Katrina needs to cut down a big mango tree that's in the way of the foundation of her Grandma's house foundation.

• She calls DaKine Tree Trimmers and they tell her the cost to remove the tree is $300 if

the tree is less than 30 feet tall. The cost will be more expensive ($2,000) if the tree is

taller than 20 feet.

• The tree looks pretty tall to Katrina, but how can she tell if it's more than 30 feet tall?

Katrina wants to use shadows on the ground and the fact that she is 5 feet tall to help her

determine if the mango tree is taller or shorter than 30 feet.

• Katrina develops a plan to collect some data and use her knowledge of similar triangles:

a. She determines that at a specific time during the day, she can stand a few feet

away from the tree so that her shadow lies directly on the tree’s shadow and both

shadows end at the same point on the ground

b. At that specific moment, Katrina’s friend determi

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is

i dont know

step-by-step explanation:

let x and 400 - x be the two numbers.  

==> 0.80x + 0.85(400 - x) = 400 - 68 from the statement of the problem.  

< ==> 0.80x + 0.85(400 - x) = 400 - 68  

==> 340 - 0.05x = 332  

< ==> -0.05x = -8 ==> x = 160, the first number ==> 400 - x = 240, the second number.