Question:
(a) Find the equation for the family of linear functions with slope 2 and sketch several members of the family.
(b) Find an equation for the family of linear functions such that f(2)=1 and sketch several members of the family.
(c) Which functions belong to both families?
Slope-intercept form
Equation of slope-intercept form is given as y=mx+b where m is the slope of the line and c is the y-intercept. m is used to measure the steepness of the graph. This form is simply the method of writing the equation of a line so that the slope and y-intercept are rapidly apparent.

An equation to represent this proportional relationship is y = 65x.

Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:

y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

Where:

Next, we would determine the linear equation representing the line which passes through the points (3, 195) and (6, 390) by using the point-slope form as follows:

y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)

y - 195 = (390 - 195)/(6 - 3)(x - 3)

y - 195 = 195/3(x - 3)

y - 195 = 65(x - 3)

y = 65x - 195 + 195

y = 65x

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Yes, this is reasonable. The circumcenter of a triangle is found by taking the average of the x-coordinates of the three points and the average of the y-coordinates of the three points, so for this triangle, the circumcenter would be at (5.67, 2.67).

The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.

1. Calculate the average of the x-coordinates of the three vertices: (1 + 7 + 8) / 3 = 16 / 3 = 5.67

2. Calculate the average of the y-coordinates of the three vertices: (5 + 5 + 0) / 3 = 10 / 3 = 2.67

3. Therefore, the circumcenter of the triangle is (5.67, 2.67).

The circumcenter of the triangular plot of land with vertices at (1, 5), (7, 5), and (8, 0) is at (5.67, 2.67), which is reasonable.

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The general solution of the first-order linear differential equation y' - (ln x)y = [tex]3 x^x[/tex] is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]

As per the give,n data the given differential equation is:

y' - (ln x) y = 3 [tex]x^x[/tex]

Here have to determine the general solution of the first-order linear differential equation.

The differential equation is linear if the dependent variable y and its derivative only occur in the first degree.

Then, [tex]$\frac{d y}{d x}-(\ln x) y=3 x^x$[/tex]

This is of the form [tex]$\frac{d y}{d x}[/tex] + P(x)y = Q(x) which is the linear equation.

In order to solve this kind of differential equation, we have to multiply it by an integrating factor.

Here, P = - ln (x), Q(x) = 3 [tex]x^x[/tex]

I F = [tex]e^{\int P d x}[/tex]

I F = [tex]e^{-\int \ln (x)}[/tex]

I F = [tex]e^{-(x \ln x-x)}[/tex]

I F = [tex]e^{x-x \ln x}[/tex]

I F = [tex]\frac{e^x}{e^{x \ln x}}[/tex]

I F = [tex]\frac{e^x}{x^x}[/tex]

Hence, the general solution is

[tex]& y(I F)=\int Q(x)(I F) d x+c \\[/tex]

[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 x^x\left(\frac{e^x}{x^x}\right) d x+c \\[/tex]

[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=\int 3 e^x d x+c \\[/tex]

[tex]& \Rightarrow y\left(\frac{e^x}{x^x}\right)=3 e^x+c \\[/tex]

[tex]& \Rightarrow y=3 x^x+c x^x e^{-x}[/tex]

Hence, the general solution is [tex]y=3x^{x} + cx^{x} e^{-x}[/tex]

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c. +.80 is correct.

lllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll

Answer:

see below

Step-by-step explanation:

there are 3 points given

diff in y / diff in x = slope

so plug in any 2 points' Y and x and get the slope

because it's downward shaped, you  know the slope MUST be negative.

so diff in Y = 23-29 = -6

diff in X = 3-7 =2

so slope is +3

intercept is given, when x=0 y = 32

it represents what F is when it's 0C°

The set X can therefore be written as follows: The expression "A is the set of elements x such that x is a natural number less than 7" can be translated as "A is the set of elements x such that x is a natural number less than 7." A = x: x N, x 7 is another way to express the above set.

The Complete Question is  Set Builder .

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Li earns more than 78percentage of recent college graduates, and is in the 78th percentile of salaries earned.

1. Calculate the total number of recent college graduates surveyed: Multiply the total number of responses to the survey by 100 to get the total number of graduates surveyed.

2. Calculate the number of recent college graduates who earn less than or equal to Li's salary: Multiply the percentile (78%) by the total number of graduates surveyed to get the number of graduates who earn less than or equal to Li's salary.

3. Calculate the percentage of recent college graduates who earn less than or equal to Li's salary: Divide the number of graduates who earn less than or equal to Li's salary by the total number of graduates surveyed to get the percentage of graduates who earn less than or equal to Li's salary. The result will be 78%.

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1/6

The probability of an event is the number of ways the event can happen divided by the number of possible outcomes. In this case, the possible outcomes are the numbers on the die, which are 1, 2, 3, 4, 5, and 6.

The event of rolling a number greater than 5 or less than 3 can happen in two ways: rolling a 6 or rolling a 1 or 2. So the probability of this event is:

P(greater than 5 or less than 3) = (number of ways the event can happen) / (number of possible outcomes) = 2/6 = 1/3

So the answer is option D. 1/6

149.0848502 decibels are emitted from a jet plane with a sound intensity of 8.1*10²

Decibels are units for expressing the ratio between two physical quantities, usually amounts of acoustic or electric power, or for measuring the relative loudness of sounds.

Number of watts per square meter

d = 10*log(I/IO)

IO = 10⁻¹²

Therefore: d = 10 * log(I/10⁻¹²

jet plane has a sound intensity of 8.1*10² watts per square meter.

Therefore: d = 10*log((8.1*10²) / 10⁻¹²)

10²/10⁻¹² = 10²⁽⁻¹²⁾ = 10⁽²⁺¹²⁾ = 10¹⁴

Therefore: d = 10 * log(8.1 * 10¹⁴)

log(8.1 * 10¹⁴) = 14.90848502

10 * that = 149.0848502 decibels

That's the value of d.

In conclusion, 149.0848502 decibels are emitted from a jet plane with a sound intensity

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No, it is not true that GCD(A, B, C).

What is the greatest common divisor?

The greatest common factor (GCF) that divides two or more numbers is known as the greatest common divisor (GCD). The highest common factor is another name for it (HCF). For instance, since both 15 and 10 can be divided by 5, 5 is the biggest common factor between both.

Here, we have

Given: Aisha's number and Benoit's number have a common divisor greater than 1. Aisha's number and Carleen's number also have a common divisor greater than 1. Benoit's number and Carleen's number also have a common divisor greater than 1.

We have to determine if is it necessarily true that the greatest common divisor of all three numbers is greater than 1.

Here, we solve this with an example.

A = 6 = 2*3,

B = 14 = 2*7,

C = 21 = 3*7

There is no GCD greater than 1 that divides all of A, B and C.

Hence, No, it is not true that GCD(A, B, C).

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The output is determined by the pattern of the input.

Pattern is a repeated design or motif used to create a visually pleasing effect. Patterns are often seen in nature, architecture, clothing, and artwork. Patterns can be used to create shapes, textures, and decorations. They can add interest and depth to a design. Patterns can be made up of geometric shapes, lines, curves, and combinations of those elements. They can be created with a variety of materials and techniques, including weaving, printing, embroidery, and painting. Patterns can be used to create continuity, emphasize a focal point, or provide a sense of balance. Patterns can be used to draw the eye to a particular area, or to create a sense of order and organization.

In this example, each output number is the sum of the two numbers before it. Therefore, the output is 6 (1 + 2), 12 (2 + 4), 18 (4 + 5), 24 (5 + 6), and 30 (6 + 8).

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Answer:

x = 56

First number = 56

Second number = 280

Third number = 156

Total 331

Step-by-step explanation:

Graph A.

Proportional relationships have to go through the origin, (0,0).

The sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.

What is the eigenvalue?

Eigenvalues are the special set of scalar values that are associated with the set of linear equations most probably in the matrix equations. The eigenvectors are also termed characteristic roots.

To find the eigenvalues of matrix A, we can solve the characteristic equation |A - λI| = 0, where λ is a scalar and I is the identity matrix.

|A - λI| = 3- λ 1 4 0 2- λ 6 0 0 5- λ

= (3-λ)(5-λ) - 24 = λ^2 - 8λ - 15

Setting λ^2 - 8λ - 15 = 0, we can find the eigenvalues of the matrix by solving the quadratic equation.

λ^2 - 8λ - 15 = 0

λ = (8 ± √(8^2 + 4*15))/2

λ = (8 ± √(64 + 60))/2

λ = (8 ± √124)/2

So the eigenvalues of matrix A are λ_1 = (8 + √124)/2 and λ_2 = (8 - √124)/2

The sum of eigenvalues is λ_1 + λ_2 = (8 + √124)/2 + (8 - √124)/2 = 8

The product of eigenvalues is λ_1 * λ_2 = (8 + √124)/2 * (8 - √124)/2 = -15

Hence, the sum of the eigenvalues of matrix A is 8 and the product of eigenvalues is -15.

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(s+12)^3

I am wasting space here as you can tell but no fr the answer is (s+12)^3

Answer:

  332 cm²

Step-by-step explanation:

You want to know the surface area of a tin can that is 7 cm in diameter and 11.6 cm high.

The area of a cylinder is given by the formula ...

  SA = πd(d/2 +h) . . . . . where d is the diameter and h is the height

Using the given values, d=7 and h=11.6, we find the area to be ...

  SA = (3.14)(7 cm)(3.5 +11.6 cm) ≈ 332 cm²

About 332 square centimeters of tin are required to make the can.

The table indicates that purchase price is a function of demand, as each demand is mapped to a single purchase price.

To verify whether a relation represents a function, we need to observe if each input is mapped to only one output.

The input and output variables for this problem are given as follows:

In the table, there are no repeated demand values, meaning that the purchase price is a function of the demand, as there are no inputs mapped to multiple outputs.

The table is given by the image presented at the end of the answer.

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The angular momentum of the flywheel is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s.

1. Determine the angular momentum of the flywheel:

Angular momentum = Torque × Time × Moment of Inertia

= 2.5 Nm × 10.0 s × 2.0 kg m2

= 50 kg m2/s

The angular momentum of an object can be determined from the product of the applied torque, the time interval, and the moment of inertia. The moment of inertia is the rotational inertia of an object, which is the resistance to changes in its angular velocity. The angular momentum of the flywheel in this question is equal to the product of the applied torque, the time interval, and the moment of inertia. Therefore, the angular momentum of the flywheel will be 2.5 Nm × 10.0 s × 2.0 kg m2 = 50 kg m2/s. This means that the flywheel will have an angular momentum of 50 kg m2/s after the 10-second interval when the torque is applied. The angular momentum of the flywheel will remain constant until another torque is applied to change it.

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Work Shown:

4/3 = 72/x

4x = 3*72

4x = 216

x = 216/4

x = 54

Explanation:

Each fraction in the first step is of the form A/B, where A is the amount of punch and B is the amount of cranberry juice. Both measured in cups. In the 2nd step, I cross multiplied. Afterward, divide both sides by 4 to isolate x.

Out of the given functions, a ,b, c, d , the function with complex roots are b and d.

What are complex roots?

Complex roots, also known as non-real roots, are roots of an equation that are not real numbers but instead are complex numbers. Complex roots are usually represented in the form of a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1.

The functions which have complex roots are b and d.

hence, out of the given functions, a ,b, c, d , the function with complex roots are b and d.

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Answer: there would be 8 men

Step-by-step explanation:

can you give me brainliest

Answer: I believe there would be 25 men

Step-by-step explanation: We can see there are 40 women and the ration is 5 (men) to 8 (women)

If we take 40 and divide it by 8 we get 5

so for every 8 women there are 5 men and we do that 5 times

we get: 40 women and 25 men.

I'm pretty sure the answer is D.mean absolute deviation.

I hope it'll help you.

The elements of each set are given as follows:

a) A and C: {1, 3, 7}.

b) B U C = {1, 2, 3, 4, 6, 7, 8, 10}

c) C U C' = U.

The intersection operation between two sets is composed by the elements that belong to both sets, hence:

A and C: {1, 3, 7}.

(as the elements 1, 3 and 7 belong to both of the sets).

The union operation between two sets is composed by the elements that belong to at least one of the sets, hence:

B U C = {1, 2, 3, 4, 6, 7, 8, 10}

The union between a set and it's complement is always the universal set, hence:

C U C' = U.

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The domain of a function is the set of possible values that can be plugged into it.

The range of values that can be plugged into a function is known as its domain. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.

The collection of all possible inputs and outputs constitutes a function's domain and range, respectively. Important features of a function are the domain and range. The domain accepts all potential input values from the set of real numbers, and the range accepts all function output values.

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Let's call the grandmother's current age G and the grandson's current age S.

From the first piece of information given, we know that:

G = S + 48

From the second piece of information given, we know that:

G - 14 = 13S

We can use the first equation to substitute for G in the second equation:

(S + 48) - 14 = 13S

S + 34 = 13S

34 = 12S

S = 34/12

S = 2.8 years

So the grandson is 2.8 years old.

Now we can use this information to find the grandmother's age:

G = S + 48

G = 2.8 + 48

G = 50.8 years

So, the grandmother is 50.8 years old and the grandson is 2.8 years old.

The expression are matched to the simplest form as shown below

simplest form   Equation

12 - 1/2r              (13 - 3/2 r) - (1 - r)

r - 13/6                (7r - 3/2) - (2/3 + 6r)

13r + 20              (6r + 7) + (13 + 7r)

-12 + r                 (-8 - r) + (2r - 4)

The simplest form is solved by evaluating each of the equation in the problem

Evaluating the expressions

(6r + 7) + (13 + 7r)

collecting like terms

6r + 7r + 13 + 7

13r + 20

(13 - 3/2 r) - (1 - r)

opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)

13 - 3/2 r - 1 + r

collecting like terms

13 - 1 - 3/2 r + r

12 - 1/2 r

(-8 - r) + (2r - 4)

collecting like terms

-8 - 4 - r + 2r

-12 + r

(7r - 3/2) - (2/3 + 6r)

opening the parenthesis (the negative sign before the second parenthesis changes the sign in the second parenthesis)

7r - 3/2 - 2/3 - 6r

collecting like terms

7r - 6r - 3/2 - 2/3

r - 13/6

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The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.

1. Start by subtracting the largest coin value from the total amount.

2. If the difference is greater than 0, add the coin to the total and repeat the process.

3. If the difference is 0, move onto the next smallest coin value.

4. Repeat the process until the total amount is reached.

5. Once the total amount is reached, the minimum amount of coins needed to arrive at the total will be displayed.

The solution is a simple process of subtracting the largest coin value from the total amount, adding any coins that fit, and repeating the process until the total amount is reached. This algorithm guarantees that the minimum number of coins needed to arrive at the total will be displayed.

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The probability that the student is female or earned grade C is 0.6

You should recall that probability is the chance of occurrence of an event E

P(E) = (Number of required outcome)/(number of possible outcomes)

The given parameters are

We'll use this table (below) to answer the questions

                         A B C Total

Male           16 17 11 44

Female           14 6 3 23

Total          30 23 14 67

Pr(E) = 23/67 + 14/67

Simplifying the fractions to have

37/67 = 0.55

Therefore this is approximately rounded to 1 decimal place as  0.6

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x is an int variable and y is a double variable and the input is: 10 20.7.The output will be x = 10, y = 20.7

given that

x is an int variable

y is a double variable

The C++ double should have a floating-point precision of up to 15 digits as it contains a precision that is twice the precision of the float data type.

When you declare a variable as double, you should initialize it with a decimal value. For example, 3.0 is a decimal number. However, if you initialize it with 3, it will also work fine because although 3 and 3.0 seem to be identical i.e., an integer, there is a big difference in their internal representation.

the input is: 10, 20.7

after execution of the statement

cin >> x >> y

The output will be x = 10, y = 20.7

because x is declared as integer variable so it will print the same

y is declared as double integer variable so it will print same as given input , if it is declared as integer variable then it will be printed as 20

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1. The coupon will save: $6.

2. The sales tax is of: $1.44.

3. The total price paid for the meal is of: $25.44.

The total cost is obtained applying the proportions in the context of this problem.

The initial fee for the meal is of:

$30.

With the coupon of 20% off, the amount paid is of:

0.8 x 30 = $24.

Meaning that the amount saved is of:

30 - 24 = $6.

After the sales tax, the total price is of:

1.06 x 24 = $25.44.

Meaning that the tax is of $1.44.

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