Consider the compound inequality x greater than 4 or x less than a. If a=4 what would the solution be?
1 answer:
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Answer:
Part A) The graph in the attached figure (see the explanation)
Part B) The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)
Step-by-step explanation:
Part 1) Graph the system of inequalities
we have
----> inequality A
The solution of the inequality A is the shaded area above the dashed line
The slope pf the dashed line A is positive m=5
The y-intercept of the dashed line A is (0,5)
The x-intercept of the dashed line A is (-1,0)
----> inequality B
The solution of the inequality B is the shaded area above the dashed line
The slope pf the dashed line B is negative m=-1/2
The y-intercept of the dashed line B is (0,1)
The x-intercept of the dashed line B is (2,0)
The solution of the system of inequalities is the shaded area above the dashed line A and above the dashed line B
using a graphing tool
see the attached figure
Part B) Is the point (-2, 5) included in the solution area for the system? Justify your answer mathematically
we know that
If a ordered pair is a solution of the system of inequalities, then the ordered pair must satisfy both inequalities
substitute the value of x and the value of y in each inequality
For x=-2, y=5
<em>Verify inequality A</em>
---> is true
so
The ordered pair satisfy inequality A
<em>Verify inequality B</em>
---> is true
so
The ordered pair satisfy inequality B
therefore
The ordered pair is a solution of the system of inequalities (is included in the solution area for the system)
Answer:
B
Step-by-step explanation:
Given a parabola in standard form
y = ax² + bx + c ( a ≠ 0 )
Then the x- coordinate of the vertex is
x = -
y = 3x² + 6x + 1 ← is in standard form
with a = 3 and b = 6 , then
= -
= - 1
Substitute x = - 1 into y for corresponding y- coordinate
y = 3(- 1)² + 6(- 1) + 1
= 3(1) - 6 + 1
= 3 - 5
= - 2
vertex = (- 1, - 2 )