Describe the relationship between the point D(6, 9) and the point A(8, 12) in terms of dilations

Answer:

Step-by-step explanation:

A square root function has a restricted domain because the square root operation is only defined for non-negative numbers. The square root of a negative number is not a real number, so the domain of a square root function is limited to non-negative values. This means that the input of a square root function must be greater than or equal to zero in order to obtain a real output.

On the other hand, a cube root function has a domain (-∞, ∞) because the cube root operation is defined for all real numbers. Unlike the square root, the cube root function can take both positive and negative inputs and still produce a real output. This is because raising a number to the power of 1/3 (cube root) results in a real number for any real input. Therefore, the cube root function has a domain that extends from negative infinity to positive infinity.

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Answer:

1200

Step-by-step explanation:

(6.4 x 103) + (5.2 x 104)

659.2+540.8

1200

So 1200 is the answer

Answer:

1200

Step-by-step explanation:

\((6.4 *103) + (5.2 * 104)\)

\(6.4*103=659.2\)

\(5.2*104=540.8\)

\(659.2 + 540.8\)

\(=1200\)

\((6.4 *103) + (5.2 * 104) = 1200\)

The statements are a. False b. True c. True d. False e. True f. False g. True h. False i. True  j. True

23. a. False. The equality AC = BC, where C is invertible, does not imply that A = B. Multiplying both sides by C^(-1) does not guarantee that A and B are equal since matrix multiplication is not necessarily commutative.

b. True. If AB = O (the zero matrix) and B is invertible, then multiplying both sides by B^(-1) gives A = O. In other words, if the product of an invertible matrix and another matrix is the zero matrix, then the other matrix must be the zero matrix as well.

c. True. If AB = C and two of the matrices A, B, and C are invertible, then the third matrix is also invertible. This is because if A and B are invertible, then their inverses exist, and multiplying AB = C on both sides by (AB)^(-1) gives C(AB)^(-1) = I, where I is the identity matrix. Thus, C is invertible.

d. False. If AB = C and two of the matrices A, B, and C are singular (non-invertible), it does not necessarily mean that the third matrix is also singular. Singular matrices can still multiply to produce a non-singular matrix.

e. True. If A^2 is invertible, then A is also invertible. This is because if A^2 is invertible, it means that the square of A has an inverse. Taking the inverse of A^2 will give (A^2)^(-1) = (A^(-1))^2, which implies that A^(-1) exists and A is invertible.

f. False. If A^3 is invertible, it does not necessarily mean that A^2 is invertible. The powers of a matrix do not have a direct relationship in terms of invertibility.

g. True. Every elementary matrix is invertible. Elementary matrices are obtained by performing a single elementary row operation on the identity matrix, and these operations are reversible.

h. False. Not every invertible matrix is an elementary matrix. Invertible matrices can have various forms and can be obtained through multiple operations, not just a single elementary row operation.

i. True. If A and B are invertible matrices, then A + B is also invertible. Moreover, the inverse of A + B is given by (A + B)^(-1) = A^(-1) + B^(-1). This can be proven by multiplying (A + B) with (A^(-1) + B^(-1)) and showing that it equals the identity matrix.

j. True. If A and B are invertible matrices, then AB is also invertible. Additionally, the inverse of AB is given by (AB)^(-1) = B^(-1)A^(-1). This can be proven by multiplying (AB) with (B^(-1)A^(-1)) and demonstrating that it equals the identity matrix.

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The complete question is:

23. Mark each of the following True or False. The statements involve matrices A, B, and C, which are assumed to be of appropriate size.

a. If AC = BC and C is invertible, then A = B.

b. If AB = O and B is invertible, then A = 0.

c. If AB = C and two of the matrices are invertible, then so is the third.

d. If AB = C and two of the matrices are singular, then so is the third.

e. If A^2 is invertible, then A^3 is invertible.

f. If A^3 is invertible, then A^2 is invertible.

g. Every elementary matrix is invertible.

h. Every invertible matrix is an elementary matrix.

i. If A and B are invertible matrices, then so is A + B, and (A + B)^(-1) = A^(-1) + B^(-1).

j. If A and B are invertible, then so is AB, and (AB)^(-1) = A^(-1)B^(-1).

The correct answer is C) The initial population at the time of the estimation

Explanation:

A mathematical function represents the relationship between two variables by showing how one increases or decreases as the other changes. In the case presented, the variables are the time in years represented by x and the population represented by f (x). In this context, the value 160.000 in column f(x) represents the population on the year 0, this means the current population or initial population when the function or estimation is created. On the other hand, other values represent the population in the future, for example, the value 173189 represents the population in 4 years.

Answer:

yes the 3ed answer in correct on ENG 2022

To prove that the sum of the interior angles of a convex n-sided polygon is (n-2) times 180 degrees, we can use the fact that any polygon can be divided into n-2 triangles by drawing n-3 non-intersecting diagonals from any one vertex.  Each triangle has interior angles that sum to 180 degrees, so the sum of the interior angles of the polygon is (n-3) times 180 degrees plus the sum of the interior angles of the last triangle. Since the last triangle is formed by connecting the two endpoints of the last diagonal with the vertex from which all the other diagonals were drawn, it has one angle that is the same as the vertex angle of the polygon (the angle between the two sides that the diagonal connects) and two angles that are supplementary to the angles adjacent to the vertex angle.

Therefore, the sum of the interior angles of the last triangle is equal to the vertex angle plus 180 degrees. Substituting this into the previous equation, we get:
sum of interior angles of polygon = (n-3) x 180 degrees + vertex angle + 180 degrees
Simplifying this expression, we get:
sum of interior angles of polygon = (n-2) x 180 degrees + vertex angle
Since the vertex angle of any convex polygon is the same for all vertices, we can say that the sum of the interior angles of a convex n-sided polygon is (n-2) times 180 degrees.  Therefore, we have proved that the sum of the interior angles of a convex n-sided polygon is (n-2) times 180 degrees, assuming that the sum of the interior angles of a triangle is 180 degrees.

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Answer:

-0.4........................

There are 9,999 natural numbers that have no more than 4 digits.

To determine the number of natural numbers that have no more than 4 digits, we consider the range of numbers from 1 to 9,999.

The natural numbers with no more than 4 digits include all numbers from 1 to 9 (which form the single-digit numbers), all numbers from 10 to 99 (which form the two-digit numbers), all numbers from 100 to 999 (which form the three-digit numbers), and all numbers from 1,000 to 9,999 (which form the four-digit numbers).

To calculate the total count, we can add the number of single-digit numbers, two-digit numbers, three-digit numbers, and four-digit numbers:

Single-digit numbers: 9 (from 1 to 9)

Two-digit numbers: 90 (from 10 to 99)

Three-digit numbers: 900 (from 100 to 999)

Four-digit numbers: 9,000 (from 1,000 to 9,999)

Adding these counts together:

9 + 90 + 900 + 9,000 = 9,999

Therefore, there are 9,999 natural numbers that have no more than 4 digits.

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Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

Now, According to the question :

What is Vertical line?

A vertical line is a line, parallel to y-axis and goes straight, up and down, in a coordinate plane. Whereas the horizontal line is parallel to x-axis and goes straight, left and right.

Is a vertical line positive or negative?

The slope of a line can be positive, negative, zero, or undefined. A horizontal line has slope zero since it does not rise vertically (i.e. y1 − y2 = 0), while a vertical line has undefined slope since it does not run horizontally (i.e. x1 − x2 = 0).

Hence, Vertical lines do not have positive slopes or negative slopes. They have undefined slopes.

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a) The moment-generating function (MGF) of X= (1/5) * [(e^(3t) - e^(-2t)) / t]

To find the moment-generating function (MGF) of X, we use the formula:

M_X(t) = E[e^(tX)]

For a uniform distribution on the interval (-2, 3), the probability density function (PDF) is constant within this interval. The PDF is given by:

f(x) = 1 / (b - a) = 1 / (3 - (-2)) = 1 / 5

Now, we can calculate the MGF:

M_X(t) = ∫[from -2 to 3] e^(tx) * (1/5) dx

= (1/5) ∫[from -2 to 3] e^(tx) dx

= (1/5) * [e^(tx) / t] [from -2 to 3]

= (1/5) * [(e^(3t) - e^(-2t)) / t]

b) To find P(X < 1), we integrate the PDF from -2 to 1:

P(X < 1) = ∫[from -2 to 1] f(x) dx

= ∫[from -2 to 1] (1/5) dx

= (1/5) * [x] [from -2 to 1]

= (1/5) * (1 - (-2))

= (1/5) * 3

= 3/5

Therefore, P(X < 1) = 3/5.

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Answer:

Your change is $2.20

Step-by-step explanation:

4 x $1.50 = $6

2 x $.90 = $1.80

$6 + $1.80 = $7.80

$10 - $7.80 = $2.20

So it's $2.20. Have a nice day :D

Answer:

$2.20

Step-by-step explanation:

4 bags of cotton candy

$1.50 x 4 = $6.00

2 soft drinks

$0.90 x 2 = $1.80

$6.00 + $1.80 = $7.80

$10.00 - $7.80 = $2.20

The value of chi-square statistic (\(X^{2}\)) is 11.26

As per the given question

the sample space of all the four cases are 30

the proportions that land upright are the same when the dropping height is 3, 5, 10, and 20 cm.

the formula of chi-squared test is

\(X^2=\sum\frac{(O_i-E_i)^2}{E}\)

where

\(X^{2}\) is chi-square

\(O_i\) is the observed value

\(E_i\) is the expected value

the upright observed value are 20,23,27,29

the upright expected values are 24.75

now

the chi-square at 3cm height is

\(X^2=\(\frac{(20-24.75)^2}{24.75}\)

=> \(X^2=0.91\)

the chi- square at 5cm height is

\(X^2=\(\frac{(23-24.75)^2}{24.75}\)

=> \(X^2=0.12\)

the value of chi-square at 10cm is

\(X^2=\(\frac{(27-24.75)^2}{24.75}\)

=>\(X^2=0.20\)

the value of chi-square at 20cm is

\(X^2=\(\frac{(29-24.75)^2}{24.75}\)

=> \(X^2=1.97\)

the not upright observed values are

10,7,3,1

the not upright expected values are 5.25

the chi-square test at 3cm height is

\(X^2=\(\frac{(10-5.25)^2}{5.25}\)

=> \(X^2=4.30\)

the chi-square test at 5cm height is

\(X^2=\(\frac{(7-5.25)^2}{5.25}\)

=> \(X^2=0.58\)

the chi-square test at  10cm height is

\(X^2=\(\frac{(3-5.25)^2}{5.25}\)

=> \(X^2=0.96\)

the chi-square test at 20 cm is

\(X^2=\(\frac{(1-5.25)^2}{5.25}\)

=> \(X^2=3.44\)

now,

the total

chi-square value at 3cm height is

=>X^2=0.91+4.30

=> \(X^{2}\)= 5.21

chi-square at 5cm height is

=> \(X^{2}=0.12+0.58\)

=> \(X^2=0.71\)

chi-square at 10cm is

=> \(X^{2}=0.20+096\)

=> \(X^2=1.16\)

chi-square at 20 cm is

=> \(X^{2}=0.73+3.44\)

=> \(X^{2}=4.17\)

now ,

the total chi-square statistic is

=>\(X^{2}=\)5.21+0.71+1.17+4.17

=>\(X^{2}=\) 11.26

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Answer:

B

Step-by-step explanation:

The 20% discount is only $6.40.

32 X .2 = 6.40

Answer:

50%

Step-by-step explanation:

Answer:

9

Step-by-step explanation:

1. Just input the x value with -180:

24 (+) -180 / 12 = answer

2. Follow PEMDAS to solve, which in this case division comes before addition:

24 + (-180 / 12)

24 + (-15)

3. Addition

24 + (-15) or 24 - 15

= 9

Therefore, 24 (+) -180 / 12 equals 9.

Answer:

-168

Step-by-step explanation:

because  f(x) = 8 - 10xg(x) = 5x + 4

(fg)(x) = (8 - 10x)(5x + 4)(fg)(x) = 40x + 32 - 50x^2 - 40x(fg)(x) = 32 - 50x^2

(fg)(-2) = 32 - 50(-2)^2(fg)(-2) = 32 - 200(fg)(-2) = -168

Answer:

1,250 millileters

Step-by-step explanation:

The computation of the number of milliters of the sports drink left is shown below:

Given that

The 2-liter sports drink is purchased

And, drank 250 millimeters and than drank one-half liter of the drink

Now convert liter to millileter

1 litre = 1000 milliliter.

2 liters = 2 × 1000 milliliters.

= 2000 milliliters.

Now the left drink would be

= (2000 - 250) - (250 × 2)

= 1,750 - 500

= 1,250 millileters

We found that the probability is approximately 0.2435. This means that there is a 27.85% chance of selecting exactly three classical songs out of the 50 sampled songs from Colin's music library

To calculate the probability that three out of 50 sampled songs from Colin's music library are classical, we need to use the binomial probability formula. The probability of getting exactly k successes (classical songs) in n trials (sampled songs) can be calculated using the formula:

P(X= k) = (nCk) * p^k * (1-p)^(n-k)

Where:

- P(X = k) is the probability of getting k successes,

- (nCk) represents the number of ways to choose k items from a set of n items,

- p is the probability of success (probability of selecting a classical song), and

- (1-p) is the probability of failure (probability of selecting a non-classical song).

In this case, n = 50, k = 3, and p = 0.08 (probability of selecting a classical song). The probability can be calculated as follows:

P(X = 3) = (50C3) * (0.08)^3 * (1-0.08)^(50-3)

Using the combination formula and performing the calculations, we find:

P(X = 3) ≈ 0.2435

Therefore, the probability that three out of 50 sampled songs are classical is approximately 0.2785.

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Answer:

275

Step-by-step explanation:

Answer:

drop the money

Step-by-step explanation:

hotdoog plss

Part (i)

1) AB is perpendicular to BC, ED is perpendicular to CD, BC = CD (given)

2) Angles ABC and CDE are right angles (perpendicular lines form right angles)

3) Angles ABC and CDE are equal (all right angles are equal)

4) Angles ACB and DCE are equal (vertical angles are equal)

5) Triangles ABC and EDC are congruent (ASA)

Part (ii)

6) AB = DE (corresponding parts of congruent triangles are equal)

Answer: The point (4, 1) is a solution to this system of equations.

Step-by-step explanation:

To determine if (4, 1) is a solution to this system, you must plug it in to both of the equations. It is in the form of (x, y); so x = 4, and y = 1

Equation #1: y = -x + 5

                     1 = -(4) + 5

                     1 = 1      <————— This is part of the solution to this equation.

Equation #2: y = 2x - 7

                      1 = 2(4) - 7

                      1 = 8 - 7

                      1 = 1       <———- This is part of the solution to this equation.

The point (4, 1) is a solution to this system of equations.

The steps to create attached screenshot of the inscribed circle of triangle ΔABC using GeoGebra tools includes;

1) Clicking on the Geometry link, under Powerful Math Apps group

2) On the opened Geometry page click on the Polygon icon and follow the instructions that come up, which is Select all vertices and then the first vertex (selected) again (a second time)

3) Once the triangle is created, select the Angle Bisector icon, under the Construct group; A message will appear, asking to Select three points or two lines, select three vertex, of the triangle created with a mouse click, with the vertex A in the center, such as BAC, or CAB a straight line representing the angle bisector of angle ∠A is created

4) Repeat the above to create the angle bisector of angle ∠B

5) Click on the Point button under the Basic Tools group, then click on the intersection of the two angle bisectors created above, the point will be automatically labelled point D

6) Click on the Perpendicular Line, icon under the Construct group, then click on point D, and then the line AB to draw the perpendicular from D to AB

7) Click on the point Point icon and then the intersection point of the perpendicular from D and AB to label the point E

8) Click on the Circle with Center basic tool and then points D and E above, to create the inscribed circle of triangle ΔABC

9) Select the Segment tool, then select the center of the circle and a point

on the circumference. Click on the label, from the pop up options, select

the label option AA then change the label of the segment created to Radius

and select Show Label and Show Value. The inscribed circle of ΔABC created with GeoGebra tools is attached

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Answer:

Step-by-step explanation: from edmentum

Given the following equation:

You know, based on the information given in the exercise, that it is a true equation. You can notice that the sum (the result of the Addition) of the terms on the left side of the equation, is:

Then, knowing the above and having the following expression:

You can substitute the sum of the equation into the expression:

Finally, adding the numbers, you get that the value of the expression is:

The total height of the two tallest trees will be 30 1/2 feet and the difference in the height of tallest and the shortest tree will be 5 feet.

We are given a line plot graph representing the heights of the different trees in a park.

a)

We can see that the height of the two tallest trees are:

15 1/2 feet and 15 feet

The total height of the two tallest trees will be:

Total height = 15 1/2 feet + 15 feet

Total height = 30 1/2 feet.

b)

Also,

Height of tallest tree = 15 1/2 feet

Height of shortest tree = 10 1/2 feet

Difference in the height of tallest and the shortest tree = 15 1/2 feet - 10 1/2 feet

Difference = 5 feet.

Therefore, we get that, the total height of the two tallest trees will be 30 1/2 feet and the difference in the height of tallest and the shortest tree will be 5 feet.

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Answer:

A. line KM

Step-by-step explanation:

radius is half of the diameter

Answer:

A

Step-by-step explanation:

The radius of a circle is a segment from the centre to the circumference.

KM is a radius as it satisfies this criterion.

The capital intensity ratio of the firm is 3.20. This means that the firm requires $3.20 of assets to generate $1 in sales.

A business metric known the capital intensity ratio can be used to assess how efficient to a company runs. A low capital intensity ratio indicates that a business is making the majority of its profits from the revenue it derives of  its assets.

Comparing capital  costs will reveal the capital intensity. High operational leverage and depreciation costs are typical of capital-intensive businesses. All assets divided by sales results in the capital intensity ratio.

The capital intensity ratio measures the amount of capital required to generate a certain level of sales. It is calculated as the ratio of total assets to sales revenue.

In this case, if the firm requires $3.20 of assets to generate $1 in sales, the capital intensity ratio would be:

Capital Intensity Ratio = Total Assets / Sales Revenue

Capital Intensity Ratio = $3.20 / $1

Capital Intensity Ratio = 3.20

Therefore, the capital intensity ratio of the firm is 3.20. This means that the firm requires $3.20 of assets to generate $1 in sales.

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Answer:

First term: 3

Common difference: 8

Function: 1 = 3 + (8 - 1)8

Step-by-step explanation:

First,

lay out the given information

O O O 27 O O O 59

Then, find the pattern to get from 27 to 59.

In this case, I found out that you can add by 8 to get 59.

3   11   19   27   35   43   51   59

Now, to write the function,

an = a1 + (n - 1)d

an = nth term in the sequence

a1 = first term in the sequence

n = number of terms in the sequence

d = common difference

Which means,

1 = 3 + (8 - 1)8

Hope this helps!!

Please give me brainliest if I am correct :)

Answer: $1.05

Step-by-step explanation:

quarters= 25 cents

4 x 25=100 cents

pennies=1 cent

5 x 1 = 5 cents

100+5=$1.05 or 105 cents

Answer:

x = 6       la cantidad de estantes

y = 65    cantidad de libros

Step-by-step explanation:

LLamemos "x" la cantidad de estantes que tiene Marta, y llamaremos "y" la cantidad de libros.

La primera condición que se debe cumplir es que cuando Marta coloca 12 libros en cada estante entonces le faltan 7, esto lo expresamos así:

y  +  7  = 12*x        (1)

La segunda condición establece que si Marta coloca los libros en número de 10 por estante le quedan 5 sin colocar, luego esto en lenguaje matemático se expresa así:

y  -   5   = 10*x     (2)

Ahora hemos obtenido un sistema de dos ecuaciones con dos incógnitas que se resuelve por cualquiera de los métodos conocidos, usaremos el método de sustitución.

Despejamos   y en la primera ecuación y lo sustituimos en la segunda, de esa forma obtendremos el valor de x

y  =  12*x  - 7

(12*x - 7 ) - 5  = 10*x

2*x  -12 = 0

2*x = 12

x = 6       la cantidad de estantes, y

y  =  12*x -7

y  =  72  -  7

y =  65    cantidad de libros