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The document presents a step-by-step solution to a problem involving coconuts and monkeys. It establishes equations to model the situation where each subsequent monkey takes 6/7 of the remaining coconuts. Through algebraic manipulation of the equations, it determines that the original number of coconuts (X) must be 5,764,795 and the amount each monkey received (I) must be 279,935.
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The document presents a step-by-step solution to a problem involving 7 monkeys sharing coconuts. It sets up a system of equations modeling the number of coconuts remaining after each monkey eats. By solving this system, it determines that the original number of coconuts must have been at least 5,764,795 and each monkey received at least 279,935 coconuts.
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i need the answers to these questions today.
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This document provides the answers to homework problems from Lesson 7-6 of a textbook. It works through the steps of 6 sample problems, providing the solutions. It then lists the answers to 20 additional problems. It concludes by directing students to work as a group on an activity from Pearson SuccessNet, dividing up problems to complete within 10 minutes.
Algebra 6
This document discusses multiplication and division of integral expressions. It begins by explaining the rules for multiplying powers of the same base. When powers of the same base are multiplied, the base does not change and the exponents are added. It then explains how to multiply monomials by distributing coefficients and adding exponents of the same variables. Examples are provided to illustrate multiplying powers, monomials, and applying the rules to example problems involving distances and speeds.
Lesson 4.3 regular
1) The document discusses solving quadratic equations by factoring, including using the zero factor property.
2) It provides examples of solving quadratic equations by factoring them into two binomial factors and setting each factor equal to zero.
3) The document also shows how to solve word problems by setting up and solving quadratic equations derived from the problem information.
S 8
The document discusses strategies for two games: Tic Tac Toe and the Pirate Game.
For Tic Tac Toe, it shows that there are 362,880 possible games that can be played. It then calculates the number of strategies for the first 2 and 3 moves of player X, showing that there are over 1 billion possible strategies for the first 3 moves.
For the Pirate Game, it suggests that pirate A, who proposes the distribution of 100 gold coins, should take 98 coins and give 1 coin each to pirates C and E, with nothing for B and D. This maximizes A's coins while getting agreement from C and E based on their own self-interest in survival and coins.
5th period review cartawithanswers
This document contains a review worksheet with 20 questions covering topics in probability, solving linear systems of equations, factoring polynomials, numerical sequences, counting techniques, angle relationships, and calculating volumes of geometric shapes. The questions include word problems, multiple choice, showing work, and drawing figures. Sample solutions are provided for some of the questions. The document provides a complete practice review to assess understanding of key mathematical concepts.
5th period review carta WITH ANSWERS
This document contains a review worksheet with 20 questions covering topics in probability, solving linear systems of equations, factoring polynomials, numerical sequences, counting techniques, angle relationships, and calculating volumes of geometric shapes. The questions include word problems, multiple choice, showing work, and drawing figures. Sample solutions are provided for some of the questions. The document provides a complete practice review to assess understanding of key mathematical concepts.
5th period review carta WITH ANSWERS
This document contains a review worksheet with 20 questions covering topics in probability, solving linear systems of equations, factoring polynomials, numerical sequences, counting techniques, angle relationships, and calculating volumes of geometric shapes. The questions include word problems, multiple choice, showing work, and drawing figures. Sample solutions are provided for some of the questions. The document provides a complete practice review to assess understanding of key mathematical concepts.
MATH: REV. QUIZ INEQUALITIES
This document provides a review for a quiz on solving inequalities. It contains 11 practice problems involving solving linear inequalities algebraically and graphing their solutions on number lines. The problems cover solving single-variable inequalities for x, compound inequalities, and choosing the graph that represents the solution set of a given inequality.
Lesson 5.3 honors
This document discusses solving quadratic equations by factoring. It begins by defining a quadratic equation in standard form and explaining the zero factor property. It then provides examples of solving quadratic equations through factoring and setting each factor equal to zero. Finally, it demonstrates solving word problems by setting up and solving the resulting quadratic equation.
Solving linear systems by the substitution method
The document discusses solving systems of linear equations using substitution and elimination methods. It provides 4 examples of solving systems of 2 equations with 2 unknowns. The substitution method involves solving one equation for one variable in terms of the other and substituting it into the second equation. The elimination method involves multiplying equations by constants and adding/subtracting them to eliminate one variable. Both methods are shown to yield the solution point that satisfies both equations.
Distance between two points
The document explains how to calculate the distance between two points using the distance formula. It shows that if points are horizontal or vertical, you can use their x- or y-coordinates alone, but otherwise you need to use the Pythagorean theorem to form a right triangle and find the hypotenuse. The distance formula is given as the square root of the sum of the squared differences between corresponding x- and y-coordinates of the two points. An example using points (3, -5) and (-1, 4) demonstrates applying the formula to find the distance between two points.
Question 11. Determine which of the following points lies on .docx
Question 1
1. Determine which of the following points lies on the graph of the equation:
(0,7)
(0,6)
(0,5)
(6,5)
(1,5)
Question 2
Complete the table. Use the resulting solution points to sketch the graph of the equation.
Question3
Graphically estimate the x- and y- intercepts of the graph:
y = x3 - 9x
x-intercept: (±3,0),(0,0)
y-intercept: (0,0)
x-intercept: (3,0),(0,0)
y-intercept: (0,0)
x-intercept: (-3,0),(0,0)
y-intercept: (0,0)
x-intercept: (0,±3),(0,0)
y-intercept: (0,0)
x-intercept (0,3),(0,0)
y-intercept (0,0)
Question 4
Find the x- and y-intercepts of the graph of the equation
y=49-7x
x-intercept: (7,0)
y-intercept: (0,-7)
x-intercept: (49,0)
y-intercept: (0,7)
x-intercept: (-7,0)
y-intercept: (0,-49)
x-intercept: (49,0)
y-intercept: (0,49)
x-intercept: (7,0)
y-intercept: (0,49)
Question 5
Determine whether the value of x=7 is a solution of the equation:
2.
no
yes
Question 6
Solve the equation 8-5x=6
Question 7
Solve the equation and check your solution.
-2-4x=30
9
-11
-8
7
-10
Question 8
Solve the equation and check your solution.
5y + 1 = 6y - 5 + 8y
2/3
3/2
6/5
5/6
-2/3
Question 9
Solve the equation and check your solution.
67x - 24 = 3x + 8(8x-3)
3
67
-3
-67
All real numbers
Question 10
Solve the equation and check your solution.
10
6
7
9
8
Question 11
Solve the equation and check your solution. (If not possible, explain why.)
2
5
6
4
10
Question 12
3.
4. Solve the equation and check your solution. (If not possible, explain why)
5.
-18
7
11
No solution. The variable is divided out.
20
Question 13
Write the quadratic equation in general form.
4x2 = 8 - 9x
4x2 + 9x + 8 = 0
4x2 + 9x = -8
4x2 - 9x - 8 = 0
-4x2 + 9x - 8 = 0
4x2 + 9x - 8 = 0
Question 14
Solve the quadratic equation by factoring.
x2 - 6x + 5 = 0
-1, 5
-1,-5
1,-5
1,5
6,5
Question 15
Solve the quadratic equation by factoring.
x2 + 8x + 16 = 0
4
-1/4
-4
±4
1/4
Question 16
Solve the equation by extracting square roots.
(x+6)2 = 5
6 + √5
-6 ± √5
-6 -√5
6 ± √5
-6 + √5
Question 17
Use the Quadratic Formula to solve
x2 + 20x + 98 = 0
x = -8, x = -12
x = -√2 - 10, x = √2 - 10
x = -√3 - 10, x = √3 - 10
x = 10, x = -10
x = -√2 - 9, x = √2 - 9
Question 18
Write the complex number in standard form.
√ -9
3i
-3i
9i
4i
-9i
Question 19
Find real numbers a and b such that the equation is true.
a + bi = 14 + 2i
a=16, b=4
a=18, b=6
a=14, b=2
a=15, b=14
a=17, b=5
Question 20
Find all solutions to the following equation.
x = -17/4
x=9
no solution
x=-17
x=-8
Question 1
1. Determine which ...
Lesson 9 8 integer equations
The document provides instructions for solving integer equations using inverse operations. It lists the rules for adding, subtracting, multiplying and dividing integers. It then provides 21 practice problems to solve integer equations using the inverse operations and integer rules. The problems include solving equations with addition, subtraction, multiplication and division of integers.
Lesson 9 8 integer equations
The document provides instructions on solving integer equations using inverse operations. It lists the rules for adding, subtracting, multiplying and dividing integers. It then provides 21 practice problems to solve integer equations, with the solutions shown. The goal is to use inverse operations to isolate the variable term and apply the integer rules to determine its value.
Numeros reales, inecuaciones y desigualdades
En el presente trabajo encontraremos conceptos básicos sobre números reales al igual que ejemplos. También conceptos sobre inecuaciones y desigualdades y sus ejercicios, operaciones con conjuntos
Quadratic eq and discriminant
The document discusses the quadratic formula and how to use it to solve quadratic equations. It introduces the quadratic formula as x = (-b ±√(b2 - 4ac))/2a and explains how to use it to solve equations by plugging in the a, b, and c coefficients. It also defines the discriminant b2 - 4ac and explains what types of roots (real, complex, rational, irrational) an equation will have depending on whether the discriminant is positive, negative, or zero. Several examples are worked through to demonstrate applying the quadratic formula.
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i need the answers to these questions today.1Use the quotient ru.docx
i need the answers to these questions today.1Use the quotient ru.docx
Question 11. Determine which of the following points lies on .docx
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Seven monkeys gathered coconuts during the day and agreed to split them evenly. That night, each monkey secretly took a pile for themselves by dividing the coconuts into seven piles and throwing the extra into the ocean, hiding one pile and combining the rest. By morning, the pile was much smaller due to each monkey stealing a share, meaning they must have started with at least 49 coconuts, with each monkey receiving 7.
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Fgrsdg
- 2. The amount of coconuts after on monkey has finished will equal b = (6/7)*(x-1) where b is the number of coconuts.
- 3. Use the same equation for the remaining monkeys
- 4. So the equation set would be
- 5. b = (6/7)*(x-1) = amount after 1 monkey,
- 6. c = (6/7)*(b-1) = amount after 2 monkeys,
- 7. d = (6/7)*(c-1) = amount after 3 monkeys,
- 8. e = (6/7)*(d-1) = amount after 4 monkeys,
- 9. f = (6/7)*(e-1) = amount after 5 monkeys,
- 10. g = (6/7)*(f-1) = amount after 6 monkeys,
- 11. h = (6/7)*(g-1) = amount after 7 monkeys,
- 12. i = (1/7)*(h-1) = amount each got at the end.
- 13. This works as the original number of coconuts must be able to be subtracted from 6/7 when one is subtracted from the original number and form an integer
- 15. b = (6/7)*(x-1) Multiply each side by 7
- 16. 7B=6*(x-1) Distribute out the 6
- 17. 7B=6x-6 Put the six on one side of the equation and the variables on the other
- 18. 6=7B+6x
- 19. Repeat this process with the remaining equations; you get
- 20. 6a - 7b = 6,
- 21. 6b - 7c = 6,
- 22. 6c - 7d = 6,
- 23. 6d - 7e = 6,
- 24. 6e - 7f = 6,
- 25. 6f - 7g = 6,
- 26. 6g - 7h = 6,
- 27. h - 7i = 1
- 29. 6^1x - 7^1b = 6*(7^1 - 6^1)
- 30. 6^2x - 7^2c = 6*(7^2 - 6^2)
- 31. 6^3x - 7^3d = 6*(7^3 - 6^3)
- 32. 6^4x - 7^4e = 6*(7^4 - 6^4)
- 33. 6^5x - 7^5f = 6*(7^5 - 6^5)
- 34. 6^6x - 7^6g = 6*(7^6 - 6^6)
- 35. 6^7x - 7^7h = 6*(7^7 - 6^7)
- 36. 6^7x - 7^8i = 7^8 – 6^8
- 37. In the last problem X: Is going to be -6(match the 6^7X on the left side to the -6^8 on the right. You need a negative and one more six to make the two terms equal)
- 38. In the last problem;I is going to equal -1(again match the -7^8i on the left to the 7^8 on the right)
- 40. X=-6 + 7^8*T
- 41. And
- 42. I=-1 + 6^7*T
- 43. T is any integer
- 44. Set T equal to one, as that is the lowest positive integer
- 45. X=-6+7^8(1)
- 46. X=5,764,795
- 47. I=-1+6^7(1)
- 48. I=279,935