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15390..15419 , 15420..15449 , 15450..15479 , 15480..15509 , 15510..15539 , 15540..15569 , 15570..15599 , 15600..15629 , 15630..15659, >>NextRectangles/577414: if the length of a rectangle is increased by 20% and the width is decreased by 20%then what will be the change in area and how much?
1 solutions
Answer 370271 by ankor@dixie-net.com(15652)   on 2012-02-24 21:21:33 (Show Source):
You can put this solution on YOUR website!if the length of a rectangle is increased by 20% and the width is decreased by 20% then what will be the change in area and how much?
:
Multiplier for 20% increase = 1.2
Multiplier for 20% decrease = .8
:
change in area:
c = L * W - 1.2L*.8W
c = 1LW - .96LW
c = .04 which is a 4% change in area, how much will depend on the actual dimensions you're dealing with here
:
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Geometry_Word_Problems/577617: I am a rectangular prism, so I have a height (h), a width (w) and a depth (d). Here are your clues to determining each of my dimensions...my depth is 3 more units than my width, my height is 1.5 units less than my depth, and the sum of my 3 dimensions is slightly > 25 units. Finally, my volume is 595 cubic units while my surface area is 429 square units.
What are my 3 dimensions? List the depth, height and width
1 solutions
Answer 370260 by ankor@dixie-net.com(15652) on 2012-02-24 20:20:33 (Show Source):
You can put this solution on YOUR website!I am a rectangular prism, so I have a height (h), a width (w) and a depth (d).
:
Write an equation for each statement:
:
" depth is 3 more units than my width,"
d = w + 3
or
w = (d-3)
:
"height is 1.5 units less than my depth,"
h = (d-1.5)
:
"the sum of my 3 dimensions is slightly > 25 units."
h + w + d > 25
:
" volume is 595 cubic units"
h*w*d = 595
:
"surface area is 429 square units."
2(h*w) + 2(h*d) + 2(w*d) = 429
:
Replace h and w in the sum equation
h + w + d > 25
(d-1.5) + (d-3) + d > 25
3d - 4.5 > 25
3d > 25 + 4.5
3d > 29.5
d > 29.5/3
d > 9.833
d = 10 is the depth
then
w = 10-3
w = 7 is the width
and
h = 10-1.5
h = 8.5 is the height
:
Find vol with these values
8.5 * 7 * 10 = 595, checks out
:
Check the surface area
2(8.5*7) + 2(8.5(10) + 2(7*10) =
119 + 170 + 140 = 429
:
Summarize: h = 8.5; w = 7; d = 10
|
test/577384: The time (t) of travel of an automobile trip varies inversely as the speed (v).
At an average speed of 65mph, a trip took 4h. The return trip took 5h.
Find the average speed of the return trip.
1 solutions
Answer 370247 by ankor@dixie-net.com(15652) on 2012-02-24 19:13:42 (Show Source):
You can put this solution on YOUR website!The time (t) of travel of an automobile trip varies inversely as the speed (v).
At an average speed of 65mph, a trip took 4h. The return trip took 5h.
Find the average speed of the return trip.
:
Let s = the speed on the return trip
;
the distance there and back is the same
:
Write a distance equation; dist = speed * time
:
5s = 4(65)
5s = 260
s = 260/5
s = 52 mph on the return trip
:
:
check solution by finding the distances, should be the same
65 * 4 = 260
52 * 5 = 260
|
Expressions-with-variables/127778: Find the width and length of the rectangle so that it has the given perimeter:
P = 60 inches, width is x, and length is 3x – 5.
1 solutions
Answer 370223 by ankor@dixie-net.com(15652) on 2012-02-24 17:10:02 (Show Source):
You can put this solution on YOUR website!Find the width and length of the rectangle so that it has the given perimeter:
P = 60 inches, width is x, and length is 3x – 5.
:
The perimeter equation:
2(3x-5) + 2x = 60
6x - 10 + 2x = 60
6x + 2x = 60 + 10
8x = 70
x = 
x = 8.75 is the width
then
3(8.75) - 5 =
26.25 - 5 = 21.25 is the length
:
:
Check the perimeter
2(21.25) + 2(8.75 =
42.5 + 17.5 = 60
|
Quadratic_Equations/5549: the width of a rectangle is 3 inches less than its length. The area of the rectangle is 340 square inches. What are the length and widthof the rectangle?
1 solutions
Answer 370196 by ankor@dixie-net.com(15652) on 2012-02-24 13:35:29 (Show Source):
You can put this solution on YOUR website!he width of a rectangle is 3 inches less than its length.
The area of the rectangle is 340 square inches.
What are the length and width of the rectangle?
:
We know the Area is: L * W = 340
Given that,"The width of a rectangle is 3 inches less than its length."
W = L - 3
Replace W with (L-3) in the area equation
L * (L-3) = 340
L^2 - 3L = 340
L^2 - 3L - 340 = 0; a quadratic equation
factors to
(L-20)(L+17) = 0
The positive solution
L = 20 inches is the Length
then
w = 20 - 3 = 17 inches is the width
:
:
Check by finding the area: 20 * 17 = 340
|
Travel_Word_Problems/577439: A man calculated that if his speed had been increased by 4km/h he would have completed his 48km journey 1 hour sooner.determine his speed.
1 solutions
Answer 370170 by ankor@dixie-net.com(15652) on 2012-02-24 08:14:48 (Show Source):
You can put this solution on YOUR website!A man calculated that if his speed had been increased by 4km/h he would have completed his 48km journey 1 hour sooner.
determine his speed.
:
Let s = his speed
then
(s+4) = his faster speed
:
Write a time equation: time = dist/speed
:
normal time - faster time = 1 hr
 -  = 1
Multiply by s(s+4)
s(s+4)* - s(s+4)* = 1s(s+4)
cancel the denominators
48(s+4) - 48s = s^2 + 4s
48s + 192 - 48s = s^2 + 4s
0 = s^2 + 4s - 192 = 0
Factors to
(s-12)(s+16) = 0
the positive solution
s = 12 mph his speed
:
:
Check this by finding the actual times
48/12 = 4 hrs
48/16 = 3 hrs
---------------
diff is 1 hr
|
Rectangles/576912: The length of a rectangle is 3cm less than twice the width. The perimeter of the rectangle is 72cm. Find the length and width of the rectangle.
I need help setting up the correct formula to find the answer, I tried a couple and my answer is still wrong.
1 solutions
Answer 370154 by ankor@dixie-net.com(15652) on 2012-02-23 21:49:06 (Show Source):
You can put this solution on YOUR website!The length of a rectangle is 3cm less than twice the width.
The perimeter of the rectangle is 72cm.
Find the length and width of the rectangle.
:
The perimeter
2L + 2W = 72
:
It say's,"The length of a rectangle is 3cm less than twice the width.". therefore:
L = 2W - 3
:
Replace L in the 1st equation with (2W-3)
2(2W-3) + 2W = 72
Mult what's inside the brackets
4W - 6 + 2W = 72
4W + 2W = 72 + 6
6W = 78
W = 
W = 13
:
Now you should be able to find L. Then check the perimeter with those values
|
Numbers_Word_Problems/576705: the sum of the two numbers is 380. the difference between the two numbers is 138. what is the smaller number and what is the greater number.
1 solutions
Answer 370153 by ankor@dixie-net.com(15652) on 2012-02-23 21:39:49 (Show Source):
You can put this solution on YOUR website!the sum of the two numbers is 380. the difference between the two numbers is 138.
what is the smaller number and what is the greater number.
:
A good problem for the elimination method
a + b = 380
a - b = 138
---------------adding eliminates b, find a. Then find b, It's easy
|
Exponential-and-logarithmic-functions/576749: The half-life of a radioactive substance is the time it takes for half of the substance to decay. The half-life if carbon-14 is 5700 years.
A.) write a exponential function to model the decay of a 240-my sample.
B.) explain what each value in the function model represents.
C.) to the nearest hundredth, find the amount of carbon-14 remaining after 2353 years. Explain how you found this amount.
1 solutions
Answer 370013 by ankor@dixie-net.com(15652) on 2012-02-23 08:42:10 (Show Source):
You can put this solution on YOUR website!The half-life of a radioactive substance is the time it takes for half of the substance to decay.
The half-life if carbon-14 is 5700 years.
:
The radioactive decay formula: A = Ao*2^(-t/h)
where
A = amt after t time
Ao = initial amt (t=0)
t = time of decay
h = half-life of the substance
:
A.) write a exponential function to model the decay of a 240-my sample.
A = 240(2^(-t/5700)
:
B.) explain what each value in the function model represents.
see above
:
C.) to the nearest hundredth, find the amount of carbon-14 remaining after 2353 years.
A = 240(2^(-2353/5700)
A = 240(2^(-.4128))
using a calc
A = 240*75116
A = 180.3 grams remain after 2,353 yrs
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Quadratic_Equations/576831: 3(x^2-3) = 35x + 19
please use the quadratic formula thankssss
1 solutions
Answer 370011 by ankor@dixie-net.com(15652) on 2012-02-23 08:22:06 (Show Source):
You can put this solution on YOUR website!3(x^2-3) = 35x + 19
put the equation in the standard form: ax^2 + bx^2 + c = 0
3x^2 - 9 - 35x - 19 = 0
3x^2 - 35x - 28 = 0
:
the quadratic formula
:
a=3, b = -35; c = -28
:
:
Two solutions
x = 
x = 12.42
and
x = 
x = -.75
:
:
You can confirm this by replacing x in the original equation with these values
|
Triangles/576714: what is the base of a right triangle with a height of 5 and a hypotenuse of 8?
1 solutions
Answer 370009 by ankor@dixie-net.com(15652) on 2012-02-23 08:00:22 (Show Source):
You can put this solution on YOUR website!what is the base of a right triangle with a height of 5 and a hypotenuse of 8?
:
Got old Pythagoras out of bed for this one: a^2 + b^2 = c^2
5^2 + b^2 = 8^2
25 + b^2 = 64
b^2 = 64 - 25
b^2 = 39
b = 
b ~ 6.245 is the base
:
:
You can check this on your calc: enter 
|
Mixture_Word_Problems/576674: Plese help me solve this problem: erika wants to dilute a 12% salt solution with water to make 36 ounces of 8% salt solution. How much water and how much 12% salt solution should she mix together?
1 solutions
Answer 369966 by ankor@dixie-net.com(15652) on 2012-02-22 21:45:04 (Show Source):
You can put this solution on YOUR website!dilute a 12% salt solution with water to make 36 ounces of 8% salt solution.
How much water and how much 12% salt solution should she mix together?
;
Let x = amt of 12% solution required
the resulting amt is to be 36 oz, therefore
(36-x) = amt of water required
:
Write an amt of salt equation, the amt of salt remains the same only the percent changes
:
.12x = .08(36)
.12x = 2.88
x = 
x = 24 oz of 12% solution
then
36 - 24 = 12 oz of water
|
Human-and-algebraic-language/576539: The second of three numbers is 3 times the first. The third is 5 more than the second. If the second is decreased by twice the third. The result is 5. What are the three numbers?
The greater of two numbers is 3 more than the smaller. If twice the smaller is added to the greater, the result is 30. What are the numbers?
1 solutions
Answer 369955 by ankor@dixie-net.com(15652) on 2012-02-22 21:20:26 (Show Source):
You can put this solution on YOUR website!Let the three number be a, b, c
:
The second of three numbers is 3 times the first.
b = 3a
:
The third is 5 more than the second.
c = b+5
:
If the second is decreased by twice the third, the result is 5.
b - 2c = 5
From the above we can replace c with (b+5)
b - 2(b+5) = 5
b - 2b + 10 = 5
-b = 5 - 10
-b = -5
b = 5
then
c = 5 + 5
c = 10
and
b = 3a
5 = 3a
a = 
:
What are the three numbers?: , 5, 10
:
:
The greater of two numbers is 3 more than the smaller.
a = b+3
:
If twice the smaller is added to the greater, the result is 30.
a + 2b = 30
Replace a with (b+3)
(b+3) + 2b = 30
3b = 30 - 3
3b = 27
b = 
b = 9
then
a = 9 + 3
a = 12
:
What are the numbers? 12 and 9
|
Travel_Word_Problems/576301: Two airplanes depart simultaneously from an airport. One flies due south; the other flies due
east at a rate 30 mph faster than that of the first airplane. After 3 hours, radar indicates that
the airplanes are 450 miles apart. What is the ground speed of each airplane
1 solutions
Answer 369902 by ankor@dixie-net.com(15652) on 2012-02-22 19:20:30 (Show Source):
You can put this solution on YOUR website!Two airplanes depart simultaneously from an airport.
One flies due south; the other flies due east at a rate 30 mph faster than that of the first airplane.
After 3 hours, radar indicates that the airplanes are 450 miles apart.
What is the ground speed of each airplane.
:
let s = speed of the southbound airplane
then
(s+30) = speed of the eastbound
:
dist = time * speed, therefore
3s = distance traveled by the southbound plane
and
3(s+30) = distance traveled by the eastbound plane
:
This is a right triangle problem: a^2 + b^2 = c^2, where
a = 3s
b = 3(s+30)
c = 450
:
(3s)^2 + (3(s+30))^2 = 450^2
9s^2 + (3s+90)^2 = 202500
9s^2 + 9s^2 + 270s + 270s + 8100 - 202500 = 0
18s^2 + 540s - 194400 = 0
simplify, divide by 18
s^2 + 30s - 10800 = 0
you can use the quadratic formula to find s, but this will factor to:
(s+120)(s-90) = 0
the positive solution is all we want here
s = 90 mph, speed of the southbound plane
then
90+30 = 120 mph, speed of the eastbound
:
:
Check this out on your calc: enter  results 450
|
Travel_Word_Problems/576213: Mrs. Sanchez ran 3/5 of a mile. Mrs. Fritz ran 2/3 as far as Mrs. Sanchez. How far did Mrs. Fritz run? How much farther than Mrs. Fritz did Mrs. Sanchez run? Show work.
1 solutions
Answer 369857 by ankor@dixie-net.com(15652) on 2012-02-22 16:53:52 (Show Source):
You can put this solution on YOUR website!Mrs. Sanchez ran 3/5 of a mile. Mrs. Fritz ran 2/3 as far as Mrs. Sanchez.
How far did Mrs. Fritz run?
 *  =  reduces to  mi by Fritz (you could have just canceled the 3's)
:
How much farther than Mrs. Fritz did Mrs. Sanchez run?
- =  mi further
|
Age_Word_Problems/576434: I am desperately trying to help my niece with homework while her parents are out of town. I am not a math guru. Here is the word problem:
Joe is 2 years older than his brother. The sum of their ages is 12. How old is his brother?
She knows the answers are ages 5 and 7 (5+7=12) but I do not know how to help her figure out the mathematical equation.
Can you PLEASE HELP????
1 solutions
Answer 369856 by ankor@dixie-net.com(15652) on 2012-02-22 16:46:23 (Show Source):
You can put this solution on YOUR website!Let j = Joe's age
Let b = his brother's age
;
Write an equation for each statement
:
"Joe is 2 years older than his brother."
j = b + 2
:
"The sum of their ages is 12."
j + b = 12
In first equation we know that j = (b+2), replace j with (b+2) in the above equation
(b+2) + b = 12
add the b's
2b + 2 = 12
subtract 2 from both sides
2b = 12 - 2
2b = 10
Divide both sides by 2
b= 10/2
b = 5 yrs is brothers age.
:
Use the 1st equation to find Joes age
:
Check your solutions in the 2nd equatiion
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Age_Word_Problems/575980: Three siblings have a combines age of 108 yrs. The oldest is 8 years older than the youngest. what are the ages of the siblings?
1 solutions
Answer 369709 by ankor@dixie-net.com(15652) on 2012-02-21 21:41:14 (Show Source):
You can put this solution on YOUR website!Three unknowns, two equations, calls for some reasoning here.
Three siblings have a combined age of 108 yrs.
a + b + c = 108
;
The oldest is 8 years older than the youngest.
a = c + 8
:
a + b + c = 108
(c+8) + b + c = 108
2c + b = 108 - 8
2c = b = 100
b = -2c + 100
we know b is < 8 and > 1 yr more than c
c = 31
b = -2(31) + 100
b = 38
or
c = 32
b = -2(32) + 100
b = 36
and
c = 33
b = -2(33) + 100
b = 34
:
So we have three possibilities:
a = 39
b = 38
c = 31
or
a = 40
b = 36
c = 32
or
a = 41
b = 34
c = 33
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Travel_Word_Problems/575977: a bus travels 1800m from your school to the first stop.the entire trip takes 2 minutes what is the average speed of the bus in meters per second?
1 solutions
Answer 369693 by ankor@dixie-net.com(15652) on 2012-02-21 20:50:58 (Show Source):
You can put this solution on YOUR website!a bus travels 1800m from your school to the first stop.the entire trip takes 2 minutes
what is the average speed of the bus in meters per second?
:
Change 2 min to 120 sec
:
 = 15 m/sec
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Percentage-and-ratio-word-problems/575934: If it takes 4 hours for 3 paint mixers to mix a fixed amount of paint.The number of hours varies inversely as the number of paint mixers used. How long would it take 8 paint mixers to do the same job?
1 solutions
Answer 369691 by ankor@dixie-net.com(15652) on 2012-02-21 20:44:16 (Show Source):
You can put this solution on YOUR website!If it takes 4 hours for 3 paint mixers to mix a fixed amount of paint.
Find how many man-hours to do the job
3 * 4 = 12 man-hrs to complete the job
:
How long would it take 8 paint mixers to do the same job?
let h = no. of hrs to do it with 6 men
8h = 12
h = 12/8
h = 1.5 hrs for 8 men to do it
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Quadratic_Equations/575890: A rain gutter is to be made of a sheet that is 10in wide by turning up the edges 90 degrees.
I have developed the formula for the cross sectional area by letting x define the unknown quantity of depth that is to be the independent value.
my formula is f(x)= 2x^2 + 10x
My question is, what happens to the cross sectional area as depth size increases?
What x and y values make sense for this problem? (restricted domain and range)
1 solutions
Answer 369690 by ankor@dixie-net.com(15652) on 2012-02-21 20:40:06 (Show Source):
You can put this solution on YOUR website!A rain gutter is to be made of a sheet that is 10in wide by turning up the edges 90 degrees.
:
Using the depth as x,
then
(10-2x) = the width of the gutter
;
y = the cross sectional area
:
y = depth * width
y = x(10-2x)
y = -2x^2 + 10x
or
f(x) = -2x^2 + 2x
:
Graphing this would make it clear
You can see the domain is >0 to < 5, with max area when x= 2.5
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Average/576018: Show me how one arrive at the answer 77 for this problem. A total of 50 juniors and seniors were given a mathematics test. The 35 juniors attained and average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test? I know the answer is 77. I'm just not sure how to arrive at this answer. Is there a algebra formula that one can use to solve this problem and if so would you show me how to solve it using the algebra formula? My e-mail is zippor21@gmail.com
1 solutions
Answer 369688 by ankor@dixie-net.com(15652) on 2012-02-21 20:28:48 (Show Source):
You can put this solution on YOUR website!A total of 50 juniors and seniors were given a mathematics test.
The 35 juniors attained and average score of 80 while the 15 seniors attained an average of 70.
What was the average score for all 50 students who took the test?
:
av = 
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Money_Word_Problems/575970: What Number increased by 12% and then decreased by 12% = 86.7328
I can't set up the equation properly, Thanks in advance for your help.
1 solutions
Answer 369685 by ankor@dixie-net.com(15652) on 2012-02-21 20:18:50 (Show Source):
You can put this solution on YOUR website!What Number increased by 12% and then decreased by 12% = 86.7328
:
an increase of 12%, the multiplier is 1.12
a decrease of 12%, the multiplier is .88
:
.88(1.12x) = 86.7328
.9856x = 86.7328
x = 
x = 88
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Rate-of-work-word-problems/575909: You have a rectangular pool that is 20 ft by 10 ft and a depth of 8ft. How do I solve and find out how much water you need to fill the pool? Also i would like to know how I can use pythagoreans theorem to solve it.
1 solutions
Answer 369672 by ankor@dixie-net.com(15652) on 2012-02-21 19:27:11 (Show Source):
You can put this solution on YOUR website!You have a rectangular pool that is 20 ft by 10 ft and a depth of 8ft.
How do I solve and find out how much water you need to fill the pool?
:
you don't need Pythag for this, just know that 1 cu/ft of water = 7.481 gallons
:
20 * 10 * 8 * 7.481 = 11,969.6 gallons
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