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- Core Connections Integrated I, 2013
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7.4E: Exercises
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Simplify a Complex Rational Expression by Writing it as Division
In the following exercises, simplify each complex rational expression by writing it as division.
1. \(\dfrac{\dfrac{2 a}{a+4}}{\dfrac{4 a^{2}}{a^{2}-16}}\)
\(\dfrac{a-4}{2 a}\)
2. \(\dfrac{\dfrac{3 b}{b-5}}{\dfrac{b^{2}}{b^{2}-25}}\)
3. \(\dfrac{\dfrac{5}{c^{2}+5 c-14}}{\dfrac{10}{c+7}}\)
\(\dfrac{1}{2(c-2)}\)
4. \(\dfrac{\dfrac{8}{d^{2}+9 d+18}}{\dfrac{12}{d+6}}\)
5. \(\dfrac{\dfrac{1}{2}+\dfrac{5}{6}}{\dfrac{2}{3}+\dfrac{7}{9}}\)
\(\dfrac{12}{13}\)
6. \(\dfrac{\dfrac{1}{2}+\dfrac{3}{4}}{\dfrac{3}{5}+\dfrac{7}{10}}\)
7. \(\dfrac{\dfrac{2}{3}-\dfrac{1}{9}}{\dfrac{3}{4}+\dfrac{5}{6}}\)
\(\dfrac{20}{57}\)
8. \(\dfrac{\dfrac{1}{2}-\dfrac{1}{6}}{\dfrac{2}{3}+\dfrac{3}{4}}\)
9. \(\dfrac{\dfrac{n}{m}+\dfrac{1}{n}}{\dfrac{1}{n}-\dfrac{n}{m}}\)
\(\dfrac{n^{2}+m}{m-n^{2}}\)
10. \(\dfrac{\dfrac{1}{p}+\dfrac{p}{q}}{\dfrac{q}{p}-\dfrac{1}{q}}\)
11. \(\dfrac{\dfrac{1}{r}+\dfrac{1}{t}}{\dfrac{1}{r^{2}}-\dfrac{1}{t^{2}}}\)
\(\dfrac{r t}{t-r}\)
12. \(\dfrac{\dfrac{2}{v}+\dfrac{2}{w}}{\dfrac{1}{v^{2}}-\dfrac{1}{w^{2}}}\)
13. \(\dfrac{x-\dfrac{2 x}{x+3}}{\dfrac{1}{x+3}+\dfrac{1}{x-3}}\)
\(\dfrac{(x+1)(x-3)}{2}\)
14. \(\dfrac{y-\dfrac{2 y}{y-4}}{\dfrac{2}{y-4}+\dfrac{2}{y+4}}\)
15. \(\dfrac{2-\dfrac{2}{a+3}}{\dfrac{1}{a+3}+\dfrac{a}{2}}\)
\(\dfrac{4}{a+1}\)
16. \(\dfrac{4+\dfrac{4}{b-5}}{\dfrac{1}{b-5}+\dfrac{b}{4}}\)
Simplify a Complex Rational Expression by Using the LCD
In the following exercises, simplify each complex rational expression by using the LCD.
17. \(\dfrac{\dfrac{1}{3}+\dfrac{1}{8}}{\dfrac{1}{4}+\dfrac{1}{12}}\)
\(\dfrac{11}{8}\)
18. \(\dfrac{\dfrac{1}{4}+\dfrac{1}{9}}{\dfrac{1}{6}+\dfrac{1}{12}}\)
19. \(\dfrac{\dfrac{5}{6}+\dfrac{2}{9}}{\dfrac{7}{18}-\dfrac{1}{3}}\)
20. \(\dfrac{\dfrac{1}{6}+\dfrac{4}{15}}{\dfrac{3}{5}-\dfrac{1}{2}}\)
21. \(\dfrac{\dfrac{c}{d}+\dfrac{1}{d}}{\dfrac{1}{d}-\dfrac{d}{c}}\)
\(\dfrac{c^{2}+c}{c-d^{2}}\)
22. \(\dfrac{\dfrac{1}{m}+\dfrac{m}{n}}{\dfrac{n}{m}-\dfrac{1}{n}}\)
23. \(\dfrac{\dfrac{1}{p}+\dfrac{1}{q}}{\dfrac{1}{p^{2}}-\dfrac{1}{q^{2}}}\)
\(\dfrac{p q}{q-p}\)
24. \(\dfrac{\dfrac{2}{r}+\dfrac{2}{t}}{\dfrac{1}{r^{2}}-\dfrac{1}{t^{2}}}\)
25. \(\dfrac{\dfrac{2}{x+5}}{\dfrac{3}{x-5}+\dfrac{1}{x^{2}-25}}\)
\(\dfrac{2 x-10}{3 x+16}\)
26. \(\dfrac{\dfrac{5}{y-4}}{\dfrac{3}{y+4}+\dfrac{2}{y^{2}-16}}\)
27. \(\dfrac{\dfrac{5}{z^{2}-64}+\dfrac{3}{z+8}}{\dfrac{1}{z+8}+\dfrac{2}{z-8}}\)
\(\dfrac{3 z-19}{3 z+8}\)
28. \(\dfrac{\dfrac{3}{s+6}+\dfrac{5}{s-6}}{\dfrac{1}{s^{2}-36}+\dfrac{4}{s+6}}\)
29. \(\dfrac{\dfrac{4}{a^{2}-2 a-15}}{\dfrac{1}{a-5}+\dfrac{2}{a+3}}\)
\(\dfrac{4}{3 a-7}\)
30. \(\dfrac{\dfrac{5}{b^{2}-6 b-27}}{\dfrac{3}{b-9}+\dfrac{1}{b+3}}\)
31. \(\dfrac{\dfrac{5}{c+2}-\dfrac{3}{c+7}}{\dfrac{5 c}{c^{2}+9 c+14}}\)
\(\dfrac{2 c+29}{5 c}\)
32. \(\dfrac{\dfrac{6}{d-4}-\dfrac{2}{d+7}}{\dfrac{2 d}{d^{2}+3 d-28}}\)
33. \(\dfrac{2+\dfrac{1}{p-3}}{\dfrac{5}{p-3}}\)
\(\dfrac{2 p-5}{5}\)
34. \(\dfrac{\dfrac{n}{n-2}}{3+\dfrac{5}{n-2}}\)
35. \(\dfrac{\dfrac{m}{m+5}}{4+\dfrac{1}{m-5}}\)
\(\dfrac{m(m-5)}{(4 m-19)(m+5)}\)
36. \(\dfrac{7+\dfrac{2}{q-2}}{\dfrac{1}{q+2}}\)
In the following exercises, simplify each complex rational expression using either method.
37. \(\dfrac{\dfrac{3}{4}-\dfrac{2}{7}}{\dfrac{1}{2}+\dfrac{5}{14}}\)
\(\dfrac{13}{24}\)
38. \(\dfrac{\dfrac{v}{w}+\dfrac{1}{v}}{\dfrac{1}{v}-\dfrac{v}{w}}\)
39. \(\dfrac{\dfrac{2}{a+4}}{\dfrac{1}{a^{2}-16}}\)
40. \(\dfrac{\dfrac{3}{b^{2}-3 b-40}}{\dfrac{5}{b+5}-\dfrac{2}{b-8}}\)
41. \(\dfrac{\dfrac{3}{m}+\dfrac{3}{n}}{\dfrac{1}{m^{2}}-\dfrac{1}{n^{2}}}\)
\(\dfrac{3 m n}{n-m}\)
42. \(\dfrac{\dfrac{2}{r-9}}{\dfrac{1}{r+9}+\dfrac{3}{r^{2}-81}}\)
43. \(\dfrac{x-\dfrac{3 x}{x+2}}{\dfrac{3}{x+2}+\dfrac{3}{x-2}}\)
\(\dfrac{(x-1)(x-2)}{6}\)
44. \(\dfrac{\dfrac{y}{y+3}}{2+\dfrac{1}{y-3}}\)
Writing Exercises
45. In this section, you learned to simplify the complex fraction \(\dfrac{\dfrac{3}{x+2}}{\dfrac{x}{x^{2}-4}}\) two ways: rewriting it as a division problem or multiplying the numerator and denominator by the LCD. Which method do you prefer? Why?
Answers will vary.
44. Efraim wants to start simplifying the complex fraction \(\dfrac{\dfrac{1}{a}+\dfrac{1}{b}}{\dfrac{1}{a}-\dfrac{1}{b}}\) by cancelling the variables from the numerator and denominator, \(\dfrac{\dfrac{1}{\cancel{a}}+\dfrac{1}{\cancel {b}}}{\dfrac{1}{\cancel{a}}-\dfrac{1}{\cancel{b}}}\). Explain what is wrong with Efraim’s plan.
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Lesson 7.1.1, lesson 7.1.2, lesson 7.1.3, lesson 7.1.4, lesson 7.1.5, lesson 7.1.6, lesson 7.1.7, lesson 7.2.1, lesson 7.2.2, lesson 7.2.3.
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2024 NFL Draft Rumors: ‘Jaguars Have Explored Moving Up’ and Done Homework on Top WRs
According to Sports Illustrated's Albert Breer, the Jaguars have done their homework on the top receivers in the class and have even considering a trade-up.
- Author: John Shipley
It is officially draft week.
In just a few short days, the first round of the 2024 NFL Draft will kickoff and the futures of all 32 teams will change and take shape.
For the Jacksonville Jaguars, could that future involve a blockbuster trade for a No. 1 wide receiver? Sports Illustrated's Albert Breer suggests it could.
"The Jaguars have explored moving up—and they’ve done a lot of work on the top receivers in the draft," Breer said.
"Losing Calvin Ridley, even with Christian Kirk and Gabe Davis paid, makes that spot a priority. Failing that, corner, if either Arnold or Mitchell are available here, shapes up as a possibility, too. Another would be a disruptive defensive tackle for new DC Ryan Nielsen’s scheme—maybe Murphy, if he slides a bit, or Illinois defensive tackle Jer’Zhan Newton (who’s coming off a foot fracture)."
The top wide receivers in the draft include the likes of Ohio State's Marvin Harrison Jr., Washington's Rome Odunze, and LSU's Malik Nabers. Nabers has been commonly linked to the Jaguars, with team sources indicating to Jaguar Report this offseason that the Jaguars are extremely high on the SEC standout.
“I think it’s a very good group of receivers, obviously. I think those three that everybody is talking about are really good football players," Jaguars general manager Trent Baalke said last week.
"I think there’s some guys in the next wave that are really good football players, too. I think there’s good players like that all the way through the draft in that position. There’s going to be some later round guys that make a mark for themselves at some point in their careers in this league as well. It’s a good group, there’s a lot of variations of guys, guys strictly in the slot, guys strictly out on the perimeter. There are some guys that can move around the formations a little bit more. It’s a good group of receivers.”
Baalke has traded up just three times in his career with the Jaguars. Only one such occurrence happened in the first round, with Baalke trading up to No. 27 to select linebacker Devin Lloyd during the 2022 NFL Draft.
“Well, if you talk to the analytics people, they’ll tell you never move up. Acquire as many darts as you can, keep moving back. You just got to look at the board and let the board speak," Baalke said.
"We spent 360-something days putting this thing together and to try to make something happen and force something to happen, sometimes backfires on you. You chase something and it doesn’t pan out, so you lose out there and then you lose out on the guy you would’ve picked and the two guys you would’ve picked with the other picks you gave up. If you’re going to move up, you better be right.”
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CPM Education Program proudly works to offer more and better math education to more students.
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It will be referred to as Checkpoint 7A. For each problem, write one or two equations to represent the situation and then solve. Be sure to define your variable (s) and clearly answer the question. The Lee's have three children. The oldest is twice as old as the youngest. The middle child is five years older than the youngest.
Mathleaks offers the ultimate homework help and much of the content is free to use. Browse the textbooks below or by downloading the Mathleaks app for free on Google Play or the App Store. Start CPM Educational Program. CPM Educational Program. Show more. Core Connections Integrated I, 2013. ISBN: 9781603283083.
Exercise 112. Exercise 113. Exercise 114. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Core Connections Integrated 3 1st Edition, you'll learn how to solve your toughest homework problems.
7-17. x = 15 , y = 9. 7-18. The baby is growing 1.5 inches per month; it is the slope (m). It was 23 inches long when it was born; it is the y-intercept (b). 27.5 inches. 11 months after it was born, so in December. 7-19. Both have 3 tiles in Figure 0. However, A grows by 2 tiles and B grows by 6 tiles.
Exercise 9. Exercise 10. Exercise 11. Exercise 12. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Core Connections Geometry 2nd Edition, you'll learn how to solve your toughest homework problems.
Open Up Resources Illustrative Mathematics Grade 7 OURUnit 1 Lesson 4More resources available at: mathhelp.cusd.com
Homework Help . CPM provides students with free online access to hints and/or answers to assigned homework problems. (Notes that teachers also often post answers to assigned homework problems on Canvas.) Students are encouraged to do their best to arrive at a solution on their own and to access the homework help when they need it.
Answer. 51) The velocity of a particle moving along a line is a function of time given by v(t) = 88t2 t2 + 1. Find the distance that the particle has traveled after t = 5 sec. In exercises 52 - 54, solve the initial-value problem for x as a function of t. 52) (t2 − 7t + 12)dx dt = 1, t > 4, x(5) = 0. Answer.
Learner is highly skilled, able to remember long sequences, and has a longer attention span. Part Practice is used when the skill is what 3 and the LEARNER is what 3 things? Skill is complex, has highly independent parts, and made of of individual skills. When the learner has limited memory span, is unable to focus for a long time, or having ...
On PC-A, right click the Ethernet0 and click Properties. 2. In the Ethernet0 Properties window select InternetProtocol Version 4 (TCP/IPv4) and click the Properties. 3. Select the Use the following IPv4 address and enter the IPv4 address 168.1.1 and subnet mask 255.255.255..
This is the digital version of practice problems for Grade 7, Unit 1, Lesson 4. This set includes a few problems targeting the skills in this lesson along with a mix of topics from previous lessons. Distributed practice (revisiting the same content over time) is more effective than massed practice (a large amount of practice on one topic, but all at once). Teachers may decide to assign the ...
Simplify a Complex Rational Expression by Writing it as Division. In the following exercises, simplify each complex rational expression by writing it as division. 1. 2a a + 4 4a2 a2 − 16 2 a a + 4 4 a 2 a 2 − 16. Answer. 2. 3b b − 5 b2 b2 − 25 3 b b − 5 b 2 b 2 − 25. 3. 5 c2 + 5c − 14 10 c + 7 5 c 2 + 5 c − 14 10 c + 7.
CPM Educational Program Discover the Newest CPM Curriculum Inspiring Connections is a new multimodal curriculum series by CPM Educational Program that utilizes different venues that turn your classrooms into communities of mathematical risk-takers. This series builds on a 30+ year tradition of inspiring mathematics students and teachers through exemplary curriculum, professional learning, and ...
Review for Team Quiz HW Key.pdf. Ch 7 Review HW KEY.pdf ...
Looking for help on 7.1.4 and 7.1.5. Hey folks, first time posting. I'm looking for help on Square and Triple. I've been using the code from the video, seen below. function triple (x) {. var tripleX = 4 * x; println (tripleX); I've got a 5/9 on Square and 4/9 on Triple. Any help is greatly appreciated.
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Illustrative Mathematics Grade 7 Open Up Resources OURUnit 3 Lesson 4More resources available at: mathhelp.cusd.com
1.8 (6 reviews) 7.1.1: Fetch. Click the card to flip 👆. // This is the start of my code. function start () {. goUp (); move (); move (); takeBall ();
View Homework Help - 7.4 Homework Solutions.pdf from MATH 1372 at University of Minnesota-Twin Cities. AI Homework Help. Expert Help. Study Resources. Log in Join. 7.4 Homework Solutions.pdf. Doc Preview. Pages 7. Total views 100+ University of Minnesota-Twin Cities. MATH. MATH 1372. pepeadad. 9/14/2017.
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Sports Illustrated's Albert Breer suggests it could. "The Jaguars have explored moving up—and they've done a lot of work on the top receivers in the draft," Breer said. "Losing Calvin Ridley ...