Answer:
Part 1)
Part 2)
Step-by-step explanation:
Step 1
Find the length of MD
we know that
The incenter is the intersection of the angle bisectors of the three vertices of the triangle. Is the point forming the origin of a circle inscribed inside the triangle
so
In this problem
------> is the radius of a circle inscribed inside the triangle
we have that
therefore
Step 2
Find the length of DC
we know that
In the right triangle MDC
Applying the Pythagoras theorem
we have
substitute
Answer:
Step-by-step explanation:
Let x = the number of bottles of paint that Carmen can buy
Let y = the number of boxes of colored pencils that Carmen can buy
A bottle of paint costs $2
A box of colored pencils costs $3.50
She can spend no more than $42 on art supplies. This means
She can buy bottles of paint worth 2×x = $2x
She can buy boxes of colored pencils
worth 3.5 × y = $3.5y
Since the total amount she can spend cannot exceed $42, the equation becomes
2x + 3.5y lesser than or equal to 42
This is shown in the attached photo
b) three different solutions to the inequality would be three different possible values that x and y can take. These are
x = 7 while y = 8
x = 10 while y = 6
x = 14 and y = 4
