Area of the shaded region is 2868.61 square inches.
Solution:
Diameter of the smaller circle = 20.4 in
Radius of the smaller circle = 20.4 ÷ 2 = 10.2 in
Area of the smaller circle = πr²
= 3.14 × (10.2)²
Area of the smaller circle = 326.6856 in²
Radius of the larger circle = (10.2 + 21.7) in = 31.9 in
Area of the larger circle = πR²
=3.14 × (31.9)²
Area of the larger circle = 3195.2954 in²
Area of shaded region = Area of larger circle – Area of smaller circle
= 3195. 2954 in² – 326.6856 in²
= 2868.6098 in²
= 2868.61 in²
Area of the shaded region is 2868.61 square inches.
Answer:
x = 10
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</u>
6(x - 1) = 9(x - 4)
<u>Step 2: Solve for </u><em><u>x</u></em>
- Distribute: 6x - 6 = 9x - 36
- Subtract 6x on both sides: -6 = 3x - 36
- Isolate <em>x</em> term: 30 = 3x
- Isolate <em>x</em>: 10 = x
- Rewrite: x = 10
<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>: 6(10 - 1) = 9(10 - 4)
- Subtract: 6(9) = 9(6)
Here we see that the 2 expressions are exactly the same.
∴ x = 10 is the solution to the equation.
The answer to your question is y = 3
Answer:
y = ½x - 11
Step-by-step explanation:
The equation of the line that goes through (8, -7) and is parallel to -2x + 4y = 100, will have the same slope as the line, but different y-intercept (b).
Let's find the slope of -2x + 4y = 100 by rewriting in the slope-intercept form.
-2x + 4y = 100
Add 2x to both sides
4y = 2x + 100
Divide both sides by 4
y = 2x/4 + 100/4
y = ½x + 25
The slope of the given line is ½. Since the line that goes through (8, -7) is parallel to -2x + 4y = 100, therefore the slope (m) is also ½.
To find the y-intercept (b), substitute m = ½, x = 8, and y = -7 into y = mx + b.
-7 = ½(8) + b
-7 = 4 + b
-7 - 4 = b
-11 = b
b = -11
Substitute m = ½ and b = -11 into y = mx + b to get the equation of the line that is parallel to -2x + 4y = 100.
y = ½x + (-11)
y = ½x - 11