Answer:
x > 1/5
Step-by-step explanation:
All of these three triangle inequalities must be satisfied:
AB +BC > AC
BC +CA > BA
CA +AB > CB
___
Taking these one at a time, we have ...
AB +BC > AC
3x +4 + 2x +5 > 4x
x +9 > 0 . . . . . subtract 4x
x > -9
__
BC +CA > BA
2x +5 + 4x > 3x +4
3x > -1 . . . . . . subtract 3x+5
x > -1/3 . . . . . divide by 3
__
CA + AB > CB
4x + 3x +4 > 2x +5
5x > 1 . . . . . . subtract 2x+4
x > 1/5
___
The only values of x that satisfy all of these inequalities are those such that ...
x > 1/5
Answer:
(2, 4)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtract Property of Equality
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = 2x
x = -y + 6
<u>Step 2: Solve for </u><em><u>y</u></em>
<em>Substitution</em>
- Substitute in <em>x</em>: y = 2(-y + 6)
- Distribute 2: y = -2y + 12
- Isolate <em>y</em> terms: 3y = 12
- Isolate <em>y</em>: y = 4
<u>Step 3: Solve for </u><em><u>x</u></em>
- Define equation: x = -y + 6
- Substitute in <em>y</em>: x = -4 + 6
- Add: x = 2
The tax is $2.80 but the total is $42.80
Answer: 17/20
<u>Divide</u>
34/40 ÷ 2/2 = 17/20
Divide each side by 2 so it'll be 2/2.