(a) Find area of shaded part of a circle in an 8cm x 8cm square with 4 shaded corners.
(b) Find area of shaded part with no additional information provided.
Describe the possible lengths of a rectangular parking lot with a perimeter of 420 ft and an area of at least 9800 sq ft. The length is between □ and □ feet.
Find the lengths of two chords intersecting in a circle, given that one chord has segments of length 21 and 28, and the other chord has segments in a 3:1 ratio.
Given point P(2∣3∣4). a) Project P parallel to x2-axis onto x1x3 plane, obtain P′ coordinates. b) Project P onto x1x2 and x2x3 planes, obtain P′′ and P′′′ coordinates. c) Reflect P across x1x3 plane, give coordinates of reflected point.
Three baseball players are playing catch. Find the distance Franco needs to throw the ball to reach Elijah, given their positions. Round to nearest tenth if needed. 32+52 meters.
Find the coordinates of point B(-4,6) after a dilation of scale factor 2 centered at the origin. A.) B′(−2,3)
B.) B′(−8,−12)
C.) B′(4,12)
D.) B′(−8,12)
Determine if the following statements are always, sometimes, or never true: (a) Two nonintersecting lines are parallel. (b) Two points are collinear. (c) Three collinear points determine exactly one plane.
Find height OI=42 of triangle OAB in a square pyramid. Calculate the area S=122 of triangle OAB and the surface area S′=4(62)+16=642+16 of the square pyramid.
12. Find another point on a line with slope −32 and point A at (−1,−5). 13. A ladder leans against a wall. Its base is 1.5m from the wall, and its top touches the wall 4m above the ground. Find the ladder's slope.
Write the equation of a parabola in vertex form and intercept form, then show they are equivalent. Identify the axis of symmetry from each equation form. Parabola vertex: (2,−9), opens upwards. Vertex form: y=a(x−2)2−9
Intercept form: y=a(x−p)(x−q)
Show equivalence by converting to general form: y=ax2+bx+c The axis of symmetry is given by x=h in vertex form and the average of the x-intercepts in intercept form.
Determine validity of argument using Euler diagram: "All mockingbirds have wings. All wings have feathers. All mockingbirds have feathers." Is this argument valid or invalid?
Determine if the following polygon pairs are always, sometimes, or never similar:
40. two obtuse triangles
41. a trapezoid and a parallelogram
42. two right triangles
43. two isosceles triangles
44. a scalene triangle and an isosceles triangle
45. two equilateral triangles
Find the lengths of the legs of a right triangle where the first leg is 1 cm longer than the second, and the hypotenuse is 6 cm. First Leg: 36−x2+1 cmSecond Leg: 36−x2 cm
Identify the principle that best describes a rose window's repeating pattern around a central point. Options: balance, emphasis, harmony, rhythm, variety.
Andre wants to make an open-top box by cutting out corners of a 22 in x 28 in poster board and folding up the sides. Find the volume V(x) of the box, where x is the side length of the square cutout. Determine the volume when x=6 and the reasonable domain for V.
Determine if JKLM is a parallelogram. Find lengths of JK, LM, JM, KL. Conclude if JKLM is a parallelogram based on side congruence. J(1,−7),K(−4,−5),L(−1,3),M(4,1)
Length of JK:
Length of LM:
Length of JM:
Length of KL:
Is JKLM a parallelogram?
Find the height and width of a 10-gallon aquarium that is 2 inches taller than it is wide, with a length of 23 inches and a volume of 1840 cubic inches. Height: □□ inches
Width: □□ inches
Find the rectangular field dimensions that maximize the enclosed area given 800 feet of fencing to create 3 identical smaller plots. Express answers as reduced fractions.
Find the areas and volumes of a round 11-inch and 8-inch by 10-inch rectangular pan. Determine which has the larger volume. a) Area of round pan: π(11/2)2
Area of rectangular pan: 8×10
b) Volume of round pan: π(11/2)2×2
Volume of rectangular pan: 8×10×2
c) Compare the volumes to determine the larger pan.
Find the amount of wrapping paper needed to cover a 5 in. by 7 in. cylindrical gift box, including the top, bottom, and sides. Use π=3.14. Round to the nearest tenth of a square inch.
Ladder on wall: top slips down as base moves away at 5 m/s. Find (29) rate of top when 5 m from ground, and (30) rate of area change when top is 5 m from ground.