course Mth152 r???????????????E?assignment #020020. `query 20
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16:04:03 query 9.1.36 Ray MO U ray OM **** How do you express the intersection of the two rays?
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RESPONSE --> The elements would be M O. They are common in both lines.
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16:05:29 ** STUDENT SOLUTION: The intersection of the two rays consists of the elements common to both sets, which would be MO. However, a union symbol is used in the question and a union is composed of all the elements found in atleast one of the two sets, which would also be MO. **
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RESPONSE --> Correct
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16:09:00 **** query 9.1.54 lines SR and TP intersecting at Q **** What are the names of the pairs of vertical angles for this figure?
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RESPONSE --> The pairs of vertical angles are angles SQT and PQR and the angles SQP and RQT
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16:09:21 ** STUDENT SOLUTION: The vertical angles are SQT and PQR; SQP and TQR **
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RESPONSE --> Correct
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16:16:51 **** query 9.1.60 5x - 129 vert with 2x - 1 **** What is the value of x and how did you obtain it?
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RESPONSE --> 5x-129 = 2x-21 5x-2x = 21-129 3x=108 x=36 5(36)-129 = 51 2(36)-21 = 51 The measure of the angles is 51 degrees.
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16:17:15 *&*& Starting with 5x - 129 = 2x - 21 to get 3x - 129 = -21. Add 129 to both sides to get 3x = 108. Divide both sides by 3 to get x = 36. To check substitute 36 in for x in the equation and simplify, getting 51 = 51.
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RESPONSE --> Correct.
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16:21:31 **** What equation did you solve to obtain x, and how did you get the equation?
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RESPONSE --> 5x-129=2x-21 The equations are provided in the book as the measure of the angles. I simply solved for x and then substituted the value of x in the equations.
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16:22:20 Since the angles are vertical angles, they are equal to eachother, therefore, I set them up to be equal to eachother and then solved.To check myself, I then substituted my answer in for x on both sides of the equation to make sure they were equal.
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RESPONSE --> Correct. The angles are equal to each other.
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16:43:16 **** query 9.1.72 complement 10 deg less that 1/5 of suppl **** What is the measure of the angle and how did you get it?
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RESPONSE --> The measure of the angle is 80 degrees. The equation is 1/5 (180-x)-10 = 90-x. 36-1/5x-10 = 90-x 26 -1/5x =90 - x -1/5x = 64 -x x-1/5x =64 4/5 x = 64 5/4 *4/5 x = 64 * 5/4 x=320/4 x= 80
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16:46:36 ** Let x be the degree measure of the angle. Then the supplement is 180 ?x; 10 deg less than 1/5 the supplement is 1/5(180 - x) ?10. The complement is 90 - x. So the equation is 90 - x = 1/5(180 - x) ?10. Multiplying both sides by 5 we get 450 ?5 x = 180 ?x ?50 so that 450 ?5 x = 130 ?x. Adding x ?450 to both sides we get -4x = -320 so thatx = 80. The complement of 80 deg is 10 deg. The supplement of 80 deg is 100 deg; 1/5 the supplement is 1/5 * 100 deg = 20 deg, so the complement 10 deg is 10 deg less than the supplement 20 deg. **
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RESPONSE --> I did not finishing solving the problem. I found the 80 degrees and I see how you derived at the rest.
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16:47:09 **** What equation did you solve to obtain the measure of the angle?
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RESPONSE --> 1/5(180-x) -10= 90-x
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16:47:30 Student Response: I determined which equations represented the degree measure of the angle, complement, and supplement. I then substituted those in the equation using the worded problem. 90 - x (complement) = 10 (10 less than) - 1/5 (1/5 of the supplement) 180 - x (supplement).
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RESPONSE --> Correct
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16:47:39 **** Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> None.
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16:47:52 The query was basically what I expected it to be.
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RESPONSE --> Correct
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K?????|?????assignment #021 021. `query 21 Liberal Arts Mathematics II 03-28-2009
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17:49:43 Liberal Arts Mathematics II
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RESPONSE --> Correct
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17:49:50 Asst # 21
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RESPONSE --> Correct
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17:49:58 03-25-2003
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RESPONSE --> Date
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17:53:21 **** query 9.2.6 sq must be rhombus **** Is the statement true or false and why?
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RESPONSE --> True. A rhombus is parallelogram and has sides with all equal lengths.
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17:54:01 ** This statement is true. A parallelogram is a quadrilateral with two pairs of parallel sides and a rhombus is a parallelogram with all sides having equal length. All sides of a square have equal length. If a square were not a rhombus then all sides would not be of equal length. It is not true that a rhombus must be a square. The angles of a rhombus do not have to be right angles, while the angles of a square do. **
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RESPONSE --> Correct. Good point on the square and right angels.
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17:57:06 **** query 9.2.10 parallelogram must be rect and rect must be parallelogram **** Is the statement true or false and why?
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RESPONSE --> False. Parallelogram does not have right angles for the corners but rectangle does.
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17:59:19 ** A rectangle is a parallelogram but a parallelogram is not necessarily a rectangle, so the statement is false. **
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RESPONSE --> I see. A rhombus is a parallelogram also and is not a rectangle.
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18:02:21 **** query 9.2.18 rb with 4 loops **** Is the curve simple, closed, both or neither?
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RESPONSE --> It is closed but not simple because it crosses itself .
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18:02:43 This is only a closed curve because its starting point and ending point are the same and it can be drawn without lifting the pencil from the paper. It is not simple because some points are passed through twice.
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RESPONSE --> Correct
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18:05:42 **** query 9.2.24 ellipse **** Is the region inside the curve convex or not, and why?
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RESPONSE --> Convex. Line segment would fit inside it completely.
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18:06:00 The region inside is convex because the line segment connecting any two points is completely inside the figure.
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RESPONSE --> Correct
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18:12:04 **** query 9.2.48 A 30 deg more than B which equals C **** What are the measures of the three angles?
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RESPONSE --> angle A is 30+x angle B is x angle C is x 30+x+x+x = 180 3x=180-30 3x =150 x=50 30+50 +50+50 =180
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18:12:29 Angle A + Angle B + Angle C = 180 deg. If x is the degree measure of B then angle A has measure x + 30 degrees and angle C has measure x degrees. So we have x + x +30 + x = 180 3x + 30 = 180 3x = 150 x = 50 Angle B and Angle C are both equal to x, i.e., to 50 deg. Angle A = 50 deg + 30 deg = 80 deg To check, 80 + 50 + 50 = 180.
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RESPONSE --> correct
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18:13:10 **** What equation did you solve to obtain your answer, and how did you use the solution to determine all angles?
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RESPONSE --> 30+x+x+x =180
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18:13:32 Student Response: The definition for the angle sum of a triangle says the sum of the measures of the angles of any triangle is 180 deg. I used x to represent angles B and C and x + 30 to represent angle A since it is 30 deg higher than the other two. All this equaled 180 deg. I solved for x to get the degree measure of angles B and C and then added 30 on to x to get the degree measure for angle A.
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RESPONSE --> Correct
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18:13:40 **** Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> None.
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18:13:48 There were no really big surprises.
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RESPONSE --> No.
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{???????|????w?|?assignment #022 022. `query 22 Liberal Arts Mathematics II 03-28-2009
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18:40:00 **** query 9.3.12 area of parallelogram **** What is the area of the given parallelogram and how did you obtain it?
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RESPONSE --> A= bh A = 4*2 1/2 A = 10 in
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18:40:17 The formula for the area of a parallelogram is A = bh ( area = base times height) From the figure the base is 4 and the altitude is 2.5 so we have A = 4 * 2.5 = 10. The area is 10 in.
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RESPONSE --> Correct
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18:43:03 **** query 9.3.18 area of trapezoid **** What is the area of the given trapezoid and how did you obtain it?
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RESPONSE --> A= 1/2 h(b+B) A= 1/2 (3) (4+5) A= 1.5 * 9 A= 13.5 cm
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18:43:44 The formula for finding the area of a trapezoid is A = 1/2h ( b + B ) h = 3, b = 4, B = 5 A = 1/2 (3) (4 + 5) A = 1/2 (3) (9) A = 1/2 (27) A = 13.5 The area is 13.5
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RESPONSE --> Correct
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18:47:32 **** query 9.3.24 dim of rect with lgth 20 more than wdth and perimeter 176 **** What are the dimensions of the rectangle?
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RESPONSE --> P= 2l+2w P=2(20)+2(176) P= 40+352 P=392 in
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18:52:39 ** The perimeter of a rectangle is P = 2l + 2w, where l and w are length and width. From the given information Length = 20 + w Perimeter = 176 This gives us the equation 176 = 2 (20 + w) + 2w which we proceed to solve for w: 176 = 40 + 2w + 2w by the Distributive Law. Simplifying we get 176 = 40 + 4w Subtract 40 from both sides to get 136 = 4w Divide both sides by 4 to get w = 34 l = w + 20 so l = 34 + 20 = 54 We have Length = 54 and Width = 34 Checking, we have perimeter = 2 * length + 2 * width so we should have 176 = 2(54) + 2(34). The right-hand side does give us 176 so the solution checks out. **
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RESPONSE --> I see. I missed some of the information in the problem and therefore solved for the incorrect thing. I went back and reworked it to get the width instead of the perimeter.
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18:59:05 **** query 9.3.48 trap bases x, x+4 alt 3 area 30 **** What is the value of x?
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RESPONSE --> A= 1/2 h(b+B) 30 = 1/2 (3) (x+x+4) 30 = 1.5 (2x+4) 30 = 3x+6 24=3x 8=x
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18:59:42 The formula for finding the area of a trapezoid is A = 1/2h ( b + B). We have A = 30 h = 3 B = x + 4 b = x 30 = 1/2(3) ( x + x+4) 30 = 1.5 ( x+x+4) 30 = 1.5x + 1.5x + 6 30 = 3x + 6 Subtract 6 from both sides 24 = 3x Divide both sides by 3 x = 8 The answer is 8.
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RESPONSE --> Correct
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19:08:10 **** query 9.3.54 $60 to paint ceiling of 9 x 15 rm, how much to paint if dimensions 18 x 30 **** What is the cost for the second ceiling? **** How did you use the results of exercise 53 to obtain your result?
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RESPONSE --> The area of 9*15 room is 135 sqft . The area of 18* 30 room is 540 sqft . The 18*30 ft room is 4 times as much sqft so $60*4 would be $240.
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19:08:35 The sides doubled from 9 ft. to 18 ft. and from 15 ft. to 30 ft. When the sides are doubled the area increases by a factor of 4. So the cost is $60 * 4 = $240 The cost for the second ceiling is $240
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RESPONSE --> Correct
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19:15:20 **** query 9.3.60 triangle alt 9 on top of 10 x 4 rect; parallelogram alt 3 under **** What is the area of the given figure and how did you obtain your result?
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RESPONSE --> First we find the area of the triangle A= 1/2bh = 1/2 (10)(9) = 1/2(90) = 45 Second we find the area of the rectangle A = lw = (10)(4) = 40 Third we find the area of the parallelogram A=bh = (10)(3) = 30 Fourth we add these together to get the total area 45+40+30 = 115
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19:15:49 ** Here's a solution by a student from a previous semester: I found the area of each figure and then added those three results together. Area of Triangle = 1/2bh A = 1/2 (10) (9) A = 1/2 (90) A = 45 Area of Rectangle = lw A = (10) (4) A = 40 Area of Parallelogram = bh A = (10) (3) A = 30 45 + 40 + 30 = 115 Area = 115 **
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RESPONSE --> Correct
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19:39:12 **** query 9.3.67 26 m diam circle inscribed in sq; area outside circle **** What is the area of the shaded region and how did you obtain it?
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RESPONSE --> find area of circle - a=3.14*r^2 = 3.14* 13^2 = 3.14*169 = 530.66 Then find area of square- a=s^2 =26^2 = 676 next subtract shaded area from the rest 676 - 530.66 = 145.34 m ^2
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19:39:34 ** The circle has diameter 26 m so its radius is 13 m and its area is A = pi r^2 = pi * (13 m)^2 = 169 pi m^2 = 531 m^2. The area of the square is the square of its side A = (26 m)^2 = 676 m^2. The area of the shaded region is the difference } 676 m^2 - 531 m^2 = 145 m^2. **
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RESPONSE --> Correct
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19:54:14 **** query 9.3.72 10, 12, 14 in pizzas for 11.99, 13.99, 14.99 **** Which pizza is the best buy and how did you
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RESPONSE --> The best deal is the 14 in pizza. 10 in A=3.14(5)^2=78.5 11.99/78.5 = .15cents 12 in A=3.14(6)^2=113.04 13.99/113.04 = .12cents 14 in A=3.14(7)^2=153.36 14.99/153.36= .10cents
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19:54:28 obtain your result?
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RESPONSE --> Shown previously
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19:55:06 Student Solution: The thickness is about the same for all three pizzas so the amount of pizza can be measured by its area. I therefore found the area of each. A = 3.14 * r^2 and radius is 1/2 the circumference. So we get areas A = 3.14 (5)^2 = 78.5 A = 3.14 (6)^2 = 113.04 A = 3.14 (7)^2 = 153.86 I then divide the prices and these answers to get the price per square inch. $11.99 / 78.5 = 15.3 $13.99 / 113.04 = 12.4 $14.99 / 153.86 = 9.7 Since 9.7 is the least, and since this is the result for the 14 inch pizza, the 14 in. pizza for $14.99 is the best buy.
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RESPONSE --> Correct. I rounded on out to the whole cents.
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19:55:13 **** Query Add comments on any surprises or insights you experienced as a result of this assignment.
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RESPONSE --> none
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19:55:18 There weren't any big surprises.
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RESPONSE --> no
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