You have a coupon for 30% off. If your subtotal is $65, what is the price of your final bill once the discount is applied?
1 answer:
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Given parameters:
Equation of the line is y = - + 8
Unknown:
Slope of line parallel to this line = ?
Slope of line perpendicular = ?
Solution:
A line parallel to this line will have the same slope with it.
A line perpendicular will have the negative inverse of this slope;
Slope of line = -
Slope of line parallel to this line =
Slope of line perpendicular = negative inverse = -( -()) = 2
So, the slope of line parallel to this line is - 1/2 and that perpendicular is 2
Answer:
Option A is the correct choice.
Step-by-step explanation:
Let d be the number of boxes of duck calls and t be the number of boxes of turkey calls.
We have been given that a company sells boxes of duck calls for $35 and boxes of turkey calls (t) for $45, so the revenue earned from selling d boxes of duck and t boxes of turkey call will be 35d and 45t respectively.
Further, the company plan to make $300. We can represent this information as:
We are also told that they make batches of duck calls that fill 6 boxes and batches of turkey calls that fill 8 boxes. the company only has 42 boxes. We can represent this information as:
Therefore, our desired system of equation will be:
<span>Differentiate implicitly:
</span>
<span>
Solve for y
</span>
<span>When the tangent is parallel to the x-axis we have y'=0, so we must solve
</span>
<span>To find the actual value of x we plug this expression for y into the original equation
</span>![x^3-3x^3+27x^6=0 \\ \\x^3(27x^3-2)=0\implies x=\{0,{\sqrt[3]2\over3}\}](https://tex.z-dn.net/?f=x%5E3-3x%5E3%2B27x%5E6%3D0%0A%5C%5C%0A%5C%5Cx%5E3%2827x%5E3-2%29%3D0%5Cimplies%20x%3D%5C%7B0%2C%7B%5Csqrt%5B3%5D2%5Cover3%7D%5C%7D)
<span>Plugging this into the formula for y above gives the points
</span>![(0,0)\text{ and }({\sqrt[3]2\over3},{\sqrt[3]4\over3})](https://tex.z-dn.net/?f=%280%2C0%29%5Ctext%7B%20and%20%7D%28%7B%5Csqrt%5B3%5D2%5Cover3%7D%2C%7B%5Csqrt%5B3%5D4%5Cover3%7D%29)
<span>which is where our tangent will be parallel to the x-axis.</span>
<span>
</span>
</span>
<span>
Solve for y
</span>
<span>When the tangent is parallel to the x-axis we have y'=0, so we must solve
</span>
<span>To find the actual value of x we plug this expression for y into the original equation
</span>
<span>Plugging this into the formula for y above gives the points
</span>
<span>which is where our tangent will be parallel to the x-axis.</span>
<span>
</span>