Jane: Think: the hypotenuse of her ramp is 14 inches and the angle opposite the rise is 30 degrees. Thus, cos 30 deg = (adj side) / (hyp) = (adj side) / (14 in).
Solving for (adj side), we get (adj side) = (14 in)(sqrt(3)/2) = 7 sqrt(3) 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.
Answer:
60cm^2
Step-by-step explanation:
We assume that is a circumscribing quadrilateral, rather than one that is circumscribed. It is also called a "tangential quadrilateral" and its area is ...
K = sr
where s is the semi-perimeter, the sum of opposite sides, and r is the radius of the incircle.
K = (12 cm) (5cm) = 60 cm²
_____
A quadrilateral can only be tangential if pairs of opposite sides add to the same length. Hence the given sum is the semiperimeter.
Answer:
Jill earned $22,500 more total income for the year.
Step-by-step explanation:
