Use the image to answer the question.
An illustration shows two school crossing signs labeled Figure A and Figure B. The signs are pentagons. A silhouette of a walking man and woman are centrally located on the signs. Starting at the bottom left vertex of both figures, the vertices are labeled A, B, C, D, and E. A line inside Figure A connects the vertices B and D. A vertical perpendicular line extends down from the top vertex C to the base side A E. Lines inside Figure B connect the vertices A and C, B and D, and C and E.
Select the correct decomposition into triangles of the sign shaped as a pentagon.
Choose 1 for Figure A, 2 for Figure B, or 3 for both Figure A and Figure B.
(1 point)
3 for both Figure A and Figure B.
Use the image to answer the question.
An illustration of a hendecagon with the vertices labeled upper A, upper B, upper C, upper D, upper E, upper F, upper G, upper H, upper I, upper J, and upper K clockwise from the top.
Find the sum of the interior angles of a hendecagon (11-sided polygon).
(1 point)
The sum of the interior angles of a hendecagon is
°.
The sum of the interior angles of a hendecagon (11-sided polygon) can be calculated using the formula:
Sum of interior angles = (n – 2) * 180 degrees
where n is the number of sides of the polygon.
Substituting the value n = 11 for a hendecagon into the formula, we get:
Sum of interior angles = (11 – 2) * 180 degrees
= 9 * 180 degrees
= 1620 degrees
Therefore, the sum of the interior angles of a hendecagon is 1620 degrees.
If triangle DEF has sides measuring 50, 40, and 32, is the triangle a right triangle? If it is a right triangle, answer with the number 90. If it is not a right triangle, answer with the number 0.(1 point)
To determine if triangle DEF is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Let's calculate:
50^2 = 2500
40^2 = 1600
32^2 = 1024
If triangle DEF is a right triangle, the sum of the squares of the two shorter sides (1600 and 1024) should be equal to the square of the longest side (2500).
1600 + 1024 = 2624
Since 2624 is not equal to 2500, triangle DEF is not a right triangle.
Therefore, the answer is 0.
If a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth, if necessary.(1 point)
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To find the length of the other leg of a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Let's denote the length of the other leg as "x". We are given that one leg has a length of 12 and the hypotenuse has a length of 16.
According to the Pythagorean theorem:
12^2 + x^2 = 16^2
Simplifying the equation:
144 + x^2 = 256
Subtracting 144 from both sides:
x^2 = 256 - 144
x^2 = 112
Taking the square root of both sides:
x = √112
x ≈ 10.6
Therefore, the length of the other leg is approximately 10.6 units.
Use the image to answer the question.
An illustration shows a square with smaller squares representing baseball plates on the top left, top right, and bottom right vertices. The bottom left vertex has a pentagon that represents home plate. A stick figure is located on the top of the square and the measurement from the right vertex to the stick figure is labeled 30 feet. A dashed diagonal line runs from the stick figure to the inner right side of the square, forming the hypotenuse of a triangle. The top right side of the square forms the right angle of the triangle and is marked with a right angle symbol. The outer right side of the square is labeled 90 feet.
A shortstop is standing in the base path between second and third base when she fields the ball. She is 30 feet from second base and needs to make the throw to first base. Assuming the field is square, how far does she need to throw the ball? Round your answer to the nearest tenth.
(1 point)
feet
Based on the information provided, we can infer that the square represents the playing field, with the smaller squares representing baseball plates.
The shortstop is standing in the base path between second and third base, which means she needs to throw the ball to first base. From the given information, we know that she is 30 feet from second base and the distance from the right vertex to the stick figure (representing the shortstop) is 30 feet.
Since the field is square, and the right side of the square is labeled as 90 feet, we can determine that each side of the square is equal to 90 feet.
To find the distance the shortstop needs to throw the ball, we need to calculate the length of the diagonal line (hypotenuse) of the triangle formed by the stick figure, the right side of the square, and the dashed diagonal line.
Using the Pythagorean theorem, the formula for finding the length of the hypotenuse is:
hypotenuse^2 = leg1^2 + leg2^2
In this case, the length of the right side of the square (leg1) is 90 feet, and the distance from the right vertex to the stick figure (leg2) is 30 feet.
hypotenuse^2 = 90^2 + 30^2
hypotenuse^2 = 8100 + 900
hypotenuse^2 = 9000
Taking the square root of both sides to solve for the hypotenuse:
hypotenuse ≈ √9000
hypotenuse ≈ 94.9 feet
Therefore, the shortstop needs to throw the ball approximately 94.9 feet to reach first base.