Answer:
16.5 inches
Step-by-step explanation:
Use the Pythagorean Theorem
a² + b² = c²
a² + 13² = 21²
a² + 169 = 441
Subtract 169 from both sides
a² = 272
Take the square root of both sides
a = 16.4924225025
Rounded
a = 16.5 inches
Answer:
Answer: 3 1/2 and -10 1/2 are the two numbers.
Step-by-step explanation:
Let x and y be the two unknown numbers.
x+y=-7 [Given]
x-y=14 [Given]
x-y=14 [Given]
x=y+14 [Add y to both sides]
x+y=-7 [Given]
(y+14)+y=-7 [Subtitution]
2y+14=-7 [Combine like terms]
2y=-21 [Subtract 14 from both sides]
y=-21/2 [Divide both sides by 2]
y=-10 1/2 [Division]
x-y=14 [Given]
x=y+14 [Add y to both sides]
x=-10 1/2 + 14 [Substitution]
x= 3 1/2 [Addition]
Check:
x+y=-7 [Given]
3 1/2 + -10 1/2?=-7 [Substition]
-7=-7 [Addition]
QED
x-y=14 [Given]
3 1/2 - -10 1/2?=14 [Substitution]
3 1/2 + 10 1/2?=14 [Change the sign of the subtrahend and add]
14=14 [Addition]
QED
Answer: 3 1/2 and -10 1/2 are the two numbers.
Answer:
a=-3/7 b=-2/8 c=-0.2
Step-by-step explanation:
From right to left
2
20
200
2000
20000
200000
Answer:
x = 1
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
Step-by-step explanation:
<u>Step 1: Define Equation</u>
3(4x - 5) - 4x + 1 = -6
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute 3: 12x - 15 - 4x + 1 = -6
- Combine like terms: 8x - 14 = -6
- Isolate <em>x</em> term: 8x = 8
- Isolate <em>x</em>: x = 1
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
- Substitute in <em>x</em>: 3(4(1) - 5) - 4(1) + 1 = -6
- Multiply: 3(4 - 5) - 4 + 1 = -6
- Subtract: 3(-1) - 4 + 1 = -6
- Multiply: -3 - 4 + 1 = -6
- Subtract: -7 + 1 = -6
- Add: -6 = -6
Here we see that -6 does indeed equal -6.
∴ x = 1 is the solution to the equation.
