Answer:
D) k = 79
Step-by-step explanation:
Given equation: [tex]\sf\sqrt{k+2}-x=0[/tex]
Steps:
1. Substitute 9 as the value of x in the equation:
[tex]\sf\sqrt{k+2}-9=0[/tex]
2. Add 9 to both sides:
[tex]\sf\sqrt{k+2}-9+9=0+9\\\\\Rightarrow \sqrt{k+2}=9[/tex]
3. Square both sides of the equation:
[tex]\sf\left(\sqrt{k+2}\right)^2=9^2\\\\\Rightarrow k+2=81[/tex]
4. Subtract 2 from both sides:
[tex]\sf k+2-2=81-2\\\\\Rightarrow k = 79[/tex]
5. Check your work:
[tex]\sf\sqrt{k+2}-x=0\ \textsf{[ substitute 79 for k, and 9 for x ]}\\\\\sqrt{79+2}-9=0\ \textsf{[ add ]}\\\\\sqrt{81}-9=0\ \textsf{[ take the square root ]}\\\\9-9=0\ \textsf{[ subtract ]}\\\\0=0\ \checkmark[/tex]
