Please help! Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact valu
e in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problems b), c), and d) are involving portions of a square. Please answer with your work, explanation, and answers to perimeter and area to the shaded region.
1 answer:
Answer:
Step-by-step explanation:
Given that the figure is made up of portion of a square and a semicircle, we have;
BC ≅ AB = 6 cm
The area of semicircle BC with radius BC/2 = 3 is 1/2×π×r² = 1/2×π×3² = 4.5·π cm²
Triangle ABC = 1/2 × Area of square from which ABC is cut
The area of triangle ABC = 1/2×Base ×Height = 1/2×AB×BC = 1/2×6×6 = 18 cm²
The area of the figure = The area of semicircle BC + The area of triangle ABC
The area of the figure = 4.5·π cm² + 18 cm² = .
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Answer:
x = 4
Step-by-step explanation:
A trapezium is a quadrilateral (has four sides and four angles) with one pair of parallel sides. A trapezium is said to be isosceles if the bases are parallel, the two other sides known as the legs are equal and diagonals of the trapezium are equal to each other.
In trapezoid ABCD, BC and AD are the diagonals.
Hence BC = AD (property of isosceles trapezoid)
9x + 1 = 12x - 11
Simplifying:
12x - 9x = 1 + 11
3x = 12
Dividing both sides by 2:
x = 4
The true statement is:
"The range of the function is all real numbers less than or equal to 9."
<h3>Which statements are true?</h3>
Here we have the quadratic function:
And we want to see which of the given statements are true.
The first one is:
"The domain is al real numbers less than or equal to -2"
This is false, for all quadratic functions the domain is the set of all real numbers (unless the domain is defined).
The second statement is:
" The domain of the function is all real numbers less than or equal to 9."
Also false
Third one:
" The range of the function is all real numbers less than or equal to −2"
The range of a quadratic function with a negative leading coefficient will be the set of all the values smaller than the y-value of the vertex.
In this case, the quadratic function is:
So the vertex is at:
Then the y-value of the vertex is:
So the range is the set of all real numbers less than or equal to 9.
So the above statement is false, and the final one:
"The range of the function is all real numbers less than or equal to 9."
Is the true statement.
If you want to learn more about quadratic functions:
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