Algebra 1 Chapter 4 Review

The relationship between the number of sports teams a person belongs to and the amount of free time they have per week is a linear function. This means that as the number of sports teams increases, the amount of free time decreases or vice versa, and the relationship can be represented by a straight line on a graph.

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The given function states that the number of jumping jacks you can do in x minutes is equal to 27 times x. To find out how many jumping jacks can be done in 15 minutes, we substitute x with 15 in the function. Therefore, j(15) = 27 * 15 = 405. So, the correct answer is 405.

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The given sequence is arithmetic because there is a common difference between each term. The common difference is -0.5, as each term is obtained by subtracting 0.5 from the previous term.

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The pattern in the given sequence is that each term is obtained by multiplying the previous term by 2. Therefore, to find the next two terms, we multiply the previous term (8) by 2. This gives us 16 as the next term, and multiplying 16 by 2 gives us 32 as the term after that.

The given answer states that the relation is not a function. This means that there exists at least one element in the domain that is associated with more than one element in the range. In a function, each element in the domain should be associated with only one element in the range. Therefore, if the given relation violates this condition, it is not a function.

The given correct answer states that the domain of the relation is -9, 3, and 5, while the range is -10, -4, 1, and 14. This means that the relation consists of the values -9, 3, and 5 as inputs, and the values -10, -4, 1, and 14 as outputs.

The relation is not a function because it fails the vertical line test. This means that there exists at least one vertical line that intersects the graph of the relation at more than one point. In a function, each input (x-value) should correspond to only one output (y-value), but in this case, there are multiple y-values for at least one x-value, violating the definition of a function.

The sequence is not arithmetic because there is no consistent difference between consecutive terms. The difference between the first two terms is 5, the difference between the second and third terms is 6, and the difference between the third and fourth terms is 7. Since the differences are not the same, the sequence is not arithmetic.

The snail will travel 12.9 feet in 6 minutes. This can be calculated by multiplying the rate of 2.15 feet per minute by the time of 6 minutes.

The rule to describe the function is that the tomato plant grows approximately 0.7 centimeters per day. To find out after how many days the tomato plant will be 18.7 centimeters tall, we can subtract the initial height of 11 centimeters from the target height of 18.7 centimeters. Then, we divide this difference by the growth rate of 0.7 centimeters per day. This gives us the number of days it will take for the tomato plant to reach 18.7 centimeters tall, which is approximately 12 days.

The correct answer is "The perimeter, P, is equal to the length of the base of one triangle multiplied by the number of triangles in the figure, n, plus two times the length of another side. The equation for the perimeter is P=4n+14." This is because the equation correctly represents the relationship between the number of triangles and the perimeter of the figure. The equation states that the perimeter is equal to the length of the base of one triangle multiplied by the number of triangles, n, plus two times the length of another side. This accurately describes how the perimeter is determined based on the number of triangles in the figure.

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The rule to represent the balance in the account as an arithmetic sequence is: each month, the balance decreases by $32.40. To find out how many months you can pay your phone bill without depositing any more money, you need to divide the initial balance of $740.00 by the decrease amount of $32.40. This gives you approximately 22.84 months. Since you cannot have a fraction of a month, you can pay your phone bill for 22 months without depositing any more money.

The rule that represents this function is y = x^2. This can be determined by observing that the second element in each ordered pair is the square of the first element.

The function rule for the situation is C=14n, where C represents the cost of n DVDs. This means that the cost of the DVDs is directly proportional to the number of DVDs purchased. The graph of this function would be discrete because the number of DVDs purchased can only be a whole number, resulting in discrete points on the graph.

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For part a), to find the employee's earnings for a week with $600 total sales, we can substitute d = 600 into the function rule f(d) = 280 + 0.03d. So, f(600) = 280 + 0.03(600) = $298.

For part b), to find the employee's total sales for a week when her earnings were $670, we need to solve the equation 670 = 280 + 0.03d for d. Subtracting 280 from both sides gives 390 = 0.03d. Dividing both sides by 0.03 gives d = 13000.

Therefore, the employee's earnings for a week with $600 total sales is $298, and her total sales for a week when her earnings were $670 is $13000.

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The domain of the function represents the possible input values, which in this case is the number of cups of flour. Since we have 8 cups of flour, a reasonable domain would be any non-negative number less than or equal to 8. Therefore, the domain is [0, 8].

The range of the function represents the possible output values, which in this case is the number of cookies. Since it takes 1 cup of flour to make 24 cookies, a reasonable range would be any non-negative multiple of 24. Therefore, the range is [0, infinity).

The graph of the function would be a straight line with a positive slope, passing through the origin (0,0) and extending indefinitely in the positive y-direction.