After completing Lesson 22, it’s important to check your answers to ensure that you understand the material and have completed the assignments correctly. This answer key provides the correct answers for the homework questions in Lesson 22, allowing you to compare your own responses and make any necessary corrections.
The answer key covers a range of topics and exercises, including grammar, vocabulary, and reading comprehension. Each question is accompanied by its correct answer, providing you with a clear understanding of where you went wrong, if applicable. By using this answer key, you can assess your performance and identify areas for improvement.
It’s crucial to review your homework and understand any mistakes you may have made. This answer key serves as a valuable tool for self-assessment and improvement. By comparing your answers to the correct ones provided, you can validate your understanding and make necessary adjustments for future lessons. Remember, practice is key to mastering any language, so take advantage of this resource to enhance your English skills.
Lesson 22 Homework Answer Key
In this lesson, we will go over the answer key for the homework assigned in Lesson 22. The homework consisted of several exercises aimed at reinforcing the concepts learned in the lesson. Let’s review the answers together.
Exercise 1:
- Biology: The study of living organisms and their interactions with the environment.
- Chemistry: The study of matter, its properties, and how it changes.
- Physics: The study of matter, energy, and the interactions between them.
- Geology: The study of the Earth’s solid materials, such as rocks and minerals.
- Astronomy: The study of celestial objects, such as stars, planets, and galaxies.
Exercise 2:
- Aquifers: Underground layers of rock or sediment that hold water.
- Desalination: The process of removing salt and other minerals from seawater to make it drinkable.
- Turbidity: The cloudiness or haziness of a fluid caused by suspended particles.
- Water table: The upper level of an underground surface in which the soil or rocks are permanently saturated with water.
- Watershed: An area of land where all the water that falls in it drains to a common outlet.
Exercise 3:
For this exercise, students were required to conduct research on a specific environmental issue and write a short paragraph summarizing their findings. The topic for research was chosen by the students themselves, so the answers may vary. Some of the possible topics could include air pollution, deforestation, climate change, or water scarcity.
These were just a few of the exercises in the homework assignment for Lesson 22. By completing these exercises, students were able to practice and solidify their understanding of key concepts related to science and the environment.
Problem 1 Solution
In problem 1, we are given a system of equations to solve:
Equation 1: 3x + 2y = 10
Equation 2: 4x + 3y = 16
To solve this system, we can use the method of substitution. Let’s start by solving Equation 1 for x:
Note: We will solve for x in terms of y, so we can substitute this expression into Equation 2 to find the value of y.
To solve for x, we isolate x on one side of the equation:
Equation 1: 3x + 2y = 10
3x = 10 – 2y
x = (10 – 2y)/3
Now that we have x in terms of y, we can substitute this expression into Equation 2:
Equation 2: 4x + 3y = 16
4((10 – 2y)/3) + 3y = 16
(40 – 8y)/3 + 3y = 16
40 – 8y + 9y = 48
40 + y = 48
y = 8
Now that we have the value of y, we can substitute it back into Equation 1 to find the value of x:
Equation 1: 3x + 2(8) = 10
3x + 16 = 10
3x = -6
x = -2
Therefore, the solution to the system of equations is x = -2 and y = 8.
Solution to Problem 2
The second problem in the homework assignment can be solved by following a step-by-step approach. Here is the solution:
Step 1: List all the given information and variables involved in the problem. This will help you have a clear understanding of what you are working with.
- Given value A: 10
- Given value B: 5
- Given value C: 3
- Given equation: A + B * C
Step 2: Evaluate the expression A + B * C using the given values. Apply the order of operations (PEMDAS).
- Multiply B and C: 5 * 3 = 15
- Add A and the result of the multiplication: 10 + 15 = 25
Step 3: Write down the final result of the expression.
The final result of the expression A + B * C is 25.
By following these steps, you can solve problem 2 of the homework assignment and obtain the correct answer.
Problem 3 Solution
To solve problem 3, we need to find the sum of the following arithmetic series: 7, 14, 21, 28, …, 70. The common difference for this series is 7, as each term increases by 7. To find the sum of an arithmetic series, we can use the formula:
Sum = (n/2)(a + l)
Where n is the number of terms, a is the first term, and l is the last term. In this case, n = 10 (from 7 to 70), a = 7, and l = 70. Plugging in these values into the formula, we get:
Sum = (10/2)(7 + 70) = 5(77) = 385.
Therefore, the sum of the arithmetic series 7, 14, 21, 28, …, 70 is 385.
Problem 4 Solution
First, we need to calculate the distance of each point from the origin. We can do this by substituting the values of (x1, y1) as (0, 0) and (x2, y2) as the coordinates of each point. Then, we can use the distance formula to find the distance of each point from the origin.
Next, we compare the distances of all the points and find the smallest distance. This will give us the point that is closest to the origin. Finally, we find the y-coordinate of this point and that is our solution to problem 4.
Problem 5 Solution
In this problem, we are given a system of equations and we need to solve for the values of x and y. The system of equations is as follows:
Equation 1: 2x + 4y = 10
Equation 2: 3x – y = 5
To solve this system of equations, we can use the method of substitution. We can solve one equation for one variable and substitute that expression into the other equation.
Solving Equation 2 for y:
We can rewrite Equation 2 to solve for y:
y = 3x – 5
Now we can substitute this expression for y in Equation 1:
2x + 4(3x – 5) = 10
2x + 12x – 20 = 10
Combining like terms, we get:
14x – 20 = 10
14x = 30
x = 30/14
x ≈ 2.14
Now we can substitute this value of x back into Equation 2 to find the value of y:
3(2.14) – y = 5
6.42 – y = 5
Subtracting 5 from both sides, we get:
-y = -1.42
y ≈ 1.42
Therefore, the solution to the system of equations is:
x ≈ 2.14
y ≈ 1.42
Problem 6 Solution
Problem 6 in the homework focused on solving a linear equation using the elimination method. The equation given was:
-5x + 3y = 7
To solve the equation, we first need to eliminate one of the variables. In this case, we can eliminate the y variable by multiplying the first equation by 3 and the second equation by 5:
- First equation: -15x + 9y = 21
- Second equation: -25x + 15y = 35
Next, we subtract the second equation from the first equation:
- New equation: 10x – 6y = -14
Once we have a new equation with only one variable, we can solve for it. In this case, we can simplify the equation by dividing it by 2:
- Simplified equation: 5x – 3y = -7
Finally, we can add this simplified equation to the original second equation to eliminate the x variable:
- New equation: -5y = 28
Now, we can solve for y by dividing both sides of the equation by -5:
- y = -5.6
Substituting this value of y back into one of the original equations, we can solve for x. In this case, we’ll use the first equation:
- -5x + 3(-5.6) = 7
Simplifying this equation gives us:
- -5x – 16.8 = 7
- -5x = 23.8
- x = -4.76
Therefore, the solution to the given linear equation is x = -4.76 and y = -5.6.