Multiply (6x^3+8)(7x^2+8x+7)

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].

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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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

is this a real question?

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

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).

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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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 .

Answer:

the cherry tree is now 39 feet tall.

Step-by-step explanation:

95% of 20 is 19, so 20+19=39.

Answer:

jndkjebfjkbwejhfdkfkdsjjdsf

Step-by-step explanation:

fjdshfshdgfjahnd

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

Answer:

Slope: 6/6. Slope in simplest form: 1

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 :)

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

Answer:

he has to save $13 every week for six weeks which equals 78, and 78+9 is 87

Answer:

(0,3/2), (0,2),(6,0),(9/4,0)

I hope it helpss..

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

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.

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

Answer:

D

Step-by-step explanation:

Answer:

18%:540 20%:600 22%:660

Step-by-step explanation:

18%:540 20%:600 22%:660

20-2=18 20+2=22

The required least to the greatest number of students their favorite color is red is 540 and 660 respectively.

Given that,
A group of students was asked about their favorite colors,
20% of the students said that their favorite color is red.
There are about 3000 students in the school.
The margin of error is ±2%,
To determine what is the range of the number of students who likely say that their favorite color is red

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,
Total number of students = 3000
Number of students like red color = 20% of 3000 = 0.20 * 3000 = 600
the margin of error ±2% of 3000 = ± 0.02 * 3000 = ± 60
Least number of students their favorite color is red = 600 - 60 = 540
Greatest  number of students their favorite color is red = 600 + 60 = 660

Thus, the required least to the greatest number of students whose favorite color is red is 540 and 660 respectively.

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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

Answer:

please give brainlist

Rounding to a certain number of decimal places

If we want to round 4.732 to 2 decimal places, it will either round to 4.73 or 4.74. 4.732 rounded to 2 decimal places would be 4.73 (because it is the nearest number to 2 decimal places).

hope this helped

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

Answer: 60 rooms

Step-by-step explanation:

because in 30 rooms is 3 hour + other 3 hour are 60 rooms. =60 rooms

Answer:

3

Step-by-step explanation:

4x +14 +4x =38

8x =38 - 14

8x=24

x=24 :8

x=3

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.

Answer:

2

Step-by-step explanation:

Answer:

column 2

Step-by-step explanation:

Answer:

week 4 so D

Step-by-step explanation: