Answer:
![\Large\boxed{Distance=√(29) }](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/jjwsjko0bar98uuniwp3.png)
Explanation:
Given information
![(x_1,~y_1)=(-5,~2)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/d54i277widyvc29wxl2a.png)
![(x_2,~y_2)=(0,~4)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/udq4vzredv4h8o2hifju.png)
Given the distance formula
![Distance =√((x_2-x_1)^2+(y_2-y_1)^2)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/rk7n5ewlxho55x437y6x.png)
Substitute values into the formula
![Distance =√(((0)-(-5))^2+((4)-(2))^2)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/qq17wpfxpu79x9i4hbm6.png)
Simplify values in the parenthesis
![Distance =√((0+5)^2+(4-2)^2)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/htp6lit31txe39m140r6.png)
![Distance =√((5)^2+(2)^2)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/rva90ow356liglj6gsy2.png)
Simplify the exponents
![Distance =√(25+4)](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/lmowstoe0rruf294i958.png)
Simplify values in the radical sign
![\Large\boxed{Distance =√(29)\approx5.4}](https://img.qammunity.org/qa-images/2023/formulas/mathematics/college/vzk4h9r8ipj1jds0lpdc.png)
Hope this helps!! :)
Please let me know if you have any questions