https://file.aiquickdraw.com/mathbot/file/1725737232797fick7u9s.jpg

From the image provided, the equation appears to be:

\[
\frac{500 + 600 + 25 \times 10^2 \times \sqrt{30h}}{7} = 9 \times 10^7
\]

Below it, there is another expression:

\[
\frac{22 \times 0.84 \times 10^4}{7}
\]

Let's proceed step by step to solve these equations. I'll start with the first equation.

### First equation:
\[
\frac{500 + 600 + 25 \times 10^2 \times \sqrt{30h}}{7} = 9 \times 10^7
\]

1. Add \(500 + 600\) which gives \(1100\).

2. The expression now becomes:
   \[
   \frac{1100 + 25 \times 10^2 \times \sqrt{30h}}{7} = 9 \times 10^7
   \]

3. Multiply \(25 \times 10^2 = 2500\), so the expression becomes:
   \[
   \frac{1100 + 2500 \times \sqrt{30h}}{7} = 9 \times 10^7
   \]

4. Multiply both sides by 7 to eliminate the denominator:
   \[
   1100 + 2500 \times \sqrt{30h} = 6.3 \times 10^8
   \]

5. Subtract 1100 from both sides:
   \[
   2500 \times \sqrt{30h} = 6.299989 \times 10^8
   \]

6. Divide by 2500 to isolate the square root term:
   \[
   \sqrt{30h} = \frac{6.299989 \times 10^8}{2500}
   \]

7. Now, solve for \(h\).

Let me also simplify the second expression next.

### Second expression:
\[
\frac{22 \times 0.84 \times 10^4}{7}
\]

1. Multiply \(22 \times 0.84 = 18.48\).

2. Multiply \(18.48 \times 10^4 = 1.848 \times 10^5\).

3. Now, divide by 7:
   \[
   \frac{1.848 \times 10^5}{7} = 2.64 \times 10^4
   \]

Would you like to continue solving for \(h\) or do you need further clarifications on any of the steps? 

Here are some related questions:

1. How would you isolate the variable \(h\) in the equation?
2. What is the significance of scientific notation in simplifying large numbers?
3. How does the square root function affect the equation involving \(h\)?
4. Can you calculate the square root of complex expressions manually or with a calculator?
5. How does distributing constants over terms affect the structure of the equation?

**Tip**: Always keep track of each algebraic operation carefully to avoid mistakes, especially when working with exponents and roots.

500 + 600 + 25 x 10^2 x sqrt(30h) / 7 = 9 x 10^7 and (22 x 0.84 x 10^4) / 7

Learn how to simplify expressions involving scientific notation, exponents, and square roots. The problem starts with 500 + 600 + 25 x 10^2 x sqrt(30h) / 7 = 9 x 10^7 and proceeds step by step. Suitable for Grades 10-12.

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