What is the solution to the compound inequality 3x-8 less than or equal to -5 or 2x - 7 > 5
1 answer:
Answer:
The solution for the compound inequality = ∅
Step-by-step explanation:
The given inequality:
3x - 8 ≤ -5 & 2x - 7 > 5
<u>For the inequality 3x - 8 ≤ -5</u>
3x - 8 ≤ -5 add 8 to both sides
3x ≤ 3 divide both side by 3
x ≤ 1
So, the solution of the inequality 3x - 8 ≤ -5 ⇒ x ∈ (-∞ , 1]
<u>For the inequality 2x - 7 > 5</u>
2x - 7 > 5 add 7 to both sides
2x > 12 divide both sides 2
x > 6
So, the solution of the inequality 2x - 7 > 5 ⇒ x ∈ (6 , ∞)
The solution for the compound inequality will be:
(-∞ , 1] ∩ (6 , ∞) = ∅
See the attached figure.
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Answer:
(6, 9 ) and r = 3
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
Given
x² + y² - 12x - 18y + 108 = 0
Rearrange the x- terms and the y- terms together and subtract 108 from both sides, that is
x² - 12x + y² - 18y = - 108
To obtain standard form use the method of completing the square
add ( half the coefficient of the x and y terms )² to both sides
x² + 2(- 6)x + 36 + y² + 2(- 9)y + 81 = - 108 + 36 + 81
(x - 6)² + (y - 9)² = 9 ← in standard form
with centre = (6, 9 ) and r = = 3