Calories proportional to grams
calories= k x grams
27 = k x 3
therefore constant k = 9
Perpendicular lines have slopes that are negative reciprocals of each other, so the equation of the line in point-slope form is:
![y-4=-\frac{5}{2}(x+3)](https://tex.z-dn.net/?f=y-4%3D-%5Cfrac%7B5%7D%7B2%7D%28x%2B3%29)
Rewriting this in standard form,
![2y-8=-5(x+3) \\ \\ 2y-8=-5x-15 \\ \\ \boxed{5x+2y=-7}](https://tex.z-dn.net/?f=2y-8%3D-5%28x%2B3%29%20%5C%5C%20%5C%5C%202y-8%3D-5x-15%20%5C%5C%20%5C%5C%20%5Cboxed%7B5x%2B2y%3D-7%7D)
The <em>algebraic</em> expression
is equivalent to the <em>algebraic</em> expression
. Thus, the right choice is option D.
<h3>How to apply power and root properties to rewrite a given expression</h3>
In this question we must apply the following set of <em>algebraic</em> properties to simplify a given expression:
(1)
(2)
(3)
Where:
- <em>m</em>, <em>n</em> - Exponents
- <em>x</em> - Base
And also by apply the definition of power.
If we know that the given expression is
, then the equivalent expression is:
![x^{10/3} = \sqrt[3]{x^{10}} = \sqrt[3]{x^{9}\cdot x} = \sqrt[3]{x^{9}}\cdot \sqrt[3]{x} = x^{3}\cdot \sqrt[3]{x}](https://tex.z-dn.net/?f=x%5E%7B10%2F3%7D%20%3D%20%5Csqrt%5B3%5D%7Bx%5E%7B10%7D%7D%20%3D%20%5Csqrt%5B3%5D%7Bx%5E%7B9%7D%5Ccdot%20x%7D%20%3D%20%5Csqrt%5B3%5D%7Bx%5E%7B9%7D%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bx%7D%20%3D%20x%5E%7B3%7D%5Ccdot%20%5Csqrt%5B3%5D%7Bx%7D)
The <em>algebraic</em> expression
is equivalent to the <em>algebraic</em> expression
. Thus, the right choice is option D.
To learn more on roots, we kindly invite to check this verified question: brainly.com/question/1527773