What is the value of the expression 2j - 7jkm when j = 5, k = -14, and m = -3?
Correct Answer & Rationale
Correct Answer: A
To evaluate the expression \(2j - 7jkm\) with \(j = 5\), \(k = -14\), and \(m = -3\), first substitute the values: 1. Calculate \(2j\): \(2 \times 5 = 10\). 2. Calculate \(7jkm\): \(7 \times 5 \times -14 \times -3 = 1470\). 3. Combine the results: \(10 - 1470 = -1460\). Thus, the value of the expression is \(-1460\). Other options are incorrect because they either miscalculate the substitutions or the arithmetic operations involved, leading to different results that do not match the evaluated expression.
To evaluate the expression \(2j - 7jkm\) with \(j = 5\), \(k = -14\), and \(m = -3\), first substitute the values: 1. Calculate \(2j\): \(2 \times 5 = 10\). 2. Calculate \(7jkm\): \(7 \times 5 \times -14 \times -3 = 1470\). 3. Combine the results: \(10 - 1470 = -1460\). Thus, the value of the expression is \(-1460\). Other options are incorrect because they either miscalculate the substitutions or the arithmetic operations involved, leading to different results that do not match the evaluated expression.
Other Related Questions
What is the slope of the line shown on the graph
- A. -0.333333333
- B. -3
- C. 3
- D. 1\3
Correct Answer & Rationale
Correct Answer: D
The slope of a line represents the change in y over the change in x (rise over run). Option D, \( \frac{1}{3} \), indicates a positive slope, suggesting that for every 3 units moved horizontally to the right, the line rises by 1 unit vertically. Option A, -0.3333, represents a negative slope, which would indicate a decline rather than an ascent. Option B, -3, also indicates a steep negative slope, suggesting a significant drop. Option C, 3, indicates a positive slope but is too steep compared to the graph's gentle incline. Thus, D accurately reflects the line's moderate upward trend.
The slope of a line represents the change in y over the change in x (rise over run). Option D, \( \frac{1}{3} \), indicates a positive slope, suggesting that for every 3 units moved horizontally to the right, the line rises by 1 unit vertically. Option A, -0.3333, represents a negative slope, which would indicate a decline rather than an ascent. Option B, -3, also indicates a steep negative slope, suggesting a significant drop. Option C, 3, indicates a positive slope but is too steep compared to the graph's gentle incline. Thus, D accurately reflects the line's moderate upward trend.
Laura walks every evening on the edges of a sports field near her house. The field is in the shape of a rectangle 300 feet (ft) long and 200 ft wide, so 1 lap on the edges of the field is 1,000 ft. She enters through a gate at point G, located exactly halfway along the length of the field.
Type your answer in the box. You may use numbers, a decimal point (.), and/or negative sign (-) in your answer.
One evening on her walk, Laura walks across the field from point W back to the gate at point G. What is the distance she walks, in feet, from point W to point G?
Correct Answer & Rationale
Correct Answer: 250
To determine the distance Laura walks from point W to gate G, we can use the Pythagorean theorem. The field is a rectangle, and point W is at one corner. The length from W to G is half the length of the field (150 ft) and the width of the field (200 ft). Calculating the distance: Distance = √(150² + 200²) = √(22500 + 40000) = √62500 = 250 ft. Other options are incorrect because they do not accurately reflect the geometric relationship of the points. Distances such as 300 ft or 200 ft misinterpret the diagonal distance, while any number below 250 fails to account for both dimensions of the rectangle.
To determine the distance Laura walks from point W to gate G, we can use the Pythagorean theorem. The field is a rectangle, and point W is at one corner. The length from W to G is half the length of the field (150 ft) and the width of the field (200 ft). Calculating the distance: Distance = √(150² + 200²) = √(22500 + 40000) = √62500 = 250 ft. Other options are incorrect because they do not accurately reflect the geometric relationship of the points. Distances such as 300 ft or 200 ft misinterpret the diagonal distance, while any number below 250 fails to account for both dimensions of the rectangle.
Type your answer in the box. You may use numbers, a decimal point (.), and/or a negative sign (-) in your answer.
A company received a shipment of 8 boxes of metal brackets.
• There are 20 metal brackets in each box.
• The total weight of the shipment is 48 pounds.
What is the weight, in pounds, of each metal bracket?
Correct Answer & Rationale
Correct Answer: 0.3
To find the weight of each metal bracket, first calculate the total number of brackets by multiplying the number of boxes (8) by the number of brackets per box (20), resulting in 160 brackets. Next, divide the total weight of the shipment (48 pounds) by the total number of brackets (160). This calculation yields a weight of 0.3 pounds per bracket. Other options may include numbers that misrepresent the division or assume incorrect values for the total brackets or shipment weight. For example, using a weight of 1 pound per bracket would imply only 48 brackets, which contradicts the initial information provided.
To find the weight of each metal bracket, first calculate the total number of brackets by multiplying the number of boxes (8) by the number of brackets per box (20), resulting in 160 brackets. Next, divide the total weight of the shipment (48 pounds) by the total number of brackets (160). This calculation yields a weight of 0.3 pounds per bracket. Other options may include numbers that misrepresent the division or assume incorrect values for the total brackets or shipment weight. For example, using a weight of 1 pound per bracket would imply only 48 brackets, which contradicts the initial information provided.
Simplify: (3x - 5) + (-7x + 2)
- A. -4x^2 - 3
- B. -4x - 3
- C. 28
- D. -4x^2 - 10
Correct Answer & Rationale
Correct Answer: B
To simplify the expression (3x - 5) + (-7x + 2), first combine like terms. Start with the x terms: 3x + (-7x) results in -4x. Next, combine the constant terms: -5 + 2 equals -3. Thus, the simplified expression is -4x - 3, matching option B. Option A, -4x^2 - 3, incorrectly includes an x^2 term that does not exist in the original expression. Option C, 28, is unrelated to the simplification process. Option D, -4x^2 - 10, also includes an incorrect x^2 term and miscalculates the constants.
To simplify the expression (3x - 5) + (-7x + 2), first combine like terms. Start with the x terms: 3x + (-7x) results in -4x. Next, combine the constant terms: -5 + 2 equals -3. Thus, the simplified expression is -4x - 3, matching option B. Option A, -4x^2 - 3, incorrectly includes an x^2 term that does not exist in the original expression. Option C, 28, is unrelated to the simplification process. Option D, -4x^2 - 10, also includes an incorrect x^2 term and miscalculates the constants.