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yanalaym [24]
3 years ago
11

What is the solution to x^3 +4x^2 > x + 4

Mathematics
2 answers:
Thepotemich [5.8K]3 years ago
8 0

Answer:

B) −4<x<−1  or  x>1

Inequality Form: −4<x<−1  or  x>1

Interval Notation: (−4,−1)  ∪  (1,∞)

Step-by-step explanation:

Solve: x^3 + 4x^2 > x + 4

Subtract x from both sides of the inequality.

x^3 + 4x^2 − x > 4

Convert the inequality to an equation.

x^3 + 4x^2 − x = 4

Move 4 to the left side of the equation by subtracting it from both sides.

x^3 + 4x^

2 − x − 4 = 0

Factor the left side of the equation

(x + 4)(x + 1)(x − 1) = 0

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to 0

x + 4 = 0

x + 1 = 0

x − 1 = 0

Set x + 4 equal to 0 and solve for x

x = −4

Set x + 1 equal to 0 and solve for x

x = −1

Set x + -1 equal to 0 and solve for x

x = 1

The final solution is all the values that make (x + 4)(x + 1)(x − 1) = 0  true

x = −4, −1, 1

Use each root to create test intervals.

x < −4

−4 < x < −1

−1 < x < 1

x > 1

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the

inequality.

x < −4  ←False

−4 < x < −1  ←True

−1 < x < 1  ←False

x > 1  ←True

The solution consists of all of the true intervals.

−4 < x < −1 x > 1

xz_007 [3.2K]3 years ago
5 0

Answer:

It is C

Step-by-step explanation:

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Set c

Step-by-step explanation:

3 0
3 years ago
Suppose a car has a rating of 4.8 gallons per 100 miles. What is the miles-per-gallon rating of this car? 
bezimeni [28]

Answer:

The miles-per-gallon rating of this car is 20.83.

Step-by-step explanation:

This question can be solved by a rule of three.

What is the miles-per-gallon rating of this car?

How many miles for 1 gallon?

4.8 gallons are used for 100 miles. So

4.8 gallons - 100 miles

1 gallon - x miles

4.8x = 100

x = \frac{100}{4.8}

x = 20.83

The miles-per-gallon rating of this car is 20.83.

4 0
2 years ago
Please help me figure this out.
xz_007 [3.2K]

Answer:

Quotient: x+7

Remainder: -2

Step-by-step explanation:

Divide the terms (x² ÷ x =x)↓

(x² + 11x + 26) ÷ (x + 4) =x

Subtract x² + 4x (You have to the sign if each term)

(x² + 11x + 26) ÷ (x + 4) =x

-x² - 4x

-------------------

      7x + 26      

Divide the terms (7x ÷ x = 7)

x² + 11x + 26) ÷ (x + 4) =x + 7

Multiply the quotient by the dividend (x + 4) × 7 = 7x+28

(x² + 11x + 26) ÷ (x + 4) =x

-x² - 4x

-------------------

      7x + 26      

      7x + 28

------------------

           = -2 Remainder

4 0
3 years ago
students at a bake sale sell bags of cookies for $2.25 each and bags of miniture muffins for $1.50 each. They received a $25 don
Soloha48 [4]
2.25c+1.5m context is that 2.25c represents the price of selling bags of cookies, hint the c. 1.5m represents the price of selling muffins, hint the m. In whole the equation represent the amount of money the bake sale would make minus the $25 donation.

Please vote my answer brainliest. thanks!
3 0
3 years ago
Read 2 more answers
23.5584557678 rounded to the nearest hundredth
hram777 [196]
23.5584557678 = 23.56 <span>rounded to the nearest hundredth

hope it helps</span>
3 0
3 years ago
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