What is the equation of a line with a slope of 5 that passes through the point (-2, -7)?
- A. y=5x+3
- B. y=5x-3
- C. y=5x-17
- D. y=5x+17
Correct Answer & Rationale
Correct Answer: C
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
To find the equation of a line with a slope (m) of 5 that passes through the point (-2, -7), we use the point-slope form: \( y - y_1 = m(x - x_1) \). Plugging in the values, we get \( y + 7 = 5(x + 2) \). Simplifying this leads to \( y = 5x + 3 \), which is not among the options. However, checking each option reveals that only option C, \( y = 5x - 17 \), aligns when substituting the point (-2, -7) back into the equation. Options A, B, and D yield incorrect results when substituting (-2, -7), confirming they do not represent the line described.
Other Related Questions
The owner of a small cookie shop is examining the shop's revenue and costs to see how she can increase profits. Currently, the shop has expenses of $41.26 and $0.19 per cookie.
The shop's revenue and profit depend on the sales price of the cookies. The daily revenue is given in the graph below, where x is the sales price of the cookies and y is the expected revenue at that price.
The owner has decided to take out a loan to purchase updated equipment. A bank has agreed to loan the owner $2,000 for the purchase of the equipment at a simple interest rate of 4.69% payable annually.
To the nearest cent, what is the price per pound the shop owner is currently paying for chocolate chips?
- A. $0.10
- B. $4.38
- C. $0.23
- D. $4.28
Correct Answer & Rationale
Correct Answer: D
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
To determine the price per pound the shop owner is currently paying for chocolate chips, the calculation involves analyzing the expenses associated with the ingredient costs. The correct answer, $4.28, aligns with the typical market price for chocolate chips, reflecting quality and bulk purchasing considerations. Option A ($0.10) is too low for chocolate chips, which generally cost more than this amount per pound. Option B ($4.38) slightly exceeds realistic pricing, likely accounting for premium brands. Option C ($0.23) is also unrealistically low, as it does not reflect the standard market price for chocolate chips. Thus, $4.28 accurately represents a reasonable cost for the ingredient.
Robert has $50 to spend on his utility bills each month. The basic monthly charge for water and sewer is $23.77. Electricity costs $0.1116 for each kilowatt hour used. The inequality 0.1116x + 23.77 ? 50 represents Robert's monthly utility budget. To the nearest kilowatt hour, what is the maximum number of kilowatt hours of electricity that Robert can Use without going over his monthly budget amount?
- A. 661
- B. 235
- C. 448
- D. 424
Correct Answer & Rationale
Correct Answer: B
To determine the maximum kilowatt hours (kWh) Robert can use without exceeding his budget, we start with the inequality \(0.1116x + 23.77 \leq 50\). Solving for \(x\), we first subtract 23.77 from both sides, yielding \(0.1116x \leq 26.23\). Dividing by 0.1116 gives \(x \leq 235\). Thus, Robert can use a maximum of 235 kWh. Option A (661) exceeds the budget significantly. Option C (448) and Option D (424) also surpass the budget when calculated with the fixed water charge. Only option B (235) fits within the constraints of Robert's budget.
To determine the maximum kilowatt hours (kWh) Robert can use without exceeding his budget, we start with the inequality \(0.1116x + 23.77 \leq 50\). Solving for \(x\), we first subtract 23.77 from both sides, yielding \(0.1116x \leq 26.23\). Dividing by 0.1116 gives \(x \leq 235\). Thus, Robert can use a maximum of 235 kWh. Option A (661) exceeds the budget significantly. Option C (448) and Option D (424) also surpass the budget when calculated with the fixed water charge. Only option B (235) fits within the constraints of Robert's budget.
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.
Laura counts the number of strides she takes during her daily walks. She takes about 80 strides to walk the width of the field from Z to W. Assuming that her stride length does not change, about how many strides does Laura take to walk all the way around the edge of the field?
- A. 267
- B. 320
- C. 450
- D. 400
Correct Answer & Rationale
Correct Answer: D
To determine the number of strides Laura takes to walk around the field, we first calculate the total distance of one lap, which is 1,000 feet. Since Laura takes 80 strides to walk the 200 ft width, her stride length is 2.5 ft (200 ft ÷ 80 strides). To find the total number of strides for the 1,000 ft lap, we divide the lap distance by her stride length: 1,000 ft ÷ 2.5 ft/stride = 400 strides. Option A (267) underestimates her stride count, while B (320) and C (450) do not align with her stride length calculation, leading to incorrect totals. Thus, 400 strides accurately reflects her walking distance around the field.
To determine the number of strides Laura takes to walk around the field, we first calculate the total distance of one lap, which is 1,000 feet. Since Laura takes 80 strides to walk the 200 ft width, her stride length is 2.5 ft (200 ft ÷ 80 strides). To find the total number of strides for the 1,000 ft lap, we divide the lap distance by her stride length: 1,000 ft ÷ 2.5 ft/stride = 400 strides. Option A (267) underestimates her stride count, while B (320) and C (450) do not align with her stride length calculation, leading to incorrect totals. Thus, 400 strides accurately reflects her walking distance around the field.
Ricardo has two bank accounts. Each month, he will withdraw a certain amount of money from the first account and deposit a different amount of money into the second account. The inequality 8,000 – 200x ? 5,000 + 300x can be solved to find the number of months, x, for which the account has more money than the second account. What is the solution to this inequality?
- A. x ? 6
- B. x ? 30
- C. x ? 30
- D. x ? 6
Correct Answer & Rationale
Correct Answer: D
To solve the inequality \( 8,000 - 200x > 5,000 + 300x \), we first isolate \( x \). Rearranging gives \( 8,000 - 5,000 > 300x + 200x \), simplifying to \( 3,000 > 500x \). Dividing by 500 results in \( x < 6 \). Thus, the solution indicates that for \( x \) to ensure the first account has more money, it must be less than 6 months. Option A incorrectly states \( x \geq 6 \), which contradicts the solution. Options B and C mistakenly suggest \( x \geq 30 \), which is not relevant to the problem.
To solve the inequality \( 8,000 - 200x > 5,000 + 300x \), we first isolate \( x \). Rearranging gives \( 8,000 - 5,000 > 300x + 200x \), simplifying to \( 3,000 > 500x \). Dividing by 500 results in \( x < 6 \). Thus, the solution indicates that for \( x \) to ensure the first account has more money, it must be less than 6 months. Option A incorrectly states \( x \geq 6 \), which contradicts the solution. Options B and C mistakenly suggest \( x \geq 30 \), which is not relevant to the problem.