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Q:
6- Si se aplica una rotación respecto del origen sobre un punto \( \mathbf{M}\left(\mathbf{1 , 6 )}\right. \) en un ángulo dé \( 90^{\circ} \) en sentido antihorario, ¿Cuál es el punto que se obtiene como imagen? a) \( M^{\prime}(-6,1) \) b) \( M^{\prime}(1,-6) \) c) \( M^{\prime}(-1,-6) \) d) \( M^{\prime}(6,-1) \)
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7. Efectúe una rotación de ejes para eliminar el término \( x y \) y trace la gráfica de la cónica [videos gula: https://youtu.be/WgY7Aktr4XY?si=rwBXUSJj1UBlQgMH; https://youtu.be/x9PSF3cRfMI?si=J-Ixvx6mm2LCbrLW; https://youtu.be/j1MoHx5- Ho8?si=wzTUxU zHgmnrBEt; https://youtu.be/qotu-p7tWDUPsi=wWOLb7rsiVFOd16H https://youtu.be/KB7hFoUmRwc?si=zLET3nfXvDmpNv8A] a. \( x y+1=0 \) b. \( 5 x^{2}-2 x y+5 y^{2}=24 \) c. \( x^{2}+2 \sqrt{3} x y+3 y^{2}-2 \sqrt{3} x+2 y+16=0 \)
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14 A line passes through the origin and the point \( (3,6) \). Which point is also on the line? \( \begin{array}{ll}\text { (*) }(6,3) & \text { (C) }(2,4) \\ \text { (B) }(4,6) & \text { (D) }(1,4)\end{array} \)
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6- Si se aplica una rotación respecto del origen sobre un punto \( M(\mathbf{M}, \mathbf{6}) \) en un ángulo de \( 90^{\circ} \) en sentido antihorario, ¿Cuál es el punto que se obtiene como imagen? a) \( M^{\prime}(-6,1) \) b) \( M^{\prime}(1,-6) \) c) \( M^{\prime}(-1,-6) \) d) \( M^{\prime}(6,-1) \) 7-- Si se aplica una rotación respecto del origen sobre un punto \( \mathbf{P}(-3,5) \) en un ángulo de \( 180^{\circ} \) en sentido horario, ¿Cuál es el punto que se obtiene como imagen?
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11 A line passes through the origin and the point \( (3,6) \). Which point is also on the line?
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The ratio of a circle's radius to its diameter is always 1 to 2 . In math class, Russell uses his compass to draw a circle with a radius of 6 centimeters. What is the diameter of the circle Russell drew? centimeters
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6. ¿Cuáles ángulos te permiten generar un triángulo? A. \( 20^{\circ}, 10,60 \) B. \( 50^{\circ}, 20^{\circ}, 20^{\circ} \) C. \( 100^{\circ}, 50^{\circ}, 29^{\circ} \) D. \( 120^{\circ}, 30^{\circ}, 30^{\circ} \)
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Q. The rectangular sandbox at the local community park has a width of 24.5 meters and its length is 31.7 meters. What is the perimeter, in meters, of the rectangular sandbox?
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8. A bathtub has a perimeter of 22 feet. If the bathtub is 4 feet wide, how long is the bathtub?
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7. A chalkboard has an area of 36 square feet. If the chalkboard is 9 feet long, what is the height of the chalkboard?

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