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Interpret parts of quadratic expressions: word problems

Thousands of Law Degrees Conferred Annually in the United States This figure presents a box plot. The numbers on the horizontal axis are 99 through 4747 in increments of 22. There is a dot approximately above 9.59.5 with a horizontal line segment extending to the right from the dot to the edge of a rectangle approximately above 3030. The rectangle extends from approximately above 3030 to approximately above 39.539.5. There is a vertical line segment in the rectangle above 3636. A horizontal line segment extends from the right edge of the rectangle to a dot approximately above 44.544.5. This figure presents a box plot. The numbers on the horizontal axis are 99 through 4747 in increments of 22. There is a dot approximately above 9.59.5 with a horizontal line segment extending to the right from the dot to the edge of a rectangle approximately above 3030. The rectangle extends from approximately above 3030 to approximately above 39.539.5. There is a vertical line segment in the rectangle above 3636. A horizontal line segment extends from the right edge of the rectangle to a dot approximately above 44.544.5. The box plot depicts the numbers of law degrees (JD or LL.B), in thousands, conferred each year in the United States over a span of 474788 years. No two years had duplicate numbers of degrees conferred. If the next year, there were 474799 thousand degrees conferred, how would that affect the range, mean, and median of the numbers?
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A rectangle has a height of 22 and a width of 5x2−2x+35x^2 - 2x + 3. Express the area of the entire rectangle. Expression should be expanded. An area model for a rectangle with a height of 22 and a width of 5x2−2x+35x^2 - 2x + 3. The rectangle is broken into three rectangles to isolate each term in the width. The first rectangle has a height of 22 and a width of 5x25x^2. The second rectangle has a height of 22 and a width of negative 2x2x. The third rectangle has a height of 22 and a width of 33. An area model for a rectangle with a height of 22 and a width of 5x2−2x+35x^2 - 2x + 3. The rectangle is broken into three rectangles to isolate each term in the width. The first rectangle has a height of 22 and a width of 5x25x^2. The second rectangle has a height of 22 and a width of negative 2x2x. The third rectangle has a height of 22 and a width of 33.
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https://www.ixl.com/math/grade−8-8/checkpoint-systems-of-equations\newline□2 \square 2 \newlineMy IXL\newlineLearning\newlineAssessment\newlineAnalytics\newlineFaith\newlineEighth grade\newlineGG. 1414 Checkpoint: Systems of equations\newlineMFL\newlineYou have prizes to reveal! Go to your game board.\newlineVer en español\newlineQuestions\newlineanswered\newlineMegan has been planting young trees in her garden. One maple tree is 6666 centimeters tall and is growing 88 centimeters per month. One oak tree is 7070 centimeters tall and is growing 77\newline1111\newlinecentimeters per month.\newlineIn a few months, the two trees will be the same height. What will that height be? How long will that take?\newlineThe two trees will both be □ \square centimeters tall in □ \square months.\newlineSubmit\newlineTime\newlineelapsed\newline0000\newline2323\newline2424\newlineHR\newlineMIN\newlineSEC\newlineSmartScore\newlineout of 100100\newline4343\newlineWork it out\newlineNot feeling ready yet? These can help:
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P Quiz 99A The Financial Statements - Personal - Microsoft Edge\newlineACCT250250v99 20232023−2024-2024\newlineHaris Khan\newline0404/2323/2424 33:0303 AM\newlineInIs question: 11 point(s) possible\newlineAssume Ciliotta Inc. ended the month of July 20202020 with the following data\newline(i) (Click the icon to view the financial data.) (i) (Click the icon to view the income statement.)\newline(i) (Click the icon to view the statement of retained earnings.) (i) (Click the icon to view the balance sheet.)\newlineRequirement\newlinePrepare the statement of cash flows of the company for the month ended July 3131, 20202020. Also, explain the relationship among income statement, statement of retained earnings, balance sheet, and statement of cash flows.\newline \qquad parentheses or a minus sign when entering cash outflows. For accounts with a $0 \$ 0 balance, make sure to enter
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Song Li \mathrm{Li} \newline44\newline(b) Bank. Hosei launch a new air miles credit card*\newlineThe rewards for new sign up are listed below. Mr Choy is a first time sizn up and he can cither go for Plan C C or Plan D D .\newline\begin{tabular}{|c|c|}\newline\hline Plan C \mathrm{C} & Plan D D \\\newline\hline \begin{tabular}{l} \newlineOn top of the above, you can get a \\\newlinebonus of 3500035000 miles if you spend a \\\newlineminimum of $1000 \$ 1000 per month using \\\newlinethe credit card for the first two \\\newlineconsecutive months and with an \\\newlineannual fee payment of $235 \$ 235 (subject \\\newlineto 9% 9 \% GST) paid.\newline\end{tabular} & \begin{tabular}{l} \newlineOn top of the above, get a bonus of \\\newline3000030000 miles if you spend a \\\newlineminimum of $500 \$ 500 per month for the \\\newlinefirst two consecutive months with an \\\newlineannual foe waived
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A wind turbine uses the power of wind to generate electricity. The blades of the turbine make a noise that can be heard at a distance from the turbine. At a distance of d=0 d=0 meters from the turbine, the noise level is 105105 decibels. At a distance of d=100 d=100 meters from the turbine, the noise level is 4949 decibels.\newlineThe noise level can be modeled by the function S \mathrm{S} given by S(d)=abd S(d)=a b^{d} , where S(d) S(d) is the noise level, in decibels, at a distance of d d meters from the turbine.\newlinePart A\newline(i) Use the given data to write two equations that can be used to find the values for constants a \mathrm{a} and b \mathrm{b} in the expression for S(d) S(d) .\newline(ii) Find the values for a \mathrm{a} and b \mathrm{b} .\newlineB\newlined=100 d=100 11\newlined=100 d=100 22\newlined=100 d=100 33\newlined=100 d=100 44
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The Rock Rollers released their first album, Metamorphic, when they were still mostly unknown, and the value of the album initially declined. As the band became more famous and the album became more popular, its value started to increase. The value of the album in dollars can be modeled by the expression 0.2t2−4t+250.2t^2 - 4t + 25, where tt is the time in years after it was first released.\newlineWhat does the number 2525 represent in the expression?\newlineChoices:\newline(A)the time in years from when the album was released until its value was the same as when it was first released\newline(B)the time in years from when the album was released until its value was the least\newline(C)the album's value in dollars when it was worth the least\newline(D)the album's value in dollars when it was first released
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Mr. Randolph is putting the finishing touches on his backyard flower bed. The flower bed is 2525 feet long and 66 feet wide, and it is bordered on two sides by the backyard fence. Mr. Randolph plans to put a pathway around the other two sides of the flower bed that is the same width on both sides.\newlineThe total area of the flower bed and pathway in square feet can be modeled by the expression (x+25)(x+6)(x + 25)(x + 6), where xx is the width of the pathway in feet. This expression can also be written in the form x2+31x+150x^2 + 31x + 150. What does the quantity x2+31xx^2 + 31x represent in the expression?\newlineChoices:\newline(A)the area of the flower bed in square feet\newline(B)the area of the pathway in square feet\newline(C)the perimeter around the outside of the flower bed and pathway in feet\newline(D)the length of the flower bed and pathway together in feet
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McClure Sisters Inc., an architectural firm, is in the early phases of planning the building for the Sports and Leisure Museum. The museum will be twice as long as it is wide to accommodate the exhibit hall for sports and the exhibit hall for leisure. The museum will also have a 1515-foot-wide parking lot along two sides.\newlineThe total area of the museum and parking lot together in square feet can be modeled by the expression (2x+15)(x+15)(2x + 15)(x + 15), where xx is the width of the museum in feet. This expression can also be written in the form 2x2+45x+2252x^2 + 45x + 225. What does the quantity 45x+22545x + 225 represent in the expression?\newlineChoices:\newline(A)the area of the museum in square feet\newline(B)the length of the museum and parking lot together in feet\newline(C)the perimeter around the outside of the museum and parking lot in feet\newline(D)the area of the parking lot in square feet
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Jaylen launches his new high-powered model rocket upward during the Rocket Week demonstration. The rocket flies far up into the sky before falling back down to the ground. The rocket has an initial velocity of 147 meters per second147\,\text{meters per second}. Therefore, the rocket's height above the ground in meters, tt seconds after being launched, can be modeled by the expression −4.9t2+147t-4.9t^2 + 147t. This expression can be written in factored form as −4.9t(t−30)-4.9t(t - 30). \newlineWhat does the number 3030 represent in the expression?\newline(A)the time in seconds from when the rocket is launched until it hits the ground\newline(B)the height in meters of the rocket when it is launched\newline(C)the time in seconds from when the rocket is launched until it reaches the top of its flight\newline(D)the height in meters of the rocket when it reaches the top of its flight
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Seth, a carpenter, is helping a client remodel her backyard patio entryway. The entryway will have a set of double doors that are trimmed with moulding. The double doors will be square, and the moulding will be 22 inches wide along the top and sides of the door. The total area of the double doors and moulding in square inches can be modeled by the expression (x+4)(x+2)(x + 4)(x + 2), where xx is the width of the double doors in inches. This expression can also be written in the form x2+6x+8x^2 + 6x + 8. What does the quantity 6x+86x + 8 represent in the expression?\newline(A)the area of the moulding in square inches\newline(B)the height of the double doors and moulding together in inches\newline(C)the perimeter around the outside of the double doors and moulding in inches\newline(D)the area of the double doors in square inches
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Liz just returned from a trip to visit some of the national parks with her family, and she wants to print her favorite picture from the trip to hang on her wall. She is not quite sure what size print she wants to get, although she does know that she wants the print to be square. She also wants to add a border that is 33 inches wide around the sides of the photo.\newlineThe total area of the photo and border in square inches can be modeled by the expression (x+6)(x+6)(x + 6)(x + 6), where xx is the width of the photo in inches. This expression can also be written in the form x2+12x+36x^2 + 12x + 36. What does the quantity 12x+3612x + 36 represent in the expression?\newlineChoices:\newline(A)the length of the photo and border together in inches\newline(B)the area of the photo in square inches\newline(C)the area of the border in square inches\newline(D)the perimeter around the outside of the border in inches
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Venture Properties is looking to design a new food-truck park. The dimensions of the rectangular park will be 110110 feet by 8080 feet. The parking lot will be along two sides of the park, and it will be the same width on both sides.\newlineThe total area of the park and parking lot together in square feet can be modeled by the expression (x+80)(x+110)(x + 80)(x + 110), where xx is the width of the parking lot in feet.\newlineWhat does the quantity x+110x + 110 represent in the expression?\newline(A)the length of the park and parking lot together in feet\newline(B)the perimeter around the outside of the park and parking lot in feet\newline(C)the area of the parking lot in square feet\newline(D)the total area of the park and parking lot together in square feet
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When Bazillium released its signature trading-card game, Wandering Wizards, the value of a first-edition deck decreased at first. As the game got more popular and the deck became more rare, its value started to increase. The value of a first-edition deck in dollars can be modeled by the expression 0.25t2−4t+280.25t^2 - 4t + 28, where tt is the time in years after it was first released.\newlineWhat does the number 2828 represent in the expression?\newline(A)the time in years from when the deck was released until its value was the least\newline(B)the deck's value in dollars when it was first released\newline(C)the time in years from when the deck was released until its value was the same as when it was first released\newline(D)the deck's value in dollars when it was worth the least
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Ann wants to print and frame a photo she recently took at the beach. She plans for the print to have the dimensions 1010 inches by 88 inches, and she also plans to put a border around the photo that has an equal width all around.\newlineThe total area of the photo and border in square inches can be modeled by the expression (10+2x)(8+2x)(10 + 2x)(8 + 2x), where xx is the width of the border in inches. This expression can also be written in the form 4x2+36x+804x^2 + 36x + 80.\newlineWhat does the quantity 4x2+36x4x^2 + 36x represent in the expression?\newlineChoices:\newline(A)the perimeter around the outside of the border in inches\newline(B)the area of the photo in square inches\newline(C)the length of the photo and border together in inches\newline(D)the area of the border in square inches\newline
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Mr. Larry, of Larry's Landscaping, is designing a backyard garden for a client. For visual appeal, the client has requested that the length of the garden be equal to twice the width. The client has also asked for the garden to have a rock edging 22 feet wide around three sides, since the backyard fence will be along the fourth side.\newlineThe total area of the garden and edging in square feet can be modeled by the expression (2x+4)(x+2)(2x + 4)(x + 2), where xx is the width of the garden in feet. This expression can also be written in the form 2x2+8x+82x^2 + 8x + 8.\newlineWhat does the quantity 8x+88x + 8 represent in the expression?\newlineChoices:\newline(A)the length of the garden and edging together in feet\newline(B)the area of the edging in square feet\newline(C)the area of the garden in square feet\newline(D)the perimeter around the outside of the edging in feet
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Rockin' Jon, a music club owner, is planning for the next annual Rockin' Jon's New Year's Eve Jamfest. He has noticed that when he charges more for tickets for the show, fewer people buy tickets. Rockin' Jon's total revenue from selling tickets for the Jamfest, in dollars, can be modeled by the expression p(576−16p)p(576 - 16p), where pp is the price per ticket in dollars. This expression can be written in factored form as −16p(p−36)-16p(p - 36).\newlineWhat does the number 3636 represent in the expression?\newline(A) Rockin' Jon's minimum total revenue in dollars\newline(B) the price per Jamfest ticket in dollars so that Rockin' Jon's total revenue is zero\newline(C) Rockin' Jon's maximum total revenue in dollars\newline(D) the price per Jamfest ticket in dollars that maximizes Rockin' Jon's total revenue
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Problem 55−20-20 Annuities (LO33)\newlineA famous quarterback just signed a $15 \$ 15 million contract providing $3 \$ 3 million a year for 55 years. A less famous recelver signed a $14 \$ 14 million 55 -year contract providing $4 \$ 4 million now and $2 \$ 2 million a year for 55 years. The interest rate is 10% 10 \% .\newlinea. What is the PV of the quarterback's contract?\newlineNote: Do not round intermediate calculations. Enter your answer in millions rounded to 22 decimal places.\newlinePresent value\newlinemillion\newlineb. What is the PV of the receiver's contract?\newlineNote: Do not round intermediate calculations. Enter your answer in millions rounded to 22 decimal places.\newlinePresent value\newlinemillion
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Vocabulary\newline11. Some common geometric terms are point, line, line segment, and ray. A point is an exact location in space, A line is a straight path of points that go on and on in opposite directions. A line segment is a part of a line with two endpoints. A ray is a part of a line that has one endpoint and continues on forever in one direction. Label each figure with the correct term.\newlineG˙ \dot{G} \newline22. Angles can be classified by their measures. A right angle forms a square comer. An acute angle is open less than a right angle. An obtuse angle is open more than a right angle but is open less than a straight angle. A straight angle forms a straight line. Identify each type of angle.\newline33. Use a geometric term to describe and name each figure. Be as specific as possible.\newlineThe figure at the right is a\newlineName the figure using the points that are labeled.\newline44. The figure at the right is an angle.\newlineName the angle with the points from each ray and the shared\newlineD\newlineendpoint of the rays. The shared endpoint is the center letter.\newlineOn the Back!\newline55. Use a geometric term to describe each figure. Be as specific as possible.\newline(915915.11)
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IXL - Equations of parallel an\newlineNew Tab\newlineByteLearn\newline×1+\times 1+\newline←\leftarrow →\rightarrow C \newline\quad-- ixl.com/math/geometry/equations-of-parallel-and-perpendicular-lines\newlinee 77 th Grade Science...\newlineMicrosoft Forms\newline(144144) Hot Wheels...\newline宜家VIMLE 维姆勒\mathbb{\text{宜家VIMLE 维姆勒}}..\newlineQuizizz Creator\newlineNew Tab\newlineGeoGebra - the w...\newlineResearch for Scien...\newlineGeometry - GeoG...\newlineAll Bookmarks\newlineMy IXL Learning Assessment Analytics\newlineHarry\newlineGeometry \newline> *** E. 55 Equations of parallel and perpendicular lines VEB\newlineYou have prizes to reveal! Go to your game board. \newlineX\newlineLine \newlinecc has an equation of \newliney=−5x+3y=-5x+3. Parallel to line \newlinecc is line \newlinedd, which passes through the point \newline(2,−6)(2,-6). What is the equation of line \newlinedd ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newline←\leftarrow11\newlineSubmit\newlineVideo (←\leftarrow22)\newlineQuestions\newlineanswered\newline856856\newlineTime\newlineelapsed\newline\newline1111\newline1313\newline3535\newline\newlineHR\newlineMIN\newlineSEC\newline\newlineSmartscore\newlineout of 100100 ?\newline1717\newlinei99\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (8383) II\newlineEquations of lines (2626)\newlineLesson: Equations of parallel and perpendicular lines
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IX. IXL - Equations of parallel an\newline←→ \leftarrow \rightarrow C \newline−@(@−@) \quad-@^(@-@) ixl.com/math/geometry/equations-of-parallel-and-perpendicular-lines\newline77th Grade Science...\newlineMicrosoft Forms\newline(144144) Hot Wheels...\newlineCuEs\newline宜家VIMLE 维姆勒.. \text{宜家VIMLE 维姆勒}.. \newlineQuizizz Creator\newlineNew Tab\newlineGeoGebra - the w...\newlineResearch for Scien...\newlineGeometry - GeoG..\newlineAll Bookmarks\newlineMy IXL Learning Assessment Analytics\newlineGeometry \newline> E. 55 Equations of parallel and perpendicular lines VEB\newlineVideo (D \text{D} )\newlineQuestions\newlineThe equation for line \newliner r can be written as \newliney=12x+8 y=\frac{1}{2}x+8 . Line \newlines s , which is perpendicular to line \newliner r , includes the point \newline(2,−7) (2,-7) . What is the equation of line \newlines s ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newlineSubmit\newline−@(@−@) \quad-@^(@-@) 00\newlineSubmit\newline−@(@−@) \quad-@^(@-@) 11\newline−@(@−@) \quad-@^(@-@) 22\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (−@(@−@) \quad-@^(@-@) 33) \newlineI\newlineEquations of lines (−@(@−@) \quad-@^(@-@) 44)\newlineLesson: Equations of parallel and perpendicular lines
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IXL - Equations of parallel an\newlineByteLearn\newline×1+ \times 1+ \newline←→ \leftarrow \rightarrow C ∵ \because ixl.com/math/geometry/equations-of-parallel-and-perpendicular-lines\newline77th Grade Science...\newlineMicrosoft Forms\newline(144144) Hot Wheels...\newline宜家VIMLE 维姆勒..\newlineQuizizz Creator\newlineNew Tab\newlineGeoGebra - the w...\newlineResearch for Scien..\newlineGeometry - GeoG...\newlineAll Bookmarks\newlineMy IXL Learning Assessment Analytics\newlineHarry\newlineGeometry > > E. 55 Equations of parallel and perpendicular lines VEB\newlineVideo (D)\newlineQuestions\newlineanswered\newlineThe equation for line c c can be written as y=−37x+4 y=-\frac{3}{7} x+4 . Perpendicular to line c c is line d d , which passes through the point (2,4) (2,4) . What is the equation of line d d ?\newline847847\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newlineSubmit\newlineSubmit\newline1414\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (8383) ←→ \leftarrow \rightarrow 00\newlineEquations of lines (2626)\newlineLesson: Equations of parallel and perpendicular lines
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IXL - Equations of parallel an\newlineByteLearn\newline×1+\times 1+\newline←\leftarrow →\rightarrow C \newline:′:' ixl.com/math/geometry/equations-of-parallel-and-perpendicular-lines\newline77th Grade Science...\newlineMicrosoft Forms\newline(144144) Hot Wheels...\newline\unicode{x5BB6}VIMLE \unicode{x7EF4}\unicode{x59C6}\unicode{x52D2}..\newlineQuizizz Creator\newlineNew Tab\newlineGeoGebra - the w...\newlineResearch for Scien..\newlineGeometry - GeoG...\newlineAll Bookmarks\newlineMy IXL Learning Assessment Analytics\newlineHarry\newlineGeometry \newline> E. 55 Equations of parallel and perpendicular lines VEB\newlineVideo (D)\newlineQuestions\newlineanswered\newlineLine \newlinerr has an equation of \newliney−9=3(x−10)y-9=3(x-10). Line \newline←\leftarrow00 includes the point \newline←\leftarrow11 and is parallel to line \newlinerr. What is the equation of line \newline←\leftarrow00 ?\newlineWrite the equation in slope-intercept form. Write the numbers in the equation as simplified proper fractions, improper fractions, or integers.\newline←\leftarrow44\newline463463\newline←\leftarrow55\newlineSubmit\newlineWork it out\newlineNot feeling ready yet? These can help:\newlineSlopes of parallel and perpendicular lines (8383)\newlineEquations of lines (2626)\newlineLesson: Equations of parallel and perpendicular lines
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