Point (-3,-6) quadrant?
- A. I
- B. II
- C. III
- D. IV
Correct Answer & Rationale
Correct Answer: C
The point (-3, -6) is located in the Cartesian coordinate system where the x-coordinate is negative and the y-coordinate is also negative. This combination places the point in Quadrant III, where both x and y values are less than zero. Option A (I) is incorrect as Quadrant I contains positive x and y values. Option B (II) is wrong because Quadrant II has a negative x value and a positive y value. Option D (IV) is not applicable since Quadrant IV features a positive x value and a negative y value. Thus, the only quadrant that matches the coordinates (-3, -6) is Quadrant III.
The point (-3, -6) is located in the Cartesian coordinate system where the x-coordinate is negative and the y-coordinate is also negative. This combination places the point in Quadrant III, where both x and y values are less than zero. Option A (I) is incorrect as Quadrant I contains positive x and y values. Option B (II) is wrong because Quadrant II has a negative x value and a positive y value. Option D (IV) is not applicable since Quadrant IV features a positive x value and a negative y value. Thus, the only quadrant that matches the coordinates (-3, -6) is Quadrant III.
Other Related Questions
Caterpillar 1 ft in 7.5 min. 18 min?
- A. 2.4
- B. 8
- C. 11.5
- D. 25.5
Correct Answer & Rationale
Correct Answer: A
To determine how far the caterpillar travels in 18 minutes, first calculate its speed. It moves 1 foot in 7.5 minutes, which equates to \( \frac{1 \text{ ft}}{7.5 \text{ min}} \). In 18 minutes, the distance covered can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Converting 18 minutes into feet: \[ \text{Distance} = \left(\frac{1 \text{ ft}}{7.5 \text{ min}}\right) \times 18 \text{ min} = 2.4 \text{ ft} \] Option B (8) overestimates the distance, while C (11.5) and D (25.5) significantly exceed the calculated distance, demonstrating a misunderstanding of the speed-time relationship.
To determine how far the caterpillar travels in 18 minutes, first calculate its speed. It moves 1 foot in 7.5 minutes, which equates to \( \frac{1 \text{ ft}}{7.5 \text{ min}} \). In 18 minutes, the distance covered can be calculated using the formula: \[ \text{Distance} = \text{Speed} \times \text{Time} \] Converting 18 minutes into feet: \[ \text{Distance} = \left(\frac{1 \text{ ft}}{7.5 \text{ min}}\right) \times 18 \text{ min} = 2.4 \text{ ft} \] Option B (8) overestimates the distance, while C (11.5) and D (25.5) significantly exceed the calculated distance, demonstrating a misunderstanding of the speed-time relationship.
Rounds to 87.5 in tenths?
- A. 88
- B. 87.56
- C. 87.459
- D. 87.05
Correct Answer & Rationale
Correct Answer: C
When rounding to the nearest tenth, the digit in the hundredths place determines whether to round up or down. For 87.5, the first digit after the decimal is 5, indicating that we round up. Option A (88) rounds to the nearest whole number, not the nearest tenth. Option B (87.56) rounds to 87.6, which is higher than 87.5. Option D (87.05) rounds to 87.1, which is lower. Only option C (87.459) rounds to 87.5 when considering the tenths place, making it the only valid choice for rounding to 87.5 in tenths.
When rounding to the nearest tenth, the digit in the hundredths place determines whether to round up or down. For 87.5, the first digit after the decimal is 5, indicating that we round up. Option A (88) rounds to the nearest whole number, not the nearest tenth. Option B (87.56) rounds to 87.6, which is higher than 87.5. Option D (87.05) rounds to 87.1, which is lower. Only option C (87.459) rounds to 87.5 when considering the tenths place, making it the only valid choice for rounding to 87.5 in tenths.
P=2(L+W), P=48, W=L-4. Width?
- A. 10
- B. 12
- C. 20
- D. 24
Correct Answer & Rationale
Correct Answer: A
To find the width (W), start with the given perimeter formula \( P = 2(L + W) \). Substituting \( P = 48 \) gives \( 48 = 2(L + W) \), which simplifies to \( L + W = 24 \). Given \( W = L - 4 \), substitute this into the equation: \( L + (L - 4) = 24 \). This simplifies to \( 2L - 4 = 24 \), leading to \( 2L = 28 \) and \( L = 14 \). Thus, \( W = 14 - 4 = 10 \). Option B (12) does not satisfy the perimeter equation. Option C (20) and Option D (24) also do not fit the derived equations, confirming that W must be 10.
To find the width (W), start with the given perimeter formula \( P = 2(L + W) \). Substituting \( P = 48 \) gives \( 48 = 2(L + W) \), which simplifies to \( L + W = 24 \). Given \( W = L - 4 \), substitute this into the equation: \( L + (L - 4) = 24 \). This simplifies to \( 2L - 4 = 24 \), leading to \( 2L = 28 \) and \( L = 14 \). Thus, \( W = 14 - 4 = 10 \). Option B (12) does not satisfy the perimeter equation. Option C (20) and Option D (24) also do not fit the derived equations, confirming that W must be 10.
Order 0.68, 1/12, 1(1/5), 3/5 least to greatest?
- A. 1(1/5), 0.68, 3/5, 1/12
- B. 1/12, 3/5, 0.68, 1(1/5)
- C. 1/12, 0.68, 3/5, 1(1/5)
- D. 0.68, 1/12, 3/5, 1(1/5)
Correct Answer & Rationale
Correct Answer: B
To compare the values, first convert them to a common format. - 1(1/5) equals 1.2. - 0.68 remains as is. - 3/5 converts to 0.6. - 1/12 is approximately 0.0833. Ordering these from least to greatest gives: 1/12 (0.0833), 3/5 (0.6), 0.68, and 1(1/5) (1.2). Option A incorrectly places 1(1/5) first, while C misplaces 3/5 and 0.68. Option D also misorders the values by placing 0.68 before 1/12. Thus, B accurately reflects the correct sequence of values.
To compare the values, first convert them to a common format. - 1(1/5) equals 1.2. - 0.68 remains as is. - 3/5 converts to 0.6. - 1/12 is approximately 0.0833. Ordering these from least to greatest gives: 1/12 (0.0833), 3/5 (0.6), 0.68, and 1(1/5) (1.2). Option A incorrectly places 1(1/5) first, while C misplaces 3/5 and 0.68. Option D also misorders the values by placing 0.68 before 1/12. Thus, B accurately reflects the correct sequence of values.