Answer:
x = √47
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Define</u>
We have a right triangle. We can use PT to solve for the missing side length.
<u>Step 2: Identify Variables</u>
Leg <em>a</em> = 5
Leg <em>b </em>= <em>x</em>
Hypotenuse <em>c</em> = √72
<u>Step 3: Solve for </u><em><u>x</u></em>
- Substitute [PT]: 5² + x² = (√72)²
- Exponents: 25 + x² = 72
- Isolate <em>x</em> term: x² = 47
- Isolate <em>x</em>: x = √47
So,
#1:

Convert to like improper fractions.

Add.

So, one solution could be

.
Another solution could by 9. There is also 10, 11, 12, etc., and all numbers in between.
#2:

Convert into improper fraction form.

Multiply.

Cross-cancel, and we have our final result.

k < 96
96 is not a solution.
95 is a solution.
So is 94, 93, 92, etc, and all numbers in between.
<u>Top row - Left Row :</u>
Order : Left to Right
{11.7 - below(negative)} , {11.6 - below(negative)} , {12 - exactly filled} , {12.2 - above(positive)}
<u>Middle Row </u>:
Order : Left to Right
{11.1 - below(negative)} , {11.2 - below(negative)} , {11.9 - below(negative)} , {12.5 - above(positive)}
<u>Right Row </u>:
Order : Left to Right
{12 - exactly filled} , {11.4 - below(negative)} , {11.5 - below(negative)} , {10.8 - below(negative)}