I need help with the following ​

n < 9 makes the inequality 3(n + 1) > 5(n − 3) true.

Hence, option A) S:{ 9 } is the correct answer.

Given the inequality in the question

3(n + 1) > 5(n − 3)

To determine the integer will make the inequality true, we simply solve for n.

3(n + 1) > 5(n − 3)

Remove the parenthesis using distributive property

3×n + 3×1 > 5×n + 5×−3

3n + 3 > 5n - 15

Collect like terms

3n + 3 > 5n - 15

3n - 5n > - 15 - 3

-2n > - 18

Divide both sides by -2.

Note that; when dividing or multiplying both sides of an inequality by a negative value, the inequality sign flips to the opposite direction.

-2n/-2 < -18/-2

n < 9

n < 9 makes the inequality 3(n + 1) > 5(n − 3) true.

Hence, option A) S:{ 9 } is the correct answer.

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Answer:

a) S:{9}

Step-by-step explanation:

Given equation,

→ 3(n + 1) > 5(n - 3)

Now the value of n will be,

→ 3(n + 1) > 5(n - 3)

→ 3n + 3 > 5n - 15

→ 3n - 5n > -15 - 3

→ -2n > -18

→ n < (-18)/(-2)

→ n < 18/2

→ [ n < 9 ]

Hence, the value of n is 9.

4. The two triangles are similar by virtue of the AAA triangle congruence theorem as a result of the corresponding angles which have equal measures.

5. The length of segment CE to the nearest tenth is; 46.7 in.

4. The ∆CBD and ∆CAE are similar (congruent) following the fact that angle C is common to both triangles and the angles A and E have equal measures as E and D respectively by virtue of corresponding angles theorem. Ultimately, the two triangles; ∆CBD and ∆CAE are congruent since all three angle measures are the same in the triangles.

The corresponding angles in discuss is due to the fact that the lines ED and AE are parallel lines.

5. Also, upon establishing the congruence of the two triangles, it follows that the ratio of their corresponding sides is same for all three sides.

Therefore, we can establish that;

BD/AE = CD/CE

6/14 = 20/CE

CE = (14 × 20)/6

CE = 140/3

CE = 46.667 in.

Ultimately, the length of segment CE to the nearest tenth is; 46.7 in.

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Answer:

  11. {7, 8}

  12. {8, 9}

  13. {8, 9}

  14. {4, 5}

Step-by-step explanation:

You want consecutive integers that bracket each of the given irrational roots.

A square root of an integer will be rational only if the integer is a perfect square. The first few perfect squares are ...

You know these because you know your multiplication tables.

The square root of a number between these perfect squares will lie between the roots of the squares.

50 lies between the squares 49 = 7² and 64 = 8². That means √50 lies between 7 and 8.

Your calculator tells you that √50 ≈ 7.0710678, which is a number that lies between the integers 7 and 8.

72 lies between the squares 64 = 8² and 81 = 9². That means √72 lies between 8 and 9.

65 lies between the squares 64 = 8² and 91 = 9². That means √65 lies between 8 and 9.

23 lies between the squares 16 = 4² and 25 = 5². That means √23 lies between 4 and 5.

__

Additional comment

The purpose of questions like this appears to be to have you make use of your knowledge of integer perfect squares to guess an approximation of a square root.

A calculator can answer these questions immediately. Of course the two consecutive integers are the integer part of the root, and the next higher integer.

The question is not well-posed. The answer to "integers each value is between" could be 1 < √50 < 50. For integers greater than 1, the square root is always smaller than the integer being rooted. We've seen questions like this enough times that we can guess the intention is for you to identify consecutive integers.

Extra credit

Knowing the integer part of the root and the difference between the number and its next lower perfect square, you can approximate the root as follows:

For integer n = a² +b, the root √n lies between a +b/(2a+1) and a +b/(2a).

For example, 65 = 8²+1, so √65 lies between 8 1/17 and 8 1/16.

The cost of lighting a 500-watt outdoor light for 8 hours according to the task content is; 30 cents.

According to the task content, the energy consumption for lighting the 500-watt outdoor light for 8 hours is; 500 × 8 = 4000 watt-hour = 4 kilowatt-hour.

On this note, since electricity costs 7.5¢ per kilowatt-hour, the cost of 4 kilowatt-hour is; 7.5¢ × 4 = 30 cents.

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The number of solutions in the equation 9x - 7 = 3(3x + 2) is 0

The equation is given as

9x - 7 = 3(3x + 2)

Open the bracket in the above equation

So, we have

9x - 7 = 9x + 14

Subtract 9x from both sides of the equation

So, we have

-7 = 14

The above equation is false

Hence, the number of solutions in the equation is 0

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Answer:

Step-by-step explanation:

(x-4,9)

Answer: 18 minutes

Step-by-step explanation:

900 divided by 250 = 3.6

3.6 times 5 = 18 minutes.

Answer:

18 minutes

Step-by-step explanation:

rate =   250 w / 5 min

900 w / rate =   time   = 900 w / (250 w/ 5min) = 18 minutes

Answer:

Step-by-step explanation:

The sum of three consecutive integers is 171. What are the integers?

(171 - 3) : 3 =

168 : 3 = 56

56 + 1 = 57

57 + 1 = 58

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

56 + 57 + 58 = 171

the answer is good

[tex]\: u_{1} - u_{0}= u_{2} - u_{1} \\ - 514 + 514 = - 514 + 514 \\ 0 = 0 \\ true \: so \: u_{n} \: arithmetic \: \: (d = 0)[/tex]

[tex] \frac{u_{1}}{u_{0}} = \frac{u_{2}}{u_{1}} \\ \frac{ - 514}{ - 514} = \frac{ - 514}{ - 514} \\ 1 = 1 \\ true \: so \: u_{n} \: geometric \: (r =1 )[/tex]

[tex]conclusion = \\ u_{n} \: is \: both \: arithmetic \: and \: geometric[/tex]

Answer:

n = 16

Step-by-step explanation:

The equation is,

→ √n = 4

Solving for the value of n,

→ √n = 4

→ n = 4²

→ [ n = 16 ]

Hence, the value of n is 16.

Answer:

997

Step-by-step explanation:

75×12=900

900+45+35+17=997

Answer:

c= -18 is your answer

Answer:   -1(5a-2)(3a+1)

Step-by-step explanation:

Answer:

-(5a-2)(3a+1)

Step-by-step explanation:

Answer:

41.6

Step-by-step explanation:

You have a duplicate question. Explanation is there. Hope it helps!

All work is shown in the screenshot that is provided! :)

Julianne's weekly salary based on this annual salary is $788.46

The yearly salary that the job pays Julianne = $41K

No. of weeks in a year = 52 weeks

When referring to a Participant, the term Weekly Salary refers to the weekly rate of pay for services that the Employer had been providing to the Participant at the time of his or her termination from the Employer. According to the Employer's payroll records, the Weekly Salary of a Participant whose rate of pay for services is based on an annual rate shall be equivalent to 1/52 of the yearly such rate at the time of his or her Termination of Employment from the Employer.

Therefore, finding out the weekly salary of Julianne we get:

=Annual salary of Julianne/No. of weeks in a year

= 41000/52 = $788.46

Hence, Julianne's weekly salary based on this annual salary is $788.46

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Answer:

Data Set 2 has the same mean as Data Set 1.

and

Data Set 2 has a larger standard deviation than Data Set 1

Step-by-step explanation:

Mean of both data sets is the same = 6

Data set 2 has a larger standard deviation since the data values are further away from the mean than the data values in data set 1 are from the mean and standard deviation is a measure of variance i.e. how far data set values are from the mean

Using the midpoint formula, the midpoints of the following are:

(4, √2) and (-2, 5√2) --> M(1, 3√2)

(-⅔, ⅘) and (⅓, ½) --> (-1/6, 13/20)

The formula that is used to determine the coordinates of the midpoint of a line segment is called the midpoint formula, and it is expressed as:

M(x, y) = [(x1 + x2)/2, (y1 + y2)/2]

Find the midpoint between (4, √2) and (-2, 5√2):

Let,

(4, √2) = (x1, y1)

(-2, 5√2) = (x2, y2)

Plug in the values

M(x, y) = [(-2 + 4)/2, (5√2 + √2)/2]

M(x, y) = [2/2, (6√2)/2]

M(x, y) = (1, 3√2)

M(1, 3√2)

Find the midpoint between (-⅔, ⅘) and (⅓, ½):

Let:

(-⅔, ⅘) = (x1, y1)

(⅓, ½) = (x2, y2)

Plug in the values

M(x, y) = [(-⅔ + ⅓)/2, (⅘ + ½)/2]

M(x, y) = [(-⅓)/2, (13/10)/2]

M(x, y) = [(-⅓ × ½), (13/10 × ½)]

M(x, y) = (-1/6, 13/20)

In summary, using the midpoint formula, the midpoints of the following are:

(4, √2) and (-2, 5√2) --> M(1, 3√2)

(-⅔, ⅘) and (⅓, ½) --> (-1/6, 13/20)

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Answer: 24

Step-by-step explanation:

60/5= 12

12(kids) times 2(parents)= 24 parents for 60 kids

5(x+2)-7

5(4+2)-7

20+10-7

30-7

23

The linear relation is:

y = x + 2

This is not a proportional relationship, as the y-intercept is different than zero, and then, it does not have a constant of proportionality.

The relationship clearly shows a linear relation, so we can get the slope if we use the first two points (2, 4) and (4, 6). The slope is:

s = (6 -4)/(4 - 2) = 1

Then the linear relation is of the form:

y = 1*x + b

To find the value of b we replace the values of the first point:

4 = 1*2 + b

4 - 2  =b

2 = b

The linear relation is:

y = x + 2

This is not a proportional relationship, as the y-intercept is different than zero, and then, it does not have a constant of proportionality.

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Answer:

No, because it doesn't go through zero

Step-by-step explanation:

Answer:

Answer: They require 18 to 26 gal of water. But they may also consume 40 gal

Step-by-step explanation:

answer:48 miles per hour

Answer: 8.717 x 10^8

Step-by-step explanation:

Answer: 8.717 × 10^{8}

Step-by-step explanation:

hope this helps <3

Total cost of the candy is represented by the function f (x) is;

⇒ f (x) = $2.80x + $3.50y

Where, x is the weight of the less expensive candy (caramel candy)

and, y is the weight of chocolate candies.

What is Multiplication?

To multiply means to add a number to itself a particular number of times. Multiplication can be viewed as a process of repeated addition.

Given that;

Mark bought 10 lb of two types of candies to make Christmas present for his classmates.

Let x is the weight of the less expensive candy (caramel candy).

And, y is the weight of chocolate candies.

Now, The cost of caramel candies = $2.80x

And, The cost of chocolate candies = $3.50y

Hence, Total cost of the candy = $2.80x + $3.50y

Therefore, Total cost of the candy is represented by the function f (x) is;

⇒ f (x) = $2.80x + $3.50y

Where, x is the weight of the less expensive candy (caramel candy)

and, y is the weight of chocolate candies.

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The equivalent expression of x^4y^2 − 3x^3y^3 when rewritten using common factors is x^3y^2(x − 3y)

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

x4y2 − 3x3y3

Rewrite the above expression properly

So, we have

x^4y^2 − 3x^3y^3

Factor out x^3 from the expression

So, we have

x^4y^2 − 3x^3y^3 = x^3(xy^2 − 3y^3 )

Factor out y^2 from the expression

So, we have

x^4y^2 − 3x^3y^3 = x^3y^2(x − 3y)

Hence, the equivalent expression of x^4y^2 − 3x^3y^3 when rewritten using common factors is x^3y^2(x − 3y)

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When f(x) = 1/x is converted to g(x) = 1/x - 7, the impact that this has on the graph of f(x) is that the graph of f(x) is moved down by seven units.

The connection that exists between lines and points in a network may be described using a graph, which is a mathematical description of a network.

g(x)=1/x - 7

f(x)= 1/x

There is a negative seven when the change occurs.

As a result, the graph of f(x) is moved 7 units below.

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Answer:

0.30

Step-by-step explanation:

sum of all probabilities is 1

so:

p(x=4) = 1 - ( 0.01 + 0.04 + 0.10 + 0.12 + 0.30 + 0.11 + 0.01 +0.01)

= 1 - 0.70

= 0.30