per square foot, what will the glass cost?
:
you should know the formula for the area of a triangle A = *b*h
:
They give you the base and the height
A = *30*20
A = 300 sq ft
:
Find the cost of the glass:
Cost = 300*3 = $900
:
:
That wasn't so hard, was it?
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expressions/109108: I wanted to know what the parentheses mean around the numbers? For example the problem is 6+3[(12/4)+5]. Can you please help understand I am very confused. Thanks, TIna
1 solutions
Answer 79560 by ankor@dixie-net.com(15622) on 2007-11-10 11:04:15 (Show Source):
You can put this solution on YOUR website! wanted to know what the parentheses mean around the numbers? For example the problem is 6+3[(12/4)+5]. Can you please help understand I am very confused.
:
Start with the values inside the most inside parentheses
:
In this case it's (12/4), do the math there and remove the parentheses
:
you then have: 6 + 3[3 + 5]
:
Do the math inside these parentheses and you have
6 + 3(8);
:
Multiply 3*8 and you have:
6 + 24 = 30
:
Some other important rules:
Sometimes you can't do the math inside the parentheses, for example
3(x + 4)
but you can remove the brackets by multiplying 3 times x and 3 times 4
3x + 12
(Everything inside the brackets has to be multiplied by what's outside)
:
Another very important rule is if there is a neg outside the brackets, like
-3(x + 4)
When you multiply by -3 you must change the signs. you will have:
-3x - 4
If you had
-3(x - 4), it would be
-3x + 4, (the sign of 4 is changed to positive)
:
Hope this helps, you can email me if you have a question about what I just said here.
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Miscellaneous_Word_Problems/109098: sasha works at the botanical gardens and is planning a new rectangular rose garden 20m by 30m. She plans to build a walkway, with a uniform width, all around the garden. Her budget is $6000 and she knows it will cost $10/m2 to construct the hallway. How wide can the walkway be?
1 solutions
Answer 79559 by ankor@dixie-net.com(15622) on 2007-11-10 10:41:10 (Show Source):
You can put this solution on YOUR website!A rectangular rose garden 20m by 30m. a walkway, with a uniform width, all around the garden. budget is $6000 and it will cost $10/m2 to construct the walkway. How wide can the walkway be?
:
1st find the area of the walkway that will utilize the $6000 budget:
Area = 6000/10
A = 600 sq/m will be the area of the walkway
:
Let x = the width of the walkway:
:
Overall area: (30 + 2x) * (20 + 2x) = (600 + 100x + 4x^2);FOILed
:
30 * 20 = 600 sq/m = area of the garden only
:
The equation:
Overall area - garden area = walkway area
(4x^2 + 100x + 600) - 600 = 600
4x^2 + 100x - 600 = 0
Simplify, divide equation by 4
x^2 + 25x - 150 = 0
Factors to:
(x+30)(x-5) = 0
x = +5 meters is the solution we want here.
:
;
Check solution:
Overall area - garden area = walkway area
(40*30) - (30*20) =
1200 - 600 = 600
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