Which rule describes the composition of transformations that maps ΔJKL to ΔJ"K"L"?

90 degree rotation about point 0 composition translation of 0 units x, negative 2 units y
Translation of 0 units x, negative 2 units y composition 90 degree rotation about point 0
90 degree rotation about point 0 composition translation of negative 2 units x, 0 units y
Translation of negative 2 units x, 0 units y composition 90 degree rotation about point 0

The zeroes of the function g(x) = x² +3x -4 as given in the task content is; x = -4 and x = 1.

It follows from the task content that the function g(x) given in the task content is; g(x) = x² +3x -4.

On this note, it follows that the zeroes of the function can be determined by solving the quadratic function as follows;

x² +4x -x -4 = 0

(x+4) (x-1) = 0

Ultimately, it can be concluded that the values of x which represents the zeroes of the function are; x = -4 and x = 1.

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The formula for Observed Score is; Observed score (X) = True score (T) + measurement error (e)

The formula for Observed Score is;

Observed score (X) = True score (T) + measurement error (e)

1) True score is the score that would be obtained if an individual took a test an infinite amount of times and those test scores were averaged. The concept of true score is theoretical because you can't give someone something an infinite number of times.

2) Standard error of measurement is the standard deviation of multiple test scores (how far the sample mean of the data is likely to be from the true population mean).

The less random error (e) in the measure, the more the observed score X approximates the true score T.

Thus;

Observed score = True Score + Error

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Recall the binomial theorem.

[tex](a+b)^n = \displaystyle \sum_{k=0}^n \binom nk a^{n-k} b^k[/tex]

1. The binomial expansion of [tex]\left(1+\frac x3\right)^7[/tex] is

[tex]\left(1 + \dfrac x3\right)^7 = \displaystyle\sum_{k=0}^7 \binom 7k 1^{7-k} \left(\frac x3\right)^k = \sum_{k=0}^7 \binom 7k \frac{x^k}{3^k}[/tex]

Observe that

[tex]k = 1 \implies \dbinom 71 \left(\dfrac x3\right)^1 = \dfrac73 x[/tex]

[tex]k = 2 \implies \dbinom 72 \left(\dfrac x3\right)^2 = \dfrac73 x^2[/tex]

When we multiply these by [tex]8-9x[/tex],

• [tex]8[/tex] and [tex]\frac73 x^2[/tex] combine to make [tex]\frac{56}3 x^2[/tex]

• [tex]-9x[/tex] and [tex]\frac73 x[/tex] combine to make [tex]-\frac{63}3 x^2 = -21x^2[/tex]

and the sum of these terms is

[tex]\dfrac{56}3 x^2 - 21x^2 = \boxed{-\dfrac73 x^2}[/tex]

2. The binomial expansion is

[tex]\left(2a - \dfrac b2\right)^8 = \displaystyle \sum_{k=0}^8 \binom 8k (2a)^{8-k} \left(-\frac b2\right)^k = \sum_{k=0}^8 \binom 8k 2^{8-2k} a^{8-k} b^k[/tex]

We get the [tex]a^6b^2[/tex] term when [tex]k=2[/tex] :

[tex]k=2 \implies \dbinom 82 2^{8-2\cdot2} a^{8-2} b^2 = 28 \cdot2^4 a^6 b^2 = \boxed{448} \, a^6b^2[/tex]

The expectancy theory that could be phrased as the above question is based on the element called expectancy.

In this question,

Expectancy theory proposes that an individual will behave or act in a certain way because they are motivated to select a specific behavior over others due to what they expect the result of that selected behavior will be.

To make the connection between motivation, effort and performance, expectancy theory has three variables: Expectancy, Instrumentality and Valence.

Expectancy theory consists of three basic components:

(1) The employee's expectancy that working hard will lead to his or her desired level of performance;

(2) The employee's expectancy that working hard will thus ensure that rewards will follow; and

(3) Whether or not the employee's perception that the outcome of working hard is worth the effort or value associated with hard work.

VIE expectancy theory is often formulated using the equation MF (motivational forces) = V (valence) x I (instrumentality) x E (expectancy).

From the definition, the probability that, "if i do a good job, that there will be some kind of outcome in it for me" is comes under the element expectancy(E).

Hence we can conclude that the expectancy theory that could be phrased as the above question is based on the element called expectancy.

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The minimum number of books required to be equally distributed among the students are 1,440 books.

To find the minimum required books so that they can be equally distributed:

The number of students in three sections of class 6th are 32, 36, and 40.

Now, find the LCM od 32, 36, and 40.

The LCM od 32, 36, and 40 will be 1,440.

Therefore, the minimum number of books required to be equally distributed among the students are 1,440 books.

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Answer:

18.0  cm to 1 decimal point.

Step-by-step explanation:

First  work out the unknown side (s) of the right triangle using the Pythagoras theorem:

s^2  = 13^2 - 5^2

       = 169 - 25 = 144

s = sqrt 144 = 12 cm.

Now consider the other triangle:

s = 12

The missing angle = 180 - 65 - 40 = 75 degrees.

By the Sine Rule:

x / sin 75 = 12 / sin40

x = 12 sin 75 / sin 40

  = 18.03

    -

Answer:

Events that mutually exclusive are 1. Landing on a shaded portion and landing on a 3.2. Landing on an unshaded portion and landing on a number less than 2.

Answer:

1st option

Step-by-step explanation:

to find f(g(x)) substitute x = g(x) into f(x) , that is

f(g(x))

= f(4x - 5)

= 2(4x - 5) + 1 ← distribute parenthesis

= 8x - 10 + 1

= 8x - 9

The correct option regarding the outliers of the data-set is given by:

The greatest value, 78, is the only outlier.

The IQR for this problem is:

IQR = 37 - 13 = 24.

Hence the bounds for outliers are:

The options are:

Hence the correct option is that only 78 is an outlier.

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Hello, the solution of the geometry problem is in this photo.

AOC = 136°

BOC = 44°

It looks like the function might be defined by

[tex]f(x) = \begin{cases} 3a{}x + b & \text{if } x > 1 \\ 11 & \text{if } x = 1 \\ 5a{}x - 2b & \text{if } x < 1 \end{cases}[/tex]

To ensure continuity at [tex]x=1[/tex], we need both one-sided limits to exist and have the same value.

[tex]\displaystyle \lim_{x\to1^-} f(x) = \lim_{x\to1} (5a{}x - 2b) = 5a - 2b[/tex]

[tex]\displaystyle \lim_{x\to1^+} f(x) = \lim_{x\to1} (3a{}x + b) = 3a + b[/tex]

Both limit values must be equal to [tex]f(1) = 11[/tex], so that

[tex]\begin{cases} 5a - 2b = 11 \\ 3a + b = 11 \end{cases}[/tex]

Eliminating [tex]b[/tex], we have

[tex](5a - 2b) + 2 (3a + b) = 11 + 2\cdot11 \implies 11a = 33 \implies \boxed{a=3}[/tex]

Solving for [tex]b[/tex], we get

[tex]5\cdot3 - 2b = 11 \implies -2b = -4 \implies \boxed{b=2}[/tex]

[tex]\displaystyle\\Answer:\theta=\frac{\pi }{2}+\pi n.[/tex]

Step-by-step explanation:

[tex]\displaystyle\\7*cosec^2\theta-9*cot^2\theta=7\\7-7*cosec^2\theta+9*cot^2\theta=0\\7-\frac{7}{sin^2\theta}+9*\frac{cos^2\theta}{sin^2\theta} } =0\\\frac{7*sin^2\theta-7+9*cos^2\theta}{sin^2\theta} =0\\\frac{-7*(1-sin^2\theta)+9*cos^2\theta}{sin^2\theta} =0\\\frac{-7*cos^2\theta+9*cos^2\theta}{sin^2\theta} =0\\\frac{2*cos^2\theta}{sin^2\theta}=0\\[/tex]

[tex]2*cot^2\theta=0\\Divide\ the\ right\ and\ initial\ parts\ by\ 2:\\cot^2\theta=0\\cot\theta=0\\\theta=\frac{\pi }{2}+\pi n\ \ \ (n=0,\ 1,\ 2,\ 3\ ...).[/tex]

The area and perimeter of the picture is 576 inches square and 96 inches respectively

Given that each frame is a rectangle and four frames makes up the picture

Note that the picture takes the shape of a square

Let's find the total perimeter

Perimeter of the picture = sum of the four rectangular frame perimeters

Perimeter = 24 + 24 + 24 + 24

Perimeter = 96 inches

Formula for area of a square = a^2

Where 'a' is the length of the side  = 24 inches

Substitute the value of 'a'

Area of the picture = 24^2

Area of the picture = 576 inches square

Thus, the area and perimeter of the picture is 576 inches square and 96 inches respectively.

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The following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.

If the measuring has a level of precision of 0.01 ml, this means that the measured quantities are only sensible to the smallest hundreths. Any change less than 0.01 ml and any decimal less than a hundreths are "invisible" for measuring processes.

Hence, the following volumes of fluid can be added to 0.40 mL of liquid for the level of precision of 0.01 mL: a) 0.2 mL, b) 6 mL, c) 2.02 mL. The amounts 0.154 mL and 8.8331 mL are not possible due to given level of precision.

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Answer:

B,D,E

Step-by-step explanation:

Answer:

$75

My answer might be a bit off since I'm not really sure what you mean by "Rs 80", which I interpreted as $80, but if my interpretation is wrong, you can still use all the same steps and you should get the correct answer

Step-by-step explanation:

So we can represent the price of each tumbler as the variable "P", since it's some unknown value we're solving for. Let's also just say that "T" is the total price that she paid for all of the tumblers.

Using this equation we can derive the following equation.

1000P = T

Since multiplying the price of each glass tumbler times the price of one glass tumbler should equal the entire price.

Now she only sold 900 of them, since 100 were broken, and she sold them each for 80. So knowing this we can find how much she made in total from selling the remaining 900 glass tumblers

900 * 80 = 72,000

Now if she made a loss of 4%, that means the total money she made back, is only 96% the amount of money she paid for the product. The reason for this is (100-4)% represents a 4% loss.

Remember, how T represents the entire price, well we know that 72,000 represents 96% of it's value. To find what x% is of some number, you generally convert the percentage into a decimal by dividing by 100, so to find x% of some variable "a" you generally use the following equation: [tex]a*\frac{x}{100}[/tex] where the value of this expression will be equal to x% of a.

So let's convert 96% to decimal form: [tex]\frac{96}{100} = 0.96[/tex]. Now if we multiply this decimal 0.96 by T, we should get 72,000 since the 72,000 represents 96% of the original value

[tex]0.96T = 72,000[/tex]

To find the original value of T, we simply divide both sides by 0.96

[tex]T = 75,000[/tex]

So now that we know the original total price, we can use the original equation we derived to solve for P, which represents the price of each individual tumbler.

Original Equation

[tex]1000P = T[/tex]

Substitute 75,000 as T

[tex]1000P = 75,000[/tex]

Divide both sides by 1,000

[tex]75=P[/tex]

This means she sold each for 75

This is a telescoping sum. The K-th partial sum is

[tex]S_K = \displaystyle \sum_{k=1}^K \left(\frac1{\sqrt{k+1}} - \frac1{\sqrt{k+3}}\right) \\\\ ~~~= \left(\frac1{\sqrt2} - \frac1{\sqrt4}\right) + \left(\frac1{\sqrt3} - \frac1{\sqrt5}\right) + \left(\frac1{\sqrt4} - \frac1{\sqrt6}\right) + \left(\frac1{\sqrt5} - \frac1{\sqrt7}\right) + \cdots \\\\ ~~~~~~~~+ \left(\frac1{\sqrt{K-1}} - \frac1{\sqrt{K+1}}\right) \\\\ ~~~~~~~~+ \left(\frac1{\sqrt K} - \frac1{\sqrt{K+2}}\right) + \left(\frac1{\sqrt{K+1}} - \frac1{\sqrt{K+3}}\right)[/tex]

[tex]\displaystyle = \frac1{\sqrt2} + \frac1{\sqrt3} - \frac1{\sqrt{K+2}} - \frac1{\sqrt{K+3}}[/tex]

As [tex]K\to\infty[/tex], the two trailing terms will converge to 0, and the overall infinite sum will converge to

[tex]\displaystyle \sum_{k=1}^\infty \left(\frac1{\sqrt{k+1}} - \frac1{\sqrt{k+3}}\right) = \lim_{k\to\infty} S_k = \boxed{\frac1{\sqrt2} + \frac1{\sqrt3}}[/tex]

By the limit comparison test, the expression √[1 / (1 + 1 / k)] - √[1 / (1 + 3 / k)] has a limit, then the expression [1 / √(k + 1)] / [1 /√k] -  [1 / √(k + 3)] / [1 /√k] has a limit and the series ∑ [1 / √(k + 1)] - ∑ [1 / √(k + 3)] is convergent.

Herein we have a series that involves radical components. First, we simplify the expression given:

∑ [1 / √(k + 1) - 1 / √(k + 3)] = ∑ [1 / √(k + 1)] - ∑ [1 / √(k + 3)]

The convergence of the series can be proved by the limit comparison test, where each component of the subtraction of the series is compared with a series that is convergent. We notice that both 1 / √(k + 1) and 1 / √(k + 3) resembles the expresion 1 /√k. Then, we have the following subtraction of ratios:

[1 / √(k + 1)] / [1 /√k] - [1 / √(k + 3)] / [1 /√k]

√k / √(k + 1) - √k / √(k + 3)

√[k / (k + 1)] - √[k / (k + 3)]

Then, by using the limit property for rational functions we find the following result for n → + ∞:

√[1 / (1 + 0)] - √[1 / (1 + 0)]

√1 - √1

1 - 1

0

By the limit comparison test, the expression √[1 / (1 + 1 / k)] - √[1 / (1 + 3 / k)] has a limit, then the expression [1 / √(k + 1)] / [1 /√k] -  [1 / √(k + 3)] / [1 /√k] has a limit and the series ∑ [1 / √(k + 1)] - ∑ [1 / √(k + 3)] is convergent.

The statement is incomplete and complete form cannot be found, therefore, we decided to determine if the series is convergent or not.

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Answer: 147.2 miles

Step-by-step explanation:

We can answer this by knowing the formula [tex]speed=\frac{distance}{time}[/tex]. Here, the speed is 46 miles/hour and the time is 3.2 hours. Let's put these values into the formula and solve for distance.

[tex]46=\frac{distance}{3.2}\\46*3.2=\frac{distance}{3.2}*3.2\\d=147.2[/tex]

Alex traveled 147.2 miles.

The magnitude of the resulting vector, u - v, is approximately 5.83

and its angle of direction is approximately 59.04°.

We want to subtract vector v from vector u.

We are given;

v = <2, -3> = 2i - 3j

u = <5, 2> = 5i + 2j

u - v = 5i + 2j - (2i - 3j)

= 5i + 2j - 2i + 3j

= 3i + 5j

Resultant vector = √(3² + 5²)

Resultant vector = √34 ≈ 5.83

Angle of direction of resultant vector is;

tan θ = (5/3)

θ = tan⁻¹(5/3)

θ = 59.04°

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Answer:

PQ = 20 cm

QR = 15 cm

Step-by-step explanation:

The ordered pairs (0,13) and (10, 0) are joined to best draw the line of best fit for the given scatter plot. So, option 4 is correct.

For the given scatter plot, to draw a line of best fit, the slope is to be calculated. The slope of the required line is calculated by

m = [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]

Where,

∑xy = sum of the product of x and y values

∑x = sum of x values

∑y = sum of y values

∑x² = sum of square values of x

n = total number of scatter points

And the y-intercept is calculated by

b = [∑y - m(∑x)]/n

Where m is the slope obtained above

The given scatter plot has the coordinate points:

(0,14), (1, 11), (2, 9), (3, 10),(4, 7), (5, 7), (6, 5), (7, 5), (8, 3), (9, 1), (10, 0)

Such that n = 11

Then the required components are calculated as follows:

∑x = 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55

∑y = 14 + 11 + 9 + 10 + 7 + 7 + 5 + 5 + 3 + 1 + 0 = 72

∑xy = (0 × 14) + (1 × 11) + (2 × 9) + (3 × 10) + (4 × 7) + (5 × 7) + (6 × 5) + (7 × 5) + (8 × 3) + (9 × 1) + (10 × 0) = 220

∑x² = 0² + 1² + 2² + 3² + 4² + 5² + 6² + 7² + 8² + 9² + 10² = 385

Then the slope is calculated as follows:

slope m =  [n(∑xy) - (∑x)(∑y)]/[n(∑x²) - (∑x)²]

On substituting,

m = [11(220) - (55)(72)]/[11(385) - (55)²]

⇒ m = -14/11 = -1.2727273 ≅ -1.3

∴ m = -1.3

Then calculating the y-intercept:

we have b = [∑y - m(∑x)]/n

On substituting,

b = [72 - -1.3(55)]/11

∴ b = 13

Then the slope-intercept form of the required line is

y = -1.3x + 13

When x = 0,

y = -1.3(0) + 13 = 13

When y = 0,

0 = -1.3x + 13

⇒ 1.3x = 13

⇒ x = 13/1.3 = 10

Therefore, the coordinates (0, 13) and (10, 0) give the best draw for the line of best fit.

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One can prove congruence through transformation if they have the same shape and size.

The congruency postulates include:

In geometry, it should be noted that two figures are congruent if they have the same shape and size.

In this case, if two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent.

One can prove triangle congruence using congruency postulates by using the SSS theorem( side side side theorem).

It should be noted that the congruence postulate is used to illustrate that the triangles are equal.

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Answer:

60m3

Step-by-step explanation:

my son got the right anser

Answer:

60m^3

Step-by-step explanation:

The formula for volume of a rectangular prism is height*width*depth

We can see two distinct shapes here

First, we find the volume for the bigger shape

We can see the measurements that pertain to it...

Width is 6m, depth is 3m, and height is also 3m

Multiply those three, you get 54m^3

Now the smaller shape...

1m in width, 2m in height, and 3m in depth

Multiply those, get 6m^3

Add the two shapes together, 54+6=60m^3

Part A

Using the Pythagorean on the right triangle PQR, with PQ and QR as the legs and PR as the hypotenuse,

[tex]14^2 +6^2 =(PR)^2\\\\(PR)=\sqrt{14^2 +6^2}\\\\PR \approx \boxed{15.23 \text{ ft}}[/tex]

Part B

[tex](QR)^2 +6^2 =16^2\\\\(QR)^2 =16^2 -6^2\\\\QR=\sqrt{16^2 -6^2}\\\\QR \approx \boxed{14.83 \text{ ft}}[/tex]

Based on the scale, the actual length of the Golden Gate Bridge is  68,600 inches.

A scale drawing is a reduced form in terms of dimensions of an original image / building / object. The scale drawing is usually reduced at a constant dimension. An example of a scale drawing is a map.

The scale of a drawing is usually written in this format -  length in the drawing, a colon (:), then the matching length on the original image. An example of a scale is 1 : 19,600. This scale means that 1 inch of the postcard represents 19.600 of the original Golden Gate Bridge.

Actual length of the Bridge = scale x length of the bridge in the postcard

19,600 x 3.5 = 68,600 inches

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The volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)

The complete question is added as an attachment

From the attached image, we have:

Length = 12 - 2x

Width = 7 - 2x

Height = x

The volume is calculated as:

Volume = Length * Width * Height

Substitute the known values in the above equation

Volume = (12 - 2x) * (7 - 2x) * x

This gives

Volume = x(12 - 2x)(7 - 2x)

Hence, the volume of the box as a polynomial in the variable x is x(12 - 2x)(7 - 2x)

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(3x² - 7x + 14) + (5x² + 4x - 6)

Match 3x² and 5x² to get 8x².

Combine −7x and 4x to get −3x.

Subtract 6 from 14 to get 8.

Therefore, the expression (3x² - 7x + 14) + (5x² + 4x - 6), is equivalent to the expression "B".

(2x² - 5x -3) + (-10x² + 2x + 7)

Combine 2x² and -10x² to get −8x².

Combine −5x and 2x to get −3x.

Add −3 and 7 to get 4.

Therefore, the expression (2x² - 5x -3) + (-10x² + 2x + 7), is equivalent to the expression "A".

(12x² - 2x - 13) + (-4x² + 5x +9)

Combine 12x² and -4x² to get 8x².

Combine −2x and 5x to get 3x.

Add −13 and 9 to get −4.

Therefore, the expression (12x² - 2x - 13) + (-4x² + 5x +9), is equivalent to the expression "C".

The correct option is B.

5 pound

The number (5.3) after Decimal is <5 so it round off to 5.

It is the same to round a number to one decimal place as to the nearest tenths. At this instance, it is known which numeral is in the hundredths position. When the number in the hundredths place is higher than or equal to 5, the tenths digit is raised by one unit.

A typical rule of thumb is to glance at the digit immediately to the right of the place value you want to round to and make your choice. For instance, rounding 5.1837 to the closest hundredth would result in 5.18 (because 3<5), whereas rounding 5.184 to the nearest thousandth would result in 5.184 (because 7>5).

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I understand that the question your are looking for is:

A scale measured a 4.5-pound brick as weighing 5.3 pounds. which measurement is more accurate but less precise than 5.3 pounds?

A. 4.98 pounds

B. 5 pounds

C. 5.52 pounds

D. 6 pounds