Given the relation A = {(5,2), (7,4), (9,10), (x, 5)}. Which of the following values for x will make relation A a function?


9

4

7

According to the question The graphs of the equations intersect at two points: (6, 8) and (-2, 0).

To find the total number of points of intersection between the graphs of the equations \($2x^2 - y^2 = 8$\) and \($y = x + 2$\) , we need to solve the system of equations.

Substituting \($y$\) from the second equation into the first equation, we get:

\(\[2x^2 - (x+2)^2 = 8\]\)

Expanding and simplifying:

\(\[2x^2 - (x^2 + 4x + 4) = 8\]\)

\(\[2x^2 - x^2 - 4x - 4 = 8\]\)

\(\[x^2 - 4x - 12 = 0\]\)

Factoring the quadratic equation, we have:

\(\[(x - 6)(x + 2) = 0\]\)

Setting each factor equal to zero:

\(\[x - 6 = 0 \quad \text{or} \quad x + 2 = 0\]\)

Solving for \($x$\) :

\(\[x = 6 \quad \text{or} \quad x = -2\]\)

Now, substituting these values of \($x$\) back into the equation \($y = x + 2$\)  to find the corresponding \($y$\) values:

When \(\\$x = 6$, $y = 6 + 2 = 8$\).

When \(\\$x = -2$, $y = -2 + 2 = 0$\).

Therefore, the graphs of the equations intersect at two points: (6, 8) and (-2, 0).

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Answer:

4 ( x-1)^2

Step-by-step explanation:

4x^2 − 8x + 4.

Factor out the greatest common factor

4( x^2 -2x+1)

Factor inside the terms

4( x-1) (x-1)

4 ( x-1)^2

Step-by-step explanation:

a) y= -6x+1

1) Perpendicular Lines have a reciprocal and opposite slope considering the original function: -1/m

So the slope of that perpendicular line is m = -6

2) Examining the options, let's rewrite them into the slope-intercept form

a) y=-6x +1

b)y=1/6x +42

c) y=-x/6-6

d) -y=-1/6x+4/3

3) So the answer is a) y= -6x+1

The variance of Wi+W is k(2k+1) for k = 1, 2, 3,... . We cannot provide a simplified expression for the variance of Wi+W.

To find the variance of Wi+W, we need to first find the probability distribution of Wi, the waiting time for the process to reach state i, and then calculate the variance using the formula for variance.

In a pure birth process, the birth rates Ak are defined as A = max(4-k, 0), where k = 0, 1, 2, ...

To find the waiting time Wi for the process to reach state i, we need to consider the inter-arrival times between consecutive births.

The inter-arrival times follow an exponential distribution with rate λ, where λ is the sum of birth rates from state 0 to state i-1.

The waiting time Wi can be calculated as the sum of exponential random variables with rate λ.

The sum of exponential random variables follows a gamma distribution with shape parameter i and rate parameter λ.

The variance of a gamma distribution with shape parameter i and rate parameter λ is given by Var(X) = i/λ^2.

In our case, λ is the sum of birth rates from state 0 to state i-1, which can be calculated as λ = Σ(max(4-k, 0)) for k = 0 to i-1.

Therefore, the variance of Wi is i/λ^2 = i/(Σ(max(4-k, 0)))^2.

Finally, to find the variance of Wi+W, we need to sum the variances of Wi from i = 1 to infinity. This can be represented as Var(Wi+W) = Σ(i/(Σ(max(4-k, 0)))^2) for i = 1 to infinity.

However, the series Σ(i/(Σ(max(4-k, 0)))^2) is not easy to calculate in a closed form, so we cannot provide a simplified expression for the variance of Wi+W.

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i think the longer u clean the less dust particles u have in ur room.

since u can't drive at the age between 0-15

Answer:

(x+2)^2 - 6

Step-by-step explanation:

Answer:

a part

Step-by-step explanation:

Attachment added....

Hope it helps :)

Answer:

\(\frac{-2}{5}\) > x

or x < \(\frac{-2}{5}\)

Step-by-step explanation:

\(\frac{2}{5}\) - 4x > 2(1 - x)   Distribute the 2

\(\frac{2}{5}\) - 4x > 2 - 2x  Add 4x to both sides

\(\frac{2}{5}\) - 4x+ 4x > 2 - 2x + 4x  Combine like terms

\(\frac{2}{5}\) > 2 + 2x  Subtract 2 from both sides

\(\frac{2}{5}\) - 2 > 2 - 2 + 2x  Combine like terms

\(\frac{2}{5}\) - \(\frac{10}{5}\) > 2x

\(\frac{-8}{10}\) > 2x  Divide both sides by 2

\(\frac{-8}{10}\)÷ 2 > 2x ÷2

\(\frac{-8}{10}\) ÷\(\frac{20}{10}\) = \(\frac{\frac{-8}{20} }{\frac{10}{10} }\) = \(\frac{\frac{-8}{20} }{1}\) = \(\frac{-8}{20}\) = \(\frac{-2}{5}\)

\(\frac{-2}{5}\) > x

Helping in Jesus' name.

Answer:

\(5x+40=2\)

Step-by-step explanation:

Using the distributive property:

\(5(x+8)=2\)

\((5*x) + (5*8)\)

\(5x+40=2\)

Answer:

5x + 40 = 2

Step-by-step explanation:

5(x + 8) = 2

5x + 40 = 2

5x = -38

x = -7.6

Best of Luck!

The best answer that describes the meaning of the multiplicities next to the number 1 in the preceding diagram is: the number 1 represents the solution that repeats thrice.

A multiplicity is a mathematical concept used to describe the number of times a value appears as a root of a polynomial equation. The number of times a specific value appears as a root of a polynomial is referred to as the multiplicity of that value.

In the given diagram, the number 1 represents the solution of the equation x = 1. The multiplicities of the number 1 are represented by the number 3.

Therefore, the number 1 has a multiplicity of 3. This means that the solution of the equation x = 1 repeats thrice. This can be better understood by looking at the graph of the equation.

The graph of the equation x = 1 is a vertical line that intersects the x-axis at 1.

Since the equation has a multiplicity of 3, the vertical line intersects the x-axis three times.

This means that the point (1, 0) occurs three times on the graph. This is shown in the diagram as three dots along the x-axis.

Therefore, the meaning of the multiplicities next to the number 1 in the preceding diagram is that the number 1 represents the solution that repeats thrice.

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Required polynomial in the form p(x) is: \(\[f(x)=\boxed{x^3-2x^2+4x-3+\frac{5}{x-1}}\]\)

We are given the following polynomial: \(\[f(x)=\frac{x^4-3x^3+2x^2-7x-2}{x-1}\]\)

To perform polynomial long division we divide the highest degree terms of the numerator and denominator. Then we write the quotient and remainder on top of each other and multiply the denominator of the original problem with the quotient to check if the answer is correct.

Let's start with the highest degree terms.

\(\[\begin{array}{r r c r r} &x^3 &-2x^2 &+4x &-3\\ \cline{2-5} x-1 & x^4 &-3x^3&+2x^2&-7x&-2 \\ & \underline{x^4} &-\underline{x^3} & & & \\ & & -2x^3 & +2x^2 & & \\ & & \underline{-2x^3} & +\underline{2x^2} & & \\ & & & 0x^2 & -7x & \\ & & & & -7x & +7 \\ & & & & \underline{-7x} & +\underline{7} \\ & & & & & \boxed{5} \\ \end{array}\]\)

Therefore, the required polynomial in the form p(x) is:\(\[f(x)=\boxed{x^3-2x^2+4x-3+\frac{5}{x-1}}\]\)

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Answer: 120

Step-by-step explanation:

Given : Total toppings = 6

Number of toppings needs to be selected = 3

Also if repetition of toppings is not allowed , then the number of combinations are possible = 6 x 5 x 4   [First we choose 1 out of 6 , then 1 out of remaining 5 and then 1 out of 4,then multiplying the choices for 3 toppings]

=  120

Hence, the number of different pizza topping combinations are possible if the maximum number of allowed toppings is 3 is 120 .

The table with a constant of proportionality of –3 are

A. 'x' is 1 2 3. 'y' is -3,-6,-9

A. 'x' is 1 2 3. 'y' is -3,-6,-9 C. 'x' is 1, 2, 3. 'y' is -3, -3, -3

A. 'x' is 1 2 3. 'y' is -3,-6,-9 C. 'x' is 1, 2, 3. 'y' is -3, -3, -3D. 'x' is 1, 2, 3. 'y' is -3, -3/2, -1

y = k × x

where,

k = constant of proportionality

A. 'x' is 1 2 3. 'y' is -3,-6,-9

y = k × x

-3 = k × 1

- 3 = k

k = -3

B. 'x' is 1, 2, 3. 'y' is -1, -2, 0

y = k × x

-1 = k × 1

-1 = k

k = -1

C. 'x' is 1, 2, 3. 'y' is -3, -3, -3

y = k × x

-3 = k × 1

-3 = k

k = -3

D. 'x' is 1, 2, 3. 'y' is -3, -3/2, -1

y = k × x

-3 = k × 1

-3 = k

k = -3

or

y = k × x

-3/2 = k × 2

-3/ 2 = 2k

k = -3/2 ÷ 2

k = -3/2 × 1/2

k = -3

Therefore, the table with a constant of proportionality of –3 are

A. 'x' is 1 2 3. 'y' is -3,-6,-9

A. 'x' is 1 2 3. 'y' is -3,-6,-9 C. 'x' is 1, 2, 3. 'y' is -3, -3, -3

A. 'x' is 1 2 3. 'y' is -3,-6,-9 C. 'x' is 1, 2, 3. 'y' is -3, -3, -3D. 'x' is 1, 2, 3. 'y' is -3, -3/2, -1

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Given that:

- The product of the ages (in days) of babies Simran and Jessie in two days

will be 48 more than the product of their ages today.

- Jessie is 2 days older than Simran.

Let be "j" Jessie's age (in days) and "s" Simran's age (in days).

You can set up the following System of Equations using the data given in the exercise:

You can use the Substitution Method to solve the system:

1. Substitute the second equation into the first one:

2. Solve for "s":

3. Substitute "s" into the second original equation and evaluate:

Hence, the answer is: Jessie is 12 days old and Simran is 10 days old.

The result of subtracting and simplifying the rational expression in its fully factored form is \(\frac{4n^{2} +17n - 195 }{5(n^{2} -25)}\)

From the question, we are to subtract the rational expressions and express in the factored form

The given expression is

\(\frac{n^{2} + 5n - 36 }{n^{2} -25} - \frac{n^{2} +8n +15 }{5n^{2} -125}\)

Factor 5n² - 125

\(\frac{n^{2} +5n - 36 }{n^{2} -25} - \frac{n^{2} +8n +15 }{5(n^{2} -25)}\)

\(\frac{5(n^{2} +5n - 36) - (n^{2} +8n +15) }{5(n^{2} -25)}\)

\(\frac{5n^{2} +25n - 180 - n^{2} -8n -15 }{5(n^{2} -25)}\)

Simplify

\(\frac{4n^{2} +17n - 195 }{5(n^{2} -25)}\)

Hence, the expression is \(\frac{4n^{2} +17n - 195 }{5(n^{2} -25)}\)

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Answer:

46???

Step-by-step explanation:

apples: 10

bananas: 6

oranges: 6

soo im guessing 10 + 6 x 6 = 46?????

Answer:

about 1.6090405507426917 years (round this)

Step-by-step explanation:

This question requires reverse thinking. This type of problem is usually presented like 13,500 people are there to start with and it increases by 6.5 yearly, how much will it be in a year? But this time we have to find the years and we have the end population value.

First write equation:

13,500(0.065)^x = 27000

Simplify by dividing:

0.65^x = 0.5

*Use property of log (for isolating x):

x(log(0.65)) = log(0.5)

Isolate x:

x = log(0.5)/log(0.65)

x = 1.6090405507426917

*the reason why we did log was because we need the x to not be in an exponent for but to be normal. So log makes us able to write it like that. Same works with ln or natural log. For continuously compounding or continuously depreciating you would use ln.

The total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.20.

To calculate the total cost, we need to determine the cost of each type of binder clip separately and then sum them up.

The cost of medium binder clips is $5 per pound, and Kayla purchased 0.1 pounds. Therefore, the cost of medium binder clips is 0.1 pounds * $5 per pound = $0.50.

The cost of jumbo binder clips is $6 per pound, and Kayla purchased 0.2 pounds. Thus, the cost of jumbo binder clips is 0.2 pounds * $6 per pound = $1.20.

Finally, to find the total cost, we add the individual costs together: $0.50 + $1.20 = $1.70.

Therefore, the total cost of Kayla's purchase of 0.1 pounds of medium binder clips and 0.2 pounds of jumbo binder clips is $1.70.

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Answer:

50

Step-by-step explanation:

Bruh

The sample size should be 24.

What is the sample size?

The process of deciding how many observations or replicates to include in a statistical sample is known as sample size determination. Any empirical study with the aim of drawing conclusions about a population from a sample must take into account the sample size as a crucial component.

Here, we have

Given

Margin of error = 300

confidence level = 0.9

standard deviation = 900

Assuming the standard deviation to be of population

ME = Z(0.1/2) × σ/√n

300 = 1.645 × 900/√n

n =  {(1.645 × 900)300}²

n = 24

Hence, the sample size should be 24.

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Answer:

14824

Step-by-step explanation:

the product is 14824

Answer:

1386 ft^2

Step-by-step explanation:

Area of a circle = πr²

Where : = π = pi = 22/7

R = radius  

22/7 x 21^2 = 1386 ft^2

Research has shown that competent communicators achieve effectiveness by adjusting their behaviors to the person and situation (option e).

Effective communication involves being adaptable and responsive to the specific context, individual preferences, and the needs of the situation.

Competent communicators recognize that different people have different communication styles, preferences, and expectations. They understand the importance of tailoring their communication approach to effectively connect and engage with others.

This may involve using appropriate language, tone, non-verbal cues, and listening actively to understand the needs and perspectives of others.

By adapting their behaviors, competent communicators can build rapport, foster understanding, and promote effective communication exchanges. They are mindful of the social and cultural dynamics at play, and they strive to communicate in a way that is respectful, inclusive, and conducive to achieving mutual goals.

In summary, competent communicators understand that effective communication is not a one-size-fits-all approach. They adjust their behaviors to the person and situation, demonstrating flexibility and adaptability in order to enhance communication effectiveness.

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Competent communicators achieve effectiveness mostly by adjusting their behaviors to suit the person they are communicating with and the situation they find themselves in. While other factors, like having a broad vocabulary or giving feedback, play a part in effective communication, the former is considered the most crucial.

Research suggests that competent communicators achieve effectiveness mostly through adjusting their behaviors depending on the person they are communicating with and the situation they are in. This is option e. of your question. Communicating effectively involves behaviors like active listening, understanding the other person's point of view, being able to express thoughts and ideas clearly, and being polite and respectful. While a broad vocabulary (option b.) can be useful, it is not as crucial as adapting your behavior to fit the situation. Moreover, giving feedback (option d.) is a part of effective communication but not the sole defining factor. Apologizing when offending others (option c.) is also important but it doesn't necessarily make one a competent communicator. Using the same type of behavior in various situations (option a.) might not always work, as different situations and individuals require different communication styles.

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The expression x + 80 represents the number of coins Arthur has now, since he x pennies and an additional 6 dimes and 4 nickels.

We shall convert the pennies, dimes and nickels into same unit before adding to get the expression for the number of coins Arthur will have in total.

A penny = 1 cent, so

x pennies = x cents

A dime = 10 cents so;

6 dimes = 6 × 10cents

6 dimes = 60 cents

A nickel = 5 cents so;

4 nickels = 4 × 5 cents

4 nickels = 20 cents

Arthur's coins in total = (x + 60 + 40) cents

Arthur's coins in total = (x + 80) cents.

Therefore, the expression expression x + 80 represents the number of coins Arthur will have in total, wether in pennies, dimes or nickels.

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To convert nm to m, we divide by 1e9, and to convert m to nm we multiply by 1e9. So 1 nm / 1,000,000,000 m/nm = 0.000000001 m.

In science, it's important to know how to convert between different units of measurement. One common conversion that is often needed is converting nanometers (nm) to meters (m).

A nanometer (nm) is a unit of length in the International System of Units (SI). It is defined as one billionth of a meter. One nanometer is equal to 0.000000001 meters (m).

To convert a quantity in nanometers to meters, you can simply divide the number of nanometers by 1,000,000,000. For example, if you want to convert 1 nanometer to meters, you would do the following calculation: 1 nm / 1,000,000,000 m/nm = 0.000000001 m.

It's worth noting that the conversion factor between nm and m is very small, so it is important to be careful when working with very large or very small numbers in nm.

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Therefore, the above answer is correct.

Hoped this helped.

\(BrainiacUser1357\)

Adding both of the polynomial equations we get \(x^2+y^2+4x+4\).

A polynomial equation exists an equation where a polynomial exists set equivalent to zero. i.e., it exists an equation constructed with variables, non-negative integer exponents, and coefficients together with operations and an equal sign. It includes different exponents. The highest one demonstrates the degree of the equation.

Given: \(x^2 + 2x + 1\) and \(y^2 + 2x + 3.\)

Adding both of these two equations, then we get

\(x^2+2x+1+y^2+2x+3\)

Group like terms

\(=x^2+y^2+2x+2x+3+1\)

Add similar elements \(x^2+y^2+4x+4\)

Adding both of the polynomial equations we get \(x^2+y^2+4x+4\).

Therefore, the correct answer is \(x^2+y^2+4x+4\).

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C. (∃x)(A(x) ∧ B(x)) ⇔ (∃x)A(x) → (∀y)B(y)

This statement is incorrect. The left-hand side states that there exists an x such that both A(x) and B(x) are true.

Therefore, the incorrect statement is option C.

A = {{1, 2, 3}, {4, 5}, {6, 7, 8}}

Hence. Option D is wrong.

In set theory, a subset relation is denoted by ⊆, and a proper subset relation is denoted by ⊂. A subset relation indicates that all elements of one set are also elements of another set.

In this case, let's evaluate the options:

A. ∅ ⊆ A: This option is correct. The empty set (∅) is a subset of every set, including A.

B. {6, 7, 8} ⊂ A: This option is correct. The set {6, 7, 8} is a proper subset of A because it is a subset of A and not equal to A.

C. {{4, 5}} ⊂ A: This option is correct. The set {{4, 5}} is a proper subset of A because it is a subset of A and not equal to A.

D. {1, 2, 3} ⊂ A: This option is incorrect. The set {1, 2, 3} is not a subset of A because it is not included as a whole within A. The element {1, 2, 3} is present in A but is not a subset.

In conclusion, the incorrect option is D, {1, 2, 3} ⊂ A.

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Answer:

it would take them 4 days to build the house