Question

question 13 (multiple choice worth 2 points) (perimeter and area on the coordinate plane mc) a classroom is rectangular in shape. if listed as ordered pairs, the corners of the classroom are (-12, 18), (-12, -11), (9, 18), and (9, -11). what is the perimeter of the classroom in feet? options: 29 feet, 50 feet, 100 feet, 129 feet. question 14 (multiple choice worth 2 points) (volume of rectangular prisms mc) a coach needs to fill a rectangular container with water to have available for karate practice. if the dimensions of the container are 32 inches by 22 inches by 23.8 inches, what is the maximum amount of water that the rectangular container will hold? options: 18,744.4 in³, 16,755.2 in³, 8,377.6 in³, 3,978.4 in³.

Explanation:

Question 13

Step1: Find length and width

For a rectangle with vertices \((-12,18)\), \((-12,-11)\), \((9,18)\), \((9,-11)\), the length is the difference in \(x\)-coordinates: \(9 - (-12)=21\) feet. The width is the difference in \(y\)-coordinates: \(18 - (-11)=29\) feet? Wait, no, wait: Wait, actually, the distance between \((-12,18)\) and \((9,18)\) is \(|9 - (-12)| = 21\) (length, horizontal), and between \((-12,18)\) and \((-12,-11)\) is \(|18 - (-11)| = 29\) (width, vertical)? Wait, no, perimeter of rectangle is \(2\times (length + width)\). Wait, no, wait, maybe I mixed up. Wait, the \(x\)-coordinates: from \(-12\) to \(9\) is \(21\) units (length), \(y\)-coordinates: from \(-11\) to \(18\) is \(29\) units (width)? Wait, no, perimeter formula is \(P = 2(l + w)\). Wait, but let's recalculate: the horizontal side: distance between \((-12,18)\) and \((9,18)\) is \(9 - (-12)=21\) feet. The vertical side: distance between \((-12,18)\) and \((-12,-11)\) is \(18 - (-11)=29\) feet? Wait, no, that can't be, because then perimeter would be \(2(21 + 29)=100\) feet. Ah, yes! Because \(21 + 29 = 50\), times 2 is 100. So that's the perimeter.

Step2: Calculate perimeter

Perimeter \(P = 2\times (length + width)\). Length \(l = 21\) (from \(x=-12\) to \(x=9\)), width \(w = 29\) (from \(y=-11\) to \(y=18\))? Wait, no, wait, the vertical distance is \(18 - (-11)=29\)? Wait, no, \(18 - (-11)=29\)? Wait, \(18 + 11 = 29\), yes. Then \(l = 21\), \(w = 29\)? Wait, no, maybe I got length and width reversed. Wait, actually, the horizontal distance is \(9 - (-12)=21\), vertical distance is \(18 - (-11)=29\). Then perimeter is \(2\times(21 + 29)=2\times50 = 100\) feet.

Step1: Recall volume formula

Volume of a rectangular prism is \(V = l\times w\times h\), where \(l\), \(w\), \(h\) are length, width, height.

Step2: Substitute values

Given \(l = 32\) in, \(w = 22\) in, \(h = 23.8\) in. So \(V = 32\times22\times23.8\). First, \(32\times22 = 704\). Then \(704\times23.8\). Let's calculate: \(704\times20 = 14080\), \(704\times3.8 = 704\times(3 + 0.8)=2112 + 563.2 = 2675.2\). Then total \(14080 + 2675.2 = 16755.2\) cubic inches.

Answer:

100 feet (corresponding to the option "100 feet")

Question 14