Linear equation Definition and 131 Threads

Problem statement : Let me copy and paste the problem to the right as it appears in the text. Solution attempt (mine) : There are mainly three cases to consider. (1) ##\boldsymbol{x\ge 3\; :}## Using the relevant equations given above, the problem statement reduces to $$x-3+x-2 = 1\Rightarrow...

Write a linear equation. A school district purchases a high-volume printer, copier, and scanner for $24,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment during the 10 years it...

Write a linear equation for the application. A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of 7% of sales. Write a linear equation for the salesperson’s monthly wage W in terms of monthly sales S. Solution: I am looking for W(S). S = monthly sales Let...

You are given the dollar value of a product in 2016 and the rate at which the value of the product is expected to change during the next 5 years. Use this information to write a linear equation that gives the dollar value V of the product in terms of the year t. (Let t = 16 represent 2016.)1...

A school district purchases a high-volume printer, copier, and scanner for $24,000. After 10 years, the equipment will have to be replaced. Its value at that time is expected to be $2000. Write a linear equation giving the value V of the equipment during the 10 years it will be in use. Let t =...

A pharmaceutical salesperson receives a monthly salary of $5000 plus a commission of 7% of sales. Write a linear equation for the salesperson’s monthly wage W in terms of monthly sales S. I will let W(S) = monthly wage W in terms of monthly sales S. $5000 plus a commission of 7% of sales =...

i get preparation for my university entering exam and i studying linear equation and they define it linear equation are those which graph line now my question is that why one variable linear equation called linear for example y=3 that actually give us just line why we draw line for this...

I use 2x -4 as the LCD and turn 8/(x - 2) - (13/2) = 3 into 16 - 13x - 4 = 3, I then get 12 - 13x = 3 which leads me to 13x = -9 so x = -9/13 which is the wrong answer. Where did I make a mistake?

My method is converting 14 into ##\frac {42} {3}, = \frac 7 3x## Then $$ \frac {126} { 21}, = 6$$

I don't know the terms so I'm sorry if the informations at summary above is unclear. But I add a detailed photo of my calculations below. I use Gauss' Elimination laws.

https://www.physicsforums.com/attachments/9471 ok lots of options to solve this but I would start by $R3-R1\to R3$ if I remember correctly if get a diagonal of ones and the rest zeros in A we will have B from Ax=B $\tiny{USMA = United \,States\, Military\, Academy}$

[solved] Basis for set of solutions for linear equation Hi, I have this problem I was working through, but I'm not sure that I've approached it from the right way. The problem consists of 3 parts, which build off of each other. I'm pretty confident about the first two parts, but no so much...

Homework Statement I need some help with a question on my assignment. It asks to set up a matrix from the linear equations, y=25x+70 and y=35x+40. Homework Equations How do I set this matrix up? The Attempt at a Solution I think that I have to rewrite it as 25x-y=-70 and 35x-y=-40. But then I...

Homework Statement convert: Y − 200 = −4 (X − 15) to X = −0.25 ⋅ Y + 65. with a given Δy/Δx = -36/4 Homework Equations point slope, slope intercept The Attempt at a Solution I understand point slope, slope intercept, and standard form, I understand how to convert one to the other, but I...

Imagine that you own a grove of orange trees, and suppose that from past experience you know that when 100 trees are planted, each tree will yield about 240 oranges per year. Furthermore, you've noticed that when additional trees are planted in the grove, the yield per tree decreases...

As per my understanding, a linear equation with two variables form a line segment (ax=by+c or ax+by=c) and linear equation with three variables form a plane (ax=by+cz+d or ax+by+cz=d). Am I right? And if I am right, does an equation with four variables form a cube?

Imagine that you own a grove of orange trees, and suppose that from past experiences you know that when 100 trees are planted, each tree will yield about 240 oranges per year. Furthermore, you've noticed that when additional trees are planted in the grove, the yield per tree decreases...

I have the linear equation ##a + (2a - b) \sqrt{2} = 4 + \sqrt{2}##. I commonly hear that for linear equations, if we have two variables and one equation, then the system is undertermined and there are infinitely many solutions. However, how does that jive with this example, where there is one...

The problem I am trying to write the equation for the plane on the following form ## ax + by + cz + d = 0 ## $$ \begin{cases} x = 1 + s - t \\ y = 2 - s \\ z = -1 + 2s \end{cases} $$ The attempt ## s, t ## are the parameters for the two directional vectors which "support" the plane. $$...

Hello, i have been studying for finals and i am stuck on a question on my study guide. the question is to make a scatter plot of a set of data, find the equation of the best fit line, and approximate the value of y for x = 5. the data is like this: x: 0 2 4 6 7 and the y is like : y: 2 7 14...

any particular solution plus the general solution to the homogeneous equation. I'm having difficuilty understanding this proof from my lecture notes Theorem : Let T : V → W be a linear transformation. Let w ∈ W and suppose T(u0) = w T(v) = 0. where v ∈ V (the kernel ) to prove: T(u) = w...

Am I forgetting some critical basic knowledge? It says: In the plane (identified by R^2) a linear equation ax+by=c is a straight line. If b=0 then this straight line is parallel with the y-axis; in the other case it is a straight line with slope -a/b. A (2 by 2)-system linear equation. Why is...

Homework Statement I am given the equation (m1 – m2)g = (m1 + m2 + I/R2)a and the experiment is to validate this equation. Homework Equations The Attempt at a Solution After following the lab guide, it tells you to plot the weight difference (m1– m2)g against acceleration and determine...

(x - 2)^3 = x^2(x - 6) = (x^3 - 8) = (x^3 - 6x^2) (x^3 - 8) = (x^3 - 6x^2) -x^3 -x^3 = -8 = -6x^2 I am not sure how to solve this for x

2xy'=3y' first how do i find it's solution

Hi, I wanted to know if the endpoints of an nth dimension linear equation will be guaranteed to contain a min and max over that interval. For 1D ( like a line), if I find f(x) over an interval [x0, xn], I'm guaranteed that the two end points will be either an max or min. So I was wondering if...

Homework Statement Hello! Please, take a look at the screeshot with a problem description. Homework Equations I am trying to solve this, but I seem to have a wrong understanding of the problem. The Attempt at a Solution It is said that a company charges 2.50 for the first 1/5 of a mile...

(1+y2) d2y/(dt2) + t dy/dt +y = et

In my multivariable calculus class, we briefly went over Taylor polynomial approximations for functions of two variables. My professor said that the second degree terms include any of the following: $$x^2, y^2, xy$$ What surprised me was the fact that xy was listed as a nonlinear term. In...

Homework Statement https://webwork.utpa.edu/webwork2_files/tmp/equations/2d/02a7e6a06f5b2424758fa01cc965f71.png with https://webwork.utpa.edu/webwork2_files/tmp/equations/80/81c176aa8964438a63eb096513245f1.png Homework Equations [/B] Standard form: y' + p(x)y = f(x)...

How the system of equations ##y=-2x+1## ##y=x+1## ##y=2x+1## are linearly dependent. In wiki its written for the above system of equations "one equation linearly dependent on the others"

The problem Adam is saving 1, 5 and 10 dollar bills. Adam has 165 bills. The amount of one dollar bills is twice as high as 10-dollar bills. The total value of his savings is 735 dollars. How many 5-dollar bills does Adam have? This problem was translated. Sorry for grammatical errors. The...

Homework Statement Mass 2 collides with mass 1 as shown in the image, mass 1 is attached to the stick and it is initially stationary. Consider that the stick is massless and can rotate around the point O. The entire system is on a frictionless table. Which magnitudes are conserved in the system...

I know that linear equations have variables, which have a power no greater than one. So, for example, 5x + 2 = 15 is linear, because the x is to the first power only. But what about this equation: x/x+2 = 80 This has an x in the denominator. Could we consider this linear still, because...

If I have a similar question $$\frac{y}{5}+\frac{7}{20}=\frac{5-y}{4}$$ should I go about the same process as the http://mathhelpboards.com/pre-algebra-algebra-2/solve-following-equation-12605.html? Try and cancel out the denominators of 5, 20 and 4? Which would be 20? So times the equation by 20?

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Using the maple I am trying to get quardic in q from this big linear equation. Then use Descarte’s rule of signs to determine the number of positive roots. \begin{equation} \frac{\gamma*q*P_Q}{k_p*(1-q)*P_C} = \frac{I*\alpha}{k_f+k_d+\frac{k_n*\lambda_b*\gamma*q*P_Q}{\lambda_b* \gamma...

each of two brothers can wash a car in 1hr; however, their sister can wash a car in 45min. If the three work together, how long will it take to wash the car? my solution, $\frac{1}{60}+\frac{1}{60}+\frac{1}{45}=\frac{1}{x}$ multiply by 36,480x I get $810x+1215x-36480=1350x$ solving for x I...

please I need assistance with this problem help me get started Roughing It Milo and Bernard are planning a three-day canoe trip on the Roaring Fork River. Their friend Vince will drop them off at the Highway 14 bridge. From there they will paddle upstream for 12 hours on the first day...

Olympic Track. To host the Summer Olympics, a city plans to build an eight-lane track. The track will consist of parallel 100-m straightaways with semicircular turns on either end as shown in the figure. The distance around the outside edge of the oval track is 514 m. If the track is built...

1. Average Speed. Junior drove his rig on Interstate 10 from San Antonio to El Paso. At the halfway point he noticed that he had been averaging 80 mph, while his company requires his average speed to be 60 mph. What must be his speed for the last half of the trip so that he will average 60...

1. Metallurgy. How much pure gold should be melted with 15 grams of 14-karat gold to produce 18-karat gold? 2. Road Construction. A new machine that deposits cement for a road requires 12 hours to complete a one-half mile section of road. An older machine requires 16 hours to pave the same...

I need help with these problems. 1. Speed of Sound in Air. Two seconds after firing a rifle at a target, the shooter hears the impact of the bullet. Sound travels at 1100 feet per second and the bullet at 1865 feet per second. Determine the distance to the target (to the nearest foot). 2...

If 3 m e n do a job in 12 days and two of the me n are three time s as fast as the third, how long will it take one of the faster men to do the job ? this is how I solved it let x = required time for one of the faster men to do the job alone 3x = time taken by third to finish a job...

Forty men were engaged to finish a work in 90 days. Afer 60 days, some men stopped working. The remaining men finished the job at a same rate in 40 more days. How many men stopped? this is how far I can get to let x = number of men remained 40-x = number of men stopped Please help. thanks!

here's the other problem. 1. An army of soldiers is marching down a road at 5 mi/hr. A messenger on horseback rides from the front to the rear and returns immediately, the total time taken being 10 minutes. Assuming that the messenger rides at the rate of 10mi/hr...

1. A clay contains 45% silica and 10% water. Determine the percentage of silica in the clay on a dry (water-free) basis. All percentages are by weight. my answer is 100% silica. because if the clay is water free the clay is 100% silica. is this correct? 2. A coal contains 2.4%...

please help me with this problem please use single variable only. The length of a rectangular swimming pool is twice its width. The pool is surrounded by a cement walk 4ft wide. If the area of the walk is 748 ft^2, determine the dimensions of the pool. let x = width of...

A and B can run around a circular mile track in 6 and 10 minutes respectively. If they start at the same instant from the same place, in how many minutes will they pass each other if they run around the track (a) in the same direction, (6) in opposite directions...

Hello Am I right in saying: ax+b=0 is one-variable linear equation ax+by+c=0 is two-variable linear equation ax^2+bx+c=0 is one-variable quadratic equation ax^2+bx+c=y is two-variable quadratic equation Every linear or quadratic equation in one or two variables can be represented in those...