5 exercises · 4 automatically checked · 1 written self-check · Untimed
4 questions · Shuffled order · Untimed practice
Try each question before choosing Check answer. Guide question labels stay the same when you shuffle the bank. 1 written response appears below the bank, with model answers for self-review; these are not automatically graded. Follow any rounding instruction in the question.
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Compare the reasoning as well as the answer. Equivalent valid methods are welcome. A referenced example provides a targeted repair route.
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A squared equation produces candidates 4 and −3 for = x. Which candidates satisfy the original equation?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
Only 4.
The principal square root is nonnegative, so a negative right side cannot work. At x
How many real solutions does (x2 − 16)/(x − 4) = 8 have?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
0.
The domain excludes x
A circle has radius centimeters. Find its area to the nearest tenth of a square centimeter.
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
94.2 cm2.
Use A = πr2 = π()2 = 30π ≈ 94.2477796, which rounds to 94.2. Enter 30*pi, not a rounded radius that will subsequently be squared. The exact ratio A/π
Each shuttle holds at most 12 passengers. What is the least number of shuttles needed for 137 passengers?
Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.
12.
137/12 ≈ 11.4167, but the count must be an integer with enough seats. Eleven shuttles hold only 132 passengers; twelve hold 144. The first feasible count is 12, even though ordinary rounding of the quotient would give 11. Review Example 4.10.
Review Checking answers and numerical precision
Write your complete response before opening the model answer. Compare both your answer and your reasoning.
The exact solution of an equation is 5/8. Give both an exact fraction entry and an exact decimal entry for a numeric-response field.
5/8 and .625.
Because 5 ÷ 8 0.625 also fits. Do not attach units or a percent sign unless the quantity itself has first been converted to the requested percent number. Review Example 4.04.