I need to find the ordered pairs

Given data:

The given figure is shown.

The given coordinate of B is (3, 4) and the coordinate of B'(-5, 4).

It can be understand take first reflection about y-axis, then move 2 units left.

Thus, the option (B) is correct.

Given,A = [X X X]and B = [-2 X 2].

The det(A) = 2 × 4 = 8

The determinant of a matrix does not depend on the order of its rows and columns. The first row of the matrix A and the last row of the matrix B have only one entry X in common,

so the product of these entries (X × X × X) does not affect the value of the determinant det(A).

Therefore, we can replace both A and B with the following matrices without changing the given condition:

A = [1 1 1]and

B = [-2 1 2].

Note that the sum of each row of A and B is 3.

Therefore, if we take X = 1, then the sum of the first row of A and the first row of B is 3, so we can take X = 1 and getA = [1 1 1]and B = [-2 1 2].

Therefore, the given conditions are satisfied by X = 1.

We know that the transition matrix from one basis to another is the matrix that contains the coordinates of the basis vectors of the second basis in terms of the basis vectors of the first basis.Therefore, the given transition matrix [1 P=2 0 2 305 is the matrix that contains the coordinates of u₁, u₂, and u₃ (basis vectors of S) in terms of v₁, v₂, and v₃ (basis vectors of the standard basis).

Therefore, we have

v₁ = 1u₁ + 2u₂v₂ = 0u₁ + 2u₂ + 3u₃v₃ = 5u₂

This means that

u₁ = (1/2)v₁ - v₂/4u₂

= (1/2)v₁ + v₂/4 + v₃/5u₃

= (1/5)v₃

Therefore, the coordinates of the vector u₃ (basis vector of S) in terms of the basis vectors of S are [0 0 1]T.

The given set S={(2,2,2),(2,0,1),(1,0,1)) is a basis for R if and only if the vectors in S are linearly independent and span R.The Gram-Schmidt process is a procedure for orthonormalizing a set of vectors.

If we apply this process to the given set

S={(2,2,2),(2,0,1),(1,0,1)), then we get the following orthonormal basis:{(√3/3, √3/3, √3/3), (0, -√2/2, √2/2), (0, 0, √6/6)}

The first vector is obtained by normalizing the first vector of S.

The second vector is obtained by subtracting the projection of the second vector of S onto the first vector of S from the second vector of S and then normalizing the result.

The third vector is obtained by subtracting the projection of the third vector of S onto the first vector of S from the third vector of S, subtracting the projection of the third vector of S onto the second vector of S from the result, and then normalizing the result.

T: R' × R' → R' is a map from the Euclidean inner product space R' to itself defined by

T(v) = (v, v, v) for all vectors v ∈ R'.

Therefore, T is a linear operator, because

T(c₁v₁ + c₂v₂) = (c₁v₁ + c₂v₂, c₁v₁ + c₂v₂, c₁v₁ + c₂v₂)

= c₁(v₁, v₁, v₁) + c₂(v₂, v₂, v₂)

= c₁T(v₁) + c₂T(v₂)

for all vectors v₁, v₂ ∈ R' and scalars c₁, c₂ ∈ R.

The kernel of T is the set of all vectors v ∈ R' such that

T(v) = 0.

Therefore, we haveT(v) = (v, v, v) = (0, 0, 0)if and only if v = 0.

Therefore, the kernel of T is {0}, which is a basis of ker(T).

The determinant of a linear operator is the product of its eigenvalues.

Therefore, we need to find the eigenvalues of T.

The characteristic polynomial of T isp(λ) = det(T - λI)

= det[(1 - λ)², 0, 0; 0, (1 - λ)², 0; 0, 0, (1 - λ)²]

= (1 - λ)⁶

Therefore, the only eigenvalue of T is λ = 1, and its geometric multiplicity is 3.

Therefore, the determinant of T is det(T) = 1³ = 1.

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Answer:

0.125 m²

Step-by-step explanation:

The area of a rectangle is the product of its length and breadth. Therefore:

area of the rectangle = length (l) × breadth (b) = 1 m².

l × b = 1

A triangle is cut off from that rectangle along a line connecting the midpoints of two adjacent sides, therefore the base of the triangle = length of rectangle/2 and the height of triangle = breadth of rectangle/2.

Area of triangle = 1/2(base × height) = \(\frac{1}{2}*\frac{l}{2}*\frac{b}{2}=\frac{1}{8}lb\)

since lb = 1:

Area of triangle = \(\frac{1}{8}*1=0.125m^2\)

Answer:

60% of 125

Step-by-step explanation:

60% of 30 = 18

60% of 45 = 27

60% of 125 = 75

60% of  450 = 270

branliest pls

Answer:

125

Step-by-step explanation:

i took the test :D

112.8 is the the total sound power, when three drill presses are operating

A relation is a function if it has only One y-value for each x-value.

Given that a function P(n) = 108 + 10 log(n) gives the total sound power in decibels when n drill presses are operating in a factory.

We need to find the total sound power, to the nearest decibel, when three drill presses are operating

We have to consider n as 3

P(3) = 108 + 10 log(3)

=108+10×0.477

=108+4.77

=112.77

Hence, 112.8 is the the total sound power when three drill presses are operating

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Answer:

D. it must be on the left due to it being negative

Answer:

A

Step-by-step explanation:

The number 1.368 is approximately 2 more than its cube.

To find a real number that is exactly 2 more than its cube, we can set up the equation:

x = x^3 + 2

Rearranging the equation, we have:

x^3 - x + 2 = 0

To find the solution to this equation, we can use numerical methods such as Newton's method or trial and error. Applying trial and error, we can find one such value accurate to three decimal places:

x ≈ 1.368

If we substitute this value into the equation x = x^3 + 2, we get:

1.368 ≈ (1.368)^3 + 2

1.368 ≈ 2.001

The number 1.368 is approximately 2 more than its cube.

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The explicit formula for the nth term of the sequence 14,16,18,... is aₙ = 2n + 12.

What is an explicit formula?

The explicit equations for L-functions are the relationships that Riemann introduced for the Riemann zeta function between sums over an L-complex function's number zeroes and sums over prime powers.

Here, we have

Given:  the sequence 14,16,18,….

First term a₁ = 14

Common difference d = 16 - 14 = 2

Now, plug the values into the above formula and simplify.

aₙ = a₁ + d( n - 1 )

aₙ = 14 + 2( n - 1 )

aₙ = 14 + 2n - 2

aₙ = 14 - 2 + 2n

aₙ = 2n + 12

Hence,  the explicit formula is aₙ = 2n + 12.

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Answer:

1.625 pounds of butter is my best answer for this equation.

Step-by-step explanation:

I multiplied .25 by 4.5 and then added .50

Answer:

1.625 pounds of butter, or 1 12/20

Step-by-step explanation:

First, we must recognize that 4.5 times the recipe is just asking you to multiply the butter for 1 batch by the size of the batch for the bake sale. (.25 x 4.5) =1.125

Do not forget that she must make two more batches, or .5 pounds of butter.

(.25+.25=.5)

By adding the bake sale amount by the extra batches for her family we can decifer that she needs 1.625 poinds of butter. (1.125+.5=1.625pounds)

We are required to calculate how many minutes does it take Autumn to walk to work now

The number of minutes does it take Autumn to walk to work now is 25.35 minutes

Time taken to walk to work = 39 minutes

Percentage decrease = 35%

Decrease in time = 35% of 39 minutes

= 35/100 × 39 minutes

= 0.35 × 39 minutes

= 13.65 minutes

Number of minutes does it take Autumn to walk to work now

= 39 minutes - 13.65 minutes

= 25.35 minutes

Therefore, the number of minutes does it take Autumn to walk to work now is 25.35 minutes

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Answer:

25y + 15x - 0.2y - 6 +(-2) =31.8

Answer: y = x - 4

Step-by-step explanation:

Slope intercept form is y = mx + b

    Given:

-2x = -8 -2x

    Add 2x and 2y to both sides of the equation:

2y = 2x - 8

    Divide both sides of the equation by 2:

y = x - 4

Answer:

Assuming that (3x - 3) and 6 are the sides of the rectangle,

Area:

A = l × w

y = (3x - 3) × (6)

y = 18x - 18

Perimeter:

P = 2l + 2w

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

y = 6x - 6 + 12

y = 6x + 6

The required linear equation for the area and perimeter of the rectangle is y = 18[x - 1] and z = 6[x + 1] respectively.

Given that, to determine the linear equation that represents the area and a linear equation that represents the perimeter of the rectangle.

The rectangle is 4 sided geometric shape whose opposites are equal in length and all angles are about 90°.

here,
Length  = 3x + 3
Width = 6

Area of the rectangle = y, = length × width
y = [3x - 3 ] × [6]
y = 18x - 18 = 18[x -1]

Perimeter of the rectangle = 2[length + width]
z = 2 [3x - 3 + 6]
z = 2 [3x + 3]
z = 6[x + 1]

Thus, the required linear equation for the area and perimeter of the rectangle is y = 18[x - 1] and z = 6[x + 1] respectively.

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Answer:

a. 300 minutes.

b. $53

explanation:

make equations from given information.

equation 1 from plan A :

20 + 0.11(n)

equation 2 from plan B :

14 + 0.13(n)

Solve them simultaneously,

14 + 0.13(n) = 20 + 0.11(n)

0.13(n) - 0.11(n) = 20 - 14

0.02(n) = 6

n = 300

insert n = 300 in any of the equation, to find cost.

14 + 0.13(n)

14 + 0.13(300)

$53

Answer:

x - 27

Step-by-step explanation:

Our goal here is to solve for x.

Start by performing the indicated multiplication:

-5(x+4) + -3x + -9x+-7  =>  -5x - 20 - 3x + 9x - 7

Combine like terms:  x - 27

Answer:

\(-5(x+4) + -3x + -9x+-7\)

\(\longmapsto -5\left(x+4\right)+\left(-3\right)x+\left(-9\right)x+\left(-7\right)\)

\(\longmapsto -5\left(x+4\right)-3x-9x-7\)

\(\longmapsto -5(x+4)=-5x-20\)

\(\longmapsto -5x-20-3x-9x-7\)

\(\longmapsto =-17x-27\)

\(ANSWER:=-17x-27\)

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

hope it helps....

have a great day!!

It takes a train going 50 mph approximately 11/2 miles to stop safely.

The distance a train takes to come to a stop can be determined by several factors, including the speed of the train, the weight of the train, the condition of the brakes and the track, and the reaction time of the engineer.

In general, a train going 50 mph will take about 1 1/2 miles or 8,000 feet to stop safely. This is because a train moving at 50 mph is traveling at about 75 feet per second, and it takes a significant distance to slow down a heavy object moving at such a high speed. It's important to note that this is an estimation, and the actual stopping distance may vary depending on the specific conditions.

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a) To maximize its net savings, the company should use the new machine for 7 years.  b) The net savings during the first year of use of the machine are $405 (rounded off to the nearest dollar).  c) The net savings over the period determined in part a are $1,833.33 (rounded off to the nearest cent).

Step-by-step explanation: a) To determine for how many years should the company use the new machine to maximize its net savings, we need to find the value of x that maximizes the difference between the savings and the costs.To do this, we need to first calculate the net savings, N(x), which is given by:S'(x) - C'(x) = 175 - x² - (x² + 11x) = -2x² - 11x + 175To find the maximum value of N(x), we need to find the critical values, which are the values of x that make N'(x) = 0:N'(x) = -4x - 11 = 0 ⇒ x = -11/4The critical value x = -11/4 is not a valid solution because x represents the number of years of operation of the machine, which cannot be negative. (i.e., not use it at all).However, this answer does not make sense because the company would not introduce a new machine that it does not intend to use. Therefore, we need to examine the concavity of N(x) to see if there is a local maximum in the feasible interval.

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The probability that it has a hairline crack is 19/27.

Given that;

In a shipment of 54 vials, only 16 do not have hairline cracks.

Let shipment of 54 Vials;

x(s) = 54

Let,' A ' be the event that selects 16

x(A) = 16

P(A) = x(A) / x(s)

       = 16/54

But only 16 don't have hairline Crakes;

To solve a given case;

The probability that it has a hairline crack is:

P(A') = 1 - P(A)

       = 1- 16/54

P(A') = 19/27

Hence, the probability that it has a hairline crack is 19/27.

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Answer:

20 Quarters = $5, add 10 dimes to make it $6 and 10 x 2 = 20 so your answer is 10 dimes

Step-by-step explanation:

Answer:

Question 3: 93    Question 4: -18

Step-by-step explanation:

Use Order of Operations (BEDMAS - Brackets Exponents Division Multiplication Addition and Subtraction).

Question 3:

Start with the numbers inside the brackets.

3^2 (4+6) + 3

= 3^2 (10) + 3

Then, solve the exponents.

= 9 (10) + 3

Multiply 9 and 10.

= 90 + 3

Add the numbers.

= 93

Question 4:

Again, start with the brackets.

3 (4+2) - 6^2

= 3 (6) - 6^2

Then, solve the exponent.

= 3 (6) - 36

Multiply 3 and 6.

= 18 - 36

Subtract the numbers.

= -18 (You can do 36 - 18 which is 18, then add the negative sign)

Answer:

\({ \rm{ \sqrt{ \frac{1 + \cos(x) }{1 - \cos(x) } } }} \\ \\ \)

- Rationalize the denominator of the above expression;

\({ \rm{ = \sqrt{ \frac{(1 + \cos(x)).(1 + \cos(x)) }{(1 - \cos(x)).(1 + \cos(x)) } } }} \\ \\ = { \rm \sqrt{ \frac{( {1}^{2} + 2 \cos(x) + \cos ^{2}(x)) }{( {1}^{2} - { \cos }^{2}(x)) } } } \\ \\ = { \rm\sqrt{ \frac{(1 + 2 \cos(x) + { \cos }^{2} (x)) }{(1 - { \cos }^{2}(x)) } } }\)

- From the above expression, 1 - cos²x = sin²x

\( = { \rm{ \sqrt{ \frac{1 + 2 \cos(x) + { \cos }^{2}(x) }{ { \sin }^{2}(x) } } }} \\ \)

\( = { \rm{ \sqrt{ \frac{ {(1 + \cos(x)) }^{2} }{ { \sin}^{2}x } } }} \\ \\ = { \rm{ \frac{ \sqrt{(1 + \cos(x)) {}^{2} } }{ \sqrt{ { \sin}^{2} x} } }} \\ \\ = { \rm{ \frac{1 + \cos(x) }{ \sin(x) } }} \\ \\ = { \rm{ \frac{1}{ \sin(x) } + \frac{ \cos(x) }{ \sin(x) } }} \\ \\ = { \boxed{ \rm{ \: \csc(x) + \cot(x) \: }}}\)

Answer:

-9

Step-by-step explanatio

Answer:

"statement 1: The number of boys at the school is \(\frac{4}5\) of the number of girls." is true.

Step-by-step explanation:

Given:

Ratio of Number of boys to the number of girls = 4 : 5

Total number of students = 270

To find:

Number of boys in terms of number of girls = ?

Solution:

As per given statement,

Let, Number of boys = \(4x\)

Let, Number of girls = \(5x\)

Total number of students = Number of boys + Number of girls = 270

\(\Rightarrow 4x+5x =270\\\Rightarrow 9x=270\\\Rightarrow \bold{x = 30}\)

Therefore, number of boys = 4 \(\times\) 30 = 120

And, number of girls = 5 \(\times\) 30 = 150

As per Statement 1:

Finding \(\frac{4}5\) of the number of girls:

\(\dfrac{4}{5}\times 150 = 4 \times 30 = 120\) = Number of boys.

Finding \(\frac{4}9\) of the total number of students:

\(\frac{4}{9}\times 270= 4 \times 30 = 120\) = Number of boys.

Number of boys is equal to \(\frac{4}9\) of total number of students.

So, "statement 1: The number of boys at the school is \(\frac{4}5\) of the number of girls." is true.

A histogram is an effective way to present and analyze the center, shape, and spread of continuous data, allowing the student to gain a better understanding of the distribution of rent amounts in the Gainesville area.

To study the center, shape, and spread of the data for the amount spent on rent for apartments in the Gainesville area, the student would typically create a histogram.

A histogram is a type of graph that represents the distribution of continuous data by dividing it into intervals, or bins, and displaying the frequency or count of data points falling within each interval. It provides insights into the center (central tendency), shape, and spread (dispersion) of the data.

In the student's case, the amount spent on rent for apartments would be the continuous variable, and the student would group the data into intervals (e.g., rent ranges) and count the number of apartment complexes falling within each interval.

By creating a histogram, the student can visually analyze the distribution of rent amounts, identify the most common rent ranges (mode), and observe the shape of the distribution (symmetric, skewed, etc.). The histogram can also provide insights into the spread of the data, such as the range of rent amounts and the presence of outliers.

Overall, a histogram is an effective way to present and analyze the center, shape, and spread of continuous data, allowing the student to gain a better understanding of the distribution of rent amounts in the Gainesville area.

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Answer:

slope = gradient...

gradient (m) = ∆y

∆x

= -4 - -2

2 - -3

= -4 + 2

2 + 3

= -2

5

Given:

The triangle A'B'C' is the image of triangle ABC after a translation as shown in the given graph.

To find:

The rule of translation in ARROW NOTATION.

Solution:

The general rule for translation is:

\((x,y)\to (x+a,y+b)\)        ...(i)

Where, a and b are constants.

From the given graph it is clear that the coordinate of point A are (2,3) and coordinates of point A' are (4,-2).

Using (i), the image of A(2,3) is

\(A(2,3)\to A'(2+a,3+b)\)

We have, A'(4,-2).

\(A'(2+a,3+b)=A'(4,-2)\)

On comparing both sides, we get

\(2+a=4\)

\(a=4-2\)

\(a=2\)

And,

\(3+b=-2\)

\(b=-2-3\)

\(b=-5\)

Putting \(a=2\) and \(b=-5\) in (i), we get

\((x,y)\to (x+2,y+(-5))\)

\((x,y)\to (x+2,y-5)\)

Therefore, the rule in ARROW NOTATION for the given translation is \((x,y)\to (x+2,y-5)\).

The value of T'(7) obtained after taking the first differential of the function is 36.

Given the T(p) = 36(p + 1) - 1/3

Diffentiate with respect to p

T'(p) = d/dp [36(p + 1) - 1/3]

= 36 × d/dp (p + 1) - d/dp (1/3)

= 36 × 1 - 0

= 36

This means that after 7 practice sessions, the rate of change of the time it takes to perform the task with respect to the number of practice sessions is 36 minutes per practice session.

Therefore, T'(p) = 36.

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The effective rate of interest his savings account has to earn is 1776%.

The amount of total deposits made by Peter in nine months would be:Amount of deposits in 9 months =\($1075 + $1075 + $1075 = $3225\)

Now, in order to reach a total of \($3300\)in nine months, the interest earned on the deposits should be:Interest earned in 9 months =\($3300 - $3225 = $75\)

effective rate of interest :ERI = (1 + R/n)^n - 1

Where, R = Rate of interest, n = number of times interest is compounded per year.

Now, since the deposits are being made every three months, there will be three deposits made in nine months. Therefore, the number of times interest will be compounded in one year would be 4. i.e., the deposits are made quarterly and there are four quarters in a year.

So, the formula for the amount after n years compounded quarterly would be given as:A = P(1 + (R/4)/100)^(4n)

\(3300 = 1075(1 + R/400)^(4(3/12))3300/1075 = (1 + R/400)^(4(3/12))\)

Taking logarithm of both sides:\(ln(3.07) = ln(1 + R/400)^(4/3)3ln(3.07) = 4/3 ln(1 + R/400)ln(3.07^(3/4)) = ln(1 + R/400)1.865 = ln(1 + R/400)\)

the antilogarithm of both sides\(:e^1.865 = 1 + R/4005.44 = 1 + R/400R/400 = 5.44 - 1R/400 = 4.44R = 4.44 × 400R = 1776\)

The effective rate of interest his savings account has to earn is 1776%.

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The journal entry for the July 31 sales and November 11 cash payment is shown below .

In the question ,

it is given that ,

the amount for which Qantas Industries sold electronics during July under a nine-month warranty is = $325000  ,

cost to repair defects is = 4.5 percent of sales price .

So , the cost to repair is = 4.5% × 325000 = $14625 .

So , the journal entry for July 31 is

Warranty expense    Debit   14625

Estimated warranty liability/warranty payable    Credit   14625

and the journal entry for November 11 is :

Estimated warranty liability /warranty payable    Debit    220 ,

                                                                Cash       Credit   220  .

Therefore , the Journal entry is shown above .

The given question is incomplete , the complete question is

Qantas Industries sold $325,000 of consumer electronics during July under a nine-month warranty. The cost to repair defects under the warranty is estimated at 4.5% of the sales price. On November 11, a customer was given $220 cash under terms of the warranty. Provide the journal entry for the estimated warranty expense on July 31 for July sales. Provide the journal entry for the November 11 cash payment .

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