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:
= Sh. 2281.50
Step-by-step explanation:
Area of the path;
(126 × 2.5 ) + (2.5 × (48 - (2.5×2)
= 315 + (2.5 × 43)
= 315 + 107.5
= 422.5 m²
But; the cost of graveling is sh 5.40 per square meter
Therefore; The cost of graveling the whole path;
= 422.5 × 5.40
<u>= Sh. 2281.50</u>
Answer:
7
Step-by-step explanation:
Look at the order it is in carefully
1) variable
2) value
3) absolute value (maybe)
4) natural numbers
5) whole numbers
6) integers
27 and 3/8 rounds down to 27.
- 1 and 1/10 rounds up to - 1
We are estimating the difference which tells us to subtract so 27 - (- 1) = 27 + 1 = 28
Your estimate for this equation is 28.