28.09.2020

algebra 2 analyzing quadratics answer key

. 4

Faq

Mathematics
Step-by-step answer
P Answered by Master

I DID YELLOWSTONE

Step-by-step explanation:

Make sense of the problem:

what is the estimated population for each animal at year 12.

Population 1 grizzly bear

1.  Is population 1 increasing or decreasing? (0.5 point)

Increasing

2. What is the rate of change between year 0 and year 1 for population 1? What is it between year 5 and year 10? Include calculations in your answer. (2 points)

The rate of change between year 0 and year 1 is .5 and the rate of change between year 5 and 10 is also .5

3. Predict the average rate of change from year 5 to year 6 for population 1. Use the average rate of change you found in question 2 in your prediction. (1 point)

I think the average rate of change from year 5 to year 6 is .5 this is because each year the population is increasing by .5 according to question 2.

4. What type of function best models the growth for population 1? Give a reason for your answer. (1 point)

A linear function would model population 1 the best. This is because the population is increasing by .5 each year. It increases as a steady rate so it will be a straight line.

Population 2 pocket gophers

5. What is the maximum population per square mile during the first 10 years for population 2? (0.5 point)

The maximum population per square mile during the first 10 years is 60.7.

6. What is the average rate of change for population 2 between years 5 and 10 (x = 5 to x = 10)? (1 point)

The average rate of change is 10.02

7. The average rate of change for population 2 changes by a common ratio (multiplication) of 1.5 each year. What type of function best models this growth? (1 point)

A exponential function would best model this growth.

8. Estimate the average rate of change from year 5 to year 6 for population 2. Remember, the average rate of change for this population changes by a ratio of 1.5 each year. Show your work. HINT: First find the average rate of change from year 4 to year 5. (3 points)

The rate of change from year 5 to year 6 is about 3.75 since population 2 changes by a ratio of 1.5 each year. The rate of change from year 4 to 5 is 2.5 so 2.5*1.5 is 3.75.

Population 3 Osprey

9. What is the maximum population per square mile during the first 10 years for population 3? In what year did this occur? (1 point)

The maximum population per square mile during the first 10 years is 9.0 this occured in year 5.

10. What is the average rate of change for population 3 between years 5 and 10 (x = 5 to x = 10)? Show your work. Identify the change as an increase or a decrease. (2 points)

The change is a decrease.

11. What type of function best models the growth for population 3? Give a reason for your answer. (1 point)

A quadratic function best models the growth for population 3 because at first the population increases but then it decreases.

12. Use the graph provided. When do all three populations contain the same number of animals? (1 point)

In year 0 all three populations contained the same amount of animals.

13. Use the following graphs to verify your work on this question.

A. Estimate the average rate of change from year 5 to year 8 for population 3. Show your work. (2 points)

7.2-9/8-5 = -1.8/3 = -0.6

B. Estimate the average rate of change from year 8 to year 10 for population 3. Show your work. (2 points)

4-7.2/10-8 = -3.2/2 = -1.6

C. Based on the answers to Parts A and B, estimate the number of animals in population 3 in year 15, and give a reason for your estimate. (1 point)

The number of animals in year 15 will be 0 this is because the number of animals keeps steadily going down and you cannot have a negative number of animals.

Mathematics
Step-by-step answer
P Answered by Specialist

I DID YELLOWSTONE

Step-by-step explanation:

Make sense of the problem:

what is the estimated population for each animal at year 12.

Population 1 grizzly bear

1.  Is population 1 increasing or decreasing? (0.5 point)

Increasing

2. What is the rate of change between year 0 and year 1 for population 1? What is it between year 5 and year 10? Include calculations in your answer. (2 points)

The rate of change between year 0 and year 1 is .5 and the rate of change between year 5 and 10 is also .5

3. Predict the average rate of change from year 5 to year 6 for population 1. Use the average rate of change you found in question 2 in your prediction. (1 point)

I think the average rate of change from year 5 to year 6 is .5 this is because each year the population is increasing by .5 according to question 2.

4. What type of function best models the growth for population 1? Give a reason for your answer. (1 point)

A linear function would model population 1 the best. This is because the population is increasing by .5 each year. It increases as a steady rate so it will be a straight line.

Population 2 pocket gophers

5. What is the maximum population per square mile during the first 10 years for population 2? (0.5 point)

The maximum population per square mile during the first 10 years is 60.7.

6. What is the average rate of change for population 2 between years 5 and 10 (x = 5 to x = 10)? (1 point)

The average rate of change is 10.02

7. The average rate of change for population 2 changes by a common ratio (multiplication) of 1.5 each year. What type of function best models this growth? (1 point)

A exponential function would best model this growth.

8. Estimate the average rate of change from year 5 to year 6 for population 2. Remember, the average rate of change for this population changes by a ratio of 1.5 each year. Show your work. HINT: First find the average rate of change from year 4 to year 5. (3 points)

The rate of change from year 5 to year 6 is about 3.75 since population 2 changes by a ratio of 1.5 each year. The rate of change from year 4 to 5 is 2.5 so 2.5*1.5 is 3.75.

Population 3 Osprey

9. What is the maximum population per square mile during the first 10 years for population 3? In what year did this occur? (1 point)

The maximum population per square mile during the first 10 years is 9.0 this occured in year 5.

10. What is the average rate of change for population 3 between years 5 and 10 (x = 5 to x = 10)? Show your work. Identify the change as an increase or a decrease. (2 points)

The change is a decrease.

11. What type of function best models the growth for population 3? Give a reason for your answer. (1 point)

A quadratic function best models the growth for population 3 because at first the population increases but then it decreases.

12. Use the graph provided. When do all three populations contain the same number of animals? (1 point)

In year 0 all three populations contained the same amount of animals.

13. Use the following graphs to verify your work on this question.

A. Estimate the average rate of change from year 5 to year 8 for population 3. Show your work. (2 points)

7.2-9/8-5 = -1.8/3 = -0.6

B. Estimate the average rate of change from year 8 to year 10 for population 3. Show your work. (2 points)

4-7.2/10-8 = -3.2/2 = -1.6

C. Based on the answers to Parts A and B, estimate the number of animals in population 3 in year 15, and give a reason for your estimate. (1 point)

The number of animals in year 15 will be 0 this is because the number of animals keeps steadily going down and you cannot have a negative number of animals.

Mathematics
Step-by-step answer
P Answered by Specialist

I DID YELLOWSTONE

I GOT A 100

Step-by-step explanation:

Make sense of the problem:

what is the estimated population for each animal at year 12.

Population 1 grizzly bear

1.  Is population 1 increasing or decreasing? (0.5 point)

Increasing

2. What is the rate of change between year 0 and year 1 for population 1? What is it between year 5 and year 10? Include calculations in your answer. (2 points)

The rate of change between year 0 and year 1 is .5 and the rate of change between year 5 and 10 is also .5

3. Predict the average rate of change from year 5 to year 6 for population 1. Use the average rate of change you found in question 2 in your prediction. (1 point)

I think the average rate of change from year 5 to year 6 is .5 this is because each year the population is increasing by .5 according to question 2.

4. What type of function best models the growth for population 1? Give a reason for your answer. (1 point)

A linear function would model population 1 the best. This is because the population is increasing by .5 each year. It increases as a steady rate so it will be a straight line.

Population 2 pocket gophers

5. What is the maximum population per square mile during the first 10 years for population 2? (0.5 point)

The maximum population per square mile during the first 10 years is 60.7.

6. What is the average rate of change for population 2 between years 5 and 10 (x = 5 to x = 10)? (1 point)

The average rate of change is 10.02

7. The average rate of change for population 2 changes by a common ratio (multiplication) of 1.5 each year. What type of function best models this growth? (1 point)

A exponential function would best model this growth.

8. Estimate the average rate of change from year 5 to year 6 for population 2. Remember, the average rate of change for this population changes by a ratio of 1.5 each year. Show your work. HINT: First find the average rate of change from year 4 to year 5. (3 points)

The rate of change from year 5 to year 6 is about 3.75 since population 2 changes by a ratio of 1.5 each year. The rate of change from year 4 to 5 is 2.5 so 2.5*1.5 is 3.75.

Population 3 Osprey

9. What is the maximum population per square mile during the first 10 years for population 3? In what year did this occur? (1 point)

The maximum population per square mile during the first 10 years is 9.0 this occured in year 5.

10. What is the average rate of change for population 3 between years 5 and 10 (x = 5 to x = 10)? Show your work. Identify the change as an increase or a decrease. (2 points)

The change is a decrease.

11. What type of function best models the growth for population 3? Give a reason for your answer. (1 point)

A quadratic function best models the growth for population 3 because at first the population increases but then it decreases.

12. Use the graph provided. When do all three populations contain the same number of animals? (1 point)

In year 0 all three populations contained the same amount of animals.

13. Use the following graphs to verify your work on this question.

A. Estimate the average rate of change from year 5 to year 8 for population 3. Show your work. (2 points)

7.2-9/8-5 = -1.8/3 = -0.6

B. Estimate the average rate of change from year 8 to year 10 for population 3. Show your work. (2 points)

4-7.2/10-8 = -3.2/2 = -1.6

C. Based on the answers to Parts A and B, estimate the number of animals in population 3 in year 15, and give a reason for your estimate. (1 point)

The number of animals in year 15 will be 0 this is because the number of animals keeps steadily going down and you cannot have a negative number of animals.

Mathematics
Step-by-step answer
P Answered by Master

I DID YELLOWSTONE

I GOT A 100

Step-by-step explanation:

Make sense of the problem:

what is the estimated population for each animal at year 12.

Population 1 grizzly bear

1.  Is population 1 increasing or decreasing? (0.5 point)

Increasing

2. What is the rate of change between year 0 and year 1 for population 1? What is it between year 5 and year 10? Include calculations in your answer. (2 points)

The rate of change between year 0 and year 1 is .5 and the rate of change between year 5 and 10 is also .5

3. Predict the average rate of change from year 5 to year 6 for population 1. Use the average rate of change you found in question 2 in your prediction. (1 point)

I think the average rate of change from year 5 to year 6 is .5 this is because each year the population is increasing by .5 according to question 2.

4. What type of function best models the growth for population 1? Give a reason for your answer. (1 point)

A linear function would model population 1 the best. This is because the population is increasing by .5 each year. It increases as a steady rate so it will be a straight line.

Population 2 pocket gophers

5. What is the maximum population per square mile during the first 10 years for population 2? (0.5 point)

The maximum population per square mile during the first 10 years is 60.7.

6. What is the average rate of change for population 2 between years 5 and 10 (x = 5 to x = 10)? (1 point)

The average rate of change is 10.02

7. The average rate of change for population 2 changes by a common ratio (multiplication) of 1.5 each year. What type of function best models this growth? (1 point)

A exponential function would best model this growth.

8. Estimate the average rate of change from year 5 to year 6 for population 2. Remember, the average rate of change for this population changes by a ratio of 1.5 each year. Show your work. HINT: First find the average rate of change from year 4 to year 5. (3 points)

The rate of change from year 5 to year 6 is about 3.75 since population 2 changes by a ratio of 1.5 each year. The rate of change from year 4 to 5 is 2.5 so 2.5*1.5 is 3.75.

Population 3 Osprey

9. What is the maximum population per square mile during the first 10 years for population 3? In what year did this occur? (1 point)

The maximum population per square mile during the first 10 years is 9.0 this occured in year 5.

10. What is the average rate of change for population 3 between years 5 and 10 (x = 5 to x = 10)? Show your work. Identify the change as an increase or a decrease. (2 points)

The change is a decrease.

11. What type of function best models the growth for population 3? Give a reason for your answer. (1 point)

A quadratic function best models the growth for population 3 because at first the population increases but then it decreases.

12. Use the graph provided. When do all three populations contain the same number of animals? (1 point)

In year 0 all three populations contained the same amount of animals.

13. Use the following graphs to verify your work on this question.

A. Estimate the average rate of change from year 5 to year 8 for population 3. Show your work. (2 points)

7.2-9/8-5 = -1.8/3 = -0.6

B. Estimate the average rate of change from year 8 to year 10 for population 3. Show your work. (2 points)

4-7.2/10-8 = -3.2/2 = -1.6

C. Based on the answers to Parts A and B, estimate the number of animals in population 3 in year 15, and give a reason for your estimate. (1 point)

The number of animals in year 15 will be 0 this is because the number of animals keeps steadily going down and you cannot have a negative number of animals.

Mathematics
Step-by-step answer
P Answered by Master
1. For this problem we just refer to the descriptions that you placed under the prompt. According to Malcolm's bandmate, it would be easier to solve the trinomial by subtracting 350 from both sides and then factoring the equation. Malcolm, on the other hand, thinks that we should manipulate the equation in order to make it a perfect square trinomial.

2. This trinomial would be easily solved by using Malcolm's idea. As Malcolm pointed out, you just need to apply a formula to manipulate the equation then you can find the roots in no time. Finding the factors of 350 just to solve the trinomial would be the hard way to go since you would be considering a lot of them.

3. For this item, we are just tasked to follow what Malcolm's bandmate started doing. So, we would just need to think of two numbers that would result to -350 when multiplied. To start off, let's think of something we can divide 350 by, let's say 70. Now, if we divide -350 by 70 the result would be -5 therefore that would be our two numbers (p and q). p + q would therefore just be 65.

p = 70
q = -5
p + q = 65

4. No, the factor table is not complete since you would need factors of -350 that would add up to -3, the coefficient of w. This rule is sort of a shortcut when factoring the trinomial, since expressing the roots in the form of (w + p)(w + q) would lead you to the original expression by following the rules. We do not see any factors that add up to -3 in the factor table.

5. Malcolm was almost right, but technically he missed the initial step. To make a perfect square trinomial, you first need to make sure that a (or the coefficient of the leading term) is equal to one. If not, you first need to divide the entire equation by a. Then, you apply what Malcolm says.

6. Since the coefficient of the leading term is already equal to one, we do not need to worry about the initial step anymore. For this item, we just need to divide -3 by two and square it then add the resulting number to both sides. The solution is shown below:

( \frac{-3}{2})^{2} =(-1.5)^{2}=2.25
w^{2}-3w+2.25=350+2.25
w^{2}-3w+2.25=352.25

7. To factor the trinomial, we just really need to make sense of the process we just did in the previous item. Notice that we just squared -1.5, after dividing -3 by 2. If you look at it closely, this is just the process of expanding the square of a binomial in reverse. Therefore, we know that our resulting expression is the square of (w - 1.5)

(w-1.5)^{2}=352.25

8. For this item we are just simply tasked to follow the instructions given. The process described in the item is how we are supposed to solve for the variable. The work and solution for this item is shown below:

\sqrt{ (w-1.5)^{2}}= \sqrt{352.25}
w-1.5=18.77
w=20.27

9. The solution does make sense in terms of the problem because, firstly, the answer we have arrived on is a positive number which means it is a realistic value of a measurement, and secondly, our solution in the previous item just followed basic arithmetic so we did not violate anything in the problem.

10. For this item, we can find the length by subtracting the value of the width by 3, as was dictated in the prompt. But before this, we first need to round our answer for the width to the nearest foot. 20 minus 3 is just 17. Multiplying 20 and 17 might not get us to 350 but this is just an approximation anyway. (Getting the product of the numbers before rounding off would give us an accurate one.)

w = 20 feet
l = 17 feet
Mathematics
Step-by-step answer
P Answered by Specialist
1. For this problem we just refer to the descriptions that you placed under the prompt. According to Malcolm's bandmate, it would be easier to solve the trinomial by subtracting 350 from both sides and then factoring the equation. Malcolm, on the other hand, thinks that we should manipulate the equation in order to make it a perfect square trinomial.

2. This trinomial would be easily solved by using Malcolm's idea. As Malcolm pointed out, you just need to apply a formula to manipulate the equation then you can find the roots in no time. Finding the factors of 350 just to solve the trinomial would be the hard way to go since you would be considering a lot of them.

3. For this item, we are just tasked to follow what Malcolm's bandmate started doing. So, we would just need to think of two numbers that would result to -350 when multiplied. To start off, let's think of something we can divide 350 by, let's say 70. Now, if we divide -350 by 70 the result would be -5 therefore that would be our two numbers (p and q). p + q would therefore just be 65.

p = 70
q = -5
p + q = 65

4. No, the factor table is not complete since you would need factors of -350 that would add up to -3, the coefficient of w. This rule is sort of a shortcut when factoring the trinomial, since expressing the roots in the form of (w + p)(w + q) would lead you to the original expression by following the rules. We do not see any factors that add up to -3 in the factor table.

5. Malcolm was almost right, but technically he missed the initial step. To make a perfect square trinomial, you first need to make sure that a (or the coefficient of the leading term) is equal to one. If not, you first need to divide the entire equation by a. Then, you apply what Malcolm says.

6. Since the coefficient of the leading term is already equal to one, we do not need to worry about the initial step anymore. For this item, we just need to divide -3 by two and square it then add the resulting number to both sides. The solution is shown below:

( \frac{-3}{2})^{2} =(-1.5)^{2}=2.25
w^{2}-3w+2.25=350+2.25
w^{2}-3w+2.25=352.25

7. To factor the trinomial, we just really need to make sense of the process we just did in the previous item. Notice that we just squared -1.5, after dividing -3 by 2. If you look at it closely, this is just the process of expanding the square of a binomial in reverse. Therefore, we know that our resulting expression is the square of (w - 1.5)

(w-1.5)^{2}=352.25

8. For this item we are just simply tasked to follow the instructions given. The process described in the item is how we are supposed to solve for the variable. The work and solution for this item is shown below:

\sqrt{ (w-1.5)^{2}}= \sqrt{352.25}
w-1.5=18.77
w=20.27

9. The solution does make sense in terms of the problem because, firstly, the answer we have arrived on is a positive number which means it is a realistic value of a measurement, and secondly, our solution in the previous item just followed basic arithmetic so we did not violate anything in the problem.

10. For this item, we can find the length by subtracting the value of the width by 3, as was dictated in the prompt. But before this, we first need to round our answer for the width to the nearest foot. 20 minus 3 is just 17. Multiplying 20 and 17 might not get us to 350 but this is just an approximation anyway. (Getting the product of the numbers before rounding off would give us an accurate one.)

w = 20 feet
l = 17 feet
Mathematics
Step-by-step answer
P Answered by PhD
Answer: 440 grams for 1.54 is the better value
Explanation:
Take the price and divide by the number of grams
1.54 / 440 =0.0035 per gram
1.26 / 340 =0.003705882 per gram
0.0035 per gram < 0.003705882 per gram
Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

The answer is in the image 

The answer is in the image 

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