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Recent problems solved by 'stanbon'
stanbon answered: 57178 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179, >>NextPolynomials-and-rational-expressions/160914: write as a product of linear factors and list all zeros:
f(x)= 12^4 + 7x^3 - 22x^2 - 7x +10
1 solutions
Answer 118592 by stanbon(57246)   on 2008-10-07 22:40:17 (Show Source):
You can put this solution on YOUR website!write as a product of linear factors and list all zeros:
f(x)= 12^4 + 7x^3 - 22x^2 - 7x +10
-----------------
Since the coefficients add up to zero, x=1 is a root of f(x)
------------------
Use synthetic division:
1)....12....7....-22....-7....10
........12...19....-3....-10..|..0
-1).......12....7....-10..|..0
----------------
So, you have roots at x= 1 and x=-1
You are left with a quadratic which you can solve in several ways:
x = [-7 +- sqrt(49 - 4*12*-10)]/24
x = [-7 +- sqrt(529)]/24
x = [-7 +- 23]/24
z = 16/24 or z = -30/24
z = 2.3 or z = -5/4
============================
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/160558: the sum of the digits of a two-digit number is 11. If the digit is reversed, the new number increased by 20 is twice the original number. Find the original number.
1 solutions
Answer 118391 by stanbon(57246) on 2008-10-05 22:47:43 (Show Source):
You can put this solution on YOUR website!the sum of the digits of a two-digit number is 11. If the digit is reversed, the new number increased by 20 is twice the original number. Find the original number.
------------
Original number: 10t+u where t is the tens digit and u is the units digit.
------------------
t + u = 11
-------------
Digits reversed: 10u+t
-------------
EQUATION:
10u+t+20 = 2(10t+u)
-----------------------
Rearrange the equations:
t + u = 11
19t - 8u = 20
---------------
Multiply thru 1st by 8 and add to solve for "t":
8t + 8u = 88
19t - 8u = 20
------------------
27t = 108
t = 4 (the tens digit of the original number)
Since t+u = 11, u = 7 (the units digit of the original number)
--------------------
Original Number: 47
========================
Cheers,
Stan H.
|
Percentage-and-ratio-word-problems/160561: THE MEASURES OF TWO SMALLER ANGLES IN A TRIANGLE ARE THE SAME. THE THIRD ANGLE IS TWICE THE MEASURE OF EACH ANGLE.
1 solutions
Answer 118390 by stanbon(57246) on 2008-10-05 22:40:28 (Show Source):
You can put this solution on YOUR website!THE MEASURES OF TWO SMALLER ANGLES IN A TRIANGLE ARE THE SAME. THE THIRD ANGLE IS TWICE THE MEASURE OF EACH ANGLE.
----------
Let each smaller angle be "x".
Then the largest angle is "2x".
------------
EQUATION:
x + x + 2x = 180
4x = 180
x = 45 degrees (each small angle)
2x = 90 degrees (larger angle)
=============
Cheers,
Stan H.
|
Money_Word_Problems/160563: You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back?
1 solutions
Answer 118388 by stanbon(57246) on 2008-10-05 22:33:32 (Show Source):
You can put this solution on YOUR website!You need to purchase a textbook for nursing school. The book cost $80.00, and the sales tax where you are purchasing the book is 8.25%. You have $100. How much change will you receive back?
-----------------
Book Cost = 1.0825*80 = 86.60
-------------------
Change on $100 after purchasing the booK: 100 - 86.60 = $13.40
==============
Cheers,
Stan H.
|
Linear_Algebra/160386: On Sunday a coffee shop sold 115 lb of coffee. The amount of regular coffee sold was 5 lb more than the amount of decaffeinated coffee sold. There were twice as many pounds of flavored coffee sold than there was regular coffee sold.
a. Write an equation to solve for the amount of regular coffee sold.
b. Solve the equation from part a.
1 solutions
Answer 118315 by stanbon(57246) on 2008-10-05 08:16:19 (Show Source):
You can put this solution on YOUR website!On Sunday a coffee shop sold 115 lb of coffee. The amount of regular coffee sold was 5 lb more than the amount of decaffeinated coffee sold. There were twice as many pounds of flavored coffee sold than there was regular coffee sold.
a. Write an equation to solve for the amount of regular coffee sold.
r + d + f = 115
r = d + 5
f = 2r
-----------------
Substitute to solve for r:
r + (r-5) + 2r = 115
4r = 120
r = 30 lbs (amount of regular coffee)
================================================
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/160368: This question is from textbook Algebra 1
Hello I have a question about this problem:
(30h^-2)(k^14)/ (5hk^-3)
The answer is in the back of the book and it's 6k^17/h^3, but the problem is I don't know how to reach the conclusion. I tried solving it by first diving 30 by 5 which gave me 6, but it's with the variables that I get mixed up.
1 solutions
Answer 118310 by stanbon(57246) on 2008-10-05 00:19:46 (Show Source):
You can put this solution on YOUR website!(30h^-2)(k^14)/ (5hk^-3)
= (30k^14/h^2) / (5h/k^3)
Invert the denominator and multiply to get:
= (30k^14/h^2) * (k^3/ 5h))
Cancel factors that are common to numerator and denominator such as
5
= (6k^17) / (h^3)
===============
Cheers,
Stan H.
|
test/160346: hey,
could you please solve the following question, thanks,
The graph of function y= x^2 - kx + k + 8 touches the x-axis at one point. What
is the value of k?
I will be waiting for the solution,
and thanks again,
1 solutions
Answer 118306 by stanbon(57246) on 2008-10-04 20:59:10 (Show Source):
You can put this solution on YOUR website!The graph of function y= x^2 - kx + k + 8 touches the x-axis at one point. What
is the value of k?
------------------------------
A quadratic has one solution when the discrimanant is zero.
-----------------
Your quadratic has a = 1, b = -k,c = k+8
---------
Discrimant equation:
b^2 - 4ac = 0
(-k)^2-4*1*(k+8) = 0
k^2 -4k -32 = 0
k^2-8k+4k-32 = 0
k(k-8)+4(k-8) = 0
(k-8)(k+4) = 0
k = 8 or k = -4
==============================
Cheers,
Stan H.
|
Proofs/160240: I don't understand the logic proofs
not k
not l then h
j then k
h then j
therefore l
i understand modus tollens, modus ponens, law of sillogysm and law of contrapositives but not how they apply to a proof as long as the above.
i also don't understand how to do the proofs and reasons, the above has 7 of each
1 solutions
Answer 118212 by stanbon(57246) on 2008-10-03 22:06:32 (Show Source):
You can put this solution on YOUR website!not k
not l then h
j then k
h then j
therefore l
---------------
Argument:
not k
if not k then not J
If not j then not h
if not h then not (not l)
Therefore l
=================
Cheers,
Stan H.
|
Equations/160247: Could you pls help me with these 2 problems:
- Find the remainder when 6x^6-17x^4+12x+26 is divided by (x+1)
- If 18x^2+9x-2 is factor into (ax+b)(cx+d),what is ac-bd
1 solutions
Answer 118210 by stanbon(57246) on 2008-10-03 22:02:48 (Show Source):
You can put this solution on YOUR website!- Find the remainder when 6x^6-17x^4+12x+26 is divided by (x+1)
If you know the Remainder Theorem find f(-1)
f(-1) = 6(-1)^6 - 17(-1)^4 + 12(-1) + 26
f(-1) = 6 -17 -12 + 26
f(-1) = 3
--------------
The Remainder is 3.
=========================
- If 18x^2+9x-2 is factor into (ax+b)(cx+d),what is ac-bd
18x^2+9x-2
= 18x^2 + 12x - 3x - 2
= 6x(3x+2) -(3x+2)
= (3x+2)(6x-1)
a = 3
b = 2
c = 6
d =-1
---------
ac-bd = 18 - -2 = 20
==========================
Cheers,
Stan H.
|
Travel_Word_Problems/160158: Hi-I was trying to help my 6th grader with his math homework. Many years since I have done any, the problem was from a work sheet. A Frog is in a 10 foot well, climbs 3 feet during the day and slides back 2 feet at night. At what point will the frog make it to the 10 foot level and be able to crawl out? I thought the answer would be 8 days, but I did not have a formula to use. Would you please help out a frustrated dad?? Thanks for your time.
1 solutions
Answer 118206 by stanbon(57246) on 2008-10-03 21:53:32 (Show Source):
You can put this solution on YOUR website!It really is more of a logic problem.
Each day the frog gains 1 ft.
When he gets to the 7 ft. level (7 days)
his next 3 ft. jump will get him to the
10 ft.level. That will occur on the 8th day.
--------------
You have the correct answer.
--------------
Cheers,
Stan H.
|
Linear-equations/160242: This question is from textbook Elementary & Intermediate Algebra
For this equation I need to solve the inequality, state the solution set in interval notation and sketch it's graph.
1 <3x - 2<7
1 solutions
Answer 118199 by stanbon(57246) on 2008-10-03 21:31:37 (Show Source):
You can put this solution on YOUR website!For this equation I need to solve the inequality, state the solution set in interval notation and sketch it's graph.
1 <3x - 2<7
Add 2 along the line to get:
3 < 3x < 9
Divide by 3 along the line to get:
1 < x < 3
-------------
Interval notation: (1,3)
--------------
Draw a number line.
Label two points 1 and 3
Draw an open circle around each of those points.
Connect the points with a line segment.
That is the graph.
=====================
Cheers,
Stan H.
|
Circles/160246: Do I divide the circumference of a circle by four to get the perimeter of a quadrant?
1 solutions
Answer 118198 by stanbon(57246) on 2008-10-03 21:27:52 (Show Source):
You can put this solution on YOUR website!Do I divide the circumference of a circle by four to get the perimeter of a quadrant?
-------------
Perimeter means distance around. You would only be
finding the length of the arc of the quadrant. I
think you would have to add 2 times the radius to get
the distance around the quadrant.
---------------
Cheers,
Stan H.
|
Polynomials-and-rational-expressions/160109: CAN SOMEONE PLEASE HELP ME WITH THIS PROBLEM:
If f(g(x)) = g(f(x)) = x, then what can we say about f(x) and g(x)?
a. They are functional inverses of each other
b. f(x) = g(x)
c. f(x) = g(x) = x
d. Nothing can be said about f(x) and g(x)
1 solutions
Answer 118095 by stanbon(57246) on 2008-10-02 23:14:25 (Show Source):
|
Travel_Word_Problems/160112: An object is propelled vertically upward with an initial velocity of 20 meters per second. The distance s (in meters) of the object from the ground after t seconds is s = -4.9t^2 + 20t.
(a) When will the object be 15 meters above the ground?
(b) When will it strike the ground?
(c) Will the object reach a height of 100 meters?
1 solutions
Answer 118087 by stanbon(57246) on 2008-10-02 22:53:26 (Show Source):
You can put this solution on YOUR website!An object is propelled vertically upward with an initial velocity of 20 meters per second. The distance s (in meters) of the object from the ground after t seconds is s(t) = -4.9t^2 + 20t.
---------
The equation tells you how far above the ground the object after "t" seconds.
I'll just point out the equations you should solve:
--------------------
(a) When will the object be 15 meters above the ground?
Solve -4.9t^2 + 20t = 15
You should get two solutions: one for the time as it rises and one for
the time it is decending..
--------------------------------------
(b) When will it strike the ground?
Solve -4.9t^2 + 20t = 0
You should get twon solutions. One of the solutions is t=0.
------------------------------------
(c) Will the object reach a height of 100 meters?
Solve -4.9t^2 + 20t = 100
Two solutions.
=================
Cheers,
Stan H.
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Functions/160113: can someone please help me with this problem:
Evaluate the function at the given value of the independent variable and simplify.
f(x) = -5x + 8; f(-3)
1 solutions
Answer 118084 by stanbon(57246) on 2008-10-02 22:48:23 (Show Source):
You can put this solution on YOUR website!Evaluate the function at the given value of the independent variable and simplify.
f(x) = -5x + 8; f(-3)
----------
f(-3) = -5*-3 + 8
f(-3) = 23
==============
Cheers,
Stan H.
|
Linear_Equations_And_Systems_Word_Problems/159979: About 4.9 million households had one brand of personal computers in 2001. The use of these computers grew at an average rate of .275 million households a year. In 2001, about 2.5 millions households used another type of computer. The use of these computers grew at an average rate of .7 million households a year. How long will it take for the two types of computers to be in the same number of households?
1 solutions
Answer 117949 by stanbon(57246) on 2008-10-02 08:35:58 (Show Source):
You can put this solution on YOUR website!About 4.9 million households had one brand of personal computers in 2001. The use of these computers grew at an average rate of .275 million households a year.
Eq: N = 4.9 + 0.275x million
----------------
In 2001, about 2.5 millions households used another type of computer. The use of these computers grew at an average rate of .7 million households a year.
Eq: P = 2.5 + 0.7x million
---------------------------------
How long will it take for the two types of computers to be in the same number of households?
4.9 + 0.275 = 2.5 + 0.7x
2.4 = 0.425x
x = 5.647 years
=================
Cheers,
Stan H.
|
Equations/159981: Solve:
a) I=P+Prt , for t
b) m=dV(1-e) , for e
c) mu=(m+M)v , for M
1 solutions
Answer 117947 by stanbon(57246) on 2008-10-02 08:29:00 (Show Source):
You can put this solution on YOUR website!Solve:
a) I=P+Prt , for t
t = (I-P)/Pr
--------------------
b) m=dV(1-e) , for e
1-e = m/dV
e = 1-(m/dV)
------------------
c) mu=(m+M)v , for M
m+M = mu/v
M = (mu/v)-m
================
Cheers,
Stan H.
|
Quadratic_Equations/159948: I'm having trouble with quadratice equations here is a problem that I cannot seem to solve: 9x^2+9x=2=0
1 solutions
Answer 117943 by stanbon(57246) on 2008-10-02 08:16:29 (Show Source):
You can put this solution on YOUR website!I'm having trouble with quadratic equations; here is a problem that I cannot seem to solve: 9x^2+9x+2=0
Note: I put a "+" in place of the "=".
---------------
Use the quadratic formula to get:
x = [-9 +- sqrt(81-4*9*2)]/[2*9]
x = [-9 +- sqrt(9)]/18
x = [-9 +- 3] /18
x = -12/18 or x = -6/18
x = -2/3 or x = -1/3
-----------------------
Using factoring:
9x^2+9x+2=0
9x^2 + 3x + 6x + 2 = 0
3x(3x+1) + 2(3x+1) = 0
(3x+1)(3x+2) = 0
x = -1/3 or x = -2/3
==========================
Cheers,
Stan H.
|
Linear-systems/159964: Linear Equation from slope and point: Suppose that f is a linear function with slope 2.6 and that f(5)=-3. What value of x gives f(x)=0?
2nd Question: Linear Equation from two points: Suppose f is a linear function such that f(3)=5 anf f(7)=-4. Find the equation for f.
Thank you, Andie
1 solutions
Answer 117941 by stanbon(57246) on 2008-10-02 07:59:30 (Show Source):
You can put this solution on YOUR website!Linear Equation from slope and point: Suppose that f is a linear function with slope 2.6 and that f(5)=-3. ------
y = mx + b
-3 = 2.6*5 + b
-16 = b
Equation:
f(x) = 2.6x -16
-------
What value of x gives f(x)=0?
0 = 2.6x - 16
x = 6.1538....
==================
2nd Question: Linear Equation from two points: Suppose f is a linear function such that f(3)=5 anf f(7)=-4. Find the equation for f.
-----
slope = (-4-5) / (7-3) = -9/4
intercept: 5 = (-9/4)*3 + b
b = 5+(27/4) = 47/4
Equation:'
y = (-9/4)x + (47/4)
==========================
Cheers,
Stan H.
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Finance/159980: 1. To determine the number of deer in a game preserve, a conservationist catches 484 deer, tags them and lets them loose. Later, 618 deer are caught; 206 of them are tagged. How many deer are in the preserve?
2. Jack usually mows his lawn in 6 hours. Marilyn can mow the same yard in 7 hours. How much time would it take for them to mow the lawn together?
3. Benz bicycles 7 km/h faster than praedup. In the same time it takes praedup to bicycle 48 km, Benz can bicycle 69 km. how fast does each bicyclist travel?
Praedup travels what km/h?
Benz travels what km/h?
4. Find the LCM of 5(r-7) and 35(r-7)
1 solutions
Answer 117940 by stanbon(57246) on 2008-10-02 07:48:50 (Show Source):
You can put this solution on YOUR website!To determine the number of deer in a game preserve, a conservationist catches 484 deer, tags them and lets them loose. Later, 618 deer are caught; 206 of them are tagged. How many deer are in the preserve?
-----
Total population/caught : x/484
Total Tagged population/tagged caught: 618/206
----------
Proportion Equation:
x/484 = 618/206
x = 1452 (estimate of size of total population)
========================
2. Jack usually mows his lawn in 6 hours. Marilyn can mow the same yard in 7 hours. How much time would it take for them to mow the lawn together?
---------
Jack rate + Marilyn rate = together rate
1/6 + 1/7 = 1/x
(13/42) = 1/x
13x = 42
x = 42/13 = 3.23 hours to do the job together
==============
3. Benz bicycles 7 km/h faster than praedup.
In the same time it takes praedup to bicycle 48 km, Benz can bicycle 69 km. how fast does each bicyclist travel?
-----------------------
Benz DATA :
distance = 69 km ; rate = x+7 kph ; time = d/r = 69/(x+7)
----------------
Praedup DATA:
distance = 48 km ; rate = x kph ; time = d/r = 48/x
----------------
EQUATION:
time = time
69/(x+7) = 48/x
69x = 48x + 7*48
21x = 7*48
x = 16 km/h (Praedup speed)
x+7 = 23 km/h (Benz speed)
================================
4. Find the LCM of 5(r-7) and 35(r-7)
LCM = 35*(r-7)
===============
Cheers,
Stan H.
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Geometry_Word_Problems/159957: hi, im working on complements and suplements of angles and i had a question from my worksheet.
"The measure of the complement of an angle is 45+x. The measure of the supplement of an angle is 15x-47. What is the measure of the angle?"
My work: 45 + x = 90 15x - 47 = 180 15x 227
-45 = -45 +47 = +47 ---- = --- =(x = 15.13333333)
------------- --------------- 15x 15x
(x = 45) 15x = 227
what i dont get is what to do next. the question is asking for only one of the angles but i have two x's. If i plugg them in then i have two different answers. What should i do next to finish this problem?
1 solutions
Answer 117929 by stanbon(57246) on 2008-10-01 22:06:38 (Show Source):
You can put this solution on YOUR website!The measure of the complement of an angle is 45+x. The measure of the supplement of an angle is 15x-47. What is the measure of the angle?
--------------
Let the measure of the angle be "y".
EQUATIONS:
y + 45+x = 90
y + 15x-47 = 180
----------------
Rearrange to get:
y + x = 45
y + 15x = 227
-------------
Subtract 1st from 2nd to solve for "x":
14x = 182
x = 13
--------------------
Substitute to solve for "y":
y + 13 = 45
y = 32 (final answer)
=======================
Cheers,
Stan H.
|
Linear-equations/159949: Function Value from Slope and run: Suppose f is a linear function such that f(3)=7. If the slope of f is 2.7, then what is f(5)?
I have no clue how to set this problem up!
The secons question is: Run from slope and rise: Suppose that f is a linear function with slope -3.4 and that f(1)=6.What value of x gives f(x)=0?
Please help. I am getting so far behind because I don't get this! Thank you. Andie
1 solutions
Answer 117928 by stanbon(57246) on 2008-10-01 21:52:01 (Show Source):
You can put this solution on YOUR website!Suppose f is a linear function such that f(3)=7. If the slope of f is 2.7, then what is f(5)?
y = 2.7x + b
7 = 2.7*3 + b
b = -1.1
------
EQUATION:
f(x) = 2.7x - 1.1
f(5) = 2.7*5 - 1.1
f(5) = 12.4
=================
The second question is: Run from slope and rise: Suppose that f is a linear function with slope -3.4 and that f(1)=6.
--------
y = -3.4x + b
6 -3.4*1 + b
b = 9.4
EQUATION:
f(x) = -3.4x + 9.4
-----------------
What value of x gives f(x)=0?
0 = -3.4x + 9.4
3.4x = 9.4
x = 2.765
==============
Cheers,
Stan H.
|
Miscellaneous_Word_Problems/159934: Help please.I cant solve this word problem, i think i am using the wrong formula.
A 500-pound watermelon is 99% water. As it was sitting in the sun on a hot summer day, some water evaporated and the watermelon ended up 98% water. What is the new weight of the watermelon?
Please and thank you...
1 solutions
Answer 117926 by stanbon(57246) on 2008-10-01 21:31:26 (Show Source):
You can put this solution on YOUR website!A 500-pound watermelon is 99% water. As it was sitting in the sun on a hot summer day, some water evaporated and the watermelon ended up 98% water. What is the new weight of the watermelon?
-----------
Before evaporation:
0.01*500 = 5 lbs not water: 0.99*500 = 495 lbs of water
------------
After evaporation:
Total weight = x lbs
5 lbs not water: 0.98x of water
------------
EQUATION:
5 + 0.98x = x
5 = 0.02x
x = 250 lbs (total weight after evaporation)
=============
Cheers,
Stan H.
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