1.Let x, y be any two numbers that satisfies the conditions x ≠0, y ≠0, and x<y. Based on the properties of inequality, which of the following statements must be correct?
A.−x<−y
B.y−x>0
C.y/x>1
D.x/y<1
2.A pickup truck that can hold up to 3000 pounds is carrying a big machine that is 300 pounds and a few smaller ones that each weigh 60 pounds.
At least how many small machines can you fit so that it will not exceed the weight limit of the truck?
A.no more than 50
B.no less than 50
C.no less than 45
D.no more than 45
3.It usually takes Claude 40 minutes driving at 48 miles per hour to go from home to work. But due to road maintenance today, Claude has to take a detour, which makes the trip 8 miles longer than usual. What is the minimum speed Claude should travel so that he can reach the destination in less than 48 minutes?
A.30 miles per hour
B.56 miles per hour
C.50 miles per hour
D.64 miles per hour
1.Let x, y be any two numbers that satisfies the conditions x ≠0, y ≠0, and x<y. Based on the properties of inequality, which of the following statements must be correct?
A.−x<−y
B.y−x>0
C.y/x>1
D.x/y<1
2.A pickup truck that can hold up to 3000 pounds is carrying a big machine that is 300 pounds and a few smaller ones that each weigh 60 pounds.
At least how many small machines can you fit so that it will not exceed the weight limit of the truck?
A.no more than 50
B.no less than 50
C.no less than 45
D.no more than 45
3.It usually takes Claude 40 minutes driving at 48 miles per hour to go from home to work. But due to road maintenance today, Claude has to take a detour, which makes the trip 8 miles longer than usual. What is the minimum speed Claude should travel so that he can reach the destination in less than 48 minutes?
A.30 miles per hour
B.56 miles per hour
C.50 miles per hour
D.64 miles per hour
4.Raphael is timing how fast he can do a series of 5 math questions, aiming to complete them in less than 20 minutes. He has done 3 questions so far, with each of them taking 3 minutes to complete.
On average, how much time does Raphael have on each remaining question so he can reach his goal?
A.Raphael has no more than 5 minutes and 50 seconds to complete each remaining question.
B.Raphael has less than 5 minutes and 50 seconds to complete each remaining question.
C.Raphael has less than 5 minutes and 30 seconds to complete each remaining question.
D.Raphael has no more than 5 minutes and 30 seconds to complete each remaining question.
5.A retail store is buying a 500 count for a device and another 200 count for another version of the same device that costs $100 less than the original. What is the maximum cost of the original device, given that the store did not go over the budget of $155,000?
A.no more than $150
B.no more than $250
C.less than $150
D.less than $250
Here are the answers to the Using Linear Inequalities Quick Check.
1. y−x>0
2. no more than 45
3. 50 miles per hour
4. Raphael has less than 5 minutes and 30 seconds to complete each remaining question.
5. no more than $250
I got a 100%
@connexus student is 100% right thanks:))
Connexus Student is 100% thank you!!!
so why did you post all that stuff twice?
Just erase what you don't like and start over.
Anyway,
#1. B
A. No. -3 < -2, but -(-3) > -(-2)
C. No -3 < -2 but -2/-3 = 2/3 < 1
D. No. -3 < -2 but -3/-2 = 3/2 > 1
So, what do you get for the others?
im taking this right now
1. To determine which statement must be correct based on the properties of inequality, we can analyze each option:
A. −x < −y: This statement is not guaranteed to be correct since we cannot determine the signs of x and y without additional information. It depends on the actual values of x and y.
B. y − x > 0: This statement is correct since y is greater than x, and subtracting a smaller value from a larger value will always result in a positive number.
C. y/x > 1: This statement is not guaranteed to be correct since it depends on the actual values of x and y. If x = 1 and y = 2, the inequality holds. However, if x = 1/2 and y = 1, the inequality does not hold.
D. x/y < 1: This statement is correct since x is smaller than y, and dividing a smaller value by a larger value will always result in a number less than 1.
Therefore, the correct answer is option D. x/y < 1.
2. To determine the number of small machines that can be fit in the pickup truck without exceeding the weight limit, we need to subtract the weight of the big machine from the weight limit first. Then, we can divide the remaining weight by the weight of each small machine to find the maximum number of small machines.
Weight limit - Weight of big machine = 3000 pounds - 300 pounds = 2700 pounds
Maximum number of small machines = Remaining weight / Weight of each small machine = 2700 pounds / 60 pounds = 45 machines
Therefore, the minimum number of small machines that can be fitted without exceeding the weight limit is 45.
The correct answer is option D. no more than 45.
3. To determine the minimum speed Claude should travel so that he can reach the destination in less than 48 minutes, we need to consider the additional distance created by the detour.
Since Claude usually travels at 48 miles per hour and takes 40 minutes to reach the destination, the usual distance is (48 miles per hour) × (40 minutes / 60 minutes) = 32 miles.
The detour adds 8 miles to the usual distance, making the total distance 32 miles + 8 miles = 40 miles.
To calculate the minimum speed, we divide the total distance by the maximum time allowed:
Minimum speed = Total distance / Maximum time = 40 miles / (48 minutes / 60 minutes per hour) = 40 miles / 0.8 hours = 50 miles per hour
Therefore, the minimum speed Claude should travel is 50 miles per hour.
The correct answer is option C. 50 miles per hour.
4. To determine how much time Raphael has on each remaining question, we need to calculate the total time he has spent on the 3 questions completed so far and subtract it from his goal time of 20 minutes. Then, we divide the remaining time by the number of remaining questions.
Total time spent on 3 questions = 3 questions × 3 minutes per question = 9 minutes
Remaining time = Goal time - Total time spent = 20 minutes - 9 minutes = 11 minutes
To find the time Raphael has on each remaining question, we divide the remaining time by the number of remaining questions:
Time on each remaining question = Remaining time / (Total questions - Questions completed) = 11 minutes / (5 questions - 3 questions) = 11 minutes / 2 questions = 5.5 minutes
Therefore, Raphael has no more than 5 minutes and 30 seconds to complete each remaining question.
The correct answer is option D. no more than 5 minutes and 30 seconds.
5. To determine the maximum cost of the original device, we need to consider the quantities and prices of the devices.
Let the cost of the original device be x. The cost of the second version is $100 less, so its cost would be x - $100.
The store is buying a 500 count of the original device and a 200 count of the second version. To stay within the budget of $155,000, the total cost should not exceed this amount:
(500 devices) * (x) + (200 devices) * (x - $100) ≤ $155,000
500x + 200(x - $100) ≤ $155,000
500x + 200x - $20,000 ≤ $155,000
700x ≤ $155,000 + $20,000
700x ≤ $175,000
x ≤ $175,000 / 700
x ≤ $250
Therefore, the maximum cost of the original device can be no more than $250.
The correct answer is option B. no more than $250.