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stanbon answered: 57314 problems
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56970..56999 , 57000..57029 , 57030..57059 , 57060..57089 , 57090..57119 , 57120..57149 , 57150..57179 , 57180..57209 , 57210..57239 , 57240..57269 , 57270..57299 , 57300..57329, >>Next

Inequalities/341756: Good evening. I am taking a college level business calculus class. We are currently reviewing algebra. I am stuck on one problem. It is:
A-5
---- < -1
A+2

I know to take the -1 times A + 2 to get A - 5 < A + 2 and I know to take the +2 and subtract it from A - 5 to get A - 5 - 2, but what happens to the A on the right side. Is it not supposed to be a 0? I am really confused and lost and, therefore, unable to continue because the rest of this section contains similar problems. Please help me figure this problem out.

1 solutions

Answer 244679 by stanbon(57387) About Me  on 2010-09-11 17:51:30 (Show Source):
You can put this solution on YOUR website!
A-5
---- < -1
A+2
---------------------
The boundary of the inequality is (A-5)/(A+2) = -1
-------------------
Since the denominator cannot be zero, A cannot be -2.
---
The numerator cannot be zero so A cannot be 5
-------------------------------
To solve the inequality:
1: Draw a number line
2: Plot the values A = -2 and A = 5
3: Check a test value from each of the resulting 3 intervals
to see where the solutions are for the inequality.
----
A-5
---- < -1
A+2
Check A = -10; (-10-5)/(-10+2) < -1, false so no solutions in (-inf,-2)
Check A = 0; (0-5)/(0+2)< -1, true so solutions in (-2,5)
Check A = 10; (10-5)/(10+2) < -1, false so no solutions in (5,+inf)
====
Final solution: -2< A < 5
============
Graph:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%28x-5%29%2F%28x%2B2%29%2C-1%29
============
Cheers,
Stan H.


Linear-equations/341754: how do i graph the line y+1/4 x-4
1 solutions

Answer 244676 by stanbon(57387) About Me  on 2010-09-11 17:38:13 (Show Source):
You can put this solution on YOUR website!
how do i graph the line y=(1/4)x-4
---
Plot a couple of points and draw a line thru them.
---
If x = 0, y = -4 giving you point (0,-4)
---
If x = 4, y = 1-4 = -3 giving you point (4,-3)
------
Graph:
graph%28400%2C300%2C-10%2C10%2C-10%2C10%2C%281%2F4%29x-4%29
---
Cheers,
Stan H.
========


Functions/341753: I need help with this problem:
Find the domain
x+13/x^2-1
1 solutions

Answer 244670 by stanbon(57387) About Me  on 2010-09-11 17:33:00 (Show Source):
You can put this solution on YOUR website!
I need help with this problem:
Find the domain
x+13/x^2-1
----
the denominaator cannot be zero.
---
Solve x^2-1 = 0
Factor:
(x+1)(x-1) = 0
x = -1 or x = 1
---------------------
Domain: All Real Numbers except x = 1 and x = -1
==================================
Cheers,
Stan H.


Circles/341751: The spoke of a wheel reaches from the center of the wheel to its rim. If the circumference of the
rim of the wheel is 42 inches, how long is each spoke? Round your answer to the nearest
hundredth.


A. 7 inches
B. 6.25 inches
C. 13.38 inches
D. 6.69 inches

1 solutions

Answer 244669 by stanbon(57387) About Me  on 2010-09-11 17:29:32 (Show Source):
You can put this solution on YOUR website!
The spoke of a wheel reaches from the center of the wheel to its rim. If the circumference of the rim of the wheel is 42 inches,
how long is each spoke? Round your answer to the nearest
hundredth.
----
Circumference = (pi)*diameter
diameter = 42/pi = 13.37 inches
2*radius = 13.37
radius = 6.68 inches
==========================
cheers,
Stan H.

A. 7 inches
B. 6.25 inches
C. 13.38 inches
D. 6.69 inches


Equations/341752: I am checking my answer to the following (the answer is not in the book):
A solution is 30% chlorine and another solution is 70% chlorine. How many liters of each solution should you use to make 150 liters of a solution that is 55% chlorine?
I wrote the equation like this:
.3x + .7(150-x)= .55(150)
I broke this down to x=56.25
56.25 Liters of 30% solution and 93.75 liters of 70% solution

1 solutions

Answer 244666 by stanbon(57387) About Me  on 2010-09-11 17:22:29 (Show Source):
You can put this solution on YOUR website!
A solution is 30% chlorine and another solution is 70% chlorine. How many liters of each solution should you use to make 150 liters of a solution that is 55% chlorine?
I wrote the equation like this:
.3x + .7(150-x)= .55(150)
I broke this down to x=56.25
56.25 Liters of 30% solution and 93.75 liters of 70% solution
---------------
That is correct.
Cheers,
Stan H.


Probability-and-statistics/341633: Heartless poker is played with a deck of cards in which all the hearts have been removed. Note that the deck now has 39 cards. Find the probability of getting a flush (five cards of the same suit) when drawing a five-card hand.
1 solutions

Answer 244665 by stanbon(57387) About Me  on 2010-09-11 17:18:15 (Show Source):
You can put this solution on YOUR website!
Heartless poker is played with a deck of cards in which all the hearts have been removed. Note that the deck now has 39 cards. Find the probability of getting a flush (five cards of the same suit) when drawing a five-card hand.
-----
Pick a suit: 3 ways
Pick 5 cards of that suit: 13C5 = 1287
-----
Pick 5 cards randomly = 575757
===============
P(flush) = (3*1287)/575757 = 0.0067
==============
Cheers,
Stan H.
==============


Numbers_Word_Problems/341727: Suppose that you are taking a course that has 4 tests. The first three tests are for 100 points each and the fourth test is for 200 points. To get an B in the course, you must have an average of at least 80 percent on the 4 tests. Your scores on the first 3 tests were 77, 80, and 80. What is the minimum score you need on the fourth test to get an B for the course?
1 solutions

Answer 244659 by stanbon(57387) About Me  on 2010-09-11 16:13:28 (Show Source):
You can put this solution on YOUR website!
Suppose that you are taking a course that has 4 tests. The first three tests are for 100 points each and the fourth test is for 200 points. To get an B in the course, you must have an average of at least 80 percent on the 4 tests. Your scores on the first 3 tests were 77, 80, and 80. What is the minimum score you need on the fourth test to get an B for the course?
-----
500 points are offered in the 4 tests
0.8*500 = 400
Equation:
77+80+80+2x >=400
237+2x >= 400
2x >= 163
x >= 81.5 (score needed on the 4th test)
===========================================
Cheers,
Stan H.


Polynomials-and-rational-expressions/341724: Please help me solve this problem: The dementions of a rectangle are such that its length is 5in. more than its width. If the length were doubled and if the width were decreased by 2in., the area would be increased by 52in. What are the length and width?
1 solutions

Answer 244656 by stanbon(57387) About Me  on 2010-09-11 15:54:09 (Show Source):
You can put this solution on YOUR website!
Please help me solve this problem: The dimensions of a rectangle are such that its length is 5in. more than its width.
width = w
length = w+5
---
Old Area = w(w+5) = w^2+5w sq. in.
------------------------------------
If the length were doubled and if the width were decreased by 2in., the area would be increased by 52in.
length = 2(w+5) = 2w+10
width = w-2
---
New Area = (2w+10)(w-2) = 2w^2 +6w -20 sq. in
-------------------------
Equation:
new area - old area = 52 sq in
2w^2+6w-20-(w^2+5w) = 52
---
w^2+w-20 = 0
Factor:
(w+5)(w-4) = 0
Positive solution
width = 4 inches
length = w+5 = 9 inches
==================================
Cheers,
Stan H.


Linear_Algebra/341719: Bridges on expressways often have expansion joints, which are small gaps in the roadway between one bridge section and the next. The gaps are put there so that the bridge can expand in hot weather. Suppose that a bridge has a gap of 1.3 cm at 22 degrees, and .9 cm at 30 degrees. Write an equation for gap width as a function of temperature.
1 solutions

Answer 244654 by stanbon(57387) About Me  on 2010-09-11 15:40:26 (Show Source):
You can put this solution on YOUR website!
Suppose that a bridge has a gap of 1.3 cm at 22 degrees, and .9 cm at 30 degrees. Write an equation for gap width as a function of temperature.
---------------------------
You have two points relating gap to timperature.
(22,1.3) and (30,0.9)
----
slope = (0.9-1.3)/(30-22) = -0.05
--------------
Form: g = m*t + b
0.9 = -0.05*30 + b
b = 2.4
---------------------------
Equation:
gap = -0.05(temp)+2.4
===========================
Cheers,
Stan H.


Numbers_Word_Problems/341709: One positive number is 5, times another number. The difference between the two numbers is 408, find the numbers

1 solutions

Answer 244652 by stanbon(57387) About Me  on 2010-09-11 15:30:08 (Show Source):
You can put this solution on YOUR website!
One positive number is 5 times another number. The difference between the two numbers is 408, find the numbers
-------------
Equations:
x = 5y
x - y = 408
------------
Substitute for "x" and solve for "y":
5y-y = 408
4y = 408
y = 102
---
Since x = 5y, x = 510
============================
Cheers,
Stan H.


Probability-and-statistics/341674: A complete cycle of a traffic light takes 80 seconds. During each cycle, the light is green for 40 seconds, amber for 10 seconds, and red for 30 seconds. At a randomly chosen time, what is the probability that the light will not be red?
1 solutions

Answer 244649 by stanbon(57387) About Me  on 2010-09-11 15:24:46 (Show Source):
You can put this solution on YOUR website!
A complete cycle of a traffic light takes 80 seconds. During each cycle, the light is green for 40 seconds, amber for 10 seconds, and red for 30 seconds. At a randomly chosen time, what is the probability that the light will not be red?
------
P(red) = 30/80 = 3/8
===========================
Cheers,
Stan H.


Word_Problems_With_Coins/341605: The value (in cents) of the change in a purse that contains twice as many nickels as pennies, six more dimes than nickels, and as many quarters as dimes and nickels combined; p = number of pennies
1 solutions

Answer 244620 by stanbon(57387) About Me  on 2010-09-11 08:35:41 (Show Source):
You can put this solution on YOUR website!
The value (in cents) of the change in a purse that contains twice as many nickels as pennies, six more dimes than nickels, and as many quarters as dimes and nickels combined; p = number of pennies
--------------
Equations:
n = 2p
d = n+6
q = d + n
-------
Rearrange:
2p - n + 0 + 0 = 0
0 + n - d + 0 = -6
0 + n + d - q = 0
-----
You have 4 variables, so you need one more equation.
==============
Cheers,
Stan H.


Coordinate-system/341618: The following are coordinates of points in the xy-plane. Which of these points is nearest the origin?
a (0,-1) b (0,1/2 ) c (1/2, -1/2) d (1/2,1/2) e (-1,-1)
1 solutions

Answer 244618 by stanbon(57387) About Me  on 2010-09-11 07:46:48 (Show Source):
You can put this solution on YOUR website!
The following are coordinates of points in the xy-plane. Which of these points is nearest the origin?
--
The distance (x,y) is from (0,0) is d = sqrt(x^2+y^2)
------
a (0,-1)::::::::d = 1
b (0,1/2 )::::::d = sqrt(1/4) = 1/2
c (1/2, -1/2):::d = sqrt(1/4 + 1/4) = sqrt(1/2) = (1/2)sqrt(2)= 0.7071
d (1/2,1/2):::::d = sqrt(1/4 + 1/4) = sqrt(1/2) = (1/2)sqrt(2)
e (-1,-1):::::::d = sqrt(1 + 1) = sqrt(2)
=====================================
Cheers,
Stan H.


Miscellaneous_Word_Problems/341602: A jeweler has 2 rings, each weighing 24 g, made of an alloy of 5% silver and 95% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 80%. How much silver should she add?
1 solutions

Answer 244617 by stanbon(57387) About Me  on 2010-09-11 07:39:44 (Show Source):
You can put this solution on YOUR website!
A jeweler has 2 rings, each weighing 24 g, made of an alloy of 5% silver and 95% gold. She decides to melt down the rings and add enough silver to reduce the gold content to 80%. How much silver should she add?
--------------------
Equation:
silver + silver = silver
0.05*48 + 1.00s = 0.20(48+s)
Multiply thru by 100 to get:
5*48 + 100s = 20*48+20s
80s = 15*48
s = 9 grams (amt. of pure silver she needs to add to the mix)
=======================
Cheers,
Stan H.


expressions/341619: The price of ground coffee beans is d dollars for 8 ounces and each ounce makes c cups of brewed coffee. In terms of c and d, what is the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee?
1 solutions

Answer 244616 by stanbon(57387) About Me  on 2010-09-11 07:28:45 (Show Source):
You can put this solution on YOUR website!
The price of ground coffee beans is d dollars for 8 ounces and each ounce makes c cups of brewed coffee. In terms of c and d, what is the dollar cost of the ground coffee beans required to make 1 cup of brewed coffee?
-----------------------
Each ounce of coffee beans costs d/8 dollars
----
Each ounce of coffee beans makes c cups.
1 cup requires 1/c ounces of coffee beans.
--------------------
price of 1/c ounces of coffee beans = (1/c)(d/8) = d/(8c) dollars
---------
cost of beans to make one cup = d/(8c) dollars
===================================================
Cheers,
Stan H.


Miscellaneous_Word_Problems/341621: A certain scale only registers weights that are greater than 6 pounds. A person who wanted to know the weights of a puppy, a kitten, and a bunny weighted them in pairs and go the following results.
The kitten and the bunny weighted 7 pounds.
The kitten and the puppy weighted 8 pounds.
The bubby and the puppy weighed 9 pounds.
What is the weight of the puppy?
A. 2 pounds B. 3 pounds C. 4 pounds D. 5 pounds E. 6 pounds

1 solutions

Answer 244615 by stanbon(57387) About Me  on 2010-09-11 07:17:26 (Show Source):
You can put this solution on YOUR website!
The kitten and the bunny weighted 7 pounds.
The kitten and the puppy weighted 8 pounds.
The bubby and the puppy weighed 9 pounds.
What is the weight of the puppy?
--------------
Equations:
k + b = 7
k + p = 8
b + p = 9
-----------------
Rearrange:
K + b +0 = 7
k + 0 +p = 8
0 + b +p = 9
----------------
Solve with any method you know to get:
k = 3
b = 4
p = 5
===========
Cheers,
Stan H.
===========
A. 2 pounds B. 3 pounds C. 4 pounds D. 5 pounds E. 6 pounds


Numbers_Word_Problems/341555: Is 6.4 odd or even?
1 solutions

Answer 244598 by stanbon(57387) About Me  on 2010-09-10 21:20:09 (Show Source):
You can put this solution on YOUR website!
Is 6.4 odd or even?
Ans: neither
================
Cheers,
Stan H.


Linear-equations/341557: what is the slope if it exist of (1,0) (0,-3)
1 solutions

Answer 244597 by stanbon(57387) About Me  on 2010-09-10 21:18:54 (Show Source):
You can put this solution on YOUR website!
what is the slope if it exist of (1,0) (0,-3)
-----
slope = (-3-0)/(0-1) = 3
-----------------------------
Cheers,
Stan H.
==============


Quadratic_Equations/341559: f(x)=x^2-7x-8

What is the vertex, the line of symmetry, and the x and y intercept(s)? How do you find each one?
Thanks!
1 solutions

Answer 244596 by stanbon(57387) About Me  on 2010-09-10 21:17:08 (Show Source):
You can put this solution on YOUR website!
f(x)=x^2-7x-8
What is the vertex, the line of symmetry, and the x and y intercept(s)? How do you find each one?
-------------------------
Vertex occurs at x = -b/(2a) = 7/2
f(7/2) = -20.25
---
Vertex::: (3.5,-20.25)
Line of symmetry: x = 3.5
--------
y-int = ?
Let x = 0, then y = -8
y-int = -8
-----------------
f(x)=x^2-7x-8
x-int = ?
Let y = 0
---
solve x^2-7x-8 = 0
(x-8)(x+1) = 0
x = 8 or x = -1
---
x-intercepts:
x = 8 and x = -1
======================
Cheers,
Stan H.
===========


Exponential-and-logarithmic-functions/341563: Please solve this for me with the working.
Function: I = 24e ^-0.3U
Sketch a graph of this function on for domain 0≤U≤10
Please show how you worked this out. Thanks
1 solutions

Answer 244588 by stanbon(57387) About Me  on 2010-09-10 21:10:04 (Show Source):
You can put this solution on YOUR website!
Function: I = 24e ^-0.3U
Sketch a graph of this function on for domain 0≤U≤10
------------------------------
graph%28400%2C300%2C-10%2C10%2C-10%2C50%2C24%2A2.71828%5E%28-0.3x%29%29
-------------------------
Cheers,
Stan H.


Angles/341558: 1) Use the Pythagorean Theorem to find the distance between X(7,11) and Y(-1,5)..Could you please show me your solution because I can't really understand this lesson!
2)Find the coordinates of the midpoint of a segment X(-4,3) and Y(-1,5)
3)Find the coordinates of A if B(0,5.5) is the midpoint of segment AC and C has coordinates (-3,6)
4) Find the coordinates of the missing endpoint given that S is the midpoint of segment RT: T(-4,3), S(-1,5)
Thank You very much=)
1 solutions

Answer 244587 by stanbon(57387) About Me  on 2010-09-10 20:50:56 (Show Source):
You can put this solution on YOUR website!
1) Use the Pythagorean Theorem to find the distance between
X(7,11) and Y(-1,5)..
Could you please show me your solution because I can't really understand this lesson!
---
d^2 = (change in x)^2 + (change in y)^2
d^2 = [(7--1)^2 + (11-5)^2]
d^2 = [64+36]
d^2 = 100
distance = 10
----------------------------
2)Find the coordinates of the midpoint of a segment X(-4,3) and Y(-1,5)
x = (-4+-1)/2 = -5/2
y = (3+5)/2 = 4
midpoint::: (-5/2,4)
----------------------------
3)Find the coordinates of A if B(0,5.5) is the midpoint of segment AC and C has coordinates (-3,6)
Let the coordinate of A be (x,y)
(x+-3)/2 = 0
x-3 = 0
x = 3
-------
(y+6)/2 = 5.5
y+6 = 11
y = 5
Coordinates of A:: (3,5)
--------------------------------
4) Find the coordinates of the missing endpoint given that S is the midpoint of segment RT: T(-4,3), S(-1,5)
Let the coordinates of R are (x,y)
(x+-4)/2 = -1
x-4 = -2
x = 2
----
(y+3)/2 = 5
y+3 = 10
y = 7
-----
Endpoint: (2,7)
=====================
Cheers,
Stan H.
=====================


Miscellaneous_Word_Problems/341548: Complete the following statements with never, sometimes, or always.
1. There are _______ an infinite number of solutions to a two variable equation in standard form.
2. The graph of a linear equation ________ has an x-intercept.
3. If y varies directly with x, the constant of variation k is _______ negative.
Below is the answers I got and wanted to check to make sure I understood the reading, any help with these questions is much appreciated. Thanks.
1. always
2. always
3. never
1 solutions

Answer 244586 by stanbon(57387) About Me  on 2010-09-10 20:40:26 (Show Source):
You can put this solution on YOUR website!
Complete the following statements with never, sometimes, or always.
1. There are always_ an infinite number of solutions to a two variable equation in standard form.
---------------------------------------------------------------------------
2. The graph of a linear equation sometimes__ has an x-intercept.
y=3 does not have an x-intercept.
---------------------------------------------------------------------------
3. If y varies directly with x, the constant of variation k is sometimes __ negative.
Direct variation: y = kx
If x = -3 when y = 9, k = -3
If x = 3 when y = 9, k = 3
--------------------------------------------
Cheers,
Stan H.


Inequalities/341546: hello, I am having problems solving the inequality in 3(3x+1)-(x-1)<6(x+10)
1 solutions

Answer 244585 by stanbon(57387) About Me  on 2010-09-10 20:22:14 (Show Source):
You can put this solution on YOUR website!
3(3x+1)-(x-1)<6(x+10)
9x+3-x+1 < 6x+60
8x+4 < 6x+60
2x<56
x < 28
============
Cheers,
Stan H.
============


Mixture_Word_Problems/341538: A coffee shop owner mixes two types of coffees to make a specialty blend. Alone, the coffees sell for $7.50 and $10.00 per pound. How many pounds of each type of coffee should be used to make 15 pounds of a mixture that sells for $8.95 per pound? Copy and complete the table below. (i am trying my best to copy the table...what is the difference between the cost per pound and the cost in dollars?)
AMOUNT, COST PER POUND, COST DOLLARS are on the top (labels)
COFFEE 1, COFFEE 2, MIXTURE are on the side (labels)

1 solutions

Answer 244584 by stanbon(57387) About Me  on 2010-09-10 20:20:09 (Show Source):
You can put this solution on YOUR website!
A coffee shop owner mixes two types of coffees to make a specialty blend. Alone, the coffees sell for $7.50 and $10.00 per pound. How many pounds of each type of coffee should be used to make 15 pounds of a mixture that sells for $8.95 per pound?
Quantity Eq::: x + y = 15 lbs.
Value Eq:::::7.5x+10y= 8.95*15
--------------------------------
Multiply the Quantity eq. by 75:: 75x + 75y = 75*15
Multiply the Value eq. by 10::::: 75x + 100y= 89.5*15
---------------------------------------------------------
Subtract the 1st eq. from the 2nd and solve for "y":
25y = 14.5*15
y = 8.7 lbs (amt. of $10 coffee needed in the mixture)
---
x = 15-8.7 = 6.3 lbs (amt. of $7.50 coffee needed in the mixture)
=======================================================================
Copy and complete the table below. (i am trying my best to copy the table...what is the difference between the cost per pound and the cost in dollars?)
::::::::::::AMOUNT, COST PER POUND, COST DOLLARS are on the top (labels)
COFFEE 1::::..x.........7.5...............7.5x
COFFEE 2::::..y..........10...............10x
MIXTURE:::::x+y..........8.95.............8.9*15
==================================================
Cheers,
Stan H.
=========



Exponential-and-logarithmic-functions/341535: The function Y(x)= 48.94 ln x/4.5 can be used to estimate the number of years Y(x) after 1980 required for a certain country's population to reach x million people. In which year will the country's population reach 11 million. About 2029, 2014, 2024, or 2034. to try and solve this problem I substituted 49, 34, 44, and 54 for x but still can not solve the problem can someone help me please.
e.g. Y(x)= 48.94 ln 54/4.5
1 solutions

Answer 244581 by stanbon(57387) About Me  on 2010-09-10 19:58:31 (Show Source):
You can put this solution on YOUR website!
The function Y(x)= 48.94 ln x/4.5 can be used to estimate the number of years Y(x) after 1980 required for a certain country's population to reach x million people. In which year will the country's population reach 11 million.
------------------
y(x) = 48.94*ln(x/4.5)
y(11) = 48.94*ln(11/4.5)
y(11) = 48.94*0.8938
y(11) = 43.74
---
Rounding up y(11) = 44
----
Year = 1980 + 44 = 2024
---------------------------
Cheers,
Stan H.
---------------------------

About 2029, 2014, 2024, or 2034.


Probability-and-statistics/341526: A professional chef’s work responsibilities include creating new dishes, shopping for ingredients and cooking the meals. On Thursday, Blake, a professional chef, spent 4 hours shopping for ingredients, 1 hour creating new dishes and 5 hours cooking the meals. If Blake’s work hours on Friday are spent approximately the same way they were on Thursday, what are the chances that at any given moment on Friday Blake will be creating new dishes or cooking the meals? Show step by step work! Give answer as a fraction in lowest terms.
1 solutions

Answer 244578 by stanbon(57387) About Me  on 2010-09-10 19:46:47 (Show Source):
You can put this solution on YOUR website!
On Thursday, Blake, a professional chef, spent 4 hours shopping for ingredients, 1 hour creating new dishes and 5 hours cooking the meals. If Blake’s work hours on Friday are spent approximately the same way they were on Thursday, what are the chances that at any given moment on Friday Blake will be creating new dishes or cooking the meals? Show step by step work! Give answer as a fraction in lowest terms.
-------
Total hours: 4+1+5 = 10
P(new dish or cooking) = (1+5)/10 = 6/10 = 3/5
==================================================
Cheers,
Stan H.


Pythagorean-theorem/341496: if one leg of a right triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs..
1 solutions

Answer 244558 by stanbon(57387) About Me  on 2010-09-10 18:20:07 (Show Source):
You can put this solution on YOUR website!
if one leg of a right triangle is 14 meters shorter than the other leg, and the hypotenuse is 26 meters, find the length of the two legs.
----------------------------------
Let one of the legs have length x.
Then the other leg's length is x-14.
----
Using Pythagoras you get:
26^2 = x^2 + (x-14)^2
x^2 + x^2-28x+196 = 676
2x^2 -28x -480 = 0
x^2 -14x -240 = 0
(x-24)(x+10) = 0
Positive solution:
x = 24 meters (longer leg)
x-14 = 10 meters (shorter leg)
==============================
Cheers,
Stan H.


Numbers_Word_Problems/341507: Find 3 consecutive integers in which the sum of the first two is 90 more than the last.
1 solutions

Answer 244557 by stanbon(57387) About Me  on 2010-09-10 18:10:56 (Show Source):
You can put this solution on YOUR website!
Find 3 consecutive integers in which the sum of the first two is 90 more than the last.
------------
1st: x
2nd: x+1
3rd: x+2
----------
Equation:
x + x+1 = x+2 + 90
2x+1 = x+92
x = 91
x+1 = 92
x+2 = 93
==========
Cheers,
Stan H.
==========


Linear-equations/341512: Write the equation of the line that has the indicated slope and contains the indicated point. Express the final equation in standard form. M=5, (-1,4)
1 solutions

Answer 244554 by stanbon(57387) About Me  on 2010-09-10 18:07:34 (Show Source):
You can put this solution on YOUR website!
Write the equation of the line that has the indicated slope and contains the indicated point. Express the final equation in standard form. M=5, (-1,4)
-------------------
Form: y = mx+b
4 = 5*-1 + b
4 = -5 + b
b = 9
------
Equation:
y = 5x + 9
=================
Cheers,
Stan H.
=================


Linear_Algebra/341508: 2x -3 > 23
1 solutions

Answer 244552 by stanbon(57387) About Me  on 2010-09-10 18:05:13 (Show Source):
You can put this solution on YOUR website!
2x -3 > 23
---
2x > 23+3
---
2x > 26
---
x > 13
========
Cheers,
Stan H.


Polynomials-and-rational-expressions/341494: tell wheathe the equation represents direct variation invers variation, or nither y/5=x
1 solutions

Answer 244551 by stanbon(57387) About Me  on 2010-09-10 18:03:26 (Show Source):
You can put this solution on YOUR website!
tell wheather the equation represents direct variation inversr variation, or neither
y/5=x
----
As x increases, y increases.
So the variation is direct.
-----
Cheers,
Stan H.