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the measures of an angle and its complement differ by twenty-two degrees. find the measures of the angles.
1 solutions
Answer 158127 by nerdybill(6962)   on 2009-08-27 21:39:05 (Show Source):
You can put this solution on YOUR website!the measures of an angle and its complement differ by twenty-two degrees. find the measures of the angles.
.
If two angles are complementary, the sum of the two angles equals 90 degrees.
.
Let x = lesser of two angles
then
x+22 = greater of two angles
.
x + (x+22) = 90
2x + 22 = 90
2x = 68
x = 34 degrees
.
Other angle:
x+22 = 34+22 = 56 degrees
.
The measure of the two angles are 34 and 56 degrees.
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Linear-equations/209062: 2y=x+4 need the slope and intersection
1 solutions
Answer 158023 by nerdybill(6962) on 2009-08-27 13:51:19 (Show Source):
You can put this solution on YOUR website!2y=x+4 need the slope and intersection
.
To determine the "slope" and the "y-intercept", you can manipulate the given equation into the "slope-intercept" form of a straight line:
y = mx + b
where
m is the slope
b is the y-intercept at (0,b)
.
To get it in the above form, simply divide both sides of the given equation by 2:
2y=x+4
y = (1/2)x + 2
This means:
m (slope) is 1/2
and
(0,2) is the y-intercept
.
To find the x-intercept, set y=0 and solve for 'x':
2y=x+4
2(0)=x+4
0=x+4
-4 = x
therefore,
(-4,0) is the x-intercept
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Equations/208959: One of the first mixtures of metals, called amalgams, used by dentists for tooth fillings consisted of 26.0 grams of silver, 10.8 grams of tin, 2.4 grams of copper, and 0.8 grams of zinc.
How much silver is in a 25.0 gram sample of this analgam?
thank you
1 solutions
Answer 157985 by nerdybill(6962) on 2009-08-26 23:34:19 (Show Source):
You can put this solution on YOUR website!26.0 grams of silver, 10.8 grams of tin, 2.4 grams of copper, and 0.8 grams of zinc
.
Total weight = 26.0 + 10.8 + 2.4 + 0.8 = 40 grams
.
Of the total weight, 26 grams is made up of silver Or
26/40 * 100 = 65%
.
So, if you have 25 grams of analgam, 65% would be silver:
.65 * 25 = 16.25 grams
|
logarithm/208905: Solve the equation for x.
e^(ax) = Ce^(bx), where a is not equal to b
1 solutions
Answer 157960 by nerdybill(6962) on 2009-08-26 19:57:27 (Show Source):
You can put this solution on YOUR website!Solve the equation for x.
e^(ax) = Ce^(bx), where a is not equal to b
.
Applying "log rules":
e^(ax) = Ce^(bx)
Divide both sides by e^(bx):
e^(ax)/e^(bx) = C
Rewriting the left side:
e^(ax-bx) = C
Take the ln of both sides:
ax-bx = ln(C)
Factor the left:
x(a-b) = ln(C)
Dividing we get:
x = ln(C)/(a-b)
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Divisibility_and_Prime_Numbers/208896: i need help with this math problem i am so lost it says factor completely s^2-64 and the other says v^2-1/49
1 solutions
Answer 157959 by nerdybill(6962) on 2009-08-26 19:53:04 (Show Source):
You can put this solution on YOUR website!factor completely s^2-64 and the other says v^2-1/49
.
First one:
s^2-64
Notice I can rewrite as:
s^2-8^2
Now, you have a "difference of squares" -- which should automatically trigger:
(s-8)(s+8) (this is completely factored)
.
Second one:
Similar to the first:
v^2-1/49
Can be rewritten as:
v^2-(1/7)^2
Now, you have a "difference of squares" -- which should automatically trigger:
(v-1/7)(v+1/7) (this is completely factored)
|
Travel_Word_Problems/208704: respected sir,
plz help me to solve this maths prob...
1] how many minutes does it take to travel 120 miles at 400 miles per hour?
waiting for yur reply.
thank u.
regards
Binita.
1 solutions
Answer 157847 by nerdybill(6962) on 2009-08-26 09:17:28 (Show Source):
You can put this solution on YOUR website!how many minutes does it take to travel 120 miles at 400 miles per hour?
.
You will be applying the "distance formula":
d = rt
where
d is distance
r is rate or speed
t is time
.
Let's start by solving:
d = rt
for 't':
t = d/r
.
Plugging in the given values:
t = 120/400
t = 3 hours
Since the problem wants the answer in terms of minutes:
t = 3 hours * 60 mins/hour = 180 minutes
|
Mixture_Word_Problems/208662: This question is from textbook
Tracey and Max determined that the vacation they would like to take for their anniversary would cost $2250. If they put the money saved by making their own coffee into a vacation account,would there be enough money in eight months to take their vacations?
1 solutions
Answer 157846 by nerdybill(6962) on 2009-08-26 09:11:54 (Show Source):
You can put this solution on YOUR website!Tracey and Max determined that the vacation they would like to take for their anniversary would cost $2250. If they put the money saved by making their own coffee into a vacation account,would there be enough money in eight months to take their vacations?
.
Previously, we found that Tracey and Max saves:
$180 per month if they make their own coffee
.
In 8 months, the will save:
8(180) = $1440
.
So, NO, they will not have enough for that vacation.
|
Mixture_Word_Problems/208661: This question is from textbook
If tracey and max make their own specialty blend of coffee.they estimate that it costs about $1.00 for every 2 cups of coffee. Determine how much they are saving by making their own coffee
1 solutions
Answer 157845 by nerdybill(6962) on 2009-08-26 09:09:13 (Show Source):
You can put this solution on YOUR website! If tracey and max make their own specialty blend of coffee.they estimate that it costs about $1.00 for every 2 cups of coffee. Determine how much they are saving by making their own coffee
.
Previously,
Max spends $120 per month
Tracey spends $90 per month
.
To make their own:
1(30) = $30 per month
.
Therefore, they will save:
(120+90) - 30
= 210 - 30
= $180
.
That is, they will save $180 per month if they make their own coffee instead of buying it.
|
Travel_Word_Problems/208614: 30. Two planes left an airport at noon. One flew east at a certain speed and the
other flew west at twice the speed.The planes were 2700 mi apart in 3 h. How
fast was each plane flying?
1 solutions
Answer 157842 by nerdybill(6962) on 2009-08-26 08:54:13 (Show Source):
You can put this solution on YOUR website!Two planes left an airport at noon. One flew east at a certain speed and the
other flew west at twice the speed.The planes were 2700 mi apart in 3 h. How
fast was each plane flying?
.
You will need to apply the "distance formula":
d=rt
where
d is distance
r is rate or speed
t is time
.
Let x = speed of east bound plane
then
2x = speed of west bound plane
.
3x + 3(2x) = 2700
3x + 6x = 2700
9x = 2700
x = 300 mph (speed of east bound plane)
.
speed of west bound plane:
2x = 2(300) = 600 mph
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Proportions/208673: Rise and run. If the rise is
3/2 and the run is 5, then what is
the ratio of the rise to the run?
1 solutions
Answer 157820 by nerdybill(6962) on 2009-08-26 02:58:58 (Show Source):
You can put this solution on YOUR website!The ratio of the rise over the run is the "slope":
.
slope = rise/run
.
In your case, since
rise = 3/2
and
run = 5
.
then,
slope = rise/run = (3/2)/5 = 3/10
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Proportions/208675: Rise and run. If the rise is 3/2
and the run is 5, then what is
the ratio of the rise to the run?
1 solutions
Answer 157819 by nerdybill(6962) on 2009-08-26 02:57:38 (Show Source):
You can put this solution on YOUR website!Rise and run. If the rise is 3/2
and the run is 5, then what is
the ratio of the rise to the run?
.
The ratio of the rise over the run is the "slope":
.
slope = rise/run
.
In your case, since
rise = 3/2
and
run = 5
.
then,
slope = rise/run = (3/2)/5 = 3/10
.
|
Linear-systems/208611: -3xyz(squared)
x=-4 y=-2 z=1\2
okay when i put this equation in my TI calculator i got 144 but when my teacher checked it he said it was wrong can you show me how to solve this problem? and what the correct answer would be PLEASE??????
1 solutions
Answer 157818 by nerdybill(6962) on 2009-08-26 02:03:34 (Show Source):
You can put this solution on YOUR website!-3xyz(squared)
x=-4 y=-2 z=1\2
.
Plugging in the given values:
x=-4 y=-2 z=1\2
.
order of operations (PEMDAS) says we deal with exponents first:
Next, multiplication right to left:
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Word_Problems_With_Coins/208666: My brain does not mix numbers and letters, but I'm trying to help my grandson with his summer homework. Here's one of two that he couldn't figure out. Altogether you have $3.30. If you have 9 more nickels than dimes and 12 fewer quarters than nickels, how many of each do you have?
1 solutions
Answer 157816 by nerdybill(6962) on 2009-08-26 01:56:38 (Show Source):
You can put this solution on YOUR website!. Altogether you have $3.30. If you have 9 more nickels than dimes and 12 fewer quarters than nickels, how many of each do you have?
.
Let x = number of dimes
then
x+9 = number of nickels
x+9 -12 = x-3 = number of quarters
.
.05(x+9) + .10x + .25(x-3) = 3.30
.05x+.45 + .10x + .25x-.75 = 3.30
.40x-.30 = 3.30
.40x = 3.60
x = 3.60/.40
x = 9 (number of dimes)
.
number of nickels:
x+9 = 9+9 = 18
.
number of quarters:
x-3 = 9-3 = 6
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Number-Line/208667: This is my grandson's other problem from his summer worksheet that he doesn't know how to do. Write a series of five decimal numbers that increase by 0.2 and add up to a total of 5. I think I've figured it out just by guessing (.60+.80+1.00+1.20+1.40) but I have no idea how to explain to him the right way to figure this out. There must be a logical solution other than trial and error or guessing.
1 solutions
Answer 157815 by nerdybill(6962) on 2009-08-26 01:52:03 (Show Source):
You can put this solution on YOUR website! This is my grandson's other problem from his summer worksheet that he doesn't know how to do. Write a series of five decimal numbers that increase by 0.2 and add up to a total of 5. I think I've figured it out just by guessing (.60+.80+1.00+1.20+1.40) but I have no idea how to explain to him the right way to figure this out. There must be a logical solution other than trial and error or guessing.
.
Let x = first of five decimal numbers
then
x+.2 = second
x+.4 = third
x+.6 = fourth
x+.8 = fifth
.
x + (x+0.2) + (x+0.4) + (x+0.6) + (x+0.8) = 5
Grouping like-terms:
(x+x+x+x+x) + (0.2+0.4+0.6+0.8) = 5
5x + 2 = 5
5x = 5-2
5x = 3
x = 3/5
x = 0.6 (first decimal number)
.
The five numbers are indeed:
.6, .8, 1, 1.2 and 1.4
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Problems-with-consecutive-odd-even-integers/208670: twice the greater of two consecutive odd integers is 13 less than three times the lesser. find the intergers.
1 solutions
Answer 157813 by nerdybill(6962) on 2009-08-26 01:45:52 (Show Source):
You can put this solution on YOUR website!twice the greater of two consecutive odd integers is 13 less than three times the lesser. find the intergers.
.
Let x = 1st consecutive odd integer
then
x+2 = greater consecutive odd integer
.
2(x+2) = 3x-13
2x+4 = 3x-13
4 = x-13
17 = x
.
Greater integer:
x+2 = 17+2 = 19
.
Therefore, the two integers are 17 and 19
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Expressions-with-variables/208388: How would I solve the equation listed below using the elimination method? I have tried, but I keep coming up with differnt answers.
x+5y=29
-7x+4y=70
1 solutions
Answer 157663 by nerdybill(6962) on 2009-08-25 07:38:32 (Show Source):
You can put this solution on YOUR website!x+5y=29
-7x+4y=70
.
Multiply the top equation by 7 then combine:
7x+35y=203
-7x+4y=70
----------
39y = 273
y = 7
.
Substitute the above back into equation 1 to solve for x:
x+5y=29
x+5(7)=29
x+35=29
x = 29-35
x = -6
.
Therefore, the solution is:
(x,y) = (-6, 7)
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Miscellaneous_Word_Problems/208427: the price of a coat is representedd by (2x-5) dollars. Represent the amount a man paid for (5x-3) of these coats.
1 solutions
Answer 157662 by nerdybill(6962) on 2009-08-25 07:33:54 (Show Source):
You can put this solution on YOUR website! the price of a coat is representedd by (2x-5) dollars. Represent the amount a man paid for (5x-3) of these coats.
.
"amount paid" = "number of coats" * "price of a coat"
.
c(x) = (5x-3)(2x-5)
c(x) = 10x^2-25X-6X+15
c(x) = 10x^2-31x+15
where
c(x) is the amount paid
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Linear-equations/208429: Parallel and Perpendicular Slope
Please help me solve this equation: Which lines are parallel?
a.x=7
b.y=5/6x+8
c.y=5/6x-4
d.x=9
1 solutions
Answer 157661 by nerdybill(6962) on 2009-08-25 07:30:15 (Show Source):
You can put this solution on YOUR website!Which lines are parallel?
a.x=7
b.y=5/6x+8
c.y=5/6x-4
d.x=9
.
'a' and 'd' are parallel
(both are vertical lines)
AND
'b' and 'c' are parallel
(by inspection, because of slope-intercept form y=mx+b -- both have the same slope of 5/6)
|
Square-cubic-other-roots/208437: I got this wrong.
(3x-2y)^2= (that's the equation)
9x^2-4y^2 (this is what i got by distributing the second power to everything in the parenthesis)
The book said the answer was 9x^2+4y^2-12xy.
Can you explain why I got it wrong and how to get the right answer?
1 solutions
Answer 157654 by nerdybill(6962) on 2009-08-25 01:08:57 (Show Source):
You can put this solution on YOUR website!(3x-2y)^2= (that's the equation)
9x^2-4y^2 (this is what i got by distributing the second power to everything in the parenthesis)
The book said the answer was 9x^2+4y^2-12xy
.
(3x-2y)^2
= (3x-2y)(3x-2y)
Applying FOIL:
F: (first terms) (3x)(3x) = 9x^2
O: (outer terms) (3x)(-2y) = -6xy
I: (inner terms) (-2y)(3x) = -6xy
L: (last terms) (-2y)(-2y) = 4y^2
= 9x^2 - 6xy - 6xy + 4y^2
= 9x^2 - 12xy + 4y^2
After reordering:
= 9x^2 + 4y^2 - 12xy
|
Angles/208310: This question is from textbook geometry
the means of two complementary angles are 16z-9 and 4z+3.find the measures of the angles
1 solutions
Answer 157582 by nerdybill(6962) on 2009-08-24 16:40:57 (Show Source):
You can put this solution on YOUR website! the means of two complementary angles are 16z-9 and 4z+3.find the measures of the angles
.
If two angles are "complementary", the sum of the two angles MUST equal 90 degrees.
.
(16z-9) + (4z+3) = 90
16z-9 + 4z+3 = 90
16z+4z+3-9 = 90
20z-6 = 90
20z = 96
z = 96/20
z = 24/5
.
Therefore, the two angles are:
16z-9 = 16(24/5)-9 = 16(4.8)-9 = 76.8-9 = 67.8 degrees
4z+3 = 4(24/5)+3 = 4(4.8)+3 = 19.2+3 = 22.2 degrees
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