A ( x + 3 ) < 5x + 15 - x

find the value for a for which the solution of the inequality is all real numbers

Answers

Answer 1

The value of a for which the solution of the inequality is all real numbers is a = 5.

We have to first simplify the inequality:

A(x + 3) < 5x + 15 - x

Ax + 3A < 4x + 15

Ax - 4x < 15 - 3A

Simplifying further:

x(A - 4) < 15 - 3A

Now, we need the inequality to hold for all real values of x. This means that the coefficient of x, (A - 4), must have a fixed sign, and that the right-hand side, 15 - 3A, must be unbounded.

For the coefficient of x to have a fixed sign, we need either A - 4 < 0 or A - 4 > 0. This means that A must be less than 4 or greater than 4.

For the right-hand side to be unbounded, we need 15 - 3A to be equal to positive or negative infinity. Since 15 - 3A is a linear function of A, this only occurs when A = 5.

So, the solution to the inequality for all real numbers is:

if A < 4, then the solution is x < (15 - 3A) / (4 - A)

if A > 5, then the solution is x > (15 - 3A) / (4 - A)

if A = 5, then the solution is all real numbers.

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Related Questions

which error does the following represent? a candidate is interviewing for a customer service representative job. the responsibilities will be responding to and logging calls in a timely and professional manner. the company asks the candidate to perform a detailed analysis on call-in data.

Answers

The error represented in this scenario is an inappropriate task allocation or a mismatch between job responsibilities and the assigned task during the interview process.

The primary role of a customer service representative is to interact with customers, address their concerns, and log calls professionally and efficiently. In contrast, performing a detailed analysis of call-in data falls under the domain of data analysis or business intelligence roles.

By asking the candidate to perform a task unrelated to their potential job responsibilities, the company may not accurately assess the candidate's aptitude for customer service tasks. This error could lead to selecting a candidate who may excel in data analysis but may not possess the necessary communication and problem-solving skills required for a customer service representative position.

To avoid this error, the company should focus on evaluating candidates based on their skills, experience, and performance in tasks directly relevant to the customer service role.

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I need help immediately ASAP!!!!!!!! it's due today and I don't know what will happen to me. I'm dead​

I need help immediately ASAP!!!!!!!! it's due today and I don't know what will happen to me. I'm dead

Answers

Answer:

C. y = 1/2x - 1

Step-by-step explanation:

The slope is 1/2 (line moves up 1 and right 2).

The y-intercept is -1 since that is where the line crosses the y-axis.

Haddle wrote a check to the grocery store for $156.00. However, when she looks at her check register later that night, she sees she only has

$122.66 In her checking account. Haddle has opted in to the standard overdraft practices at her bank. How many fees is Haddle likely to pay for

writing the check?

Answers

Answer:

she will have one fee for standard overdraft practices and that will prevent a fee from the grocery. store

Step-by-step explanation:

We are told she wrote a check to the grocery store for $156.00.

And that when she looked at her check register later that day, she had only $122.66.

This means she doesn't have sufficient balance for the grocery.

It means the bank will pay the overdraft and it attracts charges which may vary for different banks.

Thus, she will have one fee for standard overdraft practices and that will prevent a fee from the grocery store

The quotient of a number x and 19 is 10.
yes no

Answers

The value of the number x such that the quotient of the number,x and 19 is 10 is; 190.

What is the value of x from the word problem?

As evident in the task content, the value of x is to be determined such that the quotient of a number, x and 19 is 10.

Since the statement given above can be written algebraically as;

x / 19 = 10

By multiplying both sides of the equation by 19; we have that;

x = 10 × 19

x = 190.

Ultimately, the value of x is; 190.

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Paul received a coupon for 43 percent off one item at a clothing store let b be the original price of the item use the expression b-43 for the new price of the item write an equivalent expression by combining like terms

Answers

The equivalent expression for the new price of the item is 0.57b. With b be the original price of the item.

The original price of the item is represented by "b". Paul received a coupon for "43 percent" off one item at a clothing store. This means that the new price of the item will be the "original price" minus the discount. The discount is calculated by multiplying the original price by the percentage discount.
So, the discount is:
43 percent of b = 0.43 * b

The new price of the item is the original price minus the discount:
b - 0.43 * b = b - 0.43b

This expression can be simplified by combining the like terms. The like terms in this expression are b and -0.43b.
To combine like terms, we add the coefficients of the like terms:
1b + (-0.43)b = 0.57b

So, the equivalent expression for the new price of the item is:
0.57b

This means that the new price of the item is 57% of the original price. Therefore, the equivalent expression for the new price of the item is 0.57b.

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Find the value of a in the equation below.

5 = x - 18

Answers

Answer:

There's no A so I'm going to assume you meant X

X = 23

Step-by-step explanation:

X is equal to 23, because 23 - 18 = 5

or 5 + 18 = 23

find the equation of the line . PLEASE HELP

find the equation of the line . PLEASE HELP

Answers

Y=1/2x-3............

A drum of petrol is 3/4 full . when 30 litres is drawn from it , it is 7/12 , find the capacity of the drum.

Answers

Answer:

The drum capacity is 180 liters.

Step-by-step explanation:

Let the capacity of the drum be c.  Then the contents of the drum at the beginning are (3/4)c, and

if 30 liters are drawn out, then the contents are (3/4)c - 30 liters = (7/12)c.

Here the LCD is 12, and so we have (9/12)c - (7/12)c = 30 liters, or

(2/12)c = 30 liters, or c = (12/2)(30 liters) = 180 liters

The drum capacity is 180 liters.

Answer:

The capacity of the drum is 180 liters

Step-by-step explanation:

3/4x - 30 = 7/12x

3/4x - 7/12x = 30

9/12x - 7/12x = 30

2/12x = 30

1/6x = 30

x = 30*6

x = 180 liters

Evie takes out a loan of £600. This debt increases by 24% every year.
How much money will Evie owe after 12 years?
Give your answer in pounds (£) to the nearest 1p.

Evie takes out a loan of 600. This debt increases by 24% every year.How much money will Evie owe after

Answers

The amount that Evie will owe after 12 years is given as follows:

£7,928.8.

How to define an exponential function?

An exponential function has the definition presented as follows:

\(y = ab^x\)

In which the parameters are given as follows:

a is the value of y when x = 0.b is the rate of change.

The parameter values for this problem are given as follows:

a = 600.b = 1.24 -> amount increases bt 24% every year.

Hence the function for the debt after x years is given as follows:

\(y = 600(1.24)^x\)

The debt after 12 years is given as follows:

\(y = 600(1.24)^{12}\)

y = £7,928.8.

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a rectangular screen has a width of 2x 8. the length is 4x 1. what is the area of the entire screen?

Answers

The area of the entire screen is \(8x^2 + 34x + 8\) square units.

To find the area of the entire screen, you need to multiply its width by its length.
Width = 2x + 8
Length = 4x + 1
Area = Width × Length
Area = (2x + 8) × (4x + 1)
Now, we'll use the distributive property to multiply these expressions:
Area = 2x * 4x + 2x * 1 + 8 * 4x + 8 * 1
Area = 8x^2 + 2x + 32x + 8
Now, we'll combine the like terms:
\(Area = 8x^2 + 34x + 8\)

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Complete the square 6v^2-12v-18=0 showing work

Answers

1. All variables go on one side and all numbers with no variables go on opposite side. Remember that if you bring one number or variable to one side, you must change its sign:

6v^2 - 12v = 0 + 18


2. Combine like terms then you get your answer:

6v^2 - 12v = 18

HELPOOOO PLEAAEEEEEEEEEEE

HELPOOOO PLEAAEEEEEEEEEEE

Answers

Answer:

A

Step-by-step explanation:

He shouldn't of added the "^1" to c because its changed the value to c^5 in the final step when it should really be c^4

Round 463,751 to the nearest hundred.

Answers

Answer : 463, 800


Explanation:

Answer:

463,800

Step-by-step explanation:

:) watch this be wrong lol

Solve the augmented matrix by elementary row operations. 9. (4 points) Let A and B be 3 by 3 matrices with det (A) = 3 and det (b) = 5. Find the value of det (AB).

Answers

The value of determinant of the matrix det (AB) is 15.

Given matrices A and B are 3 by 3 matrices with

det (A) = 3 and

det (b) = 5.

We need to find the value of det (AB).

Writing the given matrices into the augmented matrix form gives [A | I] and [B | I] respectively.

By multiplying A and B, we get AB. Similarly, by multiplying I and I, we get I. We can then write AB into an augmented matrix form as [AB | I].

Therefore, we can solve the augmented matrix [AB | I] by row reducing [A | I] and [B | I] simultaneously using elementary row operations as shown below.

![image](https://www.mathsisfun.com/algebra/images/matrix-inverse-3x3-gauss-jordan-3.gif)

The determinant of AB can be calculated as det(AB) = det(A) × det(B)

= 3 × 5

= 15.

Conclusion: The value of det (AB) is 15.

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We need to find the value of determinant det(AB), using the formula: det(AB) = det(A)det(B)

=> det(AB) = 3 × 5

=> det(AB) = 15.

Hence, the value of det(AB) is 15.

The given matrices are A and B. Here, we need to determine the value of det(AB). To calculate the determinant of the product of two matrices, we can follow this rule:

det(AB) = det(A)det(B).

Given that: det(A) = 3

det(B) = 5

Now, let C = AB be the matrix product. Then,

det(C) = det(AB).

To evaluate det(C), we have to compute C first. We can use the following method to solve the augmented matrix by elementary row operations.

Given matrices A and B are: Matrix A and B:

[A|B] = [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0][A|B]

= [3 0 0|1 0 1] [0 3 0|0 1 1] [0 0 3|1 1 0].

We can see that the coefficient matrix is an identity matrix. So, we can directly evaluate the determinant of A to be 3.

det(A) = 3.

Therefore, det(AB) = det(A)det(B)

= 3 × 5

= 15.

Conclusion: Therefore, the value of det(AB) is 15.

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Alex went out to dinner with her family. The
cost of the meal came to $38.40. If they
leave a 15% tip, what will be the total amount
they will have to pay?
PLEASE SHOW WORK

Answers

Answer:

$44.16

Step-by-step explanation:

total amount to pay = $38.40 + (0.15)($38.40)

                                 = $38.40 + 5.76

                                 = $44.16

You can also just put 38.40 * 1.15 and you will get the same answer

$44.16

To do this you will take 38.40 and multiply it by .15 and get 5.76.
Add 5.76 to 38.40 and you get your answer, $44.16

Does 1 + 2 x 3 is 7 or 9?

Answers

Answer:

according to BODMAS

b_ bracket

o_of

d_division

m_mutiplication

a_addition

s_subtraction

multiplication comes before addition so

2×3+1

that is 7

Answer:

it must be 7

Step-by-step explanation:

cuz if u follow the bodmas rules where bo stands for bracket of , d stands for divide,m stands for multiply,a stands for addition s stands for substraction.In this case,multiply comes first then continued by addition.So it must be 2 times 3 equals to 6.And then 6+1 equals to 7.

what is 2-23+5x5 this is hard HELP not

Answers

Answer:

ez its 4

Step-by-step explanation:

Prob 4? I think yeah

Gravel is being dumped from a conveyor belt at a rate of 30 ft 3ymin, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high

Answers

The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.

Given the following data: Gravel is being dumped from a conveyor belt at a rate of 30 ft3/min.

Its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal.

The pile is 10 ft high.

To determine how fast the height of the pile is increasing, we need to differentiate the formula for the volume of a cone with respect to time.

We know that the volume of a cone is given by: \(V = (1/3)πr²h\)

We are given that the base diameter and the height of the cone are always equal, so we can write: r = (d/2)and h = d

where d is the diameter of the base of the cone.

The volume of the cone is given by: V = (1/3)π(d/2)²d

Simplifying, we get:\(V = (1/12)πd³\)

Differentiating both sides with respect to time, we get:

dV/dt = (1/4)πd² (dd/dt)

We are given that dV/dt = 30 ft³/min, and we want to find dd/dt when h = 10 ft.

Substituting V = (1/3)π(10/2)²(10)

= (1/3)π(25)(10)

= (250/3)π and d = 10,

we get:

30 = (1/4)π(10²)(dd/dt)

Simplifying, we get:

dd/dt = 12/π

The rate at which the height of the pile is increasing when it is 10 ft high is approximately 3.819 ft/min.

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Solve for a: 3a – 5(a – 2) = 34

Answers

3a-5(a-2)=34
3a-5a+10=34 (i developed)
-8a+10=34 (i subtracted 3a and 5a)
-8a=34-10 (brought 10 to the other side so it becomes negative)
-8a=24
a=24/-8 (multiplication become division)
a=-3

Answer:

a=12

Step-by-step explanation:

Find the area of the triangle bounded by the lines y=x y=-x and y=6.

Answers

S=6*12=72

High of triangle is 6
Find the area of the triangle bounded by the lines y=x y=-x and y=6.

The area of the triangle bounded by the lines y=x y=-x and y=6 is 36 units.

What is area of triangle?

The formula for finding area could be represented in the form of determinants as given below.

\(A = \frac{1}{2} \left[\begin{array}{ccc}x1&y1&1\\x2&y2&1\\x3&y3&1\end{array}\right]\)

First, we need to find the coordinates of the point of intersection of these lines.

y = x

y = -x

Adding the two equations,

2y = 0

y = 0

x = 0

coordinate: (0, 0)

y = x

y = 6

Subtracting the two equations,

0 = x - 6

x = 6

coordinate: (6, 6)

y = -x

y = 6

Subtracting the two equations,

- x - 6 = 0

x = -6

coordinate: (-6, 6)

Calculating area of triangle bounded by the given line:

Area of triangle =

\(\frac{1}{2}\left[\begin{array}{ccc}0&0&1\\6&6&1\\-6&6&1\end{array}\right]\)  =  \(\frac{1}{2} (36 + 36) = \frac{72}{2} = 36\)

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do waiters or waitresses earn larger tips? to answer this question, a restaurant consultant undertook a preliminary study. the study involved measuring the percentage of the total bill left as a tip for one randomly selected waiter and one randomly selected waitress from each of 50 restaurants during a 1-week period. what conclusions can be drawn from these data?

Answers

From these data, it is difficult to draw any meaningful conclusions about which waiters and waitresses earn larger tips.

The data only measure the percentage of the total bill left as a tip for one randomly selected waiter and one randomly selected waitress from each of the 50 restaurants during a 1-week period, which does not provide a large enough sample size to draw any meaningful conclusions. In order to draw more reliable conclusions, a larger, more comprehensive study should be conducted that measures the tips for multiple waiters and waitresses from each restaurant over a longer period of time.

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I don't understand this question can someone help me with this please, please explain!! and thank you for the help!! If u dont know try your best :D

I don't understand this question can someone help me with this please, please explain!! and thank you

Answers

First:

A. (First Option)

Second:

C. (Third option)

(Brainiest and thanks are appreciated)

Answer:

Question 3:

O (7 x 50) - (7 x 2) = 350 – 14 = 336

Question 3:

O (9 x 80) + (9 x 1) 729

Step-by-step explanation:

Distributive Property is used in algebraic expressions, to divide the equation, to make it easier to solve. For question 1,  since it was 20, you must subtract 8 from that answer, because 20 is 1 more than 19. For question 2, (2 x 9) + (2 x 3) would be the same thing as 2(9+3).

-kiniwih426

Which of these is an example of an output?


A
swiping on phone screen

B
the notification sound of a text message

C
typing on a keyboard

D
talking into a microphone

Answers

Answer:

d talking into microphone

10 points first person

10 points first person

Answers

Answer:

Step-by-step explanation:

a=20

b=70

c=20

d=70

e=110

Answer:

A. 20

B. 70

C.20

D.70

E. 110

Step-by-step explanation:

Hope this helps  

pls tell me if im wrong

Determine whether the statement is true or false. If a system of two equations has only one solution, the system is consistent and the equations in the system are independent. OA. The statement is true. OB. The statement is false because, if a system of two equations has only one solution, equations are dependent. OC. The statement is false because, if a system of two equations has only one solution, the system is inconsistent and the equations in the system are dependent. OD. The statement is false because a system of two equations with only one solution is inconsistent.

Answers

The statement about the system of equations is seen as: A. The statement is true.

How to Interpret the system of equations?

When it comes to system of equations we know that a system that has no solution is called inconsistent; a system with at least one solution is called consistent.

We also know that If a consistent system has exactly one solution, it is referred to as independent .

The given statement is that:
If a system of two equations has only one solution, the system is consistent and the equations in the system are independent.

From the earlier definitions, we can say that statement is true.

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The midpoint between y and 33is -7. Find Y

Answers

Answer:

-43

Step-by-step explanation:

-7 is exactly 36 units away from 33 so we need to go 36 in the other direction to find the value of y

since it's distance I'm not using negatives rn

36+7= 43

a pic if u don't believe me

The midpoint between y and 33is -7. Find Y

students no longer have to visit a physical store to buy course books because most course books can now be obtained .

Answers

Students no longer have to visit a physical store to buy course books because most course books can now be obtained online.

What should you try first if an online course is having technical issues?

If you have any questions or concerns about the material in your online course, don't be afraid to ask your teacher or a fellow student. You should speak with your teacher or Blackboard Help for Students if you are experiencing technical issues with Blackboard.

What drawbacks exist with online learning?

The fact that much online learning is one-way communication presents one of the largest obstacles. There is no communication between the teacher and the student. The experience will be radically different, and for many students, the transition may be challenging. Motivation is the second issue with online learning.

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The distance between two towns on a map is 2.5 centimeters. The map uses a scale where 1 centimeter represents 50 kilometers. What is the actual distance between these two towns in kilometers?

Answers

Answer:

125 kilometers

Step-by-step explanation:

2.5 * 50 = 125

What is the slope of the line shown?

What is the slope of the line shown?

Answers

Answer:

-2

Step-by-step explanation:

from one point to another, you go down 2 and over 1

Answer:

the answer is -2

Step-by-step explanation:

this is because for every unit it goes to the right it goes down 2 which makes it negitive if it is facing down and positive if facing up.

an experiment consists of selecting a letter at random from the letters in the word antartica and observing the outcomes. 1. what is an appropriate sample space for this experiment? a. s

Answers

The probability of appropriate sample space for this experiment is S = { A, N, T, R, I, C}.

Given that an experiment consists of selecting a letter at random from the letters in the word ANTARCTICA and observing the outcomes.

Sample Space is also known as possible outcomes. They are the set of all possible outcomes.

Notice there would be no way to tell if the first or the second A was selected, so the outcomes are just how many unique letters are in the word.

So, the probability of appropriate sample space for this experiment is S = { A, N, T, R, I, C}.

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There is a popular story (among data miners) that there is a correlation between men buying diapers and buying beer while shopping. A student tests this theory by surveying 140 male shoppers as they left a grocery store. The results are summarized in the contingency table below.Observed Frequencies: Oi'sBoughtDid NotDiapersBuy DiapersTotalsBeer74451No Beer88189Totals15125140The Test: Test for a dependent relationship between buying beer and buying diapers. Conduct this test at the 0.05 significance level.(a) What is the test statistic? Round your answer to 3 decimal places.2=(b) What is the conclusion regarding the null hypothesis?reject H0fail to reject H0(c) Choose the appropriate concluding statement.The evidence suggests that all men who buy diapers also buy beer.The evidence suggests that the probability of a man buying beer is dependent upon whether or not he buys diapers. There is not enough evidence to conclude that the probability of a man buying beer is dependent upon whether or not he buys diapers.We have proven that buying beer and buying diapers are independent variables. Scientists use GPS to measure the rate of Tectonic plate movements.Discuss do you know your memes???two boys are sitting in a hot tub five feet apart because??A there enemiesB there not gayC on is on the phone and does not want other to see What characteristic does Gilgamesh show in thispassage?Which detail from the passage best reflects thischaracteristic? Helpppppppp pleaseeeeee Help ASAP, please math question Please answer correctly !!!!!!!!!!!!!!!!!!! Will mark brainliest !!!!!!!!!!!!!!!! A mail carrier can deliver mail to 36 houses in 30 minutes. Mark wants to determine how many houses the carrier can deliver mail to in 7.5 minutes at this rate. He thinks that to find the answer, he should do the following. 1. First divide 36 houses by 30 minutes to find a unit rate of 1.2 houses per minute. 2. Then multiply 1.2 houses per minute by 7.5 minutes to get 9 houses. Which statement is correct? An electrochemical cell is based on the following two half-reactions:oxidation: Sn(s)Sn2+(aq,Sn(s)Sn2+(aq, 1.70 MM )+2e)+2ereduction: ClO2(g,ClO2(g, 0.130 atmatm )+eClO2(aq,)+eClO2(aq, 1.70 MM )Compute the cell potential at 25 CC. What happens to h the height of the mercury column, if the atmospheric pressure increases?. During lunch, 80 students were asked about their favorite type of food Twenty -four of them said Italian. If there are a total of 480 students in the cafeteria, about how many might say Italian is their favorite food? All marketing-related program decisions are based on what planners know about the priority population and their preferencesO SegmentationO Consumer OrientationO Social marketingO Market Penetration If the car in the problem above, then climbs a 12.2 m tall hill, how fast will it be going at the hump? Show your work withunits. When the english took over new york from the dutch, they continued to allow religious toleration but minimized the rights the dutch had given to:_________ Types of forest management techniques. The temperature was -3C last night. It was now -4C. what was the change in temperature? -3 (x -2) simplified Please help!!!!!!!!!!!! use a command to output the number of lines, words and file size of the readme.md file. how many lines are in the file according to this output? What genes/trait found in nature may be helpful if our food was modified to have these traits? Consider how you could modify both our meat and plants. Answer in your own words