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Answer:
x = ±25
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
x² = 625
<u>Step 2: Solve for </u><em><u>x</u></em>
- Square root both sides: x = ±25
<u>Step 3: Check</u>
<em>Plug in x into the original equation to verify it's a solution.</em>
x = -25
- Substitute in <em>x</em>: (-25)² = 625
- Exponents: 625 = 625
Here we see that 625 does indeed equal 625.
∴ x = -25 is a solution to the equation.
x = 25
- Substitute in <em>x</em>: 25² = 625
- Exponents: 625 = 625
Here we see that 625 does indeed equal 625.
∴ x = 25 is a solution to the equation.
Answer:
The length is 23 inches and the width is 6 inches.
Step-by-step explanation:
The perimeter for a rectangular shape is represented as:
P = 2L + 2W, where L represents length and W represents width
We can represent the length as:
L = 3W + 5
Substituting this into the perimeter function, we get:
P = 2 (3W + 5) + 2W
Substituting 58 for P, we get:
58 = 2 (3W + 5) + 2W
58 = 6W + 10 + 2W
58 = 8W + 10
58 - 10 = 8W + 10 - 10
48 = 8W
48 / 8 = 8W / 8
6 = W
With 6 being the established value for the width, we can substitute this back into the equation for length:
L = 3W + 5
L = 3(6) + 5
L = 18 + 5
L = 23
To check our work, we can substitute both the width and length into the perimeter equation:
P = 2L + 2W
58 = 2(23) + 2(6)
58 = 46 + 12
58 = 58
Therefore, length is 23 inches and the width is 6 inches.
To determine the 7th term of a given sequence, we use the formula given above which is
an = 30 - 4n
where an is the value at the nth term of a sequence
Therefore,
an = 30 - 4n
an = 30 - 4(7)
an = 2
(3+1)y=20
4y=20
both sides divided by four
y=5
