The ordered pair that is a solution of the system is (-2, 8).
<h3>Which ordered pair is included in the solution set to the following system?</h3>
Here we have the system of inequalities:
y > x² + 3
y < x² - 3x + 2
To check which points are solutions of the system, we can just evaluate both inequalities in the given points and see if they are true.
For example, for the first point (-2, 8) if we evaluate it in the two inequalities we get:
8 > (-2)² + 3 = 7
8 < (-2)² - 3*(-2) + 2 = 12
As we can see, both inequalities are true. So we conclude that (-2, 8) is the solution.
(if you use any other of the 3 points you will see that at least one of the inequalities becomes false).
If you want to learn more about inequalities:
brainly.com/question/18881247
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Answer:
13°
Step-by-step explanation:
sin(Ф)= opposite/ hypothenuse
sin(Ф) = 5.2/22.5
Ф= sin∧-1 (5.2/22.5)
Ф= 13.36°
6x8=48
48/8=6
6 eight times is 48
8 six times is 48
<u>We are given the equation:</u>
log₂(x-3) + log₂x - log₂(x+2) = 2
<u>When is it defined:</u>
in this equation, log₂(x-3) and log₂(x+2) can only be defined when
x-3 >0 and x+2 > 0
solving for the values of x, we get:
x > 3 and x > -2
which basically means x > 3
<em>Because we are looking for an inequality which is true for both x>-2 and x>3</em>
Hence, x will have a value greater than 3
<u>Solving for x:</u>
using the product rule <em>[logₐb + logₐc = logₐ(bc)]</em>
log₂[(x-3)(x)] - log₂(x+2) = 2
using the quotient rule <em>[logₐb - logₐc = logₐ(b/c)]</em>
log₂[(x-3)(x) / (x+2)] = 2
from the property <em>[ aˣ = b ⇒ logₐb = x]</em>
(x² - 3x) / (x+2) = 2²
x² - 3x = 4x + 8
x² - 7x - 8 = 0
x² + x - 8x - 8 = 0
x(x+1) - 8(x+1) = 0
(x-8)(x+1) = 0
(x-8) = 0 OR (x+1) = 0
x = 8 OR x = -1
We know that the equation is defined only for x > 3
We can see that x = 8 satisfies that inequality
Therefore, x = 8
