3. Write the equation Passing through ( -5, 2) with a slope of 3

All of the justifications used to demonstrate the following angles, including the alternate interior theorem justification, are valid.

When a transversal intersects two parallel lines, alternate interior angles are created that are equal to the alternate pairs of those pairs.

The angles formed on the opposing sides of the transversal are known as alternate internal angles.

Angles of the same size that are found on opposing sides of the transversal line are known as alternate angles.

Angles that alternate are equal: By creating a Z form, we can easily identify interior alternate angles: Alternate angles come in two varieties: alternate internal angles and alternate exterior angles.

All the reasons are given to prove the following angles are correct including the reason for the alternate interior theorem.

Therefore, all of the justifications used to demonstrate the following angles, including the alternate interior theorem justification, are valid.

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The value of k in the point (2, k) which lies on the line is -4.

How to find the value of k?

Every point lying on the curve of the line satisfies the equation of curve. Therefore, substitute the point in the given equation of line to find the value of k.

According to the given question:

The given equation is: 2y = - 3x - 2.

This is written as: 3x + 2y + 2 = 0.

Given the point (2, k) lies on the line given.

That means it should satisfy the given equation.

So, to find the value of 'k', simply substitute the point on the line.

So, it becomes: 3(2) + 2(k) + 2 = 0

⇒ 6 + 2k + 2 = 0

⇒ 2k = - 8

Dividing by 2 throughout, we get: k = - 4

Hence, (2, -4) lies on the line.

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The smallest possible value of x - y will be -6 when x = -4  and y = 2. The largest possible value of {2x}/{y}  will be 3/2 when x = 6  and y = 8. The largest possible value of x²+y² will be 100 when x = 6  and y = 8.

Given that -4 ≤ x ≤6 and 2≤ y ≤ 8,

The smallest possible value of x - y

⇒ (x - y)

As per the given, the smallest values of x and y are - 4 and 2

So, substitute the values of x = -4  and y = 2 in the expression (x - y)

⇒ - 4 - 2

⇒ - 6

The largest possible value of {2x}/{y}

⇒ {2x}/{y}

As per the given, the largest values of x and y are 6 and 8

So, substitute the values of x = 6  and y = 8 in the expression {2x}/{y}

⇒ 2(6)/8

⇒ 12/8

⇒ 3/2

The largest possible value of x²+y².

⇒ x²+y²

As per the given, the largest values of x and y are 6 and 8

So, substitute the values of x = 6  and y = 8 in the expression x²+y²

⇒ 6²+8²

⇒ 36 + 64

⇒ 100

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Answer:

Step-by-step explanation:

3.9875

Answer:

  h(x) = (x -2)(x -2+i)(x -2-i)

Step-by-step explanation:

You want the linear factorization of h(x) = x³ -6x² +13x -10.

A graphing calculator (attachment 2) shows the one positive real root is x = 2. This means (x-2) is a factor.

When we factor that out, we have a quadratic with no real roots. The vertex of its graph at (2, 1) tells us the roots of it are 2±√-1 = 2±i.

Each root p gives rise to a linear factor (x -p), so the factorization is ...

  h(x) = (x -2)(x -2+i)(x -2-i)

__

Additional comment

The first attachment shows these factors multiply out to give the polynomial h(x).

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The value of the h is A(2) / b when the formula is A = 1/2bh the formula is area of the triangle.

Given that,

We have a formula A = 1/2bh

We have to find h value from the formula.

We know that,

The variable h should be on one side of the equation, and the rest should be on the other. Divide the two sides in half as a good place to start. In this way, we eliminate the undesirable fraction.

A / 1/2 = 1/2bh / 1/2

Now on the right hand side left the 1/2 cancels out.

A / 1/2 = bh

And when a fraction is divided, the result is the same as multiplying it backwards.

A(2/1) = bh

Now, divide both sides by b.

A(2) / b = bh/b

On the left hand side b cancels out and we are left with the final product.

h = A(2) / b

Therefore, The value of the h is A(2) / b when the formula is A = 1/2bh the formula is area of the triangle.

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The correct answer is option A which is the ordered pair of point P’ will be (8.75, 5.25).

The scale factor is defined as the proportion of the new image's size to that of the previous image. decision-making.

If pentagon OPQRS is dilated by a scale factor of 7/4 from the origin, to create O’P’Q’R’S’, what is the ordered pair of point P’

Multiply the coordinates of point P by the scale factor 7/4  to get the coordinates of P'.

Given : P(-5,3)

P' (x,y) = P (-5 x 7/4 , 3 x 7/4)

          = P(-8.75, 5.25)

Therefore the correct answer is option A which is the ordered pair of point P’ will be (-8.75, 5.25).

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The equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

The standard form of the equation of a circle is (x - h)² + (y - k)² = r², where (h, k) is the center of the circle, and r is its radius.

We have given that circle having radius of 8 units. Thus, r = 8.

Since we know that circle having the center (10,−7).

Thus, the equation of the circle, with a radius of 8 units is;

(x - h)² + (y - k)² = r²

(x - 10)² + (y + 7)² = 8²

Thus, the equations that represent the circle having a with radius 8 and center (10,−7) are; (x - 10)² + (y + 7)² = 8²

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The  prize of the 4th place is 18

Given:

1. The second-place seller will receive twice as much as the third-place seller

2. The first-place seller will receive $20 more than the second-place seller

3. The profit portion they will share is $200

Let S, T, F and V represent the prize of the second, third, first and fourth  place respectively

Statement 1 can be written as:

S = 2T  --- (1)

Statement 2 can be written as:

F = S + 20  --- (2)

Statement 3 can be written as:

F + S + T = 200  --- (3)

Substitute (1) and (2) into (3):

F + S + T = 200

(S+20) + 2T + T= 200

(2T+20) +2T + T= 200          (Since S = 2T)

2T+20 +2T + T= 200

5T + 20 = 200

5T = 200-20

5T = 180

T = 180/5

T = 36

Thus, the third-place seller prize is 36

Since the 4th place winner received half of what the 3rd place received. Thus:

V = 1/2 × T

V =  1/2 × 36

V = 18

Therefore, the 4th place prize is 18

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After solving the equations we can conclude that each ticket for an adult costs $24 whereas each ticket for a child costs $6.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions.

For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

So, 2 equations can be formed:

Let a be adults and c be children.

3a + 4c = 96 ...(1)

2a + 3c = 68 ...(2)

Now, take equation (1):

3a + 4c = 96

3a = 96 - 4c

a = 96 - 4c/3

Now, substitute a = 96 - 4c/3 in equation (2):

2a + 3c = 68

2(96 - 4c/3) + 3c = 68

96 - 4c/3 + 3c = 68/2

96 - 4c + 3c = 34*3

-c = 102 - 96

c = $6

Now, substitute c = 6 in equation (1):

3a + 4c = 96

3a + 4(6) = 96

3a + 24 = 96
3a = 96 - 24

3a = 72

a = 72/3

a = $24

Therefore, after solving the equations we can conclude that each ticket for an adult costs $24 whereas each ticket for a child costs $6.

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The angle between 0 and 2π coterminal with the angle 23π/3 will be equal to 17π/3.

The branch of mathematics that sets up a relationship between the sides and the angles of the right-angle triangle is termed trigonometry. The trigonometric functions, also known as circular, angle, or goniometric functions in mathematics, are real functions that link the angle of a right-angled triangle to the ratios of its two side lengths.

Given that the angle between 0 and 2π coterminal with the angle 23π/3. The coterminal angle will be calculated as,

To calculate the coterminal angle subtract 2π from 23π/3. Solve mathematically,

Coternimal = ( 23π / 3 ) - 2π

Coterminal = 9 23π  - 6π ) / 3

Coterminal = 17π / 3

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The number of seats in each row would be = 271 seats.

An auditorium is defined as the establishment that can be used for various events such as presentation, seminars and celebrations.

The total number of people seated in the auditorium= 2100 seats.

The total number of seats = 2100

The number of seats per row = 8x

That is,

2100 = 8x

make X the subject of formula;

X = 2100/8

X =263 +8

X = 271 seats per row.

Therefore, the number of seats per row would be = 271 seats per row.

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Answer:

Exact form: 13/4

Decimal form: 3.25

Mixed form: 3 1/4

Step-by-step explanation:

Answer:

The number of students in the seventh grade is 550.

Step-by-step explanation:

To find the number of students in the seventh grade, we need to use the information given in the problem: the number of students in the Environmental Club (11 students) and the percentage of students in the seventh grade that the Environmental Club represents (2%).

We can set up an equation to represent this information:

11 students / 2% = X students / 100%

The left side of the equation represents the number of students in the Environmental Club and the percentage of the seventh grade that they represent. The right side of the equation represents the total number of students in the seventh grade and the percentage that represents the whole.

Since percentages are just fractions with a denominator of 100, we can rewrite the equation as:

11 students / 0.02 = X students / 1

Then, we can use algebraic techniques to solve for X. One way to do this is to cross-multiply:

X = (11 students * 1) / 0.02

= 550 students

Therefore, there are 550 students in the seventh grade.

The true statement are

Canister A can hold 30 pounds and contains 71% of its capacity

= 0.71 * 30 pounds

canister B can hold 45 pounds and is 10/18 full

= 45 * 10/18 pounds

canister C can hold 60 pounds and it's 8.8 pounds more than half capacity

= 8.8 + 60 * 1/2 pounds

The total amount available

= 0.71 * 30 + 45 * 10/18 + 8.8 + 60 * 1/2

= 85.1 pounds

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The length of QR in the quadrilateral is 58.7 units.

A quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.

Two quadrilaterals are similar if their corresponding angles are equal and also their corresponding sides must be proportional.

Therefore,

KLMN is similar quadrilateral to OPQR.

Hence,

[tex]\frac{KL}{OP} =\frac{KM}{OQ} =\frac{KN}{OR} =\frac{MN}{QR}[/tex]

[tex]\frac{11}{38} =\frac{17}{QR}[/tex]

cross multiply

11QR = 17 × 38

QR = 646 / 11

QR = 58.7272727273

QR = 58.7

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The required equation of the line is x - y + 3 = 0 which is parallel to line x-y=5.

A straight line's general equation is y = MX + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

On the y-axis, this value c is referred to as the intercept.

The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.

So, the equation of the line will be:

The needed line will have the same slope as the parallel line.

The slope of the parallel line:
x - y = 5

y = x - 5

The parallel line's slope is 1.

Equation of a line with a slope of 1 through the point (-5,-2).

(y - y1) = m(x  x1)

(y + 2) = 1(x + 5)

x - y + 3 = 0

Therefore, the required equation of the line is x - y + 3 = 0 which is parallel to line x-y=5.

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Answer:

The correct answer is [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

If she has 6 classes, then the total hours of classes are:

[tex]\frac{6}{1}[/tex] · [tex]\frac{7}{6}[/tex] = [tex]7[/tex]

[tex]7[/tex] · [tex]\frac{1}{2}[/tex] - [tex]7[/tex] = [tex]\frac{1}{2}[/tex]

There is not enough evidence to conclude that the population mean life span for Honolulu residents is less than 77 years.

At the null hypothesis, it is tested if there is not enough evidence that the mean life span is less than 77 years, that is:

[tex]H_0: \mu \geq 77[/tex]

At the alternative hypothesis, it is tested if there is enough evidence that the mean life span is less than 77 years, that is:

[tex]H_1: \mu < 77[/tex]

We are testing if the mean is less than a value, hence we have a left-tailed test, with 20 - 1 = 19 df and a significance level of 0.05, thus the critical value is of:

t = -1.7291.

Thus the conclusion, considering the test statistic t, is given as follows:

The equation to obtain the test statistic is presented as follows:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

The parameters are:

In the context of this problem, the values of these parameters are given as follows:

[tex]\overline{x} = 71.4, \mu = 77, s = 20.65, n = 20[/tex]

Hence the test statistic is of:

[tex]t = \frac{\overline{x} - \mu}{\frac{s}{\sqrt{n}}}[/tex]

[tex]t = \frac{71.4 - 77}{\frac{20.65}{\sqrt{20}}}[/tex]

t = -1.21 -> not enough evidence to reject the null hypothesis.

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Answer:2/1

Step-by-step explanation:

you just have to flip the slope if it is perpendicular.

Answer:84

Step-by-step explanation:21x4=84

The equation y= √(x-1) + 3 is a function of radical function.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

Type of function:

linear, power, quadratic, polynomial, rational, exponential, logarithmic, radical etc.

Given equation is

y= √(x-1) + 3

In the equation there is a term √(x-1).

A square root presents in the equation.

This means it is a radical function.

The given equation is of a radical function.

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The domain of the given graph is -∞>x>-2

The range of the given graph is [0,-4]

What is the range and domain of a graph?

The range is the set of possible output values, which are shown on the y-axis.

The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.

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The domain as an inequality x<-2 is { -∞>x>-2}.

The range as an inequality is [0,4]

What is the range and domain of a graph?

Functions in mathematics can be compared to the operations of a vending (soda) machine. When you put in a certain amount of money, you can select different types of sodas. Similarly, for functions, we input different numbers and we get new numbers as the result. Domain and range are the main aspects of functions. You can use quarters and one-dollar bills to buy a soda.

The machine will not give you any flavor of the soda if pennies are input. Hence, the domain represents the inputs we can have here, that is, quarters and one-dollar bills. No matter what amount you pay, you won't get a cheeseburger from a soda machine. Thus, the range is the possible outputs we can have here, that is, the flavors of soda in the machine.

The range is the set of possible output values, which are shown on the y-axis. The domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x -axis.

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Answer:

The tree is 396 feets height

Step-by-step explanation:

1 m = 3.3 ft

then

12 meters to feet is:

(12)*(3.3) = 396

Answer: Length (in feet) x width (in feet) = area in sq. ft. 

Step-by-step explanation:

This question is incomplete , I am answering this question in general as per my knowledge.

No, because you gave T a Boolean when T expected a student as its first argument and a course as its second parameter. This will be less formal if.

The expected,

T(‘‘user2012813",‘‘discrete math")=true

However, the function F(x) and A both yield either true or false (y). Thus, you are attempting to assess

T(F(‘‘user2012813"),A(‘‘discrete math"))=T(true, false)= NULL

Only the first formulation makes sense, but after relations are established, these kinds of structures can be used.

Null functions as both a value and a pointer in computer programming. A built-in constant called null has a value of zero. It is the same as how strings in C are terminated with the letter 0.

Null is another possible value for a pointer, and unless the CPU supports a unique bit pattern for a null pointer, it has the same value as zero.

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r≈10.75cm

Answer:

r≈10.75cm

V=πr^2h/3