Answer:
Part 1) The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.
Part 2)
Step-by-step explanation:
Part 1)
Let
x-----> the number of pounds of regular coffee
we know that
The inequality that represent the situation is
Solve for x
Divide by 2 both sides
The maximum number of pounds of regular coffee that you can buy is 7.5 pounds.
The solution of the inequality is the interval ------> (-∞,7.5]
but the number of pounds cannot be a negative number
therefore
The solution is the interval -----> [0,7.5]
see the attached figure
Part 2) we have
Adds m and n
Group terms that contain the same variable
Combine like terms
Answer:
f(g(x)) = 15x + 2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Distributive Property
<u>Algebra I</u>
- Functions
- Function Notation
- Composite Functions
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify</em>
f(x) = 5x + 7
g(x) = 3x - 1
<u>Step 2: Find</u>
- Substitute in functions: f(g(x)) = 5(3x - 1) + 7
- [Distributive Property] Distribute 5: f(g(x)) = 15x - 5 + 7
- [Addition] Combine like terms: f(g(x)) = 15x + 2
The area of the region is
Explanation:
The area of the region is given by
Integrating the terms inside the bracket, we get,
Now, applying the limits for x for the integrated term,
Any number to the power of zero is one. Thus, substituting the values, we get,
Adding the like terms,
Simplifying the terms, we get,
Thus, The area of the region is
Z + Y = a right angle so need to equal 90 degrees:
Find Z & Y:
2b + 6 + 3b -1 = 90
5b +5 = 90
5b = 85
b = 85/5
b = 17
Z = 2(17) +6 = 34+6 = 40 degrees
Y = 3(17) - 1 = 51 - 1 = 50 degrees
Y & W make a straight line so need to equal 180:
W = 180 - 50 = 130 degrees.
Z & X make a straight line so need to equal 180:
X = 180 - 40 = 140 degree.