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
Let the numbers be x and y. Then xy = -30 and x+y = -3.
Solve xy = -30 for y: y = -30/x
subst. -30/x for y in x+y= -3: x - 30/x = -3
Multiply all 3 terms by x: x^2 - 30 = -3x, so x^2 + 3x - 10 = 0
Solve this quadratic equation for x. x: {-5, 2}
If x = -5, then x+y = -3 becomes -5 + y = -3, and y = 2.
You should check to determine whether x=2 is also correct. If it is, what is the corresponding y value?
Answer:
x = 2
4 (x + 6) - 3x = 26
solve the parenthesis
4x + 24 - 3x = 26
subtract 24 from both sides to get x by itself
4x - 3x = 2
solve
x = 2
