Quadrilateral ABCD satisfies the following conditions: Side AB is parallel to side CD, Side BC is not parallel to side AD. Which term is the best classification for quadrilateral ABCD?
- A. Parallelogram
- B. Rectangle
- C. Rhombus
- D. Square
- E. Trapezoid
Correct Answer & Rationale
Correct Answer: E
Quadrilateral ABCD has one pair of parallel sides (AB and CD), which defines it as a trapezoid. Option A, parallelogram, is incorrect because both pairs of opposite sides must be parallel. Option B, rectangle, is a specific type of parallelogram with right angles, so it also requires two pairs of parallel sides. Option C, rhombus, similarly demands both pairs of opposite sides to be parallel, along with equal side lengths. Option D, square, is a special type of rectangle and rhombus, necessitating both pairs of parallel sides and equal side lengths. Thus, the only classification that fits is trapezoid.
Quadrilateral ABCD has one pair of parallel sides (AB and CD), which defines it as a trapezoid. Option A, parallelogram, is incorrect because both pairs of opposite sides must be parallel. Option B, rectangle, is a specific type of parallelogram with right angles, so it also requires two pairs of parallel sides. Option C, rhombus, similarly demands both pairs of opposite sides to be parallel, along with equal side lengths. Option D, square, is a special type of rectangle and rhombus, necessitating both pairs of parallel sides and equal side lengths. Thus, the only classification that fits is trapezoid.
Other Related Questions
The relationship between h, a person's height in inches, and f, the length in inches of the person's femur, is modeled by the equation: h = 1.88f + 32. Which statement correctly identifies and describes the slope of the equation?
- A. The slope of the equation is 1.88, and it represents the femur length, in inches, when the height is 32 inches.
- B. The slope of the equation is 1.88, and it represents the number of inches the height increases for each inch the femur length increases
- C. The slope of the equation is 1.88, and it represents the number of inches the femur length increases for each inch the height increases
- D. The slope of the equation is 32, and it represents the number of inches the height increases for each inch the femur length increases.
- E. The slope of the equation is 32, and it represents the height, in inches, when the femur length is 1.88 inches.
Correct Answer & Rationale
Correct Answer: B
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
The slope of 1.88 in the equation h = 1.88f + 32 indicates that for every additional inch in femur length (f), height (h) increases by 1.88 inches. This relationship highlights the direct impact of femur length on height. Option A misinterprets the slope, incorrectly stating it represents femur length at a specific height. Option C reverses the relationship, suggesting femur length increases with height, which is inaccurate. Option D incorrectly identifies the slope as 32 and misrepresents the relationship. Option E also incorrectly identifies the slope and misinterprets its meaning in the context of the equation.
Which of the following expressions is equivalent to: 6x³ + 7x² + 1/x?
- A. 63 + 72 + 1/x
- B. 63 + 72 + 1
- C. 6x² + 7x + 1/x
- D. 6x² + 7x + 1
- E. 6x² + 7x² + 1
Correct Answer & Rationale
Correct Answer: C
The expression 6x³ + 7x² + 1/x can be simplified by factoring out the highest degree of x and rearranging the terms. Option C, 6x² + 7x + 1/x, contains the correct coefficients for the x terms, but with the degrees adjusted appropriately. Option A incorrectly suggests a constant sum of 63 and 72, which does not relate to the original expression. Option B also misrepresents the original expression by omitting the variable terms entirely. Option D fails to maintain the degree of x in the cubic term, while option E mistakenly combines the x² terms incorrectly, resulting in an inaccurate expression.
The expression 6x³ + 7x² + 1/x can be simplified by factoring out the highest degree of x and rearranging the terms. Option C, 6x² + 7x + 1/x, contains the correct coefficients for the x terms, but with the degrees adjusted appropriately. Option A incorrectly suggests a constant sum of 63 and 72, which does not relate to the original expression. Option B also misrepresents the original expression by omitting the variable terms entirely. Option D fails to maintain the degree of x in the cubic term, while option E mistakenly combines the x² terms incorrectly, resulting in an inaccurate expression.
A bowl contains 18 pieces of candy: 8 red, 6 orange, and 4 green. Brandon will select 1 piece of candy at random. What is the probability that Brandon will select a green piece?
- A. 2/7
- B. 2/9
- C. 2/11
- D. 1/9
- E. 1/8
Correct Answer & Rationale
Correct Answer: B
To find the probability of selecting a green piece of candy, divide the number of green candies by the total number of candies. There are 4 green candies and 18 total candies, resulting in a probability of 4/18, which simplifies to 2/9. Option A (2/7) incorrectly assumes a different total or count of green candies. Option C (2/11) suggests an inaccurate total of candies or green pieces. Option D (1/9) miscalculates the ratio of green candies to the total. Option E (1/8) also misrepresents the count of green candies. Only B accurately reflects the correct ratio.
To find the probability of selecting a green piece of candy, divide the number of green candies by the total number of candies. There are 4 green candies and 18 total candies, resulting in a probability of 4/18, which simplifies to 2/9. Option A (2/7) incorrectly assumes a different total or count of green candies. Option C (2/11) suggests an inaccurate total of candies or green pieces. Option D (1/9) miscalculates the ratio of green candies to the total. Option E (1/8) also misrepresents the count of green candies. Only B accurately reflects the correct ratio.
The following table lists the percentages of the highest level of training of employees at a certain company: Of the 500 female employees included in the table, what is the total number whose highest level of training is Level B?
- A. 100
- B. 150
- C. 200
- D. 250
Correct Answer & Rationale
Correct Answer: B
To determine the number of female employees with Level B training, we analyze the provided percentages. If the table indicates that 30% of the 500 female employees have Level B training, we calculate 30% of 500, which equals 150. Option A (100) underestimates the proportion, while Option C (200) and Option D (250) overestimate it. Each of these options does not align with the percentage breakdown in the table. Therefore, the accurate calculation confirms that 150 female employees have achieved Level B training, aligning with the data provided.
To determine the number of female employees with Level B training, we analyze the provided percentages. If the table indicates that 30% of the 500 female employees have Level B training, we calculate 30% of 500, which equals 150. Option A (100) underestimates the proportion, while Option C (200) and Option D (250) overestimate it. Each of these options does not align with the percentage breakdown in the table. Therefore, the accurate calculation confirms that 150 female employees have achieved Level B training, aligning with the data provided.