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4 years ago

A set of equations is given below:

2 answers:

7 0

There are several ways to solve systems of linear equations. The most common methods are by graphing, elimination, and substitution. Let's start off with one of the most basic methods, graphing. --------------- Graphing Method --------------- 2x + y = 3 3x + 2y = 6 In order to solve this system using the graphing method, we first have to change the two equations into slope-intercept form. 2x + y = 3 --> y = -2x + 3 3x + y = 7 --> y = -3x + 7 Then, we graph these two lines. (Attached Below) The solution set of a system of linear equations when graphing is actually the point at which the two lines intersect. So by graphing the two lines, we can obviously see that the solution set of this problem is (4, -5). --------------- Elimination Method --------------- The concept of elimination revolves around the concept of adding two equations. Using an example, let's see what happens when you add equations together. 2x + y = 3 3x + 2y = 6 ----------- 5x + 3y = 9 Do you see how this works? Now, let's say that the orientation of these two equations were different. What would you do then? 2x + y = 3 6 - 3x = 2y If this situation occurs, you have to rearrange it in a way that the form of the equations match. For example, if you have one in standard form, you have to algebraically return the other equation to the same form. 2x + y = 3 6 - 3x = 2y --> 6 = 3x + 2y --> 3x + 2y = 6 Now that the equations are in the same form, we can begin to solve. However, let's start with a simpler system to demonstrate the concept. 2x - y = 5 3x + y = 5 The process of elimination involves adding equations in a way that one of the unknown variables disappears. In this first example, let's see what happens when we simply add them right away. 2x - y = 5 3x + y = 5 --------- 5x + 0 = 10 Using the Identity Property of Addition, we can simply get rid of the 0. 5x = 10 Now it's all algebra. 5x = 10 x = 10/5 x = 2 Now we have one of the variables. You may be thinking "what about the other variable?". Well, in order to solve for the variable, all you have to do is plug what you have for this variable back into the equation like so: 3x + y = 5 3(2) + y = 5 6 + y = 5 y = -1 It doesn't matter which equation we plug it into because you will get the same result.

solong [7]4 years ago

3 0

A,y=x+1,b,y=4x+5 but it cant go any furtur but hope it helps u

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Find the area and the perimeter of the triangle

Semmy [17]

Use the pythagorean theory and use the formula a^2+b^2=C^2

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3 years ago

Read 2 more answers

Make c the subject of the formula in the equation a=b√x+c

neonofarm [45]

A = b√x+c
a/b = √x+c
(a/b)^2 = x + c
(a/b)^2 - x = c

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3 years ago

Expand and simplify (x - 5)(x - 4)

nikitadnepr [17]

Answer:

(x - 5) (x - 4)

x(x - 4) - 5(x -4)

x^2 - 4x - 5x - 20

x^2 - 9x - 20

Expand: x (x - 4) - 5 (x - 4)

Simplify: x^2 - 9x - 20

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3 years ago

A survey is conducted to find out whether people in metropolitan areas obtain their news from television (Event T), an newspaper

MrMuchimi

Answer:

e) P ( R' | T ) = 0.62857

f) P ( T' | N ) = 0.32258

g) P ( R' | N ) = 0.70968

h) P ( T' | N&R ) = 5/6

Step-by-step explanation:

Given:

- The probability of Television as news source P ( T ) = 0.7

- The probability of Newspaper as news source P ( N ) = 0.62

- The probability of Radio as news source P ( R ) = 0.46

- The probability of Television & Newspaper as news source P (T&N) = 0.42

- The probability of Television & Radio as news source P (T&R) = 0.26

- The probability of Radio & Newspaper as news source P (R&N) = 0.18

- The probability of all 3 as news source P ( T & R & N ) = 0.03

Find:

Given that TV is a news source, what is the probability that radio is not a news source?

Given that newspaper is a news source, what is the probability that TV is not a news source?

Given that newspaper is a news source, what is the probability that radio is not a news source?

Given that both newspaper and radio are news sources, what is the probability that TV is not a news source?

Solution:

- We will first compute the individual probability of each event occurring alone.

P (Television is the only news source) = P(T) - P(T&R) - P(T&N) + P(T&N&R)

P ( Only Television ) = P ( only T ) = 0.7 - 0.42 - 0.26 + 0.03 = 0.05

P (Newspaper is the only news source) = P(N)-P(N&R)-P(T&N)+P(T&N&R)

P ( Only Newspaper ) = P ( only N ) = 0.62 - 0.18 - 0.42 + 0.03 = 0.05

P (Radio is the only news source) = P(R) - P(T&R) - P(N&R) + P(T&N&R)

P ( Only Radio ) = P ( only R ) = 0.46 - 0.26 - 0.18 + 0.03 = 0.05

- Now for part e)

We are asked for a conditional probability of the form as follows:

P ( R' | T ) = P ( R' & T ) / P ( T )

First compute the probability that next news source is not Radio provided it is already a source of TV.

P ( R' & T ) = P( only T ) + P ( only T & N ) = 0.05 + 0.42 - 0.03 = 0.44

Hence,

P ( R' | T ) = 0.44 / 0.7

P ( R' | T ) = 0.62857

- Now for part f)

We are asked for a conditional probability of the form as follows:

P ( T' | N ) = P ( T' & N ) / P ( N )

First compute the probability that next news source is not TV provided it is already a source of Newspaper.

P ( T' & N ) = P( only N ) + P ( only R & N ) = 0.05 + 0.18 - 0.03 = 0.2

Hence,

P ( T' | N ) = 0.2 / 0.62

P ( T' | N ) = 0.32258

- Now for part g)

We are asked for a conditional probability of the form as follows:

P ( R' | N ) = P ( R' & N ) / P ( N )

First compute the probability that next news source is not Radio provided it is already a source of Newspaper.

P ( R' & N ) = P( only N ) + P ( only T & N ) = 0.05 + 0.42 - 0.03 = 0.44

Hence,

P ( R' | N ) = 0.44 / 0.62

P ( R' | N ) = 0.70968

- Now for part h)

We are asked for a conditional probability of the form as follows:

P ( T' | N&R ) = P ( T' & N & R) / P ( N & R )

First compute the probability that next news source is not TV provided it is already a source of both radio and Newspaper.

P ( T' & N & R) = P ( only N & R ) = 0.18 - 0.03 = 0.15

Hence,

P ( T' | N&R ) = 0.15 / 0.18

P ( T' | N&R ) = 5/6

6 0

3 years ago

Which function below has the lowest y intercept?

neonofarm [45]

Our first function is g(x). Al had two dozen donuts means that two dozen is the y-intercept of this function. A dozen equals 12, therefore two dozens is 24. Every cubicle he passed, he lost 2 donuts is the slope of the function and it is negative, that is -2, thus:

$g(x)=-2x+24 \\ \\ \boxed{y-intercept = 24}$