Hermione has 7-$5 dollar bills and 5-$1 dollar bills.
The functions f(4x-3)≥f(2-x^2) and f(5-x^2)≥f(3x-5) are quadratic functions
The values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2
<h3>How to solve the inequalities?</h3>
<u>Inequality 1: f(4x - 3) ≥ f(2 - x^2), Df = (-8 , 4)</u>
The function increases at (-8,4).
So, we have:
4x - 3 ≥ 2 - x^2
Rewrite as:
x^2 + 4x - 2 - 3 ≥ 0
Evaluate the like terms
x^2 + 4x - 5 ≥ 0
Expand
x^2 + 5x - x - 5 ≥ 0
Factorize the expression
x(x + 5) - 1(x + 5) ≥ 0
Factor out x + 5
(x - 1)(x + 5) ≥ 0
Solve for x
x ≥ 1 or x ≥ -5
Rewrite as:
-5 ≤ x ≤ 1
<u>Inequality 2: f(5 - x^2) ≥ f(3x - 5), Df=(-∞,4)</u>
The function decreases at (-∞,4).
So, we have:
5 - x^2 ≥ 3x - 5
Rewrite as:
x^2 + 3x - 5 - 5 ≤ 0
Evaluate the like terms
x^2 + 3x - 10 ≤ 0
Expand
x^2 + 5x - 2x - 10 ≤ 0
Factorize the expression
x(x + 5) - 2(x + 5) ≤ 0
Factor out x + 5
(x - 2)(x + 5) ≤ 0
Solve for x
x ≤ 2 or x ≤ -5
Rewrite as:
-5 ≤ x ≤ 2
Hence, the values of the inequalities are -5 ≤ x ≤ 1 and -5 ≤ x ≤ 2
Read more about inequalities at:
brainly.com/question/11234618
Answer:
D.(2,-1,-1)
Step-by-step explanation:
-a+4b+2c=-8
3a+b-4c=9
b = -1
Substitute b=-1 into the other equations
-a -4 +2c = -8
3a -1 -4c =9
Multiply the first equation by 2 so we can eliminate c
-2a -8 +4c = -16
Add this to the second equation
-2a -8 +4c = -16
3a -1 -4c =9
-----------------
a -9 = -7
Add 9 to each side
a-9+9 = -7+9
a =2
b=-1
Now we need to find c
-a +4b +2c = -8
-2 -4 +2c = -8
-6+2c = -8
Add 6 to each side
-6+6 +2c = -8+6
2c = -2
Divide by 2
2c/2 = -2/2
c=-1
(2,-1,-1)