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3 years ago

What are the critical points for the inequality 2x+5/x-2≥x-1/x-2?

2 answers:

3 0

1) When the denominator equals zero that is a critical point

=> x - 2 = 0 => x = 2.

So x = 2 is a critical point

2) Simplify the numerator to find an expresion of the king p(x) ≥ 0 or p(x) ≤ 0. Where p(x) equals zero you have other(s) critical point(s)

Multiply both terms:

[2x + 5] / [ x - 2] = [x - 1] / [x - 2]

for x ≠ 2 => 2x + 5 = x - 1

=> 2x - x = - 1 - 5

=> x = - 6

Then, the two critical points are x = 2 and x = - 6.

Answer: option B.

expeople1 [14]3 years ago

3 0

Answer:

B. x=-6 and x=2

Step-by-step explanation:

Which shows all the critical points for the inequality?

x = 1, and x = 2

x = –6 and x = 2

x = –4 and x = 2

x = 2

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Two families stayed at the same hotel in identical rooms. The first family stayed for 5 nights and paid extra to use a rollaway

Vesna [10]

Part A: The system of equations that can be used is

5h + 2b = 413

3h + b = 243

Part B: The cost per night of renting a room is $73 and the cost per night using a roll away bed is $24

Step-by-step explanation:

Two families stayed at the same hotel in identical rooms

The first family stayed for 5 nights and paid extra to use a roll away bed for 2 of the nights.
Their total bill was $413
The second family stayed for 3 nights and used a roll away bed for 1 night.
Their total bill was $243

We need to write a system of equations that can be used to find, h, the cost per night of renting a room at the hotel, and b, the cost per night of using a roll away bed at the hotel and find the values of h and b using the elimination method

Part A:

∵ The first family stayed for 5 nights

∵ The cost of the renting room per night is $h

∴ The cost of the five nights = 5h

∵ The first family paid extra to use a roll away bed for 2 of the nights

∵ The cost of the roll away bed per night is $b

∴ The cost of the two nights = 2b

∵ Their total bill was $413

∴ 5h + 2b = 413 ⇒ (1)

∵ The second family stayed for 3 nights

∵ The cost of the renting room per night is $h

∴ The cost of the five nights = 3h

∵ The first family paid extra to use a roll away bed for 1 of the night

∵ The cost of the roll away bed per night is $b

∴ The cost of the two nights = b

∵ Their total bill was $243

∴ 3h + b = 243 ⇒ (2)

The system of equations that can be used is

5h + 2b = 413

3h + b = 243

Bart B:

∵ 5h + 2b = 413 ⇒ (1)

∵ 3h + b = 243 ⇒ (2)

- Multiply equation (2) by -2 to eliminate b

∴ -6h - 2b = -486 ⇒ (3)

- Add equations (1) and (3)

∴ -h = -73

- Multiply both sides by -1

∴ h = 73

Substitute the value of h in equations (1) or (2) to find b

∵ 3(73) + b = 243

∴ 219 + b = 243

- Subtract 219 from both sides

∴ b = 24

The cost per night of renting a room is $73 and the cost per night using a roll away bed is $24

Learn more:

You can learn more about the system of equations in brainly.com/question/2115716

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7 0

3 years ago