What is the solution of the inequality x3 + 3x2 > 7x + 6?
Answers
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! :)
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].
Learn more about inequality here;
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Related Questions
I WILL MARK BRAINLIEST!!!
What is 178.80 as a fraction?
Answers
Answer: 178 4/5 or as an improper fraction 894/5
Hope this helps!
Please mark Brainliest!
178.80 = 178 + 0.8 = 178 + 8/10
178 8/10 = 178 4/5 or 895/5
Given that the 3rd term in an arithmetic sequence is -2 and the 7th term is -10, tell me what the 1st term in the sequence is. Explain how you know.
Answers
Answer:
2
Step-by-step explanation:
a₃ = -2
a₇ = -10
The nth term of an arithmetic sequence is:
a = a₁ + d (n − 1)
Therefore:
-2 = a₁ + d (3 − 1) = a₁ + 2d
-10 = a₁ + d (7 − 1) = a₁ + 6d
Subtract the equations:
8 = -4d
d = -2
Plug into either equation to find the first term.
-2 = a₁ + 2(-2)
a₁ = 2
-75 - 82 plus 83 plus 54
Answers
Answer:
Hey!
Your answer is -20!
Step-by-step explanation:
(-75) - 82 gives us = -157
(-157) + 83 gives us = -74
(-74) + 54 gives us = -20
I HOPE THIS HELPED!
Answer:
The person above me is correct
Step-by-step explanation:
Order the numbers from least to greatest.
1.3 ,-2, 1.8 , 0, -1.75
Answers
Answer:
-2 , -1.75 , 0 ,1.3 , 1.8Step-by-step explanation:
[tex]1.3 ,\:-2,\: 1.8 , \:0,\: -1.75[/tex] =
[tex]-2 , -1.75 \:, 0\: ,1.3 \:, 1.8[/tex]
A negative number is a always smaller than a positive number.
The smallest negative number among the given set of data is ; -2.
The largest positive number is 1.8
For which values of a the system has at least one solution: 1.x≤7 ,x≥a
Answers
Given:
The system of inequalities
[tex]x\leq 7[/tex]
[tex]x\geq a[/tex]
To find:
The values of a for which the system has at least one solution.
Solution:
We have,
[tex]x\leq 7[/tex] ...(i)
It means all real values of x which are less than or equal to 0.
[tex]x\geq a[/tex] ...(ii)
It means all real values of x which are greater than or equal to a.
Using (i) and (ii), we get
[tex]a\leq x\leq 7[/tex]
The value of x is lies in the interval [a,7].
It means, if the value of a is less than or equal to 7, then system has at least one solution.
But if a is more than 7, then the system of inequalities have to solution.
Therefore, the value of a must be less than or equal to 7.
Find the distance between the two points (5, -3) and (2, 5). Simplify your answer, and write the exact answer in simplest radical form for an irrational answer.
Answers
Answer:
(3.5, 1)
Step-by-step explanation:
Write a system of inequalities to match the graph and prove that the coordinate point (-10, -14) is in the solution set
Answers
Answer:
y < x - 2
y ≥ 2x + 5
Step-by-step explanation:
For the equation of the dotted line,
Slope of the line = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
Since the dotted lines passes through the points (-7, -9) and (2, 0)
Slope = [tex]\frac{-9-0}{-7-2}[/tex]
[tex]m_1[/tex] = 1
Therefore, equation of the line passing through (2, 0) and slope = 1 will be,
y - y' = m₁(x - x')
y - 0 = 1(x - 2)
y = x - 2
Since, shaded area is below the dotted line,
y < x - 2 will be the inequality.
Slope of the solid line passing through (-7, -9) and (0, 5) is,
[tex]m_2=\frac{-9-5}{-7-0}[/tex]
= 2
Therefore, equation of the line passing through (0, 5) and slope = 2 will be,
y - 5 = 2(x - 0)
y = 2x + 5
Since, the given line is a solid line and shaded area is above the line,
y ≥ 2x + 5 will be the inequality.
Since, (-10, -14) is lying in the common shaded area of both the inequalities, it will be the solution set of the graphed inequalities.
tristan bought an orange that weighs 1 8th of a pound
Answers
Tristan bought an orange that weighs 1 8th of a pound. 1. See answer. Add answer. Log in to add comment.
odds against a randomly chosen household having a cat if the probability of the event that a randomly chosen household has a cat is .21
Answers
Step-by-step explanation:
Odds against = failures / successes
Probability = successes / (successes + failures)
0.21 = cats / (cats + no cats)
1 / 0.21 = (cats + no cats) / cats
4.76 = 1 + (no cats / cats)
3.76 = no cats / cats
So the odds against are 3.76 to 1.
On a test, Avery lost 5
points for each of the 6
questions she got wrong
but earned 10 points for
answering the bonus
question correctly. What
integer represents her
score in relation to a
perfect score of 100?
Answers
Answer:
bruhhhhhhhhhhhhhhhhhhhhhhhhhh
What is the meaning of the expression (4 + 5) x 2?
Answers
Answer:
18.
Step-by-step explanation:
4+5 is 9, and 9 times 2 is 18
Tip: use bedmas for similar equations
B- brackets
E- exponents
D- division
M- multiplication
A- addition
S- subtraction
(It’s the order in which you should solve)
which systems of equations have no Solutions
Answers
Brainliest?
Answer:
Inconsistent System of Equations
Explanation:
There is no solution for the system of equations that graphs as parallel lines.
Parallel lines never cross, therefore there is no intersection. This is an inconsistent system of equations.
If BC = x − 2, CD = 19, and BD = 3x − 11, what is BD? Simplify your answer and write it as a proper fraction, mixed number, or integer. Could you please type the answer in a step by step.
Answers
Answer:
UV = 15
BD= 31
Step-by-step explanation:
Since, U is the midpoint of TV.
Therefore,
TU = UV
x + 10 = 3x
x - 3x = - 10
-2x = - 10
x = - 10/-2
x = 5
UV = 3x = 3*5
UV = 15
BD = BC + CD
3x - 11 = x - 2 + 19
3x - 11 = x + 17
3x - x = 11 + 17
2x = 28
x = 28/2
x = 14
BD = 3x - 11 = 3*14-11 = 42 - 11
BD= 31
how to combine two integers
Answers
The simplest approach to do this is:
Convert both numbers to string
Concatenate both strings into one, as this is comparatively easy
Convert this concatenated string back to integer
Step-by-step explanation:
Given two integers n1 and n2, the task is to concatenate these two integers into one integer.
Example:
Input: n1 = 12, n2 = 34
Output: 1234
Input: n1 = 1, n2 = 93
Output: 193
solve. 20 x 10⁵ = what i only have 5 minutes to answer this
Answers
Answer:
2000000
Step-by-step explanation:
20 x 100,000
Answer:
2000000 or 2×10^6
Step-by-step explanation:
[tex]20\times 10^5\\\\10^5=100000\\\\=20\times \:100000\\\\=2000000\\or \\2\times 10^6[/tex]
60 divided (6 1/7 - 1/7) x 4
Answers
• She used a coupon for $3.00 off the total price of the items she
This expression can be used to determine the price of the items Nakit
(2(3.50 -0.80) + 4.85 + 2.40) – 3.00
What is the price of the items Nakita bought?
A $6.95
B $10.45
C $9.65
D $12.65
Answers
Find the surface area of a square pyramid if the area of the base is 324 cm^2 and the height is 40 cm.
Answers
Answer:
Step-by-step explanation:
Yep!
NEED HELP NOW!!!! find the measure of the angle BXE using the figure below
Answers
Answer:
bxe is a triangle
Step-by-step explanation:
Determine whether the given segments have the same length. Complete the justification of your answer,
AB and BC
The length of AB is
length
The length of BC is /
.So, AB and BC (select)
the same length
Answers
Answer:
No does not contain the same length
Step-by-step explanation:
Given that
A(-4,2) , B (1,4), C (2, -1)
Now
AB would be
= [tex]\sqrt{(1-(-4))^2 + (4-2)^2} \\\\= \sqrt{29}[/tex]
And, BC is
[tex]= \sqrt{(2-1)^2 + 1-(-4))^2} \\\\= \sqrt{26}[/tex]
As we can see that the AB and BC are not equaled
So,
AB ≠ BC
Due to the different length
Therefore they do not contains the same length
We simply applied the distance formula due to which the length could be determined and the same is to be considered
Suppose PR = 54, solve for QR
4x-1
3x-1
P
R
Answers
Answer:
[tex] QR = 23 [/tex]
Step-by-step explanation:
P, A, and R are collinear.
PR = 54
[tex] PQ = 4x - 1 [/tex]
[tex] QR = 3x - 1 [/tex]
To solve for the numerical length of PR, let's generate an equation to find the value of x.
According to the segment addition postulate:
[tex] PQ + QR = PR [/tex]
[tex] (4x - 1) + (3x - 1) = 54 [/tex] (substitution)
Solve for x
[tex] 4x - 1 + 3x - 1 = 54 [/tex]
Combine like terms
[tex] 4x + 3x - 1 - 1 = 54 [/tex]
[tex] 7x - 2 = 54 [/tex]
Add 2 to both sides
[tex] 7x - 2 + 2 = 54 + 2 [/tex]
[tex] 7x = 56 [/tex]
Divide both sides by 7
[tex] \frac{7x}{7} = \frac{56}{7} [/tex]
[tex] x = 8 [/tex]
[tex] QR = 3x - 1 [/tex]
Plug in the value of x into the equation
[tex] QR = 3(8) - 1 = 24 - 1 [/tex]
[tex] QR = 23 [/tex]
A bookstore had 60 copies of a magazine. Yesterday, it sold 1/3 of them. Today, it sold 3/5 of what remained. How many copies does the bookstore have left?
Answers
Answer: 8 copies
Step-by-step explanation:
1/3 of 60 is 20. 1/5 of 40 is 8. 8x3=24, 40-24=16
1/3 or 60 is 20 so they sold 20 and had 40 left over 1/5 of 40 is 8 8*3= 24 40-24=16
Convert 2.42 to percent
Answers
Answer:
242%
Step-by-step explanation:
Answer:
242%
Step-by-step explanation:
Whole numbers are a 100% each, so there's 200%. Tenths are 10% every tenth, so 40%, and hundredths are 1% every hundredth, so 2%.
200+40+2=242%
If it was helpful, could you plz consider giving me brainliest?
find the value of each variable. write your answers in simplest radical form
Answers
Answer:
y=3.364
x=4
Step-by-step explanation:
hope this helps
what is 360 x 4500 plsssssssssssssssss help
Answers
Answer:
1,620,000
Step-by-step explanation:
360×4500
=1,620,000
is the answer
Hey there!
[tex]Answer:\boxed{1,620,000}[/tex]
[tex]Explanation:[/tex]
[tex]360*4500[/tex]
Let's multiply to get our answer.
[tex]360*4500=1,620,000[/tex]
[tex]1,620,000[/tex]
Hope this helps!
1. Name the property the equation illustrates.
–2.1 × 1 = –2.1
Multiplication Property of –1
Inverse Property of Multiplication
Identity Property of Addition
Identity Property of Multiplication
2. Name the property the equation illustrates.
8.2 + (–8.2) = 0
Inverse Property of Multiplication
Addition Property of 0
Identity Property of Addition
Inverse Property of Addition
Answers
Answer:
1) ident. prop. of mult.
2) add. prop. of add.
Step-by-step explanation:
have a good day!
Last week, Lindsay earned $10 per hour plus a $60 bonus for good job performance. She spends StartFraction 1 Over 15 EndFractionof her paycheck on dinner with friends. If she had not earned the bonus, the amount she spent on dinner would have been StartFraction 1 Over 10 EndFraction of her paycheck. Which equation can be used to find h, the number of hours Lindsay worked last week? StartFraction 1 Over 15 EndFraction left-parenthesis 10 h plus 60 right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis(10h + 60) = StartFraction 1 Over 10 EndFraction(10h) StartFraction 1 Over 15 EndFraction(10h + 60h) = StartFraction 1 Over 15 EndFraction left-parenthesis 10 h plus 60 h right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis(10h) StartFraction 1 Over 15 EndFractionh(10 + 60) = StartFraction 1 Over 15 EndFraction h left-parenthesis 10 plus 60 right-parenthesis equals StartFraction 1 Over 10 Endfraction h left-parenthesis 10 right-parenthesish(10) StartFraction 1 Over 15 EndFraction left-parenthesis 10 plus 60 h right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis(10 + 60h) = StartFraction 1 Over 10 EndFraction(10h)
Answers
Answer:
StartFraction 1 Over 15 EndFraction left-parenthesis 10 h plus 60 right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis
Step-by-step explanation:
The desired equation equates 1/15 of the amount Lindsay earned with 1/10 the amount without the bonus:
StartFraction 1 Over 15 EndFraction left-parenthesis 10 h plus 60 right-parenthesis equals StartFraction 1 Over 10 Endfraction left-parenthesis 10 h right-parenthesis
_____
Comment on the form of the answer
If you don't like answers in this form, please do not post questions in this form. Ordinary math symbols are much appreciated.
Answer:
A
Step-by-step explanation:
edge 23
Look at the table showing different prices for oranges.
Prices for Oranges
Price A
Price B
Price C
$2.25 for 6
$1.30 for 4
$0.97 for 2
Which gives the prices in order, from least to greatest unit rate?
Price B, Price A, Price C
Price C, Price B, Price A
Price C, Price A, Price B
Price B, Price C, Price A
Answers
nswer:
1st Option is correct that is Price B , Price A , Price C
Step-by-step explanation:
0.33 < 038 < 0.49 ⇒ Price B < Price A < Price C
Approximately, it's going least to greatest
2.25/6=0.33
1.30/4= 0.38
0.97/2 = 0.49 ALL ROUNDED
Answer:
its the first one
Step-by-step explanation:
hope that helps
Answer these questions please
Answers
Step-by-step explanation:
hope This helps for you
Answer:
Step-by-step explanation:
Common factors are the number's , variables found in each of the terms
1) 21x²y = 3 * 7 * x * x * y
35xy² = 5 * 7 * x * y * y
Common factor = 7 * x * y
= 7xy
Answer :(iii) 7xy
2)a² - b² = (a + b)(a - b)
1 - x² = (1 - x) (1 +x)
(ii)
3) x³ - x = x(x² - 1)
= x(x + 1)(x - 1)
Answer: (iv)
4) 225 = 15 * 15 = 15²
x³ - 225x = x(x² - 225)
= x(x² - 15²) {a² - b² =(a + b)(a - b)}
= x(x + 15)(x - 15)
Answer: (ii)
5) 12a²b = 3 * 4 * a * a * b
15ab² = 3 * 5 * a * b * b
Common factor = 3 * a * b = 3ab
12a²b + 15ab² = 3*4*a²*b + 3*5*a*b²
= 3ab (4a + 5b)
Answer:(ii)
Determine the largest integer value of x in the solution of the following inequality. -3x +1> 7
Answers
Answer:
x<1/3
Step-by-step explanation: