Solve the following inequalities:

$x^{2} - 13 x + 40 \geq 0$

Created: 2 months ago | Updated: 2 months ago

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$x^{2} - 13 x + 40 \geq 0 \Rightarrow x^{2} - 8 x - 5 x + 40 \geq 0 \Rightarrow x (x - 8) - 5 (x - 8) \geq 0 \Rightarrow (x - 8) (x - 5) \geq 0 H e r e, t h e p r o d u c t o f (x - 8) a n d (x - 5) i s g r a t e r t h a n z e r o o r e q u a l t o z e r o . S o t h e v a l u e o f t h e s e m u s t b e b o t h p o s i t i v e o r n e g a t i v e . W h e n b o t h p o s i t i v e, (x - 8) \geq 0 \Rightarrow x > 8; (x - 5) \geq 0 \Rightarrow x \geq 5 [I t i s n o t t r u e] W h e n b o t h n e g a t i v e, - (x - 8) \geq 0 \Rightarrow x \leq 8; [I t i s n o t t r u e] - (x - 5) \geq 0 \Rightarrow x \leq 5; S o, t h e r a n g e x \geq 8 O r, x \leq 5 .$

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A box contains 75 rods; 35 are blue and 25 of these blue rods are twisted at the bottom. Th rest of them are red and 30 of the red ones are twisted. The rods that are not twisted are clear, What is the probability of drawing?

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Algebra ( বীজগণিত)

The sum of race times of two runners is 170 seconds. One of the runners took ten seconds Jess than twice the other to complete the race. What is the race time of each runner?

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Algebra ( বীজগণিত)

Shakib is twice as old as Fahim. Four years ago, Shakib was six years younger than three times of Fahims age at that time. How old will they be in two years from now?

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Average

Four students contributed to a charity drive and the average amount contribution by each student was BDT 20. If no student gave more than BDT 25, what is the minimum amount that any student could have contributed?

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Average

The sum of 15 consecutive integers is 88. What is the largest of these integers?

Created: 2 months ago | Updated: 2 months ago

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Solve the following inequalities:

x2-13x+40≥0

Related Questions

A box contains 75 rods; 35 are blue and 25 of these blue rods are twisted at the bottom. Th rest of them are red and 30 of the red ones are twisted. The rods that are not twisted are clear, What is the probability of drawing?

Algebra ( বীজগণিত)

The sum of race times of two runners is 170 seconds. One of the runners took ten seconds Jess than twice the other to complete the race. What is the race time of each runner?

Algebra ( বীজগণিত)

Shakib is twice as old as Fahim. Four years ago, Shakib was six years younger than three times of Fahims age at that time. How old will they be in two years from now?

Average

Four students contributed to a charity drive and the average amount contribution by each student was BDT 20. If no student gave more than BDT 25, what is the minimum amount that any student could have contributed?

Average

The sum of 15 consecutive integers is 88. What is the largest of these integers?

$x^{2} - 13 x + 40 \geq 0$