Answer:

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
- Subtraction Property of Equality<u>
</u>
<u>Trigonometry</u>
- [Right Triangles Only] SOHCAHTOA
- [Right Triangles Only] cosθ = adjacent over hypotenuse<u>
</u>
Step-by-step explanation:
<u>Step 1: Define</u>
Angle θ = <em>x</em>
Adjacent Leg = 5.8
Hypotenuse = 7.3
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute in variables [Cosine]:

- [Fraction] Divide:

- [Equality Property] Trig inverse:

- Evaluate trig inverse:

- Round:

Answer:
See the explanation below.
Step-by-step explanation:

Starting from 
By putting
we have:

Answer:
Domain: all real numbers. Range: (-∞, 2000]
Step-by-step explanation:
f(x)=2.5x is a simple "ramp" function, a linear function and a polynomial. As such, its domain contains "all real numbers." That value 800 defines the largest value that this f(x) can have: f(800) = 2.5(800) = 2000.
Thus, the range is "all real numbers from -∞ through and including 2000."
Answer:
Step-by-step explanation: This is the quadratic function:
h(x)=ax²+bx+c
We have two points:
(1,58)
(2,112)
Now, we calculate this quadratic funtion.
we assume that h(0)=0
Therefore:
a(0)²+b(0)+c=0
c=0
(1,58)
a(1)²+b(1)=58
a+b=58 (1)
(2,112)
a(2)²+b(2)=112
4a+2b=112
2a+b=56 (1)
With the equations (1) and (2) we make a system of equations:
a+b=58
2a+b=56
we can solve this system of equations by reduction method.
-(a+b=58)
2a+b=56
---------------------
a=-2
-2(a+b=58)
2a+b=56
-------------------
-b=-60 ⇒ b=60
The function is:
h(x)=ax²+bx+c
h(x)=-2x²+60x
Now find the height, in feet, of the rock after 10 seconds in the air.
h(10)=-2(10)²+60(10)
h(10)=-200+600=400
Answer: 400 ft.