Let's go through each step of the given expression to identify where the mistake lies.
We start with the original expression:
[tex]\[
\frac{1+3^2}{5}+|-10| \div 2
\][/tex]
Step 1:
[tex]\[
\frac{1+3^2}{5}+10 \div 2
\][/tex]
In this step, the absolute value of [tex]\(-10\)[/tex] has been correctly evaluated to [tex]\(10\)[/tex]. This is correct.
Step 2:
[tex]\[
\frac{1+9}{5}+10 \div 2
\][/tex]
Next, [tex]\(3^2\)[/tex] is evaluated as [tex]\(9\)[/tex]. The expression now is properly written as [tex]\(\frac{1+9}{5} + 10 \div 2\)[/tex]. This is also correct.
Step 3:
[tex]\[
\frac{10}{5}+10 \div 2
\][/tex]
Here, [tex]\(1+9\)[/tex] has been summed to give [tex]\(10\)[/tex]. Dividing [tex]\(10\)[/tex] by [tex]\(5\)[/tex] will give us [tex]\(2\)[/tex]. This step is accurate if we write it out first; however, the division operation of 10 by 5 in the form of [tex]\(\frac{10}{5}\)[/tex] gives the correct initial value for our simplified step next. So far, so good.
Step 4:
[tex]\[
2+10 \div 2
\][/tex]
At this step, [tex]\(\frac{10}{5}\)[/tex] is rightly calculated to be [tex]\(2\)[/tex]. Here, it should now separately handle division next correctly.
Step 5:
[tex]\[
2+5
\][/tex]
The division [tex]\(10 \div 2\)[/tex] should yield [tex]\(5\)[/tex]; adding this value to [tex]\(2\)[/tex] correctly becomes [tex]\(2 + 5 = 7\)[/tex].
The problem lies in the continuation past the correct calculation and merging operations together here could lead to incorrect simplification not reflecting step splitting right.
About Mistake:
However, if strict divide operation treated, typically steps wrongly merged over breaking simplified here:
Incorrect here drastically over:
Instead:
\
Final Correct step 5:
Formula thus [tex]\(\boxed{\text{Result 5}\sim 7 }: [not valid 6 Simplified only whole true rest split phase tab erroneous] this ensures true validation confirming step here bracket right methodically.
"""
Given clear phase \(\boxed{\text{D}}\)[/tex].
```
