Answer:

Step-by-step explanation:
![\frac{15}{\sqrt{31} - 4}\\\\=\frac{15}{\sqrt{31} - 4} \times \frac{\sqrt{31} + 4}{\sqrt{31}+ 4} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ rationalizing \ the \ denominator \ ]\\\\=\frac{15( \sqrt{31} + 4 )}{(\sqrt{31})^2 - (4)^2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [ \ (a-b)(a+b) = a^2 - b^2 \ ]\\\\=\frac{15 ( \sqrt{31} + 4)}{31 - 16}\\\\=\frac{15 (\sqrt{31} + 4)}{15}\\\\= \sqrt{31} + 4](https://tex.z-dn.net/?f=%5Cfrac%7B15%7D%7B%5Csqrt%7B31%7D%20-%204%7D%5C%5C%5C%5C%3D%5Cfrac%7B15%7D%7B%5Csqrt%7B31%7D%20-%204%7D%20%5Ctimes%20%5Cfrac%7B%5Csqrt%7B31%7D%20%2B%204%7D%7B%5Csqrt%7B31%7D%2B%204%7D%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%20%5B%20%20%5C%20rationalizing%20%5C%20the%20%5C%20denominator%20%5C%20%5D%5C%5C%5C%5C%3D%5Cfrac%7B15%28%20%5Csqrt%7B31%7D%20%2B%204%20%29%7D%7B%28%5Csqrt%7B31%7D%29%5E2%20-%20%284%29%5E2%7D%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%20%5B%20%5C%20%28a-b%29%28a%2Bb%29%20%3D%20a%5E2%20-%20b%5E2%20%5C%20%5D%5C%5C%5C%5C%3D%5Cfrac%7B15%20%28%20%5Csqrt%7B31%7D%20%2B%204%29%7D%7B31%20-%2016%7D%5C%5C%5C%5C%3D%5Cfrac%7B15%20%28%5Csqrt%7B31%7D%20%2B%204%29%7D%7B15%7D%5C%5C%5C%5C%3D%20%5Csqrt%7B31%7D%20%2B%204)
.75 Rounded to the nearest thousandth would be 0.750
Answer:
y = 
Step-by-step explanation:
Given that y varies directly as x then the equation relating them is
y = kx ← k is the constant of variation
To find k use the condition y = 7 when x = 3
k =
=
, thus
y =
x ← equation of variation
When x = 7, then
y =
× 7 = 
Answer:
ask your teacher for help
Step-by-step explanation:
Answer:
Function: 
Amount earned for 10 hours of work: 
Step-by-step explanation:
Let be "x" the number of hours worked on a project and "y" the total amount Luigi charges for a project.
Based on the data given in the exercise, you can identify that:
- $140 is a fixed amount.
- For each hour worked on the project, Luigi charges $25. This can be expressed as:

Then, the total amount he charges for a project is the sum of $140 and
. This can be represented with the following function:

To calculate the amount of money earned for 10 hours of work, you must substitute
into the function and evaluate. Then:
