For what values of x will the angle shown below be obtuse?

A. 0 < x < 90
Incorrect. To calculate the minimum value of x, use 2x + 5 > 90 and to calculate the maximum value of x, use 2x + 5 < 180.

B. 45 < x < 90
Incorrect. To calculate the minimum value of x, use 2x + 5 > 90 and solve. To calculate the maximum value of x, use 2x + 5 <180 and solve.

C. 42.5 < x < 87.5
Correct! The minimum value of x, or 2x + 5 > 90, is x > 42.5 and the maximum value of x, or 2x + 5 < 180, is x < 87.5.

D. 0 < x < 180
Incorrect. To calculate the minimum value of x, use 2x + 5 > 90 and to calculate the maximum value of x, use 2x + 5 < 180.

On a field trip to the zoo, the school brought four times as many students as chaperones. Tickets for students cost $2 each and tickets for chaperones cost $6 each. If the total charge for the students and chaperones was less than $115, not including tax, what is the maximum number of chaperones that could have attended the field trip?

A. 8
Correct! If c = number of chaperones and 6c = cost of chaperones, then 4c = number of students and 2(4c) = 8c = cost of students. So, 6c + 8c < 115, or 14c < 115 or c < 8.2. Therefore, the maximum number of chaperones is 8.

B. 32
Incorrect. Use c = number of chaperones and 6c = cost of chaperones. Determine the number and cost of the students in terms of c and calculate the maximum number of chaperones.

C. 9
Incorrect. If c = number of chaperones and 6c = cost of chaperones, then 4c = number of students and 2(4c) = 8c = cost of students. So, 6c + 8c < 115, or 14c < 115 or c < 8.2. Therefore, the maximum number of chaperones is 8.2.

D. 3
Incorrect. Use c = number of chaperones and 6c = cost of chaperones. Determine the number and cost of the students in terms of c and calculate the maximum number of chaperones.

In medicine, the systolic blood pressure is the higher number in a blood pressure reading and is the pressure generated when the heart contracts. The formula P ≤ 1 2 a + 110 can be used to determine the normal systolic blood pressure, P, based on a person's age, a. At age 16, what does 118 represent in terms of normal systolic blood pressure?

A. maximum normal systolic blood pressure
Correct! To calculate the normal systolic blood pressure, P, for a person 16 years old, use P less than or equal to one-half times 16 +110, or P less than or equal to 8 + 110, or P less than or equal to 118. Therefore, the normal systolic blood pressure for a person 16 years old should be at most 118.

B. minimum normal systolic blood pressure
Incorrect. To calculate the normal systolic blood pressure, P, for a person 16 years old, use P less than or equal to one-half times 16 +110, or P less than or equal to 8 + 110, or P less than or equal to 118.

C. equal normal systolic blood pressure
Incorrect. To calculate the normal systolic blood pressure, P, for a person 16 years old, use P less than or equal to one-half times 16 +110, or P less than or equal to 8 + 110, or P less than or equal to 118.

D. not equal normal systolic blood pressure
Incorrect. To calculate the normal systolic blood pressure, P, for a person 16 years old, use P less than or equal to one-half times 16 +110, or P less than or equal to 8 + 110, or P less than or equal to 118.

Liam plans to watch the latest movie trilogy on DVD. The cost to rent or purchase the DVD set is shown in the table below.

He believes that it would cost less to rent the DVD set rather than purchase it since he plans to keep it only 7 days before it is returned. Is his conclusion reasonable?

A. No, because if x represents the number of days it is rented, then 2.50x < 18, and 2.50(7) < 18, or 14 < 18.
Incorrect. The cost to rent the DVD set for 7 days is $17.50, rather than $14.

B. No, because if x represents the number of days it is rented, then 2.50x > 18, and 2.50(7) > 18, or 17.50 > 18.
Incorrect. 17.50 > 18 is not a true statement. Rather, 17.50 < 18.

C. Yes, because if x represents the number of days it is rented, then 2.50x < 18, and 2.50(7) < 18, or 17.50 < 18.
Correct! The cost to rent the DVD set can be calculated using 2.50x < 18, with x = number of days rented. If x = 7, then 2.50(7) < 18, or 17.50 < 18. Therefore, Liam’s conclusion is reasonable.

D. Yes, because if x represents the number of days it is rented, then 2.50x < 18, and 2.50(6) < 18, or 15 < 18.
Incorrect. The number of days that Liam plans to rent the DVD set is 7 rather than 6.

Mrs. Cooper plans to order invitations for her daughter's birthday party. The invitations cost $11.25 per box and the shipping charge is $5.00, regardless of the number of boxes ordered.

Mrs. Cooper budgeted $35.00 for the invitations. She believes that the maximum number of boxes of invitations she can order is 3. Is her conclusion reasonable?

A. Yes, because if x represents the number of boxes of invitations and the budget is $35, then 11.25x + 5 > 35. With 3 boxes ordered, 11.25(3) + 5 > 35, or 38.75 > 35.
Incorrect. The amount Mrs. Cooper spends on the invitations and shipping combined must be less than or equal to her budget of $35.

B. Yes, because if x represents the number of boxes of invitations and the budget is $35, then 11.25x < 35. With 3 boxes ordered, 11.25(3) < 35, or 33.75 < 35.
Incorrect. Mrs. Cooper must also pay a flat rate of $5 for shipping.

C. No, because if x represents the number of boxes of invitations and the budget is $35, then 11.75x + 5 < 35. With 3 boxes ordered, 11.75(3) + 5 < 35, or 40.25 < 35.
Incorrect. Mrs. Cooper planned to spend $11.25 per box of invitations, rather than $11.75.

D. No, because if x represents the number of boxes of invitations and the budget is $35, then 11.25x + 5 < 35. With 3 boxes ordered, 11.25(3) + 5 < 35, or 38.75 < 35.
Correct! If she orders 3 boxes of invitations, then she will spend 11.25(3), or $33.75 on the invitations and $5 for shipping sums to $38.75, which is more than her budget of $35.