Graph the line that passes through the points (1, -2) and (-1,-6) and
determine the equation of the line.

The algebraic description of the transformation of B(x, y) = B'(y + 0, 0 - x)

The algebraic description of the transformation of K(x, y) = K'(y + 0, 0 - x)

The endpoints of the new line segment are B'(4, -1) and K'(-3, -4).

As per the given data BK has endpoints B(1, 4) and K(4, -3).

Rotate BK clockwise 270 degrees about the origin.

Every point of a source image is transformed in a plane via a rotation that rotates it around a fixed point at a specific angle and direction. The fixed point is referred to as the rotational center.

The term "angle of rotation" refers to the rotation's amount and is expressed in degrees.

Rotating a figure 270 degrees clockwise is the same as rotating a figure 90 degrees anticlockwise.

Now, it would be (x, y) = (-y, x)

We have;

R (x, y) to R' (y, -x)

The algebraic description is simply written as;

R (x, y) = R'(y + 0, 0 - x)

B (x, y) = B'(y + 0, 0 - x)

K (x, y) = K'(y + 0, 0 - x)

To get the new endpoints, we simply write the transformation as shown;

B(1, 4) becomes B'(4, -1)

K(4, -3) becomes K'(-3, -4)

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Bacteria are important in the nitrogen cycle because they convert gaseous nitrogen into ammonia.

The nitrogen cycle is a biogeochemical process through which nitrogen is changed into a variety of forms before returning to the atmosphere after first entering the soil and then organisms.

Given:

The cycle's most crucial component is bacteria.

The nitrogen is changed between states by bacteria so it can be utilised.

Different bacteria assist nitrogen change states when it is absorbed by the soil so that it may be absorbed by plants.

Then, the plants provide the nitrogen for the animals.

Hence, Bacteria convert gaseous nitrogen into ammonia.

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Answer:

Transformation for A to B : Shift 2 unit horizontally.

Transformation for A to C : Shift 1 unit horizontally, 1 unit vertically.

Equation of Parabola A : y = - (x - 1)² + 1

Equation of Parabola B : y = - (x - 3)² + 1

Equation of Parabola C : y = - (x - 2)² + 2

Section of a right circular cone by a plane parallel to a generator of the cone is a parabola. It is a locus of a point, which moves so that distance from a fixed point (focus) is equal to the distance from a fixed line (directrix)

Fixed point is called focus.

Fixed line is called directrix.

Equation of the parabola having vertex (h, k).

y = a(x - h)² + k

Equation of Parabola A with vertex (1,1)

y = a(x - 1)² + 1

parabola A has point (0, 0) on it

0 = a (0 - 1)² + 1

a = -1

Equation of the parabola A

y = - (x - 1)² + 1

Shifting parabola A, 2 unit horizontally, we get parabola B

Equation of the parabola B

y = - (x - 3)² + 1

Shifting Parabola A, 1 unit horizontally and 1 unit vertically, we get parabola C

Equation of the parabola C

y = - (x - 2)² + 2

Hence, shifting 1 unit horizontally and 1 unit vertically in Parabola A we get parabola C and shifting 2 unit horizontally we get parabola B,

y = - (x - 1)² + 1 is equation of Parabola A.

y = - (x - 3)² + 1 is equation of Parabola B.

y = - (x - 2)² + 2 is equation of Parabola C.

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The 3 lengths that can be combined to form a right triangle will be 8, 15, and 17. Then the correct option is D.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The Pythagoras theorem formula is given as

H² = P² + B²

If the Pythagoras theorem is satisfied then the dimension is the dimension of the right triangle.

Let's check option D, then we have

17² = 8² + 15²

289 = 64 + 225

289 = 289

The 3 lengths that can be combined to form a right triangle will be 8, 15, and 17. Then the correct option is D.

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The quadrant 1 of the graph is in the place of upper right quadrant.

the term graph in math is referred as a non-linear kind of data structure made up of nodes or vertices and edges

Here we have given that we have to find the place of quadrant 1.

In order to find that we must know that definition of quadrant in math that is one other than the region/part of a cartesian plane which is obtained when the two axes intersect each other and it is used to determine the position of a point in a plane.

As we all know that the first quadrant is in the upper right-hand corner of the plane.

And here we all also know that both x and y have positive values in this quadrant.

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The height of a triangle can be found using the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Therefore, the height of a triangle can be found by rearranging the formula to height = (2 * area) / base.

To find the height of a triangle when the base is given, first use the triangle area formula, which states that the area of a triangle is equal to (1/2) * base * height. Next, rearrange the formula to height = (2 * area) / base so that the height can be found by dividing the area by the given base. Once the area is known, the height can be found by plugging the area and base into the rearranged formula. For example, if the base of a triangle is 8 and the area is 12, then the height of the triangle can be found by dividing 12 by 8, which is equal to 1.5. Therefore, the height of the triangle is 1.5.

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Therefore , the solution of the given problem of equation comes out to be  [tex]x^{2}[/tex]-2x-37/(x-8) (x+5).

An equation is a mathematical formula that connects two assertions using the equal sign (=) to denote equivalence. In algebra, an equation is a mathematical statement that establishes the equality of two mathematical expressions. For instance, an equal sign separates the components 3x + 5 and 14 in the equation 3x + 5 = 14. A mathematical formula is used to express the connection between two phrases on either side of a letter. Frequently, there is just one variable, which is also the symbol. for example, 2x - 4 = 2.

Here,

Given :([tex]x^{2}[/tex]-2x-37)/([tex]x^{2}[/tex]-3x-40)

[tex]x^{2}[/tex]-3x-40

Factor[tex]x^{2}[/tex]-2x-37

[tex]x^{2}[/tex]-2x-37/(x-8) (x+5)

Thus ,

the factors comes out to be [tex]x^{2}[/tex]-2x-37/(x-8) (x+5)

Therefore , the solution of the given problem of equation comes out to be  [tex]x^{2}[/tex]-2x-37/(x-8) (x+5).

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Answer: Probably negative 69

The error that Maria likely make is that she subtracted 1n from 5n.

In Mathematics, it is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

The value of the expression will be:

= -4n +3+9n-4

= 5n - 1

The error was because 1n was minus from 5n

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Answer:

$6.51

Step-by-step explanation:

To make a percent a decimal, divide by 100

62% = .62

.62 x 10.50 = 6.51

We know that half of 10.50 is 5.25 and 625 would be a little higher and 6.51 is a little higher.

An equation for the number of points y, and the correct answers x  is y = 10x.

One mathematical expression makes up a term. It could be a single variable (a letter), a single number (negatively or positively), or a number of variables multiplied but just never added as well as subtracted.

For the stated question-

Consequently, the total points earned equal the total points earned for each question. number of questions with accurate responses.

Consequently, points earned = 10x

y = 10x.

First geography test: x = 3

y = 10*3 = 30

Second geography test: x = 7

y = 10*7 = 70

Thus, the graph for the enrique's first and second geography test is plotted.

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The correct question is-

Enrique earns 10 points for each question that he answers correctly on a geography test. Write an equation for the number of points, y Enrique scores on the test when he answers x questions correctly.

On his first geography test, Enrique answered 3 questions correctly. On his second test, Enrique answered 7 questions correctly.

Place points on the graph to show Enrique's first and second geography test.

Answer:

65?

Step-by-step explanation:

im not to sure but maybe 65

The workers in shift B earns the bonus.

Mean of a set of data is defined as the average of all the values. It gives the exact middle point of the data set.

Mean is found by adding all the data values and then dividing with number of values in the set.

Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}

Number of data in shift A = 12

Mean = (77 + 91 + 82 + 68 + 75 + 72 + 85 + 65 + 70 + 79 + 94 + 86) / 12

         = 944 / 12

         = 78.67

Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}

Number of data in shift B = 12

Mean = (68 + 93 + 53 + 100 + 77 + 86 + 91 + 88 + 72 + 74 + 66 + 82) / 12

         = 950 / 12

         = 79.17

The workers in the shift with the highest mean will earn a bonus. It is shift B.

Hence the workers in shift B earn the bonus.

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The full question is as follows :

The following are daily outputs from shift A and shift B at a factory.

Shift A: {77, 91, 82, 68, 75, 72, 85, 65, 70, 79, 94, 86}

Shift B: {68, 93, 53, 100, 77, 86, 91, 88, 72, 74, 66, 82}

Q. Compare the means of the shift outputs. The workers in the shift with the highest mean will earn a bonus. Which shift will earn the bonus?

Answer:

C(t) = 5t for 0 < t ≤ 3

C(t) = (8t-9) for 3 < t ≤ 6

C(t) = 44 for 6 < t ≤ 10

C is given in thousands of dollars and t is given in months.

Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000

Step-by-step explanation:

We will do a piecewise analysis for this cost function.

How to obtain the total cost changes with each time interval.

In the first 3 months,

C(t) = 5t for 0 < t ≤ 3

Note that C is given in thousands of dollars

In the next 3 months,

C(t) = (8t-9) for 3 < t ≤ 6

- Here, it gets a little complex, we use the upper limit of the previous interval and the lower limit of this new interval to get the constant to be subtracted from the normal 8t that characterizes this interval.

8(3) = 24

5(3) = 15

constant = 24 - 15 = 9

In the last 4 months,

C(t) = 44 for 6 < t ≤ 10

- For the last four months, it is a single sum of $5000 plus the [8(6) - 9] from the previous inteval

C = [8(6) - 9] + 5 = 39 + 5 = 44

So, the cost of parking, tracked month after month gives

T | Cost (in thousands of dollars)

1 | 5

2 | 10

3 | 15

4 | 23

5 | 31

6 | 39

7 | 44

8 | 44

9 | 44

10 | 44

Total lump sum to be paid at the end of the 6 months for the total 10 months that the construction company works on the parking garage = $44000

Hope this Helps!!!

This is not my answer yet is a stollen verrified one.

the middle value in a data set when the values are put in order

For example, the set {3,1,2} sorts to {1,2,3} where the median is 2.

Another example: The set {1,2,3,4} has 2 and 3 tied for the middle most position. The midpoint is (2+3)/2 = 5/2 = 2.5 which is the median.

Answer:

  23.5 cm

Step-by-step explanation:

You want the height of the model of a 94 m tall roller coaster when the model scale is 1 cm = 4 m.

The model dimensions are assumed to be proportional to the real-world dimensions, so the model height h will satisfy the proportion ...

  h/(94 m) = (1 cm)/(4 m)

Multiplying by 94 m gives ...

  h = (1 cm)(94/4) = 23.5 cm

The height of the model is 23.5 cm.

The dual formula is a formula which we get when we replace the symbol ∨ by ∧ , ∧ by ∨ , T by F  or F by T.

Basically , we can say that it is obtained by replacing tautology by contradiction.

There are certain rules which are to be followed while applying dual formula which are,

S1 is a tautology if and only if S2 is a contradiction.

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There are 9 possible outcomes  to buy two new pair of pants.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

Given:

we have the following Styles

Boot cut (B), Skinny (S), and Relaxed fit (R).

So, if her buys two paints then the possible combination he can take as

Boot cut x Boot cut

Skinny x Skinny

Relaxed fit x Relaxed fit

Boot cut x Skinny

Boot cut  x Relaxed fit

Skinny x Relaxed fit

Skinny x Boot cut

Relaxed fit x Boot cut

Relaxed fit x Skinny

Hence, there are 9 possible ways.

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In the late 19th century, the Russian press used the phrase 2 + 2 = 5 to describe the moral confusion of social decline at the turn of a century, because political violence characterised much of the ideological conflict among proponents of humanist democracy and defenders of tsarist autocracy in Russia

No, 2 is not a  happy number because 2 can not become 1 after a series of stages in which each step 2 is replaced by the sum of its squares

Let's try to first comprehend what numbers are.

An arithmetic value that is calculated and utilized to represent a quantity is called a number. Numeral symbols, such as "3" are used in writing to represent numbers. A number system is a methodical technique to express numbers using digits or other symbols. The numerical system is a helpful collection of numbers that illustrates the number's algebraic and mathematical structure. presents an example that is typical.

Happy numbers If a number leads to 1 after a series of stages in which each step's number is replaced by the sum of its squares, it is said to be happy. For example, if we start with a happy number and keep replacing it with the sum of its squares, we eventually reach 1.

So 2 is not a  happy number.

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Answer:

No, I will not simplify -164

Step-by-step explanation:

You can not Simplify -164

so the answer will be you can not simplify it

The Complete is showing the length of the fence and the cost.

Length of fencing  4  6      7    9  10

Cost:                       36 54  63 81  90

In general, the term "proportion" refers to a part, share, or amount that is compared to a total.

According to the concept of proportion, two ratios are in proportion when they are equal.

A mathematical comparison of two numbers is called a proportion. According to proportion, two sets of provided numbers are said to be directly proportional to one another if they increase or decrease in the same ratio. "::" or "=" are symbols used to indicate proportions.

Given:

Length of fencing  4  6  7  x  10

Cost:                       36 y z 81 w

Now, Using proportion

4/ 36 = 6/y

4y = 36(6)

y = 54

and, 4/36 = 7/z

4z = 36 (7)

z = 63

and, 4/36 = x /81

x = 9

and, 4/36 = 10/w

360 = 4w

w= 90

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Answer:

Slope = -2  Y intercept is (0,4)

Step-by-step explanation:

Annabelle collected data from a sample of people that were convenient for her to access, such as her immediate neighbors, and used this to draw her conclusion.

Annabelle performed a convenience sample investigation, which is a type of statistical investigation. This involves collecting data from a sample of people that are convenient for the researcher to access. In this case, Annabelle asked a couple of her immediate neighbors to find out how many people in her neighborhood were going to the rock concert..

Convenience sampling is useful when time or resources are limited, however the results may not be representative of the larger population. Therefore, it is important to consider the limitations of the sample when drawing conclusions. For example, Annabelle may not have considered that the neighbors she asked may not be representative of the whole neighborhood.

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A coordinate plane is a two-dimensional surface formed by two number lines

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With the help of equations we can say that, the wedding had 96 attendees.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

We have LHS = RHS (left hand side = right hand side) in every mathematical equation.

To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.

The statement is not an equation if there is no "equal to" sign in it.

According to our question-

x is the total number of wedding attendees.

1/3 of the attendees =1/3 who chose pasta=1/3x----1

Those who selected chicken =5/12x---2

24 people opted for meat.----3

adding 1,2,3

x = 96

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According to the compound interest formula, the population is 5 years is 422,385.

The term compound interest in math is defined as the interest calculated on the principal and the interest accumulated over the previous period.

Here we have given that the population of 210,000 people is increasing by 15% each year.

And then while looking into the given question, we have identified that the value of

interest rate = 15%

principal count = 210,000

time period = 5

Here we have to convert R as a percent to r as a decimal, then we get

=> r = R/100

=> r = 15/100

=> r = 0.15 rate per year,

Now, we have to solve the equation for A

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

Apply the values on it , then we get,

[tex]A = 210,000.00(1 + \frac{0.15}{1} )^{(1)(5)}[/tex]

When we simplify this one then we get

[tex]A = 210,000.00(1 + 0.15)^5[/tex]

Therefore, the value of A is 422,385.

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The value of Isabel's account after three years can be calculated using the future value of the annuity formula.

Isabelle's budget car is:

Reason:

Monthly savings, PMT = $200

Account compound interest, r = 1.7%

t = Account value after 3 years is displayed as increase.

We know that:

[tex]FV =PMT * \frac{[(1+i)^n -1]}{i}[/tex]      --------------------- (1)

Where;

    i = r/12

⇒ n = 12 × t

From the above equation(1), we get:

[tex]FV =200 * \frac{[(1+\frac{1.7}{2} )^{12*3} -1]}{\frac{1.7}{12} }[/tex]

    ≈ 7381.4

Therefore,

The budget cars she can buy, those that require a down payment of less than $7,381.4, which  are:

The required down payment of choice 02 is $6200.

The required down payment of choice 03 is $5100.

The required down payment of choice 04 is $7250.

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