Step-by-step explanation:
21. x² - 4x - 5 > 0
→ (x - 5) (x - 1) > 0
{x - 5 > 0
{x + 1 > 0
{x - 5 < 0
{x + 1 < 0
{x > 5
{x > -1
{x < 5
{x < -1
= x < -1 or x > 5
therefore, option A is correct
22). 4p² - 1 ≤ 0
(2p - 1) (2p + 1) ≤ 0
{2p - 1 ≤ 0
{2p + 1 ≥ 0
{2p - 1 ≥ 0
{2p + 1 ≤ 0
{p ≤ 1/2
{p ≥ -1/2
{p ≥ 1/2
{p ≤ -1/2
1/2 ≤ p ≤ 1/2
{p ≥ 1/2
{p ≤ -1/2
-1/2 ≤ p ≤ 1/2
therefore, option A is correct.
23). y < 3x² + 3x - 6
3x² + 3x - 6 = 0
3x² + 6x - 3x - 6 = 0
3x(x +2) - 3(x +2) = 0
(x +2) (3) (-3) = 0
x = -2, 1
this is the correct ans. but their is no option similar to it.
25. x and y are root of
m² - 11m + 18 = 0
hence, x + y = 11
xy = 18
2xy = 36
now, x² + y²
= (x +y)² - 2xy
= (11)² - 36
= 121 - 36
= 85
therefore, option A is correct.
26. x² - 2x - 120
(x -1)² - 1 - 1² = 0
(x -1)² = 1 + 1²
x - 1² = 2
x - 1 = ±√2
1 ± √2
therefore, option A is correct.
hope this answer helps you dear..take care!
Answer:
The number line is attached.
Step-by-step explanation:
The holes are filled in since they are both inclusive of the value they hold, and there are two separate lines since they are broken apart by "or".
Answer:
t = 1
Step-by-step explanation:
1) Subtract 4 from both sides so you get -2t = -2
2) Divide both sides by 2 so you get t = 1