Find The Values Of X and Y

To enlarge this vector \((-12, 18)\) to \(50\)%, or \(-6\) and \(9\), respectively.

In science, anything with both a direction as well as a magnitude is referred to as a vector. They are typically represented by pointing arrows, the height of which denotes the size of the vector.

Lines and forms that have been mathematically specified make up vector pictures. They may therefore be scaled up and down without sacrificing any quality, according to this. They are frequently employed for drawings and logos.

Just multiply every component by half to reduce a vectors \((-12, 18)\) by only a ratio of one-half.

So, the dilated vector is:

\(-12*\frac{1}{2} ,=-6\\18*\frac{1}{2}=9\)

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Answer:

see below

Step-by-step explanation:

∠1 = 61°

∠2 = 119°

∠3 = 61°

∠4 = 119°

∠5 = 119°

∠6 = 61°

∠7 = 119°

-------------------------------

∠1 = 61°   = as given

∠2 = 119° = ( 180 - 61 ) = 119°

∠3 ≅ ∠1  opposite angles are equal (congruent)

∠4 ≅ ∠2  opposite angles are equal (congruent)

∠5 ≅ ∠2 or parallel

∠6 ≅ ∠3 ≅ ∠1

∠7 ≅ ∠5

\(\left\lceil\begin{matrix}1 & 0 & 0 & 1 \\-2 & 0 & 0 & 2 \\5 & -2 & 3 & -2 \end{matrix}\right\rceil\)

These three vectors are linearly independent and can span the space generated by the original set of vectors.

The vectors given are:
v₁ = (1, 0, 0, 1)
v₂ = (-2, 0, 0, 2)
v₃ = (5, -2, 3, -2)
v₄ = (15, -8, 12, -6)
v₅ = (14, -6, 9, -5)

To find a basis for the space spanned by these vectors, we need to determine which vectors are linearly independent.

A set of vectors is linearly independent if none of the vectors can be expressed as a linear combination of the others.

We can start by setting up an augmented matrix using these vectors:

\(\left\lceil\begin{matrix}1 & -2 & 5 & 15 & 14\\0 & 0 & -2 & -8 & -6\\0 & 0 & 3 & 12 & 9\\1 & 2 & -2 & -6 & -5\end{matrix}\right\rceil\)

We can then perform row operations to reduce the matrix to row-echelon form:

\(\left\lceil\begin{matrix}1 & -2 & 5 & 15 & 14\\0 & 0 & 3 & 12 & 9\\0 & 0 & 0 & -2 & -1\\0 & 0 & 0 & 0 & 0\end{matrix}\right\rceil\)

From the row-echelon form, we can see that the first three columns form a linearly independent set.

Therefore, a basis for the space spanned by the given vectors is:

\(\left\lceil\begin{matrix}1 & 0 & 0 & 1 \\-2 & 0 & 0 & 2 \\5 & -2 & 3 & -2 \end{matrix}\right\rceil\)

These three vectors are linearly independent and can span the space generated by the original set of vectors.

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From the row-echelon form for the space spanned by the given vectors the basis is \(\[\begin{bmatrix}1 & 0 & 0 \\1 & -2 & 0 \\0 & 2 & 5 \\\end{bmatrix}\]\).

The basis for the space spanned by the given vectors can be determined by finding a set of linearly independent vectors that span the same space. The given vectors are: \(\[ \begin{bmatrix}1 & 0 & 0 \\1 & -2 & 0 \\0 & 2 & 5 \\-2 & 3 & -2 \\15 & -8 & 12 \\-6 & 14 & -6 \\9 & -5 & 0 \\\end{bmatrix}\].\)

To find a basis, we can perform row operations on the given matrix to obtain its row-echelon form. After performing the row operations, we get:

\(\[ \begin{bmatrix}1 & 0 & 0 \\0 & 1 & 0 \\0 & 0 & 1 \\0 & 0 & 0 \\0 & 0 & 0 \\0 & 0 & 0 \\0 & 0 & 0 \\\end{bmatrix}\]\)

From the row-echelon form, we can observe that the first three rows are linearly independent, while the remaining rows are all zeros. Therefore, a basis for the space spanned by the given vectors is the set of three vectors corresponding to the first three rows of the row-echelon form:

\(\[\begin{bmatrix}1 & 0 & 0 \\1 & -2 & 0 \\0 & 2 & 5 \\\end{bmatrix}\]\).

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1. Subtract 2 from both sides of the equation

4x + 2 = 7x - 13

4x + 2 - 2 = 7x - 13 - 2

2. Simplify

4x + 2 - 2 = 7x - 13 - 2 -----> 4x = 7x - 13 - 2 -----> 4x = 7x - 15

3. Subtract 7x from both sides of the equation

4x = 7x - 15

4x - 7x = 7x - 15 - 7x

4. Simplify

4x - 7x = 7x - 15 - 7x -----> -3x = 7x - 15 - 7x -----> -3x = -15

5. Divide both sides of the equation by the same term

-3x = -15

-3x/-3 = -15/-3

6. Simplify

-3x/-3 = -15/-3

x = -15/-3

x = 5

7. Solution

x = 5

Hope that helps! :D

The sum of the measures of the exterior angles of any polygon, including a triangle, is always 360 degrees.

We have,

An exterior angle of a polygon is formed by extending one of its sides outward.

In the case of a triangle, when we extend each side, we create three exterior angles.

These exterior angles are located outside the triangle.

The key concept to understand is that the sum of the exterior angles of any polygon is always 360 degrees.

This property holds true for all polygons, regardless of their shape or size.

To visualize this, imagine starting at any vertex of a triangle and moving along its sides while measuring the exterior angles.

As you move around the triangle, the sum of the exterior angles will always add up to 360 degrees.

This is because, at each vertex, the exterior angle supplements the interior angle to form a straight angle of 180 degrees.

In a triangle, each interior angle measures less than 180 degrees.

So, when we extend each side to create the exterior angles, they collectively compensate for the deficiency of the interior angles, resulting in a sum of 360 degrees.

Therefore,

The sum of the measures of the exterior angles of a triangle is always 360 degrees.

This principle holds true for all polygons, making it a fundamental property of geometry.

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Nina will take the shortest time finishing her book.

Division is the opposite of multiplication. If you divide 12 into three equally sized groups, you will get four in each group if the three groups of four sum up to 12, which they do when you multiply. The main goal of division is to count the total number of evenly distributed groups or the total number of people in each group following a fair distribution.

Let's calculate how many pages each person reads in one day:

Then we divide the number of pages of each book by reading speed of the respective person:

Thus Nina will take the shortest time finishing her book.

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Answer:

-135, -134, -133

Step-by-step explanation:

Hi there!

Let x be equal to the first integer in the set of three consecutive integers.

Let x+1 and x+2 be the consecutive integers.

We're given that they have a sum of -402.

We can construct an equation:

\((x)+(x+1)+(x+2)=-402\)

Combine like terms:

\(x+x+1+x+2=-402\\x+x+x+1+2=-402\\3x+3=-402\\3x=-405\\x=-135\)

Therefore the first integer is -135.

The next two consecutive integers after -135 is -134 and -133.

Therefore, the three consecutive integers are -135, -134 and -133.

I hope this helps!

Answer:

.

.

.❥︎ᴀᴀɴᴋʜ ᴜᴛʜɪ ᴍᴏʜᴀʙʙᴀᴛ ɴᴇ ᴀɴɢᴅᴀɪ ʟɪ ,

.ᴅɪʟ ᴋᴀ sᴀᴜᴅᴀ ʜᴜᴀ ᴄʜᴀɴᴅɴɪ ʀᴀᴀᴛ ᴍᴇ ❣︎

.

.

Hi! The distinct letters in the word "definition" can be specified as a set using the roster method, which lists the unique elements in the set within curly brackets. In this case, the set of distinct letters is {d, e, f, i, n, t, o}.

To specify the set by roster, we first need to define what a roster is. In terms of mathematics, a roster is simply a list of elements. In this case, we are looking for the distinct letters in the word definition. The word definition has nine letters, but only six of them are distinct. Those letters are D, E, F, I, N, and T.

Therefore, the set specified by roster would be {D, E, F, I, N, T}. This set can also be written using set-builder notation as {x | x is a distinct letter in the word "definition"}. Answering this question in more than 100 words, we can also note that understanding how to specify a set by roster is an important concept in discrete mathematics and set theory. It allows us to define sets using a finite number of elements and to clearly define what elements are included in the set.
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Answer:

I think it's the 3rd one

Answer:

Step-by-step explanation:

Equation of a line giving 2 points is

y-y1=m(x-x1) where m is the slope and (x1,y1) is one of the points.

First we have to find the slope using formula

(y2-y1)/(x2-x1) where (x1,y1) and (x2,y2) are the points given

Slope m is (4-13)/(8--4) =-9/12 = -3/4

Looking at the answer choices, the only slope intercept equation that use the slope -3/4 is answer choice A

Answer:

15 × 14 = 210 of the 2,800 admitted patients remained longer than a week, so 2,800 - 210 = 2,590 of those patients were released within one week.

lm pretty sure the answer is d

The probability that the mean rent is more than $1200 is 0.0488 or 4.88%.Hence, the correct option is (B) 0.0488.

Given that the mean rent of a 3-bedroom apartment in Orlando is $1250. You randomly select 13 apartments around town. The rents are normally distributed with a standard deviation of $290. We need to find the probability that the mean rent is more than $1200.Steps to solve the problem: The sample size is 13 which is less than 30, and the population standard deviation is known.

Therefore, we use the t-distribution to find the required probability.

The formula to calculate t-score is given by:

t-score = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

Where, Sample mean = $1200 Population mean = $1250 Population standard deviation = $290Sample size = 13t-score = ($1200 - $1250) / ($290 / sqrt(13))

t-score = -1.47

Using the t-table, with a degree of freedom of 12 at a significance level of 0.05,

we get the t-value as -1.782.So, P ( t > t-score ) = P ( t > 1.47 ) = P ( t > 1.782 ) [ from t-table ] = 0.0488

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There are 3! for an individual words so that the consonants (ppl) and vowels (eoe) alternate one after the other.

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

The probability is typically defined as the proportion of positive outcomes to all outcomes in the sample space. Probability of an event P(E) = (Number of favorable outcomes) /(Sample space) is how it is stated.

There are 3! for an individual words so that the consonants (ppl) and vowels (eoe) alternate one after the other.

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Answer:

10

Step-by-step explanation:

substitute the given values into the expression

2(x + z) - y

= 2(6 + 3) - 8

= 2(9) - 8

= 18 - 8

= 10

The graph of the equation with a double root at -2 is a parabola that touches the x-axis at -2 and opens upward. It represents a quadratic function that has a repeated solution at x = -2.

When a quadratic equation has a double root at a particular value, it means that the graph of the equation touches the x-axis at that point but does not cross it. In this case, the double root is at -2, which means that the graph touches the x-axis at x = -2.

Since the root is a double root, the graph is a parabola that opens upward. This means that as you move away from the double root in either direction, the graph rises. However, it does not cross the x-axis again. The vertex of the parabola is located at the double root, which in this case is (-2, 0).

By sketching the graph, you can visually represent the behavior of the equation and understand how it relates to the given double root.

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The number of conjugacy classes in \(\(S_n\)\) is equal to the number of partitions of \(\(n\)\), which can be obtained using combinatorial methods.

The conjugacy classes of \(S_n\), the symmetric group on a set with \(n\) elements, can be described as follows:

1. Identity Element: The conjugacy class of the identity element consists solely of the identity element itself, which is the permutation that leaves all elements unchanged.

2. Cycles of Length \(k\): For any integer \(k\) such that \(1 \leq k \leq n\), the conjugacy class of \(S_n\) contains all permutations that consist of disjoint cycles of length \(k\). The number of cycles in each permutation can vary, but the total length of the cycles must equal \(k\). For example, in \(S_4\), the conjugacy class containing 3-cycles consists of permutations like (123), (124), (134), (234), etc.

3. Permutations with the Same Cycle Structure: Permutations that have the same cycle structure form a conjugacy class. The cycle structure refers to the lengths of the cycles and their multiplicities. For example, in \(S_3\), the conjugacy class containing 2-cycles consists of permutations like (12), (13), (23), (123), (132), etc.

4. Transpositions: Transpositions are permutations that exchange two elements and leave all other elements unchanged. Each transposition forms its own conjugacy class. In \(S_n\), there are \(\binom{n}{2}\) possible transpositions.

These are the main types of conjugacy classes in \(S_n\). The justification for this classification lies in the fact that conjugate elements in a group have the same cycle structure. Two permutations are conjugate if and only if they have the same cycle type, meaning that they can be transformed into each other by relabeling the elements.

It is important to note that the number of conjugacy classes in \(S_n\) is equal to the number of partitions of \(n\), which can be obtained using combinatorial methods.

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Which conjugacy classes of the symmetric group Sn seprates into 2 classes inside the alternating group An?

This happens for some classes which contains only elements of An.

Randomization is used within matching designs to option B) assign units within pairs to treatments.

Matching design refers to the process of selecting individuals or entities for comparison in an observational study. It is commonly used in retrospective case-control studies to avoid potential confounding variables. In matching, a control is chosen based on its similarities to the subject in question. Pairs are created and then one member of each pair is assigned to the treatment group and the other to the control group.

Randomization within matching designs It is frequently critical to randomize assignment to treatments for many experimental designs, but not so much for matching designs. In matching designs, randomization is still a useful tool, but it is used to assign units within pairs to treatments. Randomization is a vital component of the scientific method, as it helps to prevent the outcomes of a study from being influenced by confounding variables.

Randomization within matching designs should follow the same principles as in a typical randomized experiment, and all sample units should have an equal chance of being chosen for a treatment or control group. Hence, option B, assign units within pairs to treatments, is the right answer.

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Answer:

2-1

4-2

6-3

8-4

Step-by-step explanation: It is a pattern

Answer:

6 adults to 3 children

8 adults to 4 children

Step-by-step explanation:

it is a pattern

Answer:

The inequality is  3 > -6

Step-by-step explanation:

on a number line, first draw a circle over the number  Then if the sign includes equal to (≥ or ≤), fill in the circle. If the sign does not include equal to (> or <), leave the circle unfilled in. and then  take your number that you have filled in and put a > if the line goes to the left and a < if it goes to the right!

Kinda long but i hope this helps! Brainliest plz!

Answer:x+42+3x = 90

Combine like terms:

3x+x = 4x

42+4x = 90

Subtract 42 to both sides

90-42 = 48

Divide 4 by 48

48/4 = 12

X = 12

100% right

Step-by-step explanation:

The value of y in the triangle is 12

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

The triangle

On the triangle, we have the following equivalent ratio

y : 18 = 10 : 15

Using the above as a guide, we have the following:

Express ratio as fraction

This gives

y/18 = 10/15

So, we have

y = 18 * 10/15

Evaluate

y = 12

Hence, the value of y is 12

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Answer:

length of side of square = (4x - 5) inches

Step-by-step explanation:

We are given;

Area of square = 16x² – 40x + 25

Let's find the roots of this quadratic equation [-b ± √(b² - 4ac)]/2a

Thus;

x = [-(-40) ± √((-40)² - 4(16 × 25)]/(2×16)

x = [40 ± √(1600 - 1600)]/32

x = (40 ± 0)/32

x = 40/32

x = 5/4

Thus, the factors of the polynomial are;

(4x - 5)²

So,

Area = 16x² – 40x + 25 = (4x - 5)²

Since, the right hand side is (4x - 5)² and area of square is (length of side)², thus we can say that length of side of square is (4x - 5) inches

The length of each leg of a right triangle given that one angle is 22° and the length of the hypotenuse is 10 inches are 3.75 and 9.27 inches respectively.

In order to determine the length of the opposite side and adjacent side, we would apply both the cosine and sine trigonometry ratio because the given side lengths represent the hypotenuse of a right-angled triangle.

cos(θ) = Adj/Hyp

Where:

By substituting the parameters into the sine trigonometry ratio formula, we have the following;

sin(θ) = Opp/Hyp

sin(22) = y/10

y = 10sin(22)

y = 3.75 inches.

For the adjacent side, we have:

cos(θ) = Adj/Hyp

cos(22) = x/10

x = 10cos(22)

x = 9.27 inches.

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Answer:

the first one

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

it is going to be answer 2 because he put more in at the end

By calculating the given equations with points none of the equation represents equation of this graphed line.

What is the equation of the line?

The equation of a straight line is y=mx+c y = m x + c m is the gradient and c is the height at which the line crosses the y -axis, also known as the y-intercept.

We have given the,

y = 2x+2

y=-2x-2

y=6x+6

y=-6x-6

And, the graph.

From the line in the graph we can take the cordinate points which represents the equation of line.

point (1, 2)

By putting this point we can decide the given equation of line:

y=2(1)+2 = 4

y=-2(1)-2 = 0

y=6(1)+6 =12

y=-6(1) - 6 =-12

Hence, by calculating the given equations with points none of the equation represents equation of this graphed line.

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Answer:

\( p(s) = -24s^2 +2200 s -18000\)

If we use the valie of s =60 we have

\( p(60) = -24 (60)^2 +2200*60 -18000\)

And after solve we got:

\( p(60)= -86400 +132000 -18000 =27600\)

So then the best option for this case would be:

$27,600

Step-by-step explanation:

Using the following info in order to complete the problem:

p(s)=-24s^(2)+2200s-18000

$112,560

$27,600

$111,120

$236,400

$14,240

We have the following function given:

\( p(s) = -24s^2 +2200 s -18000\)

If we use the valie of s =60 we have

\( p(60) = -24 (60)^2 +2200*60 -18000\)

And after solve we got:

\( p(60)= -86400 +132000 -18000 =27600\)

So then the best option for this case would be:

$27,600