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x+y+2z=0
1/4x-1/4y+1/8z=1
3/2x+y+1/2z=1
1 solutions
Answer 198931 by Alan3354(30959)   on 2010-02-19 16:05:27 (Show Source):
You can put this solution on YOUR website!I'm not sure what "algebraically" means.
-------------
x+y+2z=0
1/4x-1/4y+1/8z=1 --> 2x-2y+z = 8
3/2x+y+1/2z=1 --> 3x+2y+z = 2
---------------
x + y+2z = 0
2x-2y +z = 8
3x+2y +z = 2
Eliminate y
------------
Add eqns 2 and 3
2x-2y +z = 8
3x+2y +z = 2
------------- Add
5x + 2z = 10 eqn A
--------------
Add 2x 1st eqn to 2nd
2x+2y+4z = 0
2x-2y +z = 8
------------Add
4x + 5z = 8 eqn B
20x +25z = 40 eqn B x 5
20x + 8z = 40 eqn A x 4
------------------------ Subtract
17z = 0
z = 0
------
x = 2
-----
y = -2
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Equations/271652: can you teach me how to solve parallel and perpendicular lines please?
1 solutions
Answer 198916 by Alan3354(30959) on 2010-02-19 14:47:22 (Show Source):
You can put this solution on YOUR website!Here are 2 examples:
Given 2 points example.
Find the equation of the line thru the points (2,1) and (3,5)
---------------------
This is a 2 step process. First find the slope of the line thru the points.
slope, m = diffy/diffx
m = (5-1)/(3-2)
m = 4
---------
Now use y = mx + b with either point to find b, the y-intercept.
y = mx + b
5 = 4*3 + b
b = -7
-------
y = mx + b
y = 4x - 7 is the answer.
------------------------
For further assistance, or to check your work, email me via the thank you note.
----------------------
A line and a point example.
Write in standard form the eqation of a line that satisfies the given conditions. Perpendicular to 9x+3y=36, through (1,2)
-----------------
Find the slope of the line. Do that by putting the equation in slope-intercept form, y = mx + b. That means solve for y.
9x+3y = 36
3y= - 9x + 36
y = -3x + 13
The slope, m = -3
------------------
The slope of lines parallel have the same slope.
The slope of lines perpendicular is the negative inverse, m = +1/3
----------------
Use y = mx + b and the point (1,2) to find b.
2 = (1/3)*1 + b
b = 5/3
The equation is y = (1/3)x + 5/3 (slope-intercept form)
x - 3y = -5 (standard form)
------------------------
For further assistance, or to check your work, email me via the thank you note.
|
Graphs/271763: 8x-4y=12
4y-8x=-12
What is the solution of the system?
a. no solution
b. infinitely many solutions
c. A point
Is the system consistent or inconsistent?
Are the equations dependent or independent?
1 solutions
Answer 198906 by Alan3354(30959) on 2010-02-19 14:06:32 (Show Source):
|
Graphs/270083: Graph the following linear equation by finding x- and y-intercepts.
2x – 4y = -8
Describe the graph verbally by showing the calculation of the two intercepts and giving the ordered pair for each. Describe the line you have graphed. The description should include the quadrants through which the line passes, and the direction the line leans (forward or backward).
1 solutions
Answer 198788 by Alan3354(30959) on 2010-02-18 22:02:00 (Show Source):
You can put this solution on YOUR website!Graph the following linear equation by finding x- and y-intercepts.
2x – 4y = -8
-------------------
set x = 0 to find the y-intercepts, and vice versa
x - 2y = -4 (I reduced it)
x = 0: -2y = -4
y = 2
--> (0,2) y-intercept
------------------
y=0: x = -4
--> (-4,0) x-intercept
Draw a line thru the 2 points
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Polynomials-and-rational-expressions/271535: Could I have help with this problem please.
The speed of train A is 16 mph's slower than the speed of train B. Train A
travels 200 miles in the same time it takes train B to travel 280 miles. Find
the speed of each train.
Speed of Train A is ?
Speed of Train B is ?
1 solutions
Answer 198764 by Alan3354(30959) on 2010-02-18 21:01:43 (Show Source):
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Volume/271525: find the square root Use the square root key on your calculator if necesary Round your answer to the thousandth place square root 5 and square root 96
thanks
1 solutions
Answer 198757 by Alan3354(30959) on 2010-02-18 20:37:40 (Show Source):
You can put this solution on YOUR website!
------------------------
Do you not have a calculator?
There's one on Windows
click Start, All Programs, Accessories, Calculator
|
Triangles/271509: Can a triangle have the following measures:4,9, and 8?
1 solutions
Answer 198752 by Alan3354(30959) on 2010-02-18 20:14:10 (Show Source):
You can put this solution on YOUR website!Yes, it can have those sides.
-----------------------------
If any side is >= the sum of the other 2 sides, or <= the difference of the other 2 sides, it's not possible to form a triangle.
-----------------
I can only guess that tobias checked to see it 4, 9 and 8 made a right triangle. They don't, but they can make a triangle.
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Travel_Word_Problems/270967: a plane is flying at 174 miles per hour with a heading of 50.5 degrees from due north. the wind is blowing a constant 23 miles per hour at 140.5 degrees from due north. find the ground speed and true course of the plane.
1 solutions
Answer 198750 by Alan3354(30959) on 2010-02-18 20:13:04 (Show Source):
You can put this solution on YOUR website!Is the plane flying a heading of 50.5º? If it's 50.5 "from due north", it could be 309.5º
---------------
Wind direction in aviation is the direction the wind is coming from.
Is this wind from 140.5º?
-------------------
The people writing textbooks should stick to subjects they know. Headings are given to the whole degree, no 50.5 degs
----------------------
I'll solve this, using that plane heading of 50.5, and the wind direction of 140.5 (coming from 140.5).
-----------------
Notice they're 90º apart, so it's a right triangle with sides of 174 and 23.
The resultang groundspeed is the hypotenuse:
g = 175.5 mph
--------------
The angle between the plane's heading and it course is the arctan(23/174)
=~ 7.53º
If the wind direction uses from, that makes the ground track 43º
If the wind direction uses to, it's 58º
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PS miles per hour is not used in aviation, it's knots.
It would be the "wind is 140 at 20 knots"
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Graphs/271371: what is the x-intercept of the line 5x-3y=-15
1 solutions
Answer 198701 by Alan3354(30959) on 2010-02-18 16:58:34 (Show Source):
You can put this solution on YOUR website!what is the x-intercept of the line 5x-3y=-15
It's the point where the line crosses the x-axis. That means y = 0.
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5x-3y = -15
5x-3*0 = -15
5x = -15
x = -3
The point is (-3,0)
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Rectangles/271379: explain (to a 5th grader) how to find the area of a rectangle where 1 side = 1m and the other =34cm????
1 solutions
Answer 198700 by Alan3354(30959) on 2010-02-18 16:56:38 (Show Source):
You can put this solution on YOUR website!explain (to a 5th grader) how to find the area of a rectangle where 1 side = 1m and the other =34cm?
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The area is the product of the 2 sides, or length times width. Which side is called length and width doesn't matter.
The 2 sides must have the same units. In this case, either both meters or both cm.
1 meter = 100 cm
The area is 34 cm * 100 cm = 3400 square cm
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Or, 34 cm = 0.34 meters
The area is 1 m * 0.34 m = 0.34 square meters
Both are correct. I prefer 3400 sq cm
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Money_Word_Problems/271181: 1. The backyard can be mapped onto a Cartesian coordinate (x,y) graph. Using the various items described in the yard below, answer the following questions.
a) A water line is given by the equation:
Suppose you want to put a pink flamingo lawn ornament in your backyard, but you want to avoid placing it directly over the water line, in case you need to excavate the line for repairs in the future. Could you place it at the point ? Demonstrate how you arrived at your answer with the detail calculations.
1 solutions
Answer 198581 by Alan3354(30959) on 2010-02-18 09:27:57 (Show Source):
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logarithm/270973: e x+ e -x=5
1 solutions
Answer 198483 by Alan3354(30959) on 2010-02-17 22:11:09 (Show Source):
You can put this solution on YOUR website!If you mean
e^x + e^-x = 5 then
x = inv hyperbolic cosine (2.5)
x =~ 1.566799 (via calculator)
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The long way
e^x + e^-x = 5
Multiply by e^x
e^2x + 1 = 5e^x
e^2x - 5e^x + 1 = 0
It's a quadratic in e^x
e^x = (1/2)*(5 ± sqrt(21))
e^x =~ 4.7912878, 0.2087
x = log(4.79..., 0.2087)
x = ± 1.566799
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percentage/271065: find the percent of change. tell whether the change is an increase or decrease. round to the nearest tenth of a percent.
from 87 to 108
1 solutions
Answer 198475 by Alan3354(30959) on 2010-02-17 21:39:10 (Show Source):
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