Write the equation of the line that passes through the point (-2, 7) and is PARALLEL to the line y = -4x + 1.
1 answer:
Answer:
The equation is
Step-by-step explanation:
If we want a line parallel to the line in the problem it will have the same slope. The equation given in the problem is already in slope intercept form so we can take the slope for the new equation directly from this equation.
The slope-intercept form of a linear equation is:
Where m is the slope and b is the y-intercept value.
Therefore the slope is
We can now use the point-slope formula to write the equation of the parallel line:
The point-slope formula states:
Where m is the slope and is a point the line passes through.
Substituting the information from the problem gives:
Or, we can solve for y to put the equation in slope-intercept form:
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Answer:
Approximately 3 grams left.
Step-by-step explanation:
We will utilize the standard form of an exponential function, given by:
In the case of half-life, our rate <em>r</em> will be 1/2. This is because 1/2 or 50% will be left after <em>t </em>half-lives.
Our initial amount <em>a </em>is 185 grams.
So, by substitution, we have:
Where <em>f(t)</em> denotes the amount of grams left after <em>t</em> half-lives.
We want to find the amount left after 6 half-lives. Therefore, <em>t </em>= 6. Then using our function, we acquire:
Evaluate:
So, after six half-lives, there will be approximately 3 grams left.