The population data for a certain country are as follows: year 2012 2013 2014 2015 2016 2017 population (millions) 10 10.9 11.7 12.6 13.8 14.9 obtain a function that describes these data. plot the function and the data on the same plot. estimate when the population will be double its 2004 size.

Function is y = 0.974x + 2.086

On 2006, the population will be double its 2004 size.

Step-by-step explanation:

Let x represents the number of years and y represents the population after x years,

Also, suppose reference year is 2004,

Then, the table would be,

x    8        9           10       11        12        13

y   10      10.9        11.7    12.6    13.8      14.9

Since, the value of y is increasing approximately linearly with increasing the value of x,

Thus, a linear function will best describe the given points,

For finding the equation we will follow the following steps,

Step 1 :  Make the table on the excel,

Step 2 : Select the table,

Step 3 : insert the scatter plot ( scatter plot with smooth lines )

Step 4 : choose the option 'add trendiness'

Step 5 : Mark the option 'display equation on the chart'.

By these steps we will get y = 0.974x + 2.086

For 2004, x = 0,

y = 0.974(0) + 2.086

y = 2.086

Hence, the population on 2004 is 2.086 millions,

If y = 4.172,

4.172 = 0.974x + 2.086

2.086 = 0.974x

⇒ x = 2.14168377823 ≈ 2,

Therefore, on 2006, the population will be double its 2004 size.

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

proofs involving isosceles triangles often require special consideration because an isosceles triangle has several distinct properties that do not apply to normal triangles.(more about triangle types) therefore, when you are trying to prove that two triangles are congruent, and one or both triangles, are isosceles you have a few theorems that you can use to make your life easier.

step-by-step explanation:

an isosceles triangle has two congruent sides and two congruent angles. the congruent angles are called the base angles and the other angle is known as the vertex angle. ∠bac and ∠bca are the base angles of the triangle picture on the left. the vertex angle is ∠abc