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Lerok [7]
3 years ago
7

Discussion for Applications of Linear Systems

Mathematics
1 answer:
Lostsunrise [7]3 years ago
6 0

Step-by-step explanation:

There are certain methods for solving a system of equations. Some of which are:

  • Substitution Method
  • Elimination Method
  • Graphing Method

<em>Substitution Method</em>

Substitution method to solve a system of equations is suitable if a variable of a any equation seems isolated or could comfortably be isolated without any ration/fraction resulting.

For example, for the following system of equations

x - 2y = 11....[A]

x = 5 - y....[B]

substituting the value of x = 5 - y from equation [B] into equation [A], so that

(5 - y) - 2y = 11

5 - y - 2y = 11

3y = -6

y = -2

<em>Elimination Method</em>

Elimination method to solve a system of equations is suitable if both equation are in standard form, and just adding or subtracting the equations to determine an equation in one variable.

For example, for the following system of equations

2x + 7y = -5....[C]

5x - 7y = 12....[D]

Adding Equation [C] and Equation [D].

7x + 0 = 7

x = 1

<em>Graphing Method</em>

Sometimes graphing method may be used to solve the system of the equation and visualize the solution.

For example,

y = -2....[E]

y = 3x + 1....[F]

The solution for this system of equation is the point of intersection of both the lines, which is shown in attached figure. The point of intersection is (-1, -2).

Hence, the solution of this system of equations is (-1, -2), as shown in attached figure.

<em>Keywords: system of equations, elimination method, substitution method, graphing method</em>

<em>Learn more about solution of system of equations from brainly.com/question/2643311</em>

<em>#learnwithBrainly</em>

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Consider the functions f(x) = 12^x and g(x)= -2(12)^x. Which transformations must be applied to function F to produce the graph
maksim [4K]

Answer:

Step-by-step explanation:

g(x) = -2f(x)

Vertical stretch                       by virtue of the factor 2

Reflection over the x-axis      by virtue of the factor -1

5 0
2 years ago
What are three other expressions that are equivalent to 8x-12
Kisachek [45]

Answer:

2(4x-6)

4(2x-3)

8(x-3/2)

Step-by-step explanation:

find all factors of 8 other than 1, you should have 3

divide the whole equation by the factor then multiply by the factor

2(8x-12)/2 = 2(4x-6)

4(2x-3)

8(x-3/2)

3 0
3 years ago
The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there a
Anettt [7]

Answer:

1) The size of the colony after 4 ​days is 6553 mosquitoes

2) After t = 4.9\ days

Step-by-step explanation:

To answer this question you must use the growth formula

N = N_0e ^ {kt}

Where

N_0 is the initial population of mosquitoes = 1000

t is the time in days

k is the growth rate

N is the population according to the number of days

We know that when t = 1 and N_0=1000 then N = 1600

Then we use these values to find k.

1600 = 1000e ^{k(1)}\\\\\frac{1600}{1000} = e ^ k\\\\ln(\frac{1600}{1000}) = k\\\\k = 0.47

Now that we know k we can find the size of the colony after 4 days.

N = 1000e ^ {0.47(4)}\\\\N = 6553\ mosquitoes

To know how long it should take for the population to reach 10,000 mosquitoes we must do N = 10000 and solve for t.

10000 = 1000e ^ {0.47t}\\\\10 = e ^ {0.47t}\\\\ln(10) = 0.47t\\\\t = \frac{ln(10)}{0.47}\\\\t = 4.9\ days

6 0
2 years ago
You need to rent a bowling lane. On Friday nights, you have two options. Option A is a $20 lane rental plus $3 per game. Option
ExtremeBDS [4]

For 5 games, the cost will be equal for each option.

Step-by-step explanation:

Given,

Lane rental of offer A = $20

Per game charges = $3

Let,

x be the number of games.

A(x) = 3x + 20

Lane rental is $35 for maximum 10 games.

B(x) = 35

For the cost to be same;

A(x) = B(x)

3x+20=35\\3x=35-20\\3x=15

Dividing both sides by 3

\frac{3x}{3}=\frac{15}{3}\\x=5

For 5 games, the cost will be equal for each option.

Keywords: function, division

Learn more about functions at:

  • brainly.com/question/10772025
  • brainly.com/question/10879401

#LearnwithBrainly

6 0
2 years ago
The expression cos(A-B) - cos(A+B) is equal to
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Cos (A-B) - cos (A+B) 
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=2sinAsinB

Ans: 4
6 0
2 years ago
Read 2 more answers
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