Sure, let's tackle each equation step by step.
### Question 6:
[tex]\[
\sqrt{2} + 9 + 2 + 2
\][/tex]
First, evaluate the square root of 2.
[tex]\[
\sqrt{2} \approx 1.4142135623730951
\][/tex]
Then, add all the numbers together.
[tex]\[
\sqrt{2} + 9 + 2 + 2 \approx 1.4142135623730951 + 9 + 2 + 2 = 14.414213562373096
\][/tex]
### Question 7:
[tex]\[
d + d + \gamma = 4
\][/tex]
Assume [tex]\(\gamma = 1\)[/tex].
[tex]\[
d + d + 1 = 4
\][/tex]
Combine like terms.
[tex]\[
2d + 1 = 4
\][/tex]
Subtract 1 from both sides.
[tex]\[
2d = 3
\][/tex]
Divide by 2.
[tex]\[
d = \frac{3}{2} = 1.5
\][/tex]
### Question 8:
[tex]\[
0 + \sqrt{0} + d = 6
\][/tex]
Evaluate the square root of 0.
[tex]\[
\sqrt{0} = 0
\][/tex]
Then plug in the value of [tex]\( d \)[/tex] from question 7.
[tex]\[
0 + 0 + d = 6
\][/tex]
Simplify the equation.
[tex]\[
d = 6
\][/tex]
### Question a:
[tex]\[
\alpha + \rho + d
\][/tex]
Using the value of [tex]\( d \)[/tex] from question 8.
[tex]\[
d = 6
\][/tex]
The expression becomes:
[tex]\[
\alpha + \rho + 6
\][/tex]
### Question 10:
[tex]\[
0 + 2 + d + d
\][/tex]
Using the value of [tex]\( d \)[/tex] from question 8.
[tex]\[
d = 6
\][/tex]
Substitute [tex]\( d \)[/tex] into the equation.
[tex]\[
0 + 2 + 6 + 6 = 14
\][/tex]
Add all the terms together.
[tex]\[
0 + 2 + 6 + 6 = 14
\][/tex]
### Summary of Results:
[tex]\[
6. \quad \sqrt{2} + 9 + 2 + 2 = 14.414213562373096
\][/tex]
[tex]\[
7. \quad d + d + \gamma = 4 \implies d = 1.5 \quad \text{(assuming } \gamma = 1\text{)}
\][/tex]
[tex]\[
8. \quad 0 + \sqrt{0} + d = 6 \implies d = 6
\][/tex]
[tex]\[
\text{a.} \quad \alpha + \rho + d = \alpha + \rho + 6
\][/tex]
[tex]\[
10. \quad 0 + 2 + d + d = 14 \quad (d = 6)
\][/tex]
