Due today please help important will give brainliest A TALE OF TWO TRANSLATIONS Lacy performs the translation (x, y) → (x + 5, y + 3) to an object in the coordinate plane. Kyle performs the translation (x, y) → (x – 4, y + 2) to the same object after Lacy. What single translation could have been done to achieve the same effect as Lacy and Kyle’s combined translations? Would the result have been different if Kyle did his translation first?

Part A:

Linear function

Part B:

House 1; f(x) = 7595.3·x + 178515

House 2; f(x) = 11,000·x + 179000

Part C:

Yes, there will be a significance difference

The value of house 1 after 30 years is $406,374

The value of house 2 after 30 years is $509,000

Step-by-step explanation:

The given values are

               House 1

Year 1,    186,160

Year 2,   193606.40

Year 3,   201350.66

We see that the prices of the houses have a common difference given as follows;

201,350.66 - 193606.40 = 7744.26,

193,606.40 - 186,160 = 7446.4

Which is fairly constant giving a linear function of the house after a fixed number of years

               House 2

Year 1,    190,000

Year 2,   201,000

Year 3,   212,000

We see that the prices of the houses have a common difference given as follows;

212,000 - 201,000 = 11,000,

201,000 - 190,000 = 11,000

Which is fairly constant

Which is fairly constant giving a linear function of the house after a fixed number of years

Part B:

The function for the first house  is given by the regression formula from regression analysis

Y = a + b·X

Where:

X = Value of the house at Year Y

Y = The year

Which gives;

f(x) = 7595.3·x + 178515

The function for the first house  is given by the arithmetic progression also by regression analysis as follows;

f(x) = 11,000·x + 179000

Part C

The value of house 1 after 30 years = 7595.3×30 + 178515 = $406,374

The value of house 2 after 30 years = 11,000×30 + 179000 = $509,000

Yes, there will be a significance difference between house 2 and house 1 to about 509,000 - 406,374 = $102,626.