m = 0.7
m = 1.5
m = 3
m = 1.5 is the solution to the equation.
An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.
1.6m-4.8=-1.6m
Subtract 1.6m to both sides to get
-4.8=-3.2m
Divide both sides by -3.2to get
x = 1.5
m = 1.5 is the solution to the equation.
The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true. For equations having one unknown, raised to a single power, two fundamental rules of algebra, including the additive property and the multiplicative property, are used to determine its solutions.
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Elapsed time: 30 minutes
Answer:
10:38
Step-by-step explanation:
Because your adding your numbers together
You are deciding whether to light a new factory using bulb A, bulb B, or bulb C.
Which bulb would be better to use on the factory floor?
Which bulb would be better to use in the break room?
To answer these questions, you will compare the energy usage of the three bulbs. The amount of energy the lights use is measured in units of kilowatt-hours. A kilowatt-hour is the amount of energy needed to provide 1000 watts of power for 1 hour.
1. Circle the two bulbs you picked.
incandescent
Halogen
Fluorescent
2.
3. Practice: Summarizing (3 points)
Fill in the blanks.
The energy usage of a light bulb is a function. The input for the function is _________, measured in hours.
The output of the function is energy usage, measured in ____________.
Identify the functional relationship between the variables. _________________ is a function of _________________.
The graph of the function will show energy usage on the _____________ axis and time on the _______________ axis.
4. Practice: Organizing Information (2 points)
Use the data given to complete the table for your first bulb.
DATA TABLE A
Time (hours) x Energy (kWh) y Point (time, energy) (x, y)
3
10
5. Practice: Organizing Information (2 points)
Use the data given to complete the table for your second bulb.
DATA TABLE B
Time (hours)x Energy (kWh)y Point (time, energy)(x, y)
3
10
6. Practice: Organizing Information (5 points: 1 point for labels, 2 points for each graph)
Label the axes of the graph with "Time (hours)" and "Energy (kWh)." Plot the points from Table A on the graph. Connect the points with a line. On the same graph, plot the points from Table B and connect them with a line.
7. Practice: Summarizing (1 point)
Classify each of your graphs as increasing, decreasing, or constant.
First bulb: ___________________
Second bulb:___________________
8. Practice: Summarizing (2 points)
Fill in the blanks.
First bulb: When 3 is the input, the output is _____. When 10 is the input, the output is _______.
Second bulb: When 3 is the input, the output is _____. When 10 is the input, the output is _______.
9. Practice: Summarizing (1 point)
The workers leave the lights on in the break room for stretches of about 3 hours. Which light bulb would light this room using the least amount of energy?
10. Practice: Summarizing (1 point)
The lights in the main room of the factory stay on for stretches of 9 hours. Which kind of light bulb would light this room with the least amount of energy?
Answer:
To determine which bulb would be better to use on the factory floor and in the break room, we need to compare the energy usage of the three bulbs: incandescent, halogen, and fluorescent.
1. Based on energy efficiency, we would circle the two bulbs that are more energy-efficient: halogen and fluorescent.
3. Summarizing:
- The energy usage of a light bulb is a function. The input for the function is time, measured in hours.
- The output of the function is energy usage, measured in kilowatt-hours (kWh).
- Time is a function of energy usage.
4. Organizing Information: DATA TABLE A
Time (hours) x Energy (kWh) y Point (time, energy) (x, y)
3 -
10 -
5. Organizing Information: DATA TABLE B
Time (hours) x Energy (kWh) y Point (time, energy) (x, y)
3 -
10 -
6. Organizing Information:
- Graph 1: Label the axes with "Time (hours)" and "Energy (kWh)". Plot the points from Table A and connect them with a line.
- Graph 2: Label the axes with "Time (hours)" and "Energy (kWh)". Plot the points from Table B and connect them with a line.
7. Summarizing:
- Graph 1 (First bulb) classification: Unknown, as the points are not provided.
- Graph 2 (Second bulb) classification: Unknown, as the points are not provided.
8. Summarizing:
- First bulb: When 3 hours is the input, the output (energy usage) is unknown. When 10 hours is the input, the output (energy usage) is unknown.
- Second bulb: When 3 hours is the input, the output (energy usage) is unknown. When 10 hours is the input, the output (energy usage) is unknown.
9. Summarizing:
- To determine which light bulb would consume the least amount of energy in the break room for stretches of about 3 hours, we need the data or information on energy usage for each bulb. Without that information, it's not possible to make a definitive conclusion.
10. Summarizing:
- Similarly, to determine which light bulb would consume the least amount of energy in the main room of the factory for stretches of 9 hours, we need the data or information on energy usage for each bulb. Without that information, it's not possible to make a definitive conclusion.
In summary, without the energy usage data for each bulb, we cannot determine which bulb would be better to use on the factory floor or in the break room, or which bulb would consume the least amount of energy for specific time durations.
Step-by-step explanation:
The product of two consecutive integers is 420 is 20 and 21.
Consider x one the two number
Then the successor of x = x + 1
Then x and x+1 are the consecutive numbers
Now according to the question,
The product of two consecutive integers is 420,
Then, multiply x and x+1 and equate it to 420
Therefore,
⇒ x(x+1) = 420
⇒ x² + x = 420
⇒ x² + x - 420 = 0
This is a quadratic equation
Now solve it to find the value of x
We can write it as,
⇒ x² + 21x - 20x - 420 = 0
⇒ x(x + 21) - 20(x + 21) = 0
⇒ (x+21)(x-20) = 0
⇒ x = 20 or x = -21
Since number should be an integer so - 21 is absurd.
Hence, consecutive numbers are,
20 and 21
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