Alg2 lesson 2-7
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The document provides examples of solving inequalities and determining whether boundary lines are included in solution sets. Example 1 shows testing points to determine which side of a boundary line satisfies an inequality. Example 2 involves writing and graphing an inequality about the number of students and chaperones that can ride on a bus being less than or equal to 60. Example 3 tests a point to shade the region satisfying the original inequality.
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![Example 7-1a ,[object Object],[object Object],≥ or ≤ includes the line SOLID LINE > or < does not include the line BROKEN LINE Graph](https://image.slidesharecdn.com/alg2lesson2-7-100922213814-phpapp02/85/Alg2-lesson-2-7-1-320.jpg)
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This document contains a sample GATE paper with questions from various subjects like mathematics, physics, chemistry and general aptitude. The questions include multiple choice, numerical answer type and explanation type questions. Some questions test concepts like differential equations, complex numbers, Laplace transforms, electric circuits etc. The document also contains information about an online portal for GATE preparation that has trained over 1 lakh students across India.
Linear programming problems
This document contains instructions for a mathematics exam, including:
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- No books, notes, or calculators with CAS or QWERTY keyboards are allowed. Cell phones may not be used.
- The multiple choice section includes 8 questions worth 5 points each.
- The true/false section includes 15 statements worth 15 points total.
- Three short answer questions are each worth 15 points.
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1150 day 11
Ratios, proportions, and percents can be used to compare quantities and solve problems. A ratio compares two quantities, like the number of squares to circles. Equal ratios form a proportion, which can be used to solve for unknown values. Percents represent a number out of 100. Common percent calculations include finding a percent of a number and converting between fractions, decimals, and percents. The percent proportion states that the percent equals the part divided by the whole quantity.
1150 day 10
This document covers topics related to repeating decimals, irrational numbers, and square roots. It includes examples of writing repeating decimals as fractions, ordering decimals, finding square roots, and using the Pythagorean theorem. Various math problems are presented along with step-by-step solutions to illustrate these concepts.
1150 day 9
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1150 day 7
This document discusses prime and composite numbers, greatest common divisors (GCD), and least common multiples (LCM). It provides examples of finding the GCD and LCM of various numbers using different methods like the intersection of sets method, prime factorization method, and Euclidean algorithm. Key definitions include: a prime number has exactly two distinct positive divisors, a composite number has factors other than itself and 1, the GCD is the largest integer that divides numbers, and the LCM is the smallest number that is a multiple of the given numbers.
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Alg2 lesson 2-7
- 2. Example 7-1b Test (0 , 0) . Shade the region that contains (0 , 0) . 3) Pick a test point to find the side of the line that contains points which make the inequality true. x Graph true
- 3. Example 7-1c 2x + 5y = 10 x-intercept: 2x + 5(0) = 10 2x = 10 x = 5 (5, 0) y-intercept: 2(0) + 5y = 10 5y = 10 y = 2 (0, 2) Solid or broken line? BROKEN Graph
- 4. Example 7-1c Test any point that is not on the line Test (0, 0) 2(0) + 5(0) > 10 0 + 0 > 10 0 > 10 FALSE Shade the true side Graph
- 5. Example 7-2g Class Trip Two social studies classes are going on a field trip. The teachers have asked for parent volunteers to also go on the trip as chaperones. However, there is only enough seating for 60 people on the bus. a. Write an inequality to describe the number of students and chaperones that can ride on the bus. Students + chaperones ≤ 60 Answer:
- 6. Example 7-2h b. Graph the inequality. c. Can 45 students and 10 chaperones go on the trip? Answer: yes x Answer:
- 7. Example 7-3a Test (0 , 0) . Shade the region that contains (0 , 0) . x Graph Original inequality true