Answer:
The rule of Identity. X*1=X.
Divide both sides by x, and you get
X/X = 1
What is the solution of the inequality x3 + 3x2 > 7x + 6?
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].
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there are 54 new houses built in a neighborhood. Last month, 1/3 of them were sold. This month, 5/6 of the remaining houses were sold. How many houses are left to be sold?
Answer:
Total houses = 54
House sold last month = 1/3 * 54 = 18
Remaining houses = 54-18 = 36
Houses sold this month = 5/6* 36 = 30 houses
House left to be sold = 36 - 30 = 6 houses
When Anita first planted the cherry tree in her yard, it was 20 feet tall. Now it
is 95% taller. How tall is the tree now?
Answer:
the cherry tree is now 39 feet tall.
Step-by-step explanation:
95% of 20 is 19, so 20+19=39.
How much larger is 5 than -5 ? ( if using a number line what is the difference between -5 and 5)
Answer:
-10 if moving to left 10 if moving to the right
Step-by-step explanation:
The difference is 10 because if you go from 0 to 5 and then go to -5 you're skipping 10 units to the left go there if you're going right it's positive 10 if you're going left it's negative -10
The difference is 10.
5 - (-5) = 10.
you are subtracting a negative number.
That basically means adding.
a trick to that is using the two subtraction symbols to make a plus.
I added an image in case that didn’t make sense!
I will mark Brainy just help!!!!
Answer:
D
Step-by-step explanation:
5 ( 3 squared x) + 9 ( 3 squared x)
Answer:
42x^2
Step-by-step explanation:
[tex]5(3x^{2} )+9(3x^2)\\\\=(5+9)(3x^2)\\\\=14(3x^2)\\\\=42x^2[/tex]
Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, critical value(s), and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100mm cigarettes is obtained, and the tar content of each cigarette is measure. The sample has a mean of 19.4 mg and a standard deviation of 3.52 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest about the effectiveness of the filters? What are the hypotheses? Identify the test statistic. Identify the P-value Identify the critical value(s). State the final conclusion that addresses the original claim. A. Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. B. Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. C. Fail to reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. D. Reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. What do the results suggest, if anything, about the effectiveness of the filters? A. The results are inconclusive because the sample size is less than 30. B. The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes. C. The results do not suggest that the filters are effective. D. The results suggest that the filters are effective. E. The results suggest that the filters increase the tar content.
Answer:
1) Option A: Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.
2)Option D: The results suggest that the filters are effective
Step-by-step explanation:
We are given;
Sample size; n = 25
Sample mean; x' = 19.4 mg
Standard deviation; s = 3.52 mg
Population mean; μ = 21.1 mg
Let's state the hypotheses;
Null Hypothesis;H0: μ = 21.1 mg
Alternative Hypothesis; Ha; μ < 21.1 mg
Now, since sample size is less than 30,we will use a t-test.
Thus;
t = (x' – μ)/[s/√(n)]
t = (19.4 - 21.1)/(3.52/√25)
t = -2.415
Using an online p-value from t-score calculator as attached with the parameters t = -2.415, DF = 25 - 1 = 24, significance level = 0.05, one tailed, we have;
The p-value is 0.011885.
The calculated p-value is less than the significance level of 0.05. Thus, we will fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.
Solve | | 2x + 5 | – 3 | = 8
The sum of the ages of Jacob and Jasmine is 66 years. 6 years ago, Jacob's age was 2 times Jasmine's age. How old is Jacob now?
Answer:
Jacob's age is 42
Jasmine's age is 24
Step-by-step explanation:
Let Jacob's age be x
Let Jasmine's age be y
x + y = 66
x - 6 = 2(y - 6)
x - 6 = 2y - 12
x - 2y = -12 + 6
x - 2y = -6
x + y = 66 ------- (1)
x - 2y = -6 ------- (2)
From (1),
x = 66 - y -------- (3)
Substitute the value of x in (2)
x - 2y = -6
66 - y - 2y = -6
-3y = -6 - 66
-3y = -72
y = -72/-3
y = 24
Solve for x in (1)
x + y = 66
x + 24 = 66
x = 66 - 24 = 42
x = 42, y = 24
The triangle will be enlarged by a scale factor of 10. A triangle with base 10 centimeters and height 7 centimeters. What will be the area of the new triangle?
Answer:
3500cm^2
Step-by-step explanation:
Area of a triangle= bxh/2
10x10=100
7x10=70
100x70=7000
7000/2=3500
Answer:
3500 cm²
Step-by-step explanation:
The given triangle has an area of ...
A = (1/2)bh = (1/2)(10 cm)(7 cm) = 35 cm²
The area of the enlarged triangle will be 10² = 100 times that, or 3500 cm².
__
You can see this if you use the enlarged dimensions in the area formula:
A = (1/2)bh = (1/2)(10·10 cm)(10·7 cm) = 100·35 cm² = 3500 cm
The table shows the number of pounds a dog lost or gained over the past month. A 2-column table with 4 rows. Column 1 is labeled Week with entries 1, 2, 3, 4. Column 2 is labeled pounds with entries 2 and one-half, negative 1, 1, negative 3 and one-half In which week did the dog have the greatest weight change? Week 1 Week 2 Week 3 Week 4
Answer:
column 2
Step-by-step explanation:
Answer:
week 4 so D
Step-by-step explanation:
The shortest known adult women is about 24 inches tall and tallest known adult woman is about 92 inches tall. write an absolute value equation that represents the minimum and maximum Heights. Use x to represent the heights.
Answer:
jndkjebfjkbwejhfdkfkdsjjdsf
Step-by-step explanation:
fjdshfshdgfjahnd
solve for x
[tex] - 6x + 14 = 32 - 4x[/tex]
how do I solve
Answer:
x = -9
Step-by-step explanation:
add 4x to both sides of the equal sign so then you'd have -2x + 14 = 32
then subtract 14 from both sides to where you have -2x = 18
then divide both sides by -2 and get x= -9
what is 75^58*^%23(718&^01232) *68726 function sof the equlatric erguim of the property
Answer:
2
Step-by-step explanation:
Draw a line representing the "rise" and a line representing the "run" of the line. State
the slope of the line in simplest form.
Answer:
Slope: 6/6. Slope in simplest form: 1
Help ASAP I'm bad at solving this I will give out 20 points!
Answer:
(0,3/2), (0,2),(6,0),(9/4,0)
I hope it helpss..
Factorise 4x^3 + 24x^2 Fully
Answer:
4x^2(x+6)
4x^3 is split into 4 and 3 x's
24x^2 is split into 4 and 6 and 2 x's
Cancel out what is the same so 4 and 2 x's and put it out the bracket : 4x^2(
Then put what is left over inside the bracket:
4x^2(x+6)
After factorization of the equation, the net result is 4x²(x + 6).
What is Factorization?An integer is factorized using the factorization equation. Factorization is the method of splitting a single object into two or smaller entities, or factors, whose sum equals the original estimate.
As per the provided data in the question,
4x³ consists of 4 and 3 x's
24x² consists of 4 and 6 and 2 x's.
Remove the bracket and remove anything identical, such as 4 and 2 x's: 4x²
Then put what is left over inside the bracket:
4x²(x + 6)
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.50 x 32? Please help. i will mark brainliest!
Chico is saving for new shoes that cost $87. He already has
$9 saved, and he will save the same amount each week.
Chico wants to buy the shoes in 6 weeks.
What is the least amount Chico can save each week and still
buy the new shoes in 6 weeks?
Answer:
he has to save $13 every week for six weeks which equals 78, and 78+9 is 87
The function is expressed by a formula y=0.1x+5. Find the value of the function if the variable is equal to 10; 50; 120.
Answer:
f(x) = 10: [tex]\large\boxed{6}[/tex]
f(x) = 50: [tex]\large\boxed{10}[/tex]
f(x) = 120: [tex]\large\boxed{17}[/tex]
Step-by-step explanation:
Write out the whole function using given information
f(x) = [10, 50, or 120]
Domain/y = 0.1x + 5
Substitute the possible values for x into the domain equation and solve
f(x) = 10: 0.1(10) + 5 = 1 + 5 = 6
f(x) = 50: 0.1(50) + 5 = 5 + 5 = 10
f(x) = 120: 0.1(120) + 5 = 12 + 5 = 17
Final answers:
f(x) = 10: [tex]\large\boxed{6}[/tex]
f(x) = 50: [tex]\large\boxed{10}[/tex]
f(x) = 120: [tex]\large\boxed{17}[/tex]
Hope this helps :)
solve: 3(2x+1)-2(x-5)-5(5-2x)=16 value of x?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{x = 2}}}}}[/tex]
Step-by-step explanation:
[tex] \displaystyle{ \star{ \: \: \underline{ \sf{given \: equation}}}}[/tex] :
[tex] \sf{3(2x + 1) - 2(x - 5) - 5(5 - 2x) = 16}[/tex]
Distribute 3 through the parentheses
[tex] \mapsto{\sf{6x + 3- 2(x - 5)- 5(5 -2x) = 16}}[/tex]
Distribute 2 through the parentheses
[tex] \mapsto{ \sf{6x + 3 - 2x + 10- 5(5 - 2x) = 16}}[/tex]
Distribute 5 through the parentheses
[tex] \mapsto{ \sf{6x + 3 - 2x + 10 - 25 + 10x = 16}}[/tex]
Combine ike terms and simplify it
Like terms are those which have the same base
[tex] \mapsto{ \sf{6x - 2x + 10x + 3 + 10 - 25 = 16}}[/tex]
[tex] \mapsto{ \sf{4x + 10x + 3 + 10 - 25 = 16}}[/tex]
[tex] \mapsto{ \sf{14x + 3 + 10 - 25 = 16}}[/tex]
Add the numbers : 3 and 5
[tex] \mapsto{ \sf{14x + 13 - 25 = 16}}[/tex]
The negative and positive integers are always subtracted but posses the sign of the bigger integer.
[tex] \mapsto{ \sf{14x - 12 = 16}}[/tex]
Move 17 to right hand side and change it's sign
[tex] \mapsto{ \sf{14x = 16 + 12}}[/tex]
Add the numbers: 16 and 17
[tex] \mapsto{ \sf{14x = 28}}[/tex]
Divide both sides by 14
[tex] \mapsto{ \sf{ \frac{14x}{14} = \frac{28}{14}}} [/tex]
Calculate
[tex] \mapsto{ \boxed{ \sf{x = 2}}}[/tex]
The value of x is 2
Hope I helped!
Best regards!
~TheAnimeGirl
dihsjsksiusjsueuuehehebdbbsjsshshshhs
is this a real question?
Find mDCAˆ. the question says that the angle is 3x+19 the smaller arc is 91 and the bigger is 17x-3 it is one of those problems were the difference in the arcs divided by two equals the angle
Answer: Option C.
Step-by-step explanation:
Let as consider the below figure is attached below.
We know that angle between tangent and secant is half of difference of major and minor arcs.
[tex]\angle ABC=\dfrac{arc(AD)-arc(AC)}{2}[/tex]
[tex]3x+19=\dfrac{17x-3-91}{2}[/tex]
Multiply both sides by 2.
[tex]6x+38=17x-94[/tex]
[tex]38+94=17x-6x[/tex]
[tex]132=11x[/tex]
Divide both sides by 11.
[tex]12=x[/tex]
The value of x is 12.
[tex]arc(AD)=17(12)-3[/tex]
[tex]arc(AD)=204-3[/tex]
[tex]arc(AD)=201^{\circ}[/tex]
Now,
[tex]arc(DCA)=360^\circ-arc(AD)[/tex]
[tex]arc(DCA)=360^\circ-201^{\circ}[/tex]
[tex]m\widehat {DCA}=159^{\circ}[/tex]
Therefore, the correct option is C .
which of the following pairs consists of equivalent fractions 9/24 and 21/56?
Answer:
3/8
Step-by-step explanation:
if u simplify you get half then add them the bigger dinominator is the bottom so only add the tops
Y varies directly as x. If x=7 then y = 56. Find ybwhen x=3
When something varies directly as something else, their ratio of change always stays the same.
56 / 7 = 8
Therefore,
8 * 3 = 24
If x = 3 then y = 24
How do you change a percent to a decimal? What is 6 1/2% as a decimal?
0.065
To convert a percent to a decimal, you move the decimal point to the left two times
Answer: 0.065
Step-by-step explanation:
When we divide 50 by 100 we get 0.5 (a decimal number). So, to convert from percent to decimal: divide by 100, and remove the percent symbol. So for 6.5% divided by 100=0.065
In the following figure, the teacher asks a student named Jerrica to find the length of segment AM. Jerrica sets the two sides equal to each other, does some algebra, and proclaims that the length of segment AM is 8 units long
State whether Jerrica is correct in her conclusion. If she is incorrect, explain the source of her error and give the correct length. In at least four sentences, support your response with a brief explanation. Be sure to include the terms midpoint, segment, and bisector in your explanation.
Answer/Step-by-step explanation:
Let us try to find the lenght of AM step-by-step to see if Jessica is correct or incorrect in her conclusion and possibly find out where she made an error if she's incorrect.
Now briefly, keys state some facts that explains or guides us while solving a problem like this:
1. Point M is the midpoint of segment AB.
2. The midpoint M, is a bisector of segment AB.
3. Segment AB is divided into two congruent or equal parts, AM and MB.
4. Therefore, by implication, segment AM (4x - 18) = segment MB (2x - 2).
5. To find the lenght of AM, we need to generate an equation to enable us solve for the value of x.
6. Equation to use to solve using algebra can be gotten by setting segment AM equal to segment MB. Which gives us:
4x - 18 = 2x - 2
Solve for x. Combine like terms.
4x - 2x = 18 - 2
2x = 16
Divide both sides by 2
x = 8
To find the lenght of AM = 4x - 18, replace x with 8 in the expression for the lenght of segment AM. (Note: this is what Jessica failed to do. She assumed 8 to be the length of segment AM.)
AM = 4(8) - 18 (Substitution)
AM = 32 - 18
Length of segment AM = 14 units
Jessica's error was her assuming that x = 8, is the length of segment AM. Her conclusion is wrong.
She ought to have plug in the value of x into the expression given for the lenght of segment AM.
Fill in the formula: The sum of the natural numbers from m to n is equal to…
Answer:
any sum of the form m+n′, either n′ is equal to 0, in which case the first clause applies, and the sum can be evaluated immediately, or n′ is the successor s(n) of some natural number n, in which case the second clause applies, and we can compute the sum in terms of a strictly simpler sum.
Step-by-step explanation:
I hope that helps
4x +14+ 4x=38 solve equation
Answer:
3
Step-by-step explanation:
4x +14 +4x =38
8x =38 - 14
8x=24
x=24 :8
x=3
In a hotel a servant needs to clean 30 rooms in 3 hours. How many rooms a servant needs to clean in 6 hours
Answer: 60 rooms
Step-by-step explanation:
because in 30 rooms is 3 hour + other 3 hour are 60 rooms. =60 rooms