An isosceles triangle has sides of length 17cm, 17cm and 16cm. find the area of

Step-by-step explanation:

The area of an isoceles triangle is:

A = base x height / 2

The base is the unequal side in the isosceles triangle.  You have to calculate the height using the Pythagorean Theorem.

Since two side are equal in length, if you draw a vertical lined from where these two sides meet and bisect the base, you will create two right triangles.

So a² + b² = c² where c is the hypotenuse of the right triangle.  This hypotenuse is also the two equal sides of the isosceles triangle.  They told you the length of the base but you need to divide that in half since your line bisected the base.

So now you know one side of the right triangle is 8cm which is half of 16cm.  You also know the hypotenuse is 17cm.  Solve the Pythagorean Theorem for the other side and that will give you the height of your bisecting line.

8² + b² = 17²  OR  64 + b² = 289

Solve for b

b² = 289 - 64  OR  b² = 225  and finally    b =  which is 15

So now you can calculate the area of the triangle:

A = 16 x 15 / 2   or   240 / 2  which is   120

So the area is 120 cm²

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.