A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). answer the questions about line t to write the equation. what is the slope of line t? what is the y-intercept of line t? what is the equation in slope-intercept form of line t?

The required length of line segment JK would be 16 units.

The midpoint of a line segment is the point that divides the line segment into two equal parts. So, to find the length of the line segment JK, we can first find the coordinates of point J, which is the other endpoint of the line segment.

Let the coordinate of the point J would be (x, y)

Since the midpoint of the line segment is (2, -3), and point K is located at (-6, -3), we can use the midpoint formula to find the coordinates of point J:

2 = (x+(-6))/2 ; -3 = (y+(-3))/2

4 = x - 6 ; -6 = y -3

x = 10 ; y = -3

So the coordinate of the point J :(10, -3)

Now that we have the coordinates of both endpoints of the line segment, we can use the distance formula to find the length of the line segment:

length = √((10 - (-6))² + (-3 - (-3))²)

= √((10 + 6)² + (-3 + 3)²)

= √(16² + 0)

= √(256)

= 16

Therefore, the length of line segment JK is 16 units.

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Answer and Step-by-step explanation:

Lydia must sell at least $680 worth of tacos and burritos each day, and she only has enough supplies to make 115 tacos or burritos. If she sells each taco for $4, then she can make a maximum of 115 tacos * $4/taco = $<<115*4=460>>460 by selling tacos.

Therefore, in order to make at least $680, Lydia must sell burritos in addition to the tacos. The minimum number of burritos she must sell in order to make at least $680 is $680 - $460 = $<<680-460=220>>220.

Since Lydia sells each burrito for $6.75, she must sell at least $220 / $6.75/burrito = <<220/6.75=32.5>>32.5 burritos to make at least $680. Since she only has enough supplies to make 115 tacos or burritos, and she has already accounted for 115 tacos, she must sell a minimum of 32.5 burritos to meet the requirements.

We can write '8 or more' as [tex]\geq 8[/tex], using the greater-than equal to sign.  

The greater-than sign is a mathematical symbol that denotes an inequality between two values. The widely adopted form of two equal-length strokes connecting in an acute angle at the right, >, has been found in documents dated as far back as 1631. In mathematical writing, the greater-than sign is typically placed between two values being compared and signifies that the first number is greater than the second number.

Examples of typical usage include 1.5 > 1 and 1 > −2. The less-than sign and greater-than sign always "point" to the smaller number. Since the development of computer programming languages, the greater-than sign and the less-than sign have been repurposed for a range of uses and operations.

Here, we can use an alternate to the 'greater-than' symbol: a 'greater-than equal to' symbol, denoted as ≥.

Using this, we can write:

[tex]\geq[/tex] 8, denotes a number greater-than or equal to 8.

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Answer:

1/ simplify polynomial is x^3 y^2 - x^2 y^3 + xy

2/ Answer is -86

Step-by-step explanation:

x²yxy-xy²xy +xy

Simplify each term, and I get

x^3 y^2 - x^2 y^3 + xy

I may be wrong!

Now let's put -3 in for x and 2 in y and evaluate

(-3)^3  (2)^2 -  (-3)^2  (2)^3  +  (-3 times 2)

(27) (4) - (9) (8) - 6

-86

I may be wrong, but I tried my best to help you since this question has been on for a long time, but no one answered. If I am wrong, I am sorry!

The mean squared error is 4.67. So the option a is correct.

In the given question, demand for a product and the forecasting department's forecast for a product are given.

We have to compute the mean squared error.

Period          Actual        Forecasted      Error       Absolute      Squared

                 Demand(E)    Demand (F)     (E-F)        Error |E-F|    Error |(E-F)|^2

1                12    

2                15                12              3               3             9

3                14                15              -1                1              1

4                18                16              2                2              4

                                                                Total=6        Total=14

Now we finding the mean squared error (MAE)

Mean squared error = ∑|(E−F)|^2/n

Mean squared error = 14/3

Mean squared error = 4.67

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The probability that exactly two of the students are juniors is given as follows:

0.270 = 27%.

The mass probability formula is presented as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The parameters are:

The values of these parameters for this problem are given as follows:

[tex]N = 60, n = 4, k = 18[/tex]

Hence the probability that exactly two of the students are juniors is calculated as follows:

[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}[/tex]

[tex]P(X = 2) = h(2,60,4,18) = \frac{C_{18,2}C_{42,2}}{C_{60,4}} = 0.270[/tex]

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Answer:

(D) 1/9

Step-by-step explanation:

9x-2=-3

9x=1

x=1/9

You can see that x=4 takes two different values y=7 and y=1. You should remove one of these ordered pairs (4,7) or (4,1).

What are the 4 types of function?

There are 4 types of functions:

Functions with arguments and return values. This function has arguments and returns a value: ...

Functions with arguments and without return values. ...

Functions without arguments and with return values. ...

Functions without arguments and without return values.

A function is a relation that for each input value x takes the unique value of output y.

Consider the table

x y

1 7

4 7

2 2

4 1

3 9

You can see that x=4 takes two different values y=7 and y=1. You should remove one of these ordered pairs (4,7) or (4,1).

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A mode is defined as the value that has a higher frequency in a given set of values. It is the value that appears the most number of times.

In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.

For example, the mode of the set {3, 7, 8, 8, 9}, is 8. Therefore, for a finite number of observations, we can easily find the mode. A set of values may have one mode or more than one mode or no mode at all.

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The parallel marks the northern limit of the Southern Ocean (though some organisations and countries, notably Australia, have other definitions) and of the Antarctic Treaty System.

Parallel lines are straight lines that never meet each other no matter how long we extend them

Parallel lines are any two or more lines that all lie in the same plane and never cross one another. They are equally spaced apart and have the same incline.

Numerous pairs of angles are created when a transversal line intersects any two parallel lines. While some angles are additional, others are congruent (equal).

The fundamental characteristics listed below make it simple to recognise parallel lines.

Parallel lines are defined as straight lines that are always the same distance apart.

No matter how far apart they are from one another, parallel lines can never intersect.

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The lines p and q are perpendicular in the coordinate plane.

The name of the other number line, which is a vertical one, is called the y-axis. To graph points, lines, and other objects, one can utilize the coordinate plane. A pair of numerical coordinates that uniquely identify each point in a Cartesian coordinate system in a plane are called the coordinates. These numerical coordinates are signed length measurements that represent the separations between two fixed perpendicular oriented lines and the point.

Let the equation of the line is:

y-y'=m₁(x-x')

m₁=2/6

m₁=1/3

Therefore, the equation of a line with the point (3, 4) and slope m₁=1/3

y-4=(1/3)(x-3)

y=(1/3)x-1+4

y=(1/3)x+3

And m₂= -3

The line equation that is passing through (2,7) and m₂= -3

y-7=(-3)(x-2)

y-7= -3x+6

y= -3x+13

m₁×m₂= -1

(1/3)(-3)= -1

So, the lines that are given in the coordinate plane p and q are perpendicular.

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56.6 years  is the mean of the modes of the given set of numbers.

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

                     Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

The mean is calculated by adding together all the values

                 =  (54+54+54+55+56+57+57+58+58+60+60

                  = 623

                  =  56.6 years.

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The one way of determining the factors of x³ + 4x² + 5x + 20 by grouping is (b) x²(x + 4) + 5(x + 4) .

The Grouping in a polynomial is done by the taking the GCF( greatest common factors) from the different terms .

the expression is given as : x³ + 4x² + 5x + 20 ;

in order to determine the factors by grouping ,

we first take x² common from the first two terms and 5 common from the last two terms .

we get ;

⇒ x²(x + 4) + 5(x + 4)

Therefore , the one way of determining the factors is x²(x + 4) + 5(x + 4)  .

The given question is incomplete , the complete question is

Which shows one way to determine the factors of x³ + 4x² + 5x + 20 by grouping ?

(a) x(x² + 4) + 5(x² + 4)

(b) x²(x + 4) + 5(x + 4)

(c) x²(x + 5) + 4(x + 5)

(d) x(x² + 5) + 4x(x² + 5)

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The factors of  2x² - 7x - 15 are (2x + 3) and (x - 5).

By splitting the middle term and factoring the polynomial,

2x² - 7x - 15

= 2x² - 10x + 3x - 15

= 2x(x - 5) + 3(x - 5)

= (2x + 3)(x - 5)

The factors of  2x² - 7x - 15 are (2x + 3) and (x - 5).

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Rational functions can have 3 types of asymptotes:

1. Horizontal Asymptotes

2. Vertical Asymptotes

3. Oblique Asymptotes

The ratio of two polynomial functions with a non-zero denominator is known as a rational function.

1. Horizontal Asymptotes:

A graph's horizontal asymptote is a horizontal line with the equation y = b, and when the inputs get closer to 0 or 1, the graph moves toward the line. A graph's slant asymptote is a sloped line, denoted by the equation y = mx + b, where the graph slopes toward the line when the inputs approach 0 or -1.

2. Vertical Asymptotes:

Vertical asymptotes are vertical lines that represent the zeros in a rational function's numerator. Asymptotes can also occur in other situations, such as logarithms, although you'll almost probably run into them when discussing rationals for the first time.

3. Oblique Asymptotes:

These slanted asymptotes, known as oblique asymptotes, demonstrate how a function rises or falls without bound. Slant asymptotes are another name for oblique asymptotes. The slant asymptote won't be a line because the degree of the numerator is 3 and the degree of the denominator is 1, respectively.

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If x has a percentage of 10% and that is equal to y at 100%, then x is equal to 10% of y. If x is at 100%, then the percentage of y would be 1000%.

Here's how to arrive at this answer:

First, let's set up the equation to represent the given information:

x = 10% * y

If we solve for y in this equation, we get:

y = x / (10%)

Now, if we set x equal to 100%, we get:

y = (100%) / (10%)

Simplifying this fraction gives us:

y = 10

Since y is equal to 10, the percentage of y is 1000%.

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Answer:

Step-by-step explanation:

You want the measures of the numbered angles in the figure comprised of overlapping right triangles.

The acute angles in a right triangle are complementary, as are the two angles into which a right angle is divided.

  ∠1 +35° = 90°   ⇒   ∠1 = 55°

  ∠3 +35° = 90°   ⇒   ∠3 = 55°

The angle marked 70° is exterior to the bottom right triangle, so is equal to the sum of angles 3 and 4.

  ∠3 +∠4 = 70°

  55° +∠4 = 70°   ⇒   ∠4 = 15°

Angle 2 is the other acute angle in the bottom right triangle, so ...

  ∠2 = 90° -∠4 = 90° -15°

  ∠2 = 75°

From the concept of algebra of venn diagram we obtain that
P(A or B) = 0.75.

A set is a collection of well-defined objects.

A subset contains all the elements or few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

From set theory, we know that N(A∪B) = N(A) + N(B) - N(A∩B).

It states that N(A) or N(B) is the sum of N(A) and N(B) minus the common intersecting region N(A∩B) as we have already considered the region in the sum of N(A) and N(B) twice.

Similarly, P(A or B) = P(A) + P(B) - P(A∩B)>

Therefore, P(A or B) = 0.50 + 0.40 - 0.15.

P(A or B) = 0.90 - 0.15.

P(A or B) = 0.75.

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We will write greater than 20 using Inequality sign as ( > 20).

The first number in every inequality sign tells us how the first and second numbers relate to one another, so  > 20 means "A number is greater than 20."

In mathematics, "inequality" refers to a relationship between two expressions or values that are not equal to one another.

Greater than and less than symbols are used to indicate whether one number is greater than or less than another. The greater than symbol (>) is used when the first number exceeds the second number. The less than symbol (<) is used when the first number is less than the second number.

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The symbol that represents an expression in statistics are That is option A , B and C.

Statistics is defined as the area of study that is concerned with the collection, organization, analysis, interpretation, and presentation of data.

The importance of statistics is that it helps in conducting research, evaluating results, developing critical thinking and making informed decisions.

The various symbols use in statistics include the following:

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Interest earn is $6,371.45 ≅ $6,370 (round to the nearest cent)

To receive as return for effort and especially for work done or services rendered. : to bring in by way of return.

When you earn interest on your interest earnings as well as the money you have saved, this is known as compound interest. A = P is the compound interest formula.

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

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

$530 for 9 years at 33% interest each year using the compound interest formula, where t = number of time periods elapsed

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

A= 530 (1 + 0.33/1)^9

A = $6,901.45

So to find interest I = A-P

I = $6901.45 -$530

I =  $6,371.45

Interest earn is $6,371.45 ≅ $6,370 (round to the nearest cent)

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Answer:5.6

Step-by-step explanation:

Answer: $1.40/4 = $0.35/apple

(i) Large Table Required are 3 and Small Table required are 8

(ii) Price of Student Ticket is $5.5 and Adult Ticket is $7.5

What is Linear Equation in Two Variable?

A linear equation in two variables is one that is stated in the form ax + by + c = 0, where a, b, and c are real integers and the coefficients of x and y, i.e. a and b, are not equal to zero.

Solution:

(i)

Seats in Large Table = 12

Cost of Large Table = $50

Seats in Small Table = 8

Cost of Small Table = $25

Let, Number of Large Tables = x

Number of Small Tables = y

According to the Question:

12x + 8y = 100

50x + 25y = 350

x = 3, y = 8 (refer graph 1)

(ii)

Cost of Student Ticket = x

Cost of Adult Ticket  = y

According to the Question:

16x + 3y = 110.5

12x + 4y = 96

x = $5.5, y = $7.5 (refer graph 2)

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Hannah's thought that the original photo is congruent and similar to the final image is false

From the question, we have the following parameters that can be used in our computation:

Translation creates congruent and similar shapes

However, dilation only create similar shapes,  but not congruent shapes

This means that the shapes are similar, but not congruent

Hence. Hannah is incorrect

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By using the concept of conjugate, it can be calculated that

Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]

What is conjugate?

Conjugating is the process of changing a verb in a sentence to match the person, number, gender, tense, mood, and voice of the subject. For example, the verb "to walk" changes to "walked" when conjugated in the past tense. Conjugation is important in many languages, including English, as it helps to make communication more precise. Conjugation involves making changes to the base form of the verb, such as adding suffixes or prefixes, or changing the spelling of the word. Different languages have different rules for conjugating verbs, so it is important to understand the language’s system of conjugation before attempting to use it.

Here the expression is [tex]x + \sqrt{y}[/tex]

Conjugate of [tex]x + \sqrt{y}[/tex] is [tex]x - \sqrt{y}[/tex]

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Answer:

you would take 249.50 and subtract 26.00 from it. then you would divide it by 3 for the initial cost of each dress

Step-by-step explanation:

249.50-26.00=223.05 then divide

223.05÷3= 74.05

hope that helped !

Identifying the issue, considering potential solutions, and selecting the best course of action are the three primary components of problem-solving.

Mathematical issues can be solved in a variety of methods; however, a three-step technique is a streamlined approach that can assist anybody in solving even the most challenging problem.

Three steps is here:

1. Create a mental image of the issue

Daydreaming and the mental imagery that takes place when reading a book are two frequent instances of mental pictures. The images that athletes conjure up during practice or before a competition, describing each step they will take to achieve their objective, are another example.

2. The strategy should be used to solve the issue

A strategy is a way to manipulate numbers, use connections and interactions between numbers to solve an issue. For each procedure, there are a few key tactics. The first thing you do with the statistics is frequently used to label a technique.

3. Conclude by fixing the issue

A conclusion is a claim made after a set of premises and a set of logical principles known as syllogisms have been considered. Deduction is the process of inferring conclusions from premises and syllogisms.

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If the two triangle are overlapping , then they are congruent.

The term congruent refers the triangles that have three sets of corresponding congruent sides and three sets of corresponding congruent angles.

Here we have to prove that the two overlapping triangles are congruent.

Here we know that the two triangle are overlappling.

Now we have to do the following process to prove that the overlapping triangles are also congruent.

As per the reflexive property of congruence, here when overlapping triangles share a common side or angle because the reflexive property of congruence states that a segment or angle is congruent to itself. Therefore, according to the geometry when two triangles share a side or angle this can be used to prove one set of congruent sides/angles.

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