Answer:
Step-by-step explanation:
The reciprocal of 5:
The negative reciprocal of 5:
Express this number in scientific notation: 0.0002077
2 answers:
Given the number:
0.0002077
Let's express in scientific notation.
To express the number in scientific notation, move the decimal point so that there is only one non-zero number to the left of the decimal point.
Then, the number of decimal places you move will be the exponent on 10.
If the decimal point is moved to the right, the exponent will be negative.
If the decimal pointt is moved to the left, the exponent will be positive.
In this case the decimal point will be moved to the right.
Using this description, we have the scientific notation below:
Answer:
2.077 x
Step-by-step explanation:
First, move the decimal place until we have a single digit between 1 and 10 to the left of the decimal point. In this problem, if we keep moving the decimal point to the right in 0.0002077 we will get 2.077.
Next, count how many places we moved the decimal point. If we have to move the decimal place to the right, the exponent will be negative. If we had moved the decimal place to the left, the exponent would be positive. In this case we had to move it 4 places to the right to change 0002077 to 2.077. We show that we moved it 4 places to the right by noting that the number should be multiplied by .
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Answer:
Step-by-step explanation:
y > 3x + 10
y < -3x - 1
<h3> Part A:</h3>You'd graph the given systems of linear inequalities the same way as you graph the linear equations.
To graph y > 3x + 10, plot the y-intercept, (0, 10), then use the slope, m = 3 (rise 3, run 1), to plot other points on the graph. Use a dashed line (because of the ">" symbol).
Follow the same steps for the other linear inequality. Plot the y-intercept, (0, -1), then use the slope, m = -3 (down 3, run 1) to plot other points. Use a dashed line (because of the "<" symbol).
Pick a test point on either side of the boundary line and plug it into the original problem. This will help determine which side of the boundary line is the solution. Plug in a test point that is not on the boundary line.
Use the point of origin, (0, 0) as the test point. Plug in these values into the given systems of linear inequalities to see whether it will provide a true statement.
y > 3x + 10
0 > 3(0) + 10
0 > 0 + 10
0 > 10 (False statement).
y < -3x - 1
0 < -3(0) - 1
0 < 0 - 1
0 < -1 (false statement).
Since the point of origin provided a false statement to the given systems of linear inequalities, you must shade the half-plane region where it doesn't contain the test point.
<h3>Part B: </h3>
You'll do the same process as what I've done for the test point. Plug in the values of (8, 10) into the given systems of linear inequalities. If it provides a false statement, then it means that it is not a solution to the system.
y > 3x + 10
10 > 3(8) + 10
10 > 24 + 10
10 > 34 (False statement).
y < -3x - 1
10 < -3(8) - 1
10 < -24 - 1
10 < -25 (false statement).
Therefore, (8, 10) is not a solution to the system.
