What is the solution of the inequality x3 + 3x2 > 7x + 6?

Answers

Answer 1

Answer:

Inequality form : - 5 + squareroot13 / 2 < x < - 5- squareroot13 / 2 or x > 2

Step-by-step explanation: Solve the inequality by finding the roots and creating test intervals.

I hope this helps you out! :)

Answer 2

The solution to the inequality is [tex]\rm \left (\dfrac{-5+\sqrt{13} }{2} < x < \dfrac{-5-\sqrt{13} }{2} \right ) \ or \ x > 2[/tex].

The Interval Notation is [tex]\rm \left (\dfrac{-5+\sqrt{13} }{2} , \dfrac{-5-\sqrt{13} }{2} \right ) \cup (2, \infty)[/tex].

What is inequality?

In Mathematics, the relationship between two values that are not equal is defined by inequalities.

The given inequality is;

[tex]\rm x^3 + 3x^2 > 7x + 6[/tex]

The solution to the inequality is determined in the following steps given below.

[tex]\rm x^3 + 3x^2 > 7x + 6\\\\\rm x^3 + 3x^2-7x-6 > 7x + 6-7x-6\\\\ x^3 + 3x^2-7x-6 > 0\\\rm \\ x(x^2+5x+3)-2(x^2+5x+3) > 0\\\\ \rm x^3+5x^2+3x-2x^2-10x-6 > 0\\\\ x(x^2+5x+3)-2(x^2+5x+3) > 0\\\\\rm (x-2)(x^2+5x+3) > 0[/tex]

Now finding the roots of the inequality;

[tex]\rm (x-2)(x^2+5x+3) > 0 \\\\(x-2) \left (\dfrac{-5\pm\sqrt{25-12} }{2} \right )\\\\(x-2)\left (\dfrac{-5+\sqrt{13} }{2} \right )\left (\dfrac{-5-\sqrt{13} }{2} \right )[/tex]

Hence, the solution to the inequality is [tex]\rm \left (\dfrac{-5+\sqrt{13} }{2} < x < \dfrac{-5-\sqrt{13} }{2} \right ) \ or \ x > 2[/tex].

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What Is The Solution Of The Inequality X3 + 3x2 &gt; 7x + 6?

Related Questions

Explain how to find the LCM of 8 and 10

Answers

Answer: Start by listing the first five multiples of each number. Then circle the common multiples. Finally, identify the least of these common multiples. The LCM of 8 and 10 is 40.

Step-by-step explanation:

Answer:

Start by listing the first five multiples of each number. Then circle the common multiples

Step-by-step explanation:

-7x+4y+9-4x=-7-5-5(-x-3y)

Answers

Answer:

for x = −11y/16+ 21/16

for y = 16x/11 +21/11

Step-by-step explanation:

Warren had d dollars. He bought 5 ice creams which cost x dollars each. How much money does he have left?

Answers

Answer:

The answer is: d-5x

Step-by-step explanation:

What I like to do is rewrite the problem with numbers instead of variables.

Example: Warren had 20 dollars. He bought 5 ice creams which cost 2 dollars each. How much money does he have left?

He has 20 dollars, 5x2=10 he spent 10$ on the ice cream so you have to subtract how much he had in the beginning to how much he spent, the answer with numbers would be: 20-5x2

With variables it would be d-5x

Solve the equation . Check your solution

Answers

Answer:

x=48/8=6

Step-by-step explanation:

simple form

8x-48=0

fractionized

8(x-6)=0


Solve for Xon the following Equations.
1. 4 + 7 x X = 22

Answers

Step-by-step explanation:

4 + 7 x X = 22

4+7x=22

7x=22-4

7x=18

x=18/7

You would add the 4 and 7 then get 11 x X=22. Once you get that subtract the 11 from both sides to get X=11

What is the solution set for 8(2−h)>−3h−4?

Answers

Answer:

h < 4

Step-by-step explanation:

Simplify both sides

-8h + 16 > -3h - 4

Add 3h to both sides

-5h + 16 > -4

Subtract 16 from both sides

-5h > -20

Divide both sides by -5

-20 divided by -5 = 4

Since you divided by a negative number, you change the inequality sign to < instead of >

A car is traveling down a highway at a constant speed, described by the equation d=65t, where d represents the distance, in miles, that the car travels at this speed in t hours. How many miles does the car travel in 1.5 hours?

Answers

Answer:

A car is traveling down a highway at a constant speed, described by the equation d = 65t, where d represents the distance, in miles, that the car travels - 1138… ... How many miles does it take the car to travel 26 miles at this speed? c. ... the distance, in miles, that the car travels at this speed in t hours.

Step-by-step explanation:

Hope this helps

in Sean’s fish tank, there are 6 times as many goldfish as guppies. There are a total of 21 fish in the tank. How many more goldfish are there than guppies.

Answers

Answer: There are 15 more goldfish than guppies.

Step-by-step explanation:

Since there are 6 times as many goldfish as guppies, then. Now 3 + 18 = 21 the total fish in the tank. Hence there are 3 guppies and 18 goldfish. and 18 - 3 = 15, thus there are 15 more goldfish than guppies.

What is the domain of the function f(x)=

Answers

Think of f(x) as y, because it is the same thing so find the x for your domain

Answer:

The domain of a function is the set of all possible inputs for the function.

Step-by-step explanation:the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0.

The copper content of 18-carat gold was measured by two methods for six different samples collected from a jewelry production plant. Sample Method 1 Method 2 A 2.2% 2.5% B 1.8% 2.2% C 2.5% 3.0% D 3.0% 3.2% E 2.6% 2.3% F 2.6% 2.7% Which test would you use to determine if the results obtained by the two methods agree within experimental error?

Answers

Full question attached

Answer:

Paired t test

Explanation:

The paired sample t test is used to measure or compare the mean of two observations or samples by measuring each subject two times as is seen above with the gold measurement which would result in two sets or pair of samples in a statistical procedure. We observe from the question that we measure each gold with two methods and then compare result of the two methods in terms of their mean error using the paired t test.

4|m-n| if m= -7 and n=2

Answers

4|-7-2| = 4|-9| = 4x9 = 36

- Complete the following paragraph proof.
Given: 44 -2(3x + 4) = -18
Prove: x = 9

Answers

Doing it in reverse order of operation. U can start by +2 or remove -2 on the left side :) and move it onto the -18 (right side)

Jose spent $34.50 on a bike rental in Miami, Florida. The rental store charged a base fee of $8.50 for the first hour, and an hourly rate of $3.25 for each additional hour. The following sign is displayed to show the prices for the first 4 hours.

Answers

Answer:

8.5+2.25x=34.5

edit***

18.25+3.25h=34.5

ILL MARK BRAINLIST !! SHOW WORK

Answers

Answer: Here is your answer dude

How would the underline look like

Answers

Answer:

the correct answer is C

-200 + {37}{3}4.5) -200 + 55.5

Answers

Answer:

-294.55

Step-by-step explanation:

-200+ 49.95 -200 +55.5

49.95+55.5-200-200

-294.55

On Monday a team of street sweepers cleaned 4 city blocks. Tuesday, the team cleaned 2 1/6 times as many blocks as on Monday. How many city blocks did the street sweepers clean on Tuesday?

Answers

1/5 is the answer :0000

There will be twelve and a half city blocks of the street sweepers clean on Tuesday.

What is a fraction?

The numerator, which is found at the top of the fraction number, and the denominator, which is located at the bottom, are its two component components.

It is given that, four city blocks were cleaned by a crew of street sweepers on Monday. The crew cleaned 2 1/6 as many blocks on Tuesday as they did on Monday.

Suppose the number of city blocks the street sweepers cleaned on Tuesday will be x,

x = 4 +  2 1/6 × 4

x=4+13/6×4

x=12.6≈ 12 1/2

Thus, the street sweepers will clean twelve and a half city blocks on Tuesday.

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r/4 - 1.4 =1.58 what should be the first step?

Answers

Answer:

R/4 - 1.4 =1.58

R/4 = 1.58 + 1.4

R/4 =2.98

r=11.92

Step-by-step explanation:

convert this statement into a conditional statement: 2 angles that add up to 180 degrees are supplementary

Answers

answer:
if 2 angles add up to 180 degrees, then they are supplementary

Identify three of the key messages used by advertisers when promoting their products.

Answers

Answer:

1. "Everyone is doing it"; 2. "It's fun to use our products"; 3. "You will be successful if you use our products."

Step-by-step explanation:

Are the two triangles below similar?
PLEASE HELP ME!!!!!!!!!!​

Answers

Answer:

im going with number 3 sorry if im wrong

Step-by-step explanation:

Answer:

Yes; they have congruent corresponding angles.

Step-by-step explanation:

The two triangles are similar because their angles measure are the same. This is because 70 + 28 + 92 = 180 degrees and all Euclidean triangles angles measures must have a sum of exactly 180 degrees.

9. Find the sum of the first 6 terms of the sequence: –3, 1, 5, 9, . . . options: A) 25 B) 48 C) 42

Answers

Answer:

C. 42.

Step-by-step explanation:

This is an arithmetic sequence with common difference d = 4 and first term a = -3.

Sum of n terms = (n/2)[2a + (n - 1)d]

Sum of  six terms = (6/2)[2(-3) + (6 - 1)4]

= 3 * (-6 + 20)

= 42.

Answer:

C) 42

Step-by-step explanation:

Given is an Arithmetic Sequence, where

First term a = - 3

Common Difference d = 1-(-3)= 4

n = 6

[tex]S_6=? \\ \\ \because \: S_n = \frac{n}{2} \{2a + (n - 1)d \} \\ \\ \therefore \: S_6 = \frac{6}{2} \{2 \times ( - 3) + (6 - 1)4 \} \\ \\ \therefore \: S_6 = 3 \{ - 6 + 20\} \\ \\ \therefore \: S_6 = 3 \times 14 \\ \\ \huge \red{ \boxed{ \therefore \: S_6 = 42}}[/tex]

1.For this problem, 200 meters of fencing will all be used to place fence on all four sides of the rectangle. Your task is to write the area that can be enclosed as a function of the width, w, of the rectangle.


Area equation:


What is the domain for this function (what values do you expect the width to fall between)?

Answers

Answer:

Step-by-step explanation:

Given that:

the perimeter of the fencing (rectangle)  = 200

Let recall that the area equation of a rectangle = L × w

The perimeter now = 2(L + w)

The perimeter = 2L + 2w

200 = 2L +2w

Dividing both sides by 2

100 = L + w

Making Length L the subject; we have:

- L = -100 + w

L = 100 - w

Thus;

A(w) = (100 - w) w

and the domain of the function is (0,100)

Simplify

(2x– 3) (5x4 – 7x3 + 6x2 – 9)



A. 10x5 – 29x4 + 33x3 - 18x2 18x + 27
B. 10x5 - x4-9x3 – 18x2 -18x - 27
C. 10x5 + 29x4 – 33x3 + 18x2 + 18x - 27
D. 10x5 + x4 + 33x3 + 18x2 + 18x + 27

Answers

Answer: (A)=10x5−29x4+33x3−18x2−18x+27

Step-by-step explanation:

How i solved it was by simplifying each answer there was available and (A) was the most compatiable answer!

=(2x+−3)(5x4+−7x3+6x2+−9)

=(2x)(5x4)+(2x)(−7x3)+(2x)(6x2)+(2x)(−9)+(−3)(5x4)+(−3)(−7x3)+(−3)(6x2)+(−3)(−9)

=10x5−14x4+12x3−18x−15x4+21x3−18x2+27

=10x5−29x4+33x3−18x2−18x+27

Answer:

=(2x+−3)(5x4+−7x3+6x2+−9)

=(2x)(5x4)+(2x)(−7x3)+(2x)(6x2)+(2x)(−9)+(−3)(5x4)+(−3)(−7x3)+(−3)(6x2)+(−3)(−9)

=10x5−14x4+12x3−18x−15x4+21x3−18x2+27

=10x5−29x4+33x3−18x2−18x+27

Step-by-step explanation:

can someone help ASAP plzz

Answers

Answer:

c. 84 ft²

Step-by-step explanation:

lateral area = 1/2 * base perimeter * height

where

base sides = 6 ft.

height (L) = 7

lateral area = 1/2 x (4*6) * 7

lateral area = 84 ft²

LA = 1/2pl

p = base perimeter

l = length

p = (6 * 4)

p = 24

l = 7

Use the formula and solve.

LA = 1/2(24)(7)

LA = 1/2(168)

LA = 84

Therefore, the answer is C

Best of Luck!

What number is 136% of 12.24?

Answers

Answer:

I really don't know but I'm trying to hurry for my quiz lol sorry

Answer:

cxcxcxcxcxgergddgg

Step-by-step explanation:

Find the area of a square with a side of length 2 Square root of 3+6 square root of 7 inches

Answers

Answer:

(264+24√21) in²

Step-by-step explanation:

Area of a square = Length * Length

A = L²

Given the length of a square as [tex]2\sqrt{3}+6\sqrt{7}[/tex] inches' The area of the square will be calculated as shown;

[tex]A = (2\sqrt{3}+6\sqrt{7})^2\\\\A = (2\sqrt{3}+6\sqrt{7})(2\sqrt{3}+6\sqrt{7})\\\\A =(2\sqrt{3})(2\sqrt{3})+(2\sqrt{3})(6\sqrt{7})+(6\sqrt{7})(2\sqrt{3})+(6\sqrt{7})(6\sqrt{7})\\\\A = 4\sqrt{9}+12\sqrt{21}+12\sqrt{21}+36\sqrt{49}\\\\A = 4(3)+24\sqrt{21}+36(7)\\ \\A = 12+24\sqrt{21}+252\\\\A = 264+24\sqrt{21}[/tex]

Hence the area of the square is (264+24√21) in²

To make grape juice by using frozen juice concen-trate, you must mix the frozen juice concentrate with water in a ratio of 1 to 3. How much frozen juice concentrate and how much water should you use to make 11 this problem in two different ways by reasoning about multiplication and division with quanti-ties, explaining your reasoning in each case.

Answers

Answer:

To make 11 grape juice, you will need:

11 (1 * 11) frozen juice concentrate and

33 (3 * 11) water.

Step-by-step explanation:

Since you are making 11 grape juice containers and each container requires 1 frozen juice concentrate and 3 quantities of water, to get the maximum quantities of ingredients required, you will multiply each ingredient by 11.

With the sum of ratio as 4 (1:3), we can also say that 44 (4 * 11) units of both frozen juice concentrate and water are required to produce 11 units of the grape juice.  Dividing 44 by 4 also gives 11 units.  Similarly, dividing the total ingredients of the frozen juice of 11 units by 11 juice concentrate gives 1 unit each and dividing 33 units by 11 quantity of water gives 3 units each in every unit of the juice produced.

SOMEONE HELP PLEASE.............

What is the x-coordinate of the solution of the following system of equations?

3x + y = 6
x - y = 6

A. -3
B. 0
C. 3​

Answers

Answer:

(3,-3) or x = 3

Step-by-step explanation:

I solved this problem with the help of graphing, you would start by sketching each equation. The x-value of the point where both equations intersect would be solution to your equations.

These tables of values represent continuous functions. For which functions will the y-values be the greatest for very large values of x?​

Answers

∆....A....∆

1 6

2 18

3 54

4 162

5 486

The function with the greatest y-values for very large values of x is C.

The y-values in function C increase at a much faster rate compared to the other functions as x becomes larger. In function C, the y-values are growing with a constant difference of 200 for each increase in x. This means that for every unit increase in x, the y-value increases by 200. This linear relationship results in significantly larger y-values for larger x-values.

On the other hand, the other functions (A, B, and D) do not exhibit such rapid growth. Function A has a cubic relationship, which does lead to larger values than a linear relationship, but it is still not as rapid as the linear increase in function C. Function B also has a linear relationship, but the constant difference between y-values is much smaller than in function C (only 75).

Function D has a constant difference of 5 between y-values, resulting in a very slow growth as x becomes larger.

In conclusion, function C has the greatest y-values for very large values of x due to its linear relationship with a constant difference of 200 between y-values for each unit increase in x.

To learn more about continuous functions, here

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