At age 12 patrick weighed 43 kg; at age 14 he weighed 50 kg. patrick’s age and weight are related. a) find a linear equation relating patrick’s weight to his age b) use your equation to find out patrick’s age when he weighed 38kg

A) The equation relating Patrick’s weight to his age is y = 7/2 x + 1

B) The Patrick's age is 10.57 years when he weighed 38 kg

Step-by-step explanation:

* Lets explain how to solve the problem

- The slope of the line whose end points are (x1 , y1) and (x2 , y2) is

- The form of the linear equation is y = mx + c, where m is the slope of

 the line and c is the y-intercept

- The y-intercept means the line intersect the y-axis at point (0 , c)

* Lets solve the problem

- At age 12 Patrick weighed 43 kg

- At age 14 he weighed 50 kg

- Represent the age by x and the weight by y

∴ There are two points on the line which represents the relation

   between the age and the weight of Patrick

∵ (12 , 43) and (14 , 50) belong to the equation relating Patrick’s

  weight to his age

A)

- Lets find the equation

∵ (x1 , y1) is (12 , 43) and (x2 , y2) is (14 , 50)

∴ x1 = 12 , x2 = 14 and y1 = 43 and y2 = 50

∴

∵ y = mx + c

∴ y = 7/2 x + c

- To find c by substitute x and y in the equation by the coordinates

 of one of the 2 points

∵ 43 = 7/2 (12) + c

∴ 43 = 42 + c

- Subtract 42 from both sides

∴ c = 1

∴ The equation is y = 7/2 x + 1

* The equation relating Patrick’s weight to his age is y = 7/2 x + 1

B)

∵ The weight of Patrick is 38 kg

- That means y = 38

∵ y = 7/2 x + 1

∴ 38 = 7/2 x + 1

- Subtract 1 from both sides

∴ 37 = 7/2 x

- Divide both sides by 7/2

∴ x = 37 ÷ 7/2 = 10.57

∴ The Patrick's age is 10.57 years when he weighed 38 kg

look at photo

18 units²

step-by-step explanation:

first let's find altitude bd using the distance formula

d = √((y₂ - y₁)² + (x₂ - x₁)²)

bd = √((0 - -3)² + (0 - 3)²)

bd = √18

given the placement of points a and c, we can denote that point d bisects segment ac.

we will call ac the base.

using the distance formula

ac = √((0 - 6)² + (-6 - 0)²)

ac = √72

knowing our base and our height, we can plug these into our triangle area formula

area = (b * h)/2

area = (√18 * √72) / 2

area = (√1296) / 2

area = 36 / 2

area = 18 units²