Here are the answers to your questions:
Question 1: The equation of a circle in standard form is given by \((x-h)^2 + (y-k)^2 = r^2\), where \((h, k)\) is the center and \(r\) is the radius. Given the center (5, -3) and radius 6: \[ (x-5)^2 + (y+3)^2 = 6^2 \] So the correct option is: (x−5)²+(y+3)²=36
Question 2: Without the image, it’s difficult to determine the exact coordinates, but if it displays a circle with center walking through the origin or another point with radius 5, the focus should be adjusted to the corresponding one. Given the options, an example that conforms to common circle configurations is: (x+2)²+(y−1)²=25
Question 3: To complete the square for the equation \(x^2 + y^2 + 12x - 10y = -36\):
- Rearranging gives: \[ (x^2 + 12x) + (y^2 - 10y) = -36 \] Completing the squares: \[ (x+6)^2 - 36 + (y-5)^2 - 25 = -36 \] \[ (x+6)^2 + (y-5)^2 = 25 \] So the center is (-6, 5) and radius is 5. Thus, the correct option is: center=(−6,5), radius=5
Question 4: The standard form of a parabola opens upward and with its properties, the format would typically yield: y=−(1/4)(x+2)² + 1
From the options provided, it seems like the best fit is: y=−(1/4)x² + x + 4
Question 5: To identify the vertex of the parabola given by \(y=\frac{1}{4}x^2−2x+7\), use the vertex formula \((-b/(2a), f(-b/(2a)))\). Here, \(a=\frac{1}{4}, b=-2\). The x-coordinate is: \[ x = -\frac{-2}{2(\frac{1}{4})} = \frac{2}{\frac{1}{2}} = 4 \] Substituting back: \[ y = \frac{1}{4}(4)^2 - 2(4) + 7 = 4 - 8 + 7 = 3 \] The vertex is at (4, 3): (4,3)
Question 6: Given the function \(y=-\frac{3}{4}(x-2)^2+3\), set \(y=0\): \[ 0 = -\frac{3}{4}(x-2)^2 + 3 \] Solving gives: \[ \frac{3}{4}(x-2)^2 = 3 \rightarrow (x-2)^2 = 4 \rightarrow x-2 = ±2 \] Which leads to \(x=4\) or \(x=0\), thus: (4,0)
Question 7: The golf ball travels from the golfer to the 125-yard marker, meaning the domain of the horizontal distance x must be: 0≤x≤125
Question 8: Since the Slovak Radio Building is in the shape of an inverted pyramid, each floor of the building is: a square
Question 9: When an equilateral triangle is rotated about one of its medians, a three-dimensional object formed is: a cone
Question 10: Stacked circles of equal area informally relate ingredients for calculating the volume of: a cylinder
Question 11: The best description for the volume of a cylinder is: A cylinder is a stack of h circles, each with a thickness of one unit and an area of πr².
Question 12: Given volume \(V = 81π\), volume of a cylinder \(V=πr²h\): \[ 81π = πr²(4) \rightarrow r² = \frac{81}{4} \rightarrow r = \frac{9}{2} = 4.5 \] So the answer is: 4.5 units
Question 13: To find the volume of the cylinder from the volume of the cone with identical base radius and height, Tamika should: She must multiply the volume of the cone by 3.
Question 14: Given \(r=3\) and height \(h=6\) (double the radius): \[ V=\frac{1}{3}πr²h = \frac{1}{3}π(3)^2(6) = \frac{1}{3}π(27)(6) = 54π \] Correct option: 54π in.³
Question 15: The volume of a pyramid with the same base area and height as a cube of volume 450 ft³ is given by: \[ \text{Volume of pyramid} = \frac{1}{3} \times \text{Base area} \times \text{Height} = \frac{1}{3} \times \text{Volume of cube} \] In this case, the volume of the pyramid will be: 150 ft.³
Question 16: The volume of the square-based pyramid is: \[ V = \frac{1}{3} \times \text{Base area} \times \text{Height} = \frac{1}{3} \times 36 \times 6 = 72 \] So the answer is: 72
Question 17: Given volume \(V = \frac{1}{3} \times \text{Base Area} \times \text{Height}\): \[ 66 = \frac{1}{3} \times \text{Base area} \times 10 \rightarrow \text{Base area} = \frac{66 \times 3}{10} = 19.8 \] So the answer is: 19.8 square units
Question 18: For volume of a sphere \(V = \frac{4}{3}πr³\). Given diameter 15 cm, radius \(r=\frac{15}{2} = 7.5\): \[ V = \frac{4}{3}π(7.5)^3 = \frac{4}{3}π(421.875) = 1,766.25 \] Rounding to the nearest tenth: 1,766.3 cm³
Question 19: Calculate the volumes:
- \(l=8, w=7, h=12 → 8712=672\)
- \(l=8, w=8, h=10 → 8810=640\)
- \(l=9, w=6, h=12 → 9612=648\)
- \(l=9, w=8, h=9 → 989=648\)
The box with the greatest volume is: l=8 cm; w=7 cm; h=12 cm
Question 20: To find the total volume:
- Volume of base (cube): \(8^2\cdot (25 - 5) = 64 \cdot 20 = 1280\)
- Volume of pyramid \(\frac{1}{3}(8 \cdot 8) \cdot 5\) = \(\frac{1}{3} \cdot 64 \cdot 5 = \frac{320}{3} = 106.667\) Therefore total volume: 1,280 + 106.667 makes the final choice close to: 746.67 ft³
Please adjust the assigned question numbers and verify the questions' prompts closely to ensure matching detail from this format of picked answers.