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Solve 2(x + 4) ext >= 5x - 1, graph the solution, change 111012 to base ten, and find the time when three machines produce packages simultaneously.
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Step-by-step solution
12 stepsHere are the solutions to the questions:
4a. Solve and graph the solution.
Distribute the 2 on the left side.
Subtract $2x$ from both sides.
Add 1 to both sides.
Divide by 3.
This can also be written as .
Graph the solution.
The solution means all numbers less than or equal to 3. On a number line, this is represented by a closed circle at 3 and an arrow extending to the left.
<------------------•---------------------> -1 0 1 2 3 4 5 <----- (closed circle at 3, arrow to the left)The solution is .
4b. Change to base ten numeral.
To convert a binary number to base ten, multiply each digit by the corresponding power of 2.
So, .
5a. Three machines in a factory produce packages. Machine A every 12 minutes, Machine B every 18 minutes, and Machine C every 24 minutes. Find the time (in minutes) when all three machines will produce a package at the same time.
This problem requires finding the Least Common Multiple (LCM) of 12, 18, and 24.
Find the prime factorization of each number.
Identify the highest power of each prime factor present in any of the numbers.
For prime factor 2: The highest power is (from 24).
For prime factor 3: The highest power is (from 18).Multiply these highest powers to find the LCM.
All three machines will produce a package at the same time after .
5b. If an item is sold at a 20% profit for GH¢60, find the cost price.
Let the cost price be .
The selling price (SP) is GH¢60.
The profit percentage is 20%.The selling price is the cost price plus the profit.
So,
To find , divide the selling price by 1.20.
The cost price is .
5c. Arrange the numbers in ascending order.
Ascending order means arranging numbers from the smallest to the largest.
The given numbers are: .Identify the negative numbers and arrange them.
is smaller than . So, .
Place zero.
0 comes after the negative numbers. So, .
Identify the positive numbers and arrange them.
The positive numbers are $15, 56, 4$.
Arranging them: $4, 15, 56$.Combine all numbers in ascending order.
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