this is the definition of it:
In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
Answer:
The feasible region is unbounded which is the shaded portion in the graph.
Step-by-step explanation:
Given that, the number of hours Jessie works as a teacher and tutor is y and x respectively, which can't be negative.
So, 
y\ge0\;\cdots(ii)
She works at least 36 hours a week.


She works as a teacher for al least twice the number of hours she works as a tutor.

The boundary of the inequalities from equations (i), (ii), (iii), and (iv) are
and
.
The feasible region is the shaded portion which is the unbounded region as shown in the graph. Any point P(x,y) from the feasible region will satisfies all the constraints.
Answer:
D
Step-by-step explanation:

n+4=32
n=28
Answer:
The ratio of the circumference to its diameter remains the same.
Step-by-step explanation:
Given,
diameter of circle = 6 inch
diameter is doubled.
New diameter of circle = 2 x 6 = 12 inch
We know that,
The Circumference of a circle is 2 π r or π d where r is the radius of the circle and d is the diameter of the circle.
Circumference of the circle when the diameter is 6 inches.
C₁ = 6π
Ratio of circumference to diameter
Ratio = 
Ratio = π
When the diameter is 12 inches
C₂ = 12 π
Ratio of circumference to diameter
Ratio = 
Ratio = π
Now, the correct statement is the ratio of the circumference to its diameter remains the same if the diameter is doubled.
The length of the AC is x^2 + 4x - 12.
<h3>What is a parallelogram?</h3>
That quadrilateral in which opposite sides are parallel is called a parallelogram.
Thus, a parallelogram is always a quadrilateral but a quadrilateral can or cannot be a parallelogram.
Given :
In Parallelogram ABCD, diagonals AC and BD intersect at point E.
such that
AE = x^2 - 12,
CE = 4x
We know that the diagonal of a parallelogram bisect each other.
x^2 - 12 = 4x
x^2 - 4x - 12= 0
(x-6)(x-2) = 0
Hence, the value of x = 6, 2.
AC = AE + CE = x^2 + 4x - 12.
The length of the AC is x^2 + 4x - 12.
Learn more about Parallelogram ;
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