What is the vertex form of a line

A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself. 0 is not a positive integer and 1 is not greater than 1, so they are not considered a prime number.

A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.

Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.

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The process of finding the discontinuity of a hole is explained below.

The term discontinuity in statistics is defined as a point on the graph that is undefined or is unfit for the rest of the graph.

In order to find the discontinuity of the hole we have to perform the following steps,

The first and foremost thing is to factor out the numerator and the denominator

Next we have to determine the common factors in the numerator and the denominator

After that we have to set the common factors equal to zero and find the value of x.

Then the final steps is to plot the graph and mark the point with a hole

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Answer:

[tex]x {}^{3} + 2x {}^{2} y + 2xy {}^{2} + y {}^{2} [/tex]

Step-by-step explanation:

Greetings !

[tex](x + y)( x{}^{2} + xy + y {}^{2}) [/tex]

Distribute parentheses

[tex] = xx {}^{2} + xxy + xy {}^{2} + yx {}^{2} + y {}^{2}x + y {}^{2} [/tex]

[tex] = x {}^{3} + x {}^{2} y + xy {}^{2} + yx {}^{2} + y {}^{2} x + y {}^{2} [/tex]

Collect Like terms and further simplification

[tex] = x {}^{3} + 2x {}^{2} y + 2xy {}^{2} + y {}^{2} [/tex]

Hope it helps!!!

If you have any questions and suggestions tag it on the comments. thanks

The product of (x+y)(x²+xy+y²) gives x³ + 2x²y + 2xy² + y³.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

(x+y)(x²+xy+y²)

Multiplying the terms

= x(x²+xy+y²)) + y(x²+xy+y²)

= x³ + x²y + xy² + yx² + xy² + y³

= x³ + 2x²y + 2xy² + y³

Hence, the expression gives x³ + 2x²y + 2xy² + y³.

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Three parameters, start value, stop value, and step value, are required for the range() method in Python to function. After incrementing the values by the amount specified in the step value .

The range of values between a given data collection's top and lowest values is known as the statistical range. The difference between the highest and lowest observation is another method of expressing the range. By deducting the highest value from the lowest, one may calculate the sample interval. A crucial indicator of variability for continuous variables is the sample range.

here

startNumber (optional): The series of integers that are returned begins with this number.

stopNumber: The list of integers that range() provides comes to an end before this one.

stepValue (opportunity): a number that is an integer and represents the difference between each integer in the series.

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We calculated the domain of this function is all the real numbers of independent variable X such as 0, 1, 2, 3, 4, 5, 6 etc.

An expression that indicates a relationship between an independent variable and dependent variable. A function consists of two variables with or without numbers. A function has symbols but equal sign is mandatory.

The domain of a function is the set of all possible value of independent variables. It is also called the input of a function.

In the above function, the domain is all real number of independent variable x.

For each value of x that means for each domain, we get a value of y. The set of y values are called ranges.

we put x= 0, 1, 2, 3, 4, 5, 6 and so on.

we get y = 3×0-1 = -1

     y = 3×1-1 = 2

   y =3×2-1 = 5

  y = 3×3-1 = 8

 y= 3×4-1 = 11

y = 3×5-1 = 14

y= 3×6-1= 17

The set of domains are {0, 1, 2, 3, 4, 6}

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Answer:

All three angles must add up to 180 degrees

Step-by-step explanation:

He would pay $160 after one year if the installation fee per month is $45.

The cost of installing something. charge - the cost of a good or service; "the admittance charge" Based on the Farlex clipart collection and WordNet 3.0. Installation can be divided into two major categories: physical and virtual. While a virtual installation relates to the installation of software, a physical installation concerns the installation of tangible items like computer hard drives, wires, modems, and so on.

Simple installation entails unpacking and plugging the appliance into the main electrical outlet. This excludes mounting on brackets, reinstalling in fixed units, or connecting to the gas or water.

Installment fee per month=$45

For 9 months,

9×45=405

Total fees=Installation+405

Installation+405=$565

Let the installation be x then,

x+405=565

x=565-405

x=$160

Therefore, he would pay $160 after one year if the installation fee per month is $45.

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Answer:

B

Step-by-step explanation:

13a ^2+14-17a-12a ^2+12a+6a-a^ 2

=14-17a+12a+6a

=14+a    or     a+14

Answer:

Step-by-step explanation:

The point-slope form of the equation of a line is:

[tex]y-y_1=m(x-x_1)[/tex]

So, the equation for this problem, let

[tex](x_1,y_1)=(2,-1)[/tex]

then,

[tex]y-(-1)=m(x-2)\\y+1=m(x-2)[/tex]

If line (a) is perpendicular to line (b), then [tex]m_b[/tex] is equal to [tex]-\frac{1}{m_a}[/tex].  For this problem, let

[tex]m_a=-\frac{1}{2}[/tex] and [tex]m_b=2[/tex]

So,

[tex]y+1=(2)(x-2)\\y+1=2x-4\\(y+1)-1=(2x-4)-1\\y=2x-5[/tex]

Yes, the given equation is a quadratic equation.

The meaning of quadratic equation is any equation containing one term in which the unknown is squared and no term in which it is raised to a higher power.

Given is an equation, 2x²-7x = 0

As we know that, a quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared.

On comparing equation 2x²−7x=0 with standard form of quadratic equation

ax ²+bx+c=0:

We get, a=2,b=−7,c=0

Hence, the equation 2x²−7x=0  is a quadratic equation.

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Four types of transformations are as follow:

1. Rotation : It is based on about any point.

2. Reflection : It is based on over any line.

3. Translation : It is based on a given vector.

4. Dilation : It is based on size.

As given in the question,

Four types of transformations is given by :

1. Rotation : It represent the same image but the image is rotated about a fixed point by certain degree of its preimage.

2. Reflection: It is mirror image of the given image along the line after flipping.

3. Translation: Change in the position of the image without change in the given image.

4. Dilation: In this case size of the image get enlarged or shrink as per given condition.

Therefore, the four types of transformation is given by :

1. Rotation : It is based on about any point.

2. Reflection : It is based on over any line.

3. Translation : It is based on a given vector without change in the image.

4. Dilation : It is based on size.

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Answer:

Function to be graphed is,

h(x) = 2(x - 3)²

Function 'h' is a quadratic function.

Since, the coefficient of the leading term (term with the highest power) is positive, parabola will open upwards.

Both the ends of the parabola will be upwards (towards positive infinity).

As x approaches to negative infinity, h(x) approaches to positive infinity.

As x approaches to positive infinity, h(x) approaches to positive infinity.

Step-by-step explanation:

Please give the brainliest.

The graph of the equation that is parallel to 4x – 3y = –12 is determined as: A. y = 4/3x - 3/2.

If two lines are parallel to each other, their graph will have the same slope value, m. This means if their equations are expressed as y = mx + b in slope-intercept form, they will both have the same value of m.

Given the equation of a graph as 4x - 3y = -12, rewrite it in slope-intercept form to determine the slope value:

4x - 3y = -12

-3y = -4x - 12

-3y/-3 = -4x/-3 - 12/-3

y = 4/3x + 4

This means the slope, m is 4/3. The slope of the graph that is parallel to it will also have a slope of 4/3.

The slope of y = 4/3x - 3/2 is also 4/3, therefore, the answer is: A. y = 4/3x - 3/2.

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Complete Question:

The graph of which of the following will be parallel to the graph of 4x – 3y = –12?

A. y = 4/3x - 3/2

B. 6x - 4y = -8

C. y = 3/4x +1

D. 4x – 2y = –12

Answer:

AB = 6.71

Step-by-step explanation:

See the attached worksheet.

Find the lengths of the two sides of the right triangle:

 CB = (5 - (-1)) = 6

 CA = (6-3) = 3

Use the Phythagorean Theorem to find AB.

6^2 + 3^2 = AB^2

AB^2 = 45

AB = 6.71

Therefore , we can calculate the side of the length of the square by finding the square root of the given area.

The square root of an integer, which is the outcome of multiplication alone, gives the initial number. Squares and square roots are a few of examples of exponents. Think about the number 36. Furthermore, this can be written as 6x6.

Here,

The base length times the height of any quadrilateral yields the area of that shape.

Since the shape is square, we can be certain that all of its sides are equal in length.

Using this information, we can work backwards to determine the length of one side by taking the square root of the area.

For example : Square having area of 25

We can find its length by taking square root of 25

Which comes out to be √25 = 5

Thus , 5 is a length of the side of the square.

Therefore , we can calculate the side of the length of the square by finding the square root of the given area.

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Answer:

The roots of x^3 −2=2x^2 −x can be found by using the cubic formula to solve this polynomial equation. The roots are -2, 1, and 2/3.

Step-by-step explanation:

Answer:

let x= amount she earn for each delivery

6(16.5) = 11x

99 = 11x

x = 9

$16.5 per hour * 6 hours = $99

11 deliveries * $9 = $99

Step-by-step explanation:

Answer:

Here is the answer

Step-by-step explanation:

To find the perimeter of a triangle, we need to add up the lengths of all three sides. In this case, the sides of the triangle are given by the expressions 3x2 - y2, 4x2 - 7xy + 4y, and -3x + 7xy + 8y2.

To find the perimeter, we can simply add up these three expressions:

Perimeter = 3x2 - y2 + 4x2 - 7xy + 4y - 3x + 7xy + 8y2

= 7x2 - 3xy + 12y

This is the perimeter of the triangle. Note that the perimeter is a scalar quantity, not a vector, so it does not have a direction associated with it.

For the choir, the ratio is 1/5 and for the orchestra, the ratio is also 1/5, then yes, the two groups have the same ratio

Here we just need to compute the two ratios, to do that, we need to take the quotient between the number of students with a solo and the total number of students.

For the choir, there are 25 students and 5 with a solo, so the ratio is:

5/25 = 1/5

For the orchestra, there are 20 students and 4 of them have a solo, so the ratio is:

4/20 = 1/5

So yes, both groups have the same ratio of students with a solo to total students.

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Answer:

13

Step-by-step explanation:

(x+13) find its fourth root

which will be......

x⁴+28561=-93

x⁴=-28654

x=13.01

On solving the provided question, we can say that - If you put all the numbers together by digits, the total must be a multiple of three. so answer is 17

The divisibility rule is a concise and practical approach to check, often by looking at the integer's digits, whether a given integer is divisible by a given set divisor without actually executing division. Without actually doing the division procedure, you may quickly discover if a given number can be divided by a defined divisor using the divisibility test. When dividing two numbers exactly, the quotient must be an integer and the remainder must be zero.

[tex]51, 54, 57\\60, 63, 66, 69\\72, 75, 78\\81, 84, 87\\90, 93, 96, 99[/tex]

If you put all the numbers together by digits, the total must be a multiple of three. so answer is 17

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On solving the provided question we can say that, - the factors of the given equations [tex]x^2 -11x +18[/tex] are - x= 2 and x = 9

A number that divides another number by itself with no residual is known as a factor. In other words, if multiplying two whole numbers results in the creation of a product, the numbers we are multiplying are factors of the product since the product is divisible by them. Division and multiplication are the two ways to discover factors. A number or other mathematical object is factorized or factored in mathematics by expressing it as the product of numerous factors, often smaller or simpler things of the same sort. One factorization of the polynomial x2 - 4 is 3 5, which is also a factorization of the number 15.

[tex]x^2 -11x +18[/tex]

(x-2)(x-9)

x= 2 and x = 9

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The graph of the equation x = -4 is shown in the image attached below.

In Mathematics, a graph can be defined as a type of chart that is typically used to graphically represent data points or ordered pairs on both the horizontal and vertical lines of a cartesian coordinate, which are the x-coordinate (x-axis) and y-coordinate (y-axis) respectively.

In Mathematics, the x-intercept can be defined as the point at which the graph of a function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).

By critically observing the graph (see attachment), we can reasonably infer and logically deduce that the x-intercept is equal to -4.

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Therefore ,the collar remain effective for 26.44 days.

In mathematics, there are numerous ways to use the word "order." It most frequently refers to the quantity of elements in (for example, conjugacy class order, graph order, group order, etc.) or describes the biggest term (for example, curve order, surface order, or polynomial order) that appears in a mathematical object.

Here,

=>Rate of evaporation=k=dr/dt

=> amount still present=R.

Thus ,It's a first order reaction.

So, half life=0.693/k.

20=0.693/k.

=> k=0.0346

Now,

60% of active ingredient has been evaporated.

So, 40% left.

Time taken=T=(2.303/k)log(R/0.4R)

T=(2.303/0.0346)log(5/2)

T=66.56(log5-log2)

T=66.56(0.699-0.301)

T=66.56(0.398)

T=26.44 days.

Therefore ,the collar remain effective for 26.44 days.

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The price of a single chicken is $8 and the price of a single duck is $5.

The prices can be determined by forming the linear equation in two variables.

Given that,

Michael sold last month, 50 chickens and 30 ducks for $550.

This month, he sold 44 chickens and 36 ducks for $532.

Let the price of single chicken be 'a' and the price of a single duck be 'b'. Then the linear equation will be:

50a+30b=550 ____________(1)

44a+36b=532 ____________(2)

Solving equation (1) for the value of 'b'.

b=550-50a/30

b=55/3 - 5a/3  ____________(3)

Putting the value of 'b' in equation (2).

44a+36(55/3 - 5a/3) = 532

128 = 16a

a=8

Putting the value of a in equation (3).

b= 55/3 - 5*8/3

b=5

Thus, The price of a single chicken is $8 and the price of a single duck is $5.

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Michael sold last month, 50 chickens and 30 ducks for $550.

This month, he sold 44 chickens and 36 ducks for $532.

50a+30b=550

44a+36b=532

Solving equation (1) for the value of 'b'.

b=550-50a/30

b=55/3 - 5a/3

Putting the value of 'b'

44a+36(55/3 - 5a/3) = 532

128 = 16a

a=8

Putting the value of a

b= 55/3 - 5*8/3

b=5

Thus, The price of a single chicken is $8 and the price of a single duck is $5.

Answer:

11:27 am.

Step-by-step explanation:

The time which has passed when Tom overtakes Hazel is after Hazel has walked 1 hr 15 minutes and in that time Hazel has walked

1.25 * 4.8

= 6 km.

So, Tom runs 6 km in 10:15 - 9.39 = 36 minutes

= 0.6 hrs.

So, Tom's speed is 6/0.6 = 10 km/hr.

,

and Tom will take 18/10 = 1.8 hours to finish the route,

= 1 hr 48 minutes

So he finishes the route at

9:39 + 1:48

= 11:27 am.

Answer:

transversitile multistelular projection

Answer:

Step-by-step explanation:

The perimeter of triangle ACD that is formed by two right-angle triangles ACB and DCB, approximated to 1 decimal place is: 40.1 cm.

Mean is calculated to get an idea of the average of the observations in the data set.

The average value of the observations in a data set is called the mean or average . It is calculated by dividing the sum of observations by the number of observations i.e.

u = (x1 + x2 + x3 + .... + xn)/n

where u is the mean , x1 , x2 ...,  xn are data observations and n is the number of observations.

For example, we have values as 1,2,3,4,5 and we want to calculate the mean . Then it is calculated by

u = (1+2+3+4+5) / 5 = 3.

So, the mean is 3.

Therefore, mean is calculated to get an average or an idea of a certain number of observations.

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5Fx+5Gy=5H  Qx +Ry=S is a system of equations that is equivalent to the following system.

An equivalent system of equations is a system of equations that has the same solutions as the original system, but the coefficients of the variables may be different.

To determine which of the given systems is equivalent to the original system, you need to solve each system and see if they have the same solutions.

The original system is:

Fx + Gy = H

Qx + Ry = S

The solution to this system can be found by either graphing the equations or using substitution or elimination methods.

If we solve each of the other systems in the same way, we find that the system that is equivalent to the original system is:

C. 5Fx + 5Gy = 5H

Qx + Ry = S

This is because all of the other systems have different coefficients for the variables, and therefore will not have the same solutions as the original system.

The complete question is;-

Choose an equivalent system of equations to the following system:

Fx + Gy = H

Qx + Ry = S

A. 5Fx + 5Gy = 5H

Qx − Ry = S

B. 5Fx + Gy = 5H

Qx + 5Ry = S

C.5Fx + 5Gy = 5H

Qx + Ry = S

D. Fx + 5Gy = 5H

Qx + Ry = S

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