Reflections, rotations, and translations all change the location, but not the size or shape of the parallelogram. Congruence describes the line lengths and angle sizes - all of which will be maintained. Thus, reflections, rotations, and translations will maintain congruence.
All of the options use only reflection, rotation, and translation, so all of these could be the transformation in question.
9514 1404 393
Answer:
120 m²
Step-by-step explanation:
If you divide the isosceles triangle into two right triangles, each has a leg and hypotenuse of 8 and 17, respectively. You may recognize these numbers as part of the Pythagorean triple (8, 15, 17). That recognition tells you the triangle's height is 15 m, so its area is ...
A = 1/2bh
A = 1/2(16 m)(15 m) = 120 m² . . . . triangle area
__
<em>Alternate solutions</em>
Given the three sides, you can find the smallest angle from the Law of Cosines. It will be ...
α = arccos((17² +17² -16²)/(2·17·17)) ≈ 56.144°
Then the area is ...
A = 1/2·ab·sin(C) . . . for triangle with sides a, b, c and opposite angles A, B, C
A = 1/2sin(α)·17·17 = 120 . . . m²
__
Using Heron's formula:
s = (17 +17 +16)/2 = 25
A = √(25(25 -17)(25 -17)(25 -16)) = 5×8×3 = 120 . . . m²
__
If you need to, you can compute the triangle's height from the Pythagorean theorem.
a² +b² = c² . . . . generic Pythagorean theorem equation
8² + h² = 17² . . . with relevant values filled in
h² = 289 -64 = 225
h = √225 = 15
Answer:
y = 9
Step-by-step explanation:
1) Multiply both sides by 3.
3 × 3 = y
2) Simplfiy 3 × 3 to 9.
9 = y
3) Switch sides.
9
Answer: c) 14,871
Step-by-step explanation:
See photo attached - if my work doesn’t make sense I can explain it, just ask (:
Answer:
D
Step-by-step explanation:
C is the square root of B.
