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Recent problems solved by 'stanbon'
stanbon answered: 57222 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239, >>NextQuadratic_Equations/120474: What are the EXACT values of the roots of the quadratic equation 1/2(x^2-6x)=2 ?
1 solutions
Answer 88350 by stanbon(57290)   on 2008-01-16 12:33:47 (Show Source):
You can put this solution on YOUR website!What are the EXACT values of the roots of the quadratic equation
1/2(x^2-6x)=2 ?
-------------
x^2-6x = 4
x^2-6x-4 = 0
x = [6 +- sqrt(36-4*-4)]/2
x = [6 +- sqrt(52)]/2
x = [6 +- 2sqrt(13)]/2
x = 3+sqrt(13) or x = 3-sqrt(13)
=====================
Cheers,
Stan H.
|
Quadratic_Equations/120473: If a sequence contains the terms tn=-2n^2-5n+10,what is the value of t25? I got 2385 can someone please explain?
1 solutions
Answer 88347 by stanbon(57290) on 2008-01-16 12:30:15 (Show Source):
You can put this solution on YOUR website!If a sequence contains the terms t(n)=-2n^2-5n+10,what is the value of t(25)? I got 2385 can someone please explain?
--------------------
t(25) = -2(25)^2-5(25)+10
= -2(625)-125+10
= -1250-125+10
= -1375+10
= -1365
-----------
Cheers,
Stan H.
|
Quadratic_Equations/120478: What is the equation of the quadratic function under the following transformations of the basic quadratic function y=x^2 : a vertical stretch of 2/5 , a vertical translation of -3 units and a horizontal translation of 2 units ? I said 5/2(y+3)=(x-2)^2 but I'm not sure.
1 solutions
Answer 88344 by stanbon(57290) on 2008-01-16 12:25:25 (Show Source):
|
Equations/120519: A plane flies 720 mi against a steady 30-mi/h headwind and then returns to the same point with the wind. If the entire trip takes 10 h, what is the plane’s speed in still air?
1 solutions
Answer 88339 by stanbon(57290) on 2008-01-16 12:17:56 (Show Source):
You can put this solution on YOUR website!A plane flies 720 miles against a steady 30 mph headwind and then returns to the same point with the wind, if the entire trip takes 10 hours what is the plane's speed in still air?
-----------------------
Let "p" be the plane's speed in still air.
--------------------
Upwind DATA;
Distance = 720 miles ; Rate = p-30; time = d/r = 720/(p-30) hrs.
-------------
Downwind DATa:
Distance = 720 miles ; Rate = p+30: time = d/r = 720/(p+30) hrs
--------------
EQUATION:
time up + time down = 10 hrs
720/(p-30) + 720/(p+30) = 10
------------------------
Divide thru by 10 to get:
72/(p-30) + 72/(p+30) = 1
--------------
Multiply thru by (p-30)(p+30)=p^2-900
---------------
72(p+30) + 72(p-30) = p^2-900
144p = p^2-900
p^2-144p-900= 0
(p-150)(p+6) = 0
p = 150 mph (plane speed in still air is 150 mph)
==================
Cheers,
Stan H.
|
Linear_Algebra/120517: hELLO CAN SOME ONE PLEASE SOLVE THE EQUATION BELOW?
d= D( a + 1)
------------
24
determine the dosage for the child based on this information
D = adult
d = child
adult dossage 600 milligrams and the doctor uses the formula above to estimate childs dosage at 200 milligrams how old is the child?
1 solutions
Answer 88337 by stanbon(57290) on 2008-01-16 12:15:08 (Show Source):
You can put this solution on YOUR website!d= D( a + 1)
------------
24
determine the dosage for the child based on this information
D = adult
d = child
adult dossage 600 milligrams and the doctor uses the formula above to estimate childs dosage at 200 milligrams how old is the child?
---------------
200 = 600(a+1)/24
Divide both sides by 200 to get:
1 = 3(a+1)/24
Reduce the fraction on the right side to get:
1 = (a+1)/8
Cross-multiply to get:
a+1 = 8
a = 7
The child's age is 7
=========================
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/120498: The probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probability that they do not play is 1. What is the probability that San Francisco plays in the next Super Bowl?
1 solutions
Answer 88320 by stanbon(57290) on 2008-01-16 10:33:14 (Show Source):
You can put this solution on YOUR website!The probability that San Francisco plays in the next Super Bowl is nine times the probability that they do not play in the next Super Bowl. The probability that San Francisco plays in the next Super Bowl plus the probability that they do not play is 1. What is the probability that San Francisco plays in the next Super Bowl?
------------------------
Let prob SF plays = 9x
Then probl SF does not play = x
---------------------
x + 9x = 1
10x = 1
x = 1/10
-----------------
Prob(SF plays) = 9*1/10 = 9/10 = 0.9
=============
Cheers,
Stan H.
|
Graphs/120500: How would I write and graph an equation with slope -2 and y-intercept (0,0)?
1 solutions
Answer 88319 by stanbon(57290) on 2008-01-16 10:28:47 (Show Source):
You can put this solution on YOUR website!How would I write and graph an equation with slope -2 and y-intercept (0,0)?
-------------
y = mx + b is the slope-intercept equation form of a line.
Your slope is m = -2
Your intercept is b = 0
Your equation is y = -2x
--------------------------
Let x=0, then y = 0
Let x=1, then y = -2
Let x=2, then y = -4
__________________
You have three points: (0,0),(1,-2),(2,-4)
Plot the points and draw a line thru them to see your graph.
------------------
===================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/120493: This question is from textbook
If someone can help explain these two word problems in explicit detail I would greatly appreciate it!!!!
1. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate?
2. Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?
1 solutions
Answer 88318 by stanbon(57290) on 2008-01-16 10:24:30 (Show Source):
You can put this solution on YOUR website!1. Donna invested her $33,000 bonus and received a total of $970 in interest after one year. If part of the money returned 4% and the remainder 2.25%, then how much did she invest at each rate?
---------------------
Let amt. at 4% be "x" ; interest on this is 0.04x dollars
------------------------
Amt at 2.25% is "33000-x" ; interest is 0.0225(33000-x)= 742.50-0.0225x dollars
-------------------------
EQUATION:
interest + interest = 970 dollars
0.04x + 742.50-0.0225x = 970
0.0175x = 227.50
x = 13000 (amt invested at 4%)
33000-x = 20000 (amt invested at 2.25%)
------------------------------------------------
2. Tickets for a concert were sold to adults for $3 and to students for $2. If the total receipts were $824 and twice as many adult tickets as student tickets were sold, then how many of each were sold?
-----------
Let # of adult tiks sold be "2x" ; value = 3*2x = 6x dollars
----------------
# of stud tiks sold is "x" ; value is 2x dollars
---------------
EQUATION:
value + value = 824
6x + 2x = 824
8x = 824
x = 103 (# of student tickets sold)
2x = 206 (# of adult tickets sold)
====================
Cheers,
Stan H.
|
Finance/120495: William is 1/6 as old as his faither but five years older than his sister, Mary. If the sum of all their ages is 51, how old is William?
1 solutions
Answer 88317 by stanbon(57290) on 2008-01-16 10:14:23 (Show Source):
You can put this solution on YOUR website!William is 1/6 as old as his faither but five years older than his sister, Mary. If the sum of all their ages is 51, how old is William?
------------
Let William's age be "x"
Father's age is "6x"
Sister's age is "x-5"
EQUATION:
x + 6x + x-5 = 51
8x = 56
x = 7 (William's age is seven)
===============
Cheers,
Stan H.
|
expressions/120491: (-5a^2)(-5a^3)^4 simplified, the answer is (-5)^5a^14.
What I don't understand is, how did the negative sign shift to the 5 only? Please explain. Thanks
1 solutions
Answer 88316 by stanbon(57290) on 2008-01-16 10:11:02 (Show Source):
You can put this solution on YOUR website!(-5a^2)(-5a^3)^4 simplified, the answer is (-5)^5a^14.
What I don't understand is, how did the negative sign shift to the 5 only? Please explain.
-------------
(-1) raised to an even power is 1
(-1) raised to an odd power is negative
-------------
Your problem:
(-5a^2)(-5a^3)^4
The -5 in the 1st factor is raised to the power one which is odd
so the negative survives.
The -5 in the 2nd factor is raised to the power 4 which is even
so the negative becomes positive.
---------------
(-5a^2)(-5a^3)^4
= (-5a^2)[(-5)^4(a^3)^4]
= (-5)(a^2)(-5)^4(a^12)
= (-5)^5(a^14)
===============
Cheers,
Stan H.
|
Quadratic_Equations/120482: An astronaut standing on the surface of the moon throws a rock upward. The height of the rock is given by s=-2.7t^2+27t+6.3, where s is the height in metres and t is the time in seconds.What was the initial height of the rock?
1 solutions
Answer 88314 by stanbon(57290) on 2008-01-16 10:00:33 (Show Source):
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Reduction-of-unit-multipliers/120484: This question is from textbook college algebra/ blitzer
Calculate the value of the discriminant of x squared plus 4x plus 4 equals zero
Answer:
Show your work here:
b)By examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x squared plus 4x plus 4 have? Why?
Answer:
1 solutions
Answer 88313 by stanbon(57290) on 2008-01-16 09:58:16 (Show Source):
You can put this solution on YOUR website!Calculate the value of the discriminant of x squared plus 4x plus 4 equals zero
Answer:
Show your work here:
x^2+4x+4=0
discriminant = sqrt(b^2-4ac)=sqrt(16-4*4)=0
------------------------
b)By examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x squared plus 4x plus 4 have? Why?
Answer:
The graph touches but does not pass through the x-axis at x=-2.
================
================
Cheers,
Stan H.
|
Length-and-distance/120488: the length of the shadow of a flagpole was found to be 72 feet. the shadow of a 3 foot pecket fence in line with the flagpole was 4 feet. what is the height of the flagpole?
1 solutions
Answer 88312 by stanbon(57290) on 2008-01-16 09:53:59 (Show Source):
You can put this solution on YOUR website!the length of the shadow of a flagpole was found to be 72 feet. the shadow of a 3 foot pecket fence in line with the flagpole was 4 feet. what is the height of the flagpole?
-------------
pole/shadow = fence/shadow
----------
pole/72 = 3/4
pole = 72(3/4)
pole = 54 ft
=================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/120413: THis is a factoring word problem using the principle of zero. The question says "Find two consecutive, negative integers whose product is 156." Could you please help me?
1 solutions
Answer 88250 by stanbon(57290) on 2008-01-15 20:41:32 (Show Source):
You can put this solution on YOUR website!"Find two consecutive, negative integers whose product is 156." Could you please help me?
----------------------
Let the 1st be "x"; the 2nd would be "x+1".
EQUATION:
x(x+1) = 156
x^2+x-156 = 0
x = [-1 +- sqrt(1-4*1*-156)]/2
x = [-1 +- sqrt(625)]/2
x = [-1 +- 25]/2
Negative soution:
x = (-1-25)/2 = -13 (1st negative integer)
x+1 = -12 (2nd negative integer)
==============================
Cheers,
Stan H.
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testmodule/120388: please help me solve this problem- A car is worth $9000.Each year it depreciates by 12%.What will it be worth in 5 years?
1 solutions
Answer 88247 by stanbon(57290) on 2008-01-15 20:24:36 (Show Source):
You can put this solution on YOUR website!please help me solve this problem- A car is worth $9000.Each year it depreciates by 12%.What will it be worth in 5 years?
------------------------
A 12% depreciation means the car is worth 88% of what it was worth last year.
-----------------------------
EQUATION:
Value after 5 years = 9000(0.88)^5 = $4749.59
------------------
Cheers,
Stan H.
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Numbers_Word_Problems/120402: There are 10 more boys than girls in a class. If one more girl joins the class, there will be twice as many boys as there are girls. How many boys and how many girls are there in the class?
1 solutions
Answer 88246 by stanbon(57290) on 2008-01-15 20:18:54 (Show Source):
You can put this solution on YOUR website!There are 10 more boys than girls in a class. If one more girl joins the class, there will be twice as many boys as there are girls. How many boys and how many girls are there in the class?
-----------------
Original numbers:
Let number of girls be "x", then number of boys is "x+10".
-----------------------
Numbers after the change:
# of girls = x+1 ; # of boys is still "x+10"
--------------------------------
EQUATION:
x+10 = 2(x+1)
x+10 = 2x+2
x = 8 (original # of girls) ; x+10 = 18 (original # of boys)
--------------------------------
Cheers,
San H.
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Linear_Equations_And_Systems_Word_Problems/120378: A plane flies 720 miles against a steady 30 mph headwind and then returns to the same point with the wind, if the entire trip takes 10 hours what is the plane's speed in still air?
1 solutions
Answer 88243 by stanbon(57290) on 2008-01-15 20:09:38 (Show Source):
You can put this solution on YOUR website!A plane flies 720 miles against a steady 30 mph headwind and then returns to the same point with the wind, if the entire trip takes 10 hours what is the plane's speed in still air?
-----------------------
Let "p" be the plane's speed in still air.
--------------------
Upwind DATA;
Distance = 720 miles ; Rate = p-30; time = d/r = 720/(p-30) hrs.
-------------
Downwind DATa:
Distance = 720 miles ; Rate = p+30: time = d/r = 720/(p+30) hrs
--------------
EQUATION:
time up + time down = 10 hrs
720/(p-30) + 720/(p+30) = 10
------------------------
Divide thru by 10 to get:
72/(p-30) + 72/(p+30) = 1
--------------
Multiply thru by (p-30)(p+30)=p^2-900
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72(p+30) + 72(p-30) = p^2-900
144p = p^2-900
p^2-144p-900= 0
(p-150)(p+6) = 0
p = 150 mph (plane speed in still air is 150 mph)
==================
Cheers,
Stan H.
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Money_Word_Problems/120365: This question is from textbook North carolina Algebra 1
A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold was 30. The small mower costs $249.99. The large mower costs $329.99. Find the number sold of each type of mower.
What is the answer to this problem and how do you solve it?
1 solutions
Answer 88235 by stanbon(57290) on 2008-01-15 19:31:18 (Show Source):
You can put this solution on YOUR website!A garden supply store sells two types of lawn mowers. Total sales of mowers for the year were $8379.70. The total number of mowers sold was 30. The small mower costs $249.99. The large mower costs $329.99. Find the number sold of each type of mower.
----------------------------------
Let number of 249.99 mowers be "x"; Value is 249.99x dollars
--------------------------
# of 329.99 mowers is "30-x"; Value is 329.99(30-x) dollars
-------------------------------
EQUATION:
value + value = 8379.70
249.99x + 329.99*30-329.99x = 8379.70
-80x + 9899.70 = 8379.70
-80x = -1520.00
x = 19 (number of the cheaper mowers sold)
30-x = 11 (number of more expensive mowers sold)
======================
Cheers,
Stan H.
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Miscellaneous_Word_Problems/120347: This question is from textbook
Bette drives at 60 mph for 2 1/2 hours and at 75 mph for 1 1/2 hours. What is her average rate of speed?
1 solutions
Answer 88216 by stanbon(57290) on 2008-01-15 17:44:29 (Show Source):
You can put this solution on YOUR website!Bette drives at 60 mph for 2 1/2 hours and at 75 mph for 1 1/2 hours. What is her average rate of speed?
---------------------------------
1st leg DTA:
Rate = 60 mph; time = 5/2 hrs: distance = rt = 150 miles
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2nd leg DATA:
Rate = 75 mph; time = 3/2 hrs; distance = rt = 112.5 miles
----------------------
Average rate = distance/time
average = (150+112.5)/(5/2 + 3/2) = 262.5/4 = 65.625 mph
===================
Cheers,
Stan H.
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Equations/120298: I have just started on equation substitutions. They are very confusing, and my entire 10th grade class is struggling. can you help me solve this substitution?
4x+y=-2 2x=-y
1 solutions
Answer 88171 by stanbon(57290) on 2008-01-15 13:40:46 (Show Source):
You can put this solution on YOUR website!4x+y=-2 2x=-y
-------------
Solve the "simpler" equation for "y":
y = -2x
Substitute that value of "y" in the other equation to solve for "x":
4x+(-2x)= 2
4x-2x = 2
2x = 2
x = 1
----------
Substitute that into y = -2x to solve for "y":
y = -2*1 = -2
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The solution for the system is (1,-2)
==================================
Cheers,
Stan H.
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Square-cubic-other-roots/120301: Find x, if (x) squared equals 20 times radical 3
1 solutions
Answer 88170 by stanbon(57290) on 2008-01-15 13:36:11 (Show Source):
You can put this solution on YOUR website!(x) squared equals 20 times radical 3
-----------
x^2= 20sqrt(3)
x = sqrt(20sqrt(3)) or x = -sqrt(20sqrt(3))
x = 2[sqrt(5)][4th rt. of 3] or x = -2[sqrt(5)][4th rt. of 3]
x = 2(5)^(1/2)*(3)^(1/4) or x = -2(5)^(1/2)*(3)^(1/4)
==============
Cheers,
Stan H.
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Graphs/120297: I understand everything with these graphs where the dotted lines goes and such, but I am stuck on how and where to shade them. So if someone can please explain in detail where to shade and how to shade I would greatly appreciate it..
Graph the inequality:
here is the first graph.
y<-3x+2
This is the second graph.
3x+2y>6
1 solutions
Answer 88166 by stanbon(57290) on 2008-01-15 13:22:14 (Show Source):
You can put this solution on YOUR website!first graph.
y<-3x+2
-----------
Dashed boundary line:
---------------
To determine where to shade pick any test point that
is not on the obrder. If the test point coordinates
satisfy the inequality, the half-plane containing it
is the solution set. If the coordinates do not satisfy
the inequality, the side opposite the test point side
is the solution.
---------------
Example using your problem:
Let the test point be (0,0)
Substitute into the inequality to get: 0<-3*0+2; 0<2
That is false, so the half-plane which does NOT contain
the test point is the solution area.
---------------------
the second graph.
3x+2y>6
solve for y:
y >(-3/2)x+3
Graph the boundary as a dashed line:
----------
Pick a test point, like (0,0)
Substitute: 0 > (-3/2)*0+3
0 >3
That is false.
The solution is on the other side of the
boundary from the test point.
=================
Cheers,
Stan H.
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Graphs/120288: Graph the following line: y=((5x)/3)-3
I need at least three points so if someone can explain everything about this I would really appreciate it. Thanks
1 solutions
Answer 88158 by stanbon(57290) on 2008-01-15 11:27:57 (Show Source):
You can put this solution on YOUR website!Graph the following line: y=((5x)/3)-3
-----------------
y = (5/3)x - 3
Let x=0 then y = -3
Let x=3 then y = 5-3=2
Let x=6 then y = 5*2-3 = 7
------------------------------
You have three points: (0,-3), (3,2), (6,7)
-------------------
Plot the points and draw a line thru them to get:
Graph the following line: y=((5x)/3)-3
Cheers,
Stan H.
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Graphs/120282: The national cost C in billions of dollars for dental services can be modeled by the linear equation C=2.85n +30.52 where n is the number of years since 1990. A)Find and interpret the C-intercept for the line B)Find and interpret the n-intercept for the line C) Graph the line for n ranging from 0 through 20 D) If this trend continues, then in what year will the cost of dental services reach 100 billion?
1 solutions
Answer 88155 by stanbon(57290) on 2008-01-15 11:08:14 (Show Source):
You can put this solution on YOUR website!The national cost C in billions of dollars for dental services can be modeled by the linear equation C(n)=2.85n +30.52 where n is the number of years since 1990.
A)Find and interpret the C-intercept for the line:(0,30.52)
In 1990 the cost was 30.52 billion.
------------------------------
B)Find and interpret the n-intercept for the line
0 = 2.85n+30.52
n = -30.52/2.85 = -10.71
The cost was zero in 1990-10.71= 1979 (rounded-off answer)
--------------------------------
C) Graph the line for n ranging from 0 through 20
--------------------------
D) If this trend continues, then in what year will the cost of dental services reach 100 billion?
100 = 2.85n+30.52
2.85n = 69.48
n = 24.38
Year = 1990+24.38 = 2015
===============================
Cheers,
Stan H.
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Expressions-with-variables/120274: there are three prizes. the value of the second prize is five-sixths the value of the first prize. the third prize is four-fifths that of the second prize.
I have to express the total value of the three prizes as an algebraic expression.
1 solutions
Answer 88153 by stanbon(57290) on 2008-01-15 10:58:48 (Show Source):
You can put this solution on YOUR website!there are three prizes. the value of the second prize is five-sixths the value of the first prize. the third prize is four-fifths that of the second prize.
I have to express the total value of the three prizes as an algebraic expression.
-----------------
Let 1st be "x".
2nd is (5/6)x
3rd is (4/5)(5/6)x = (2/3)x
----------------
Total value = x + (5/6)x + (4/6)x
Total value = (15/6)x or 2 1/2 x
=================================
Cheers,
Stan H.
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Graphs/120280: Graph the inequality: 3x+2y>6
1 solutions
Answer 88152 by stanbon(57290) on 2008-01-15 10:53:44 (Show Source):
You can put this solution on YOUR website!Graph the inequality: 3x+2y>6
----------------
Graph the boundary as a dashed line because it is not part of the solution:
----------
Shade the half-plane above the line; that is the solution area.
-----------
Cheers,
Stan H.
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