Total weight = 50 lb
x = count of 3-lb weights
y = count of 10-lb weights
weight from 3-lb weights = 3x
weight from 10-lb weights = 10y
overall weight = 3x + 10y
equation
3x + 10y = 50
To express the statements using quantifiers, let F(x, y) mean 'x can fool y' and W represent the entire population. a) Everyone is able to fool Fred. b) Evelyn has the ability to fool every person. c) Each individual can fool at least one other person. d) No individual can fool everyone. e) There is not a single person who can fool both Fred and Jennifer. f) Nancy manages to fool exactly two individuals.
Answer:
{x | x ≤ 6}
Step-by-step explanation:
Given:
y = √(6 - x)
Objective:
Identify the domain.
We begin by setting the expression 6 - x to be greater than or equal to 0.
Therefore:
6 - x ≥ 0
Adding x to each side yields:
6 - x + x ≥ 0 + x
Resulting in:
6 ≥ x
This can be rephrased as:
x ≤ 6
In set-builder notation, this can be expressed as: {x | x ≤ 6}
Answer:
(x+12)(x+5)
Step-by-step explanation:
Using the formula: a²+bx+c
Original equation:
-7x-60 =x² +10x
Rearranged:
x² + 17x + 60
Result:
(1)x x 60 = 60
- Identify factors of 60 that sum up to 17.
Outcomes:
10 × 6, 60 × 1, 20 × 3, 5 × 12, 4 × 15
Choosing 5 and 12 yields 60, with a sum of 17.
- Substitute 5 and 12 for 17
Updated:
x² + 5x + 12x + 60
- Separate into two expressions
Updated:
x² + 5x l 12x + 60
- Factor each expression. Ensure ( ext{ }) have identical values within.
Final result:
x(x + 5) l +12(x+5)
- Final answer: (x+12)(x+5)
