NO LINKS!!
Part 2: Graph the polygon with the given vertices and its image after the transformation. Label all vertices in both the preimage and image using the correct notation.

4. A(2, 1), B(3, -1), C(4, 2), D(3, 3)
Reflection : in the line x = -1

5. A(2, 3), B(1, 4), C(3, 4)
Rotation: 180° about the origin

6. A(5, -2), B(5, 2), C(3, 1), D(2, -1)
Rotation: 270° about the origin

Answer:

x=-3

Step-by-step explanation:

I showed my work in the picture

Answer:

[tex]\boxed{\sf x=-3}[/tex]

Step-by-step explanation:

[tex]\sf -2x+1=3x+16[/tex]

Subtract 3x from both sides:-

[tex]\sf -2x+1-3x=3x+16-3x[/tex]

[tex]\sf -5x+1=16[/tex]

Subtract 1 from both sides:-

[tex]\sf -5x+1-1=16-1[/tex]

[tex]\sf -5x=15[/tex]

Divide both sides by -5:-

[tex]\sf \cfrac{-5x}{-5}=\cfrac{15}{-5}[/tex]

[tex]\sf x=-3[/tex]

Therefore, x = -3!

______________________

Hope this helps!

Have a great day!

Answer:

A) The standard formula of the equation of a circle that has a center of (-4,-2) and contains the points (-1,2) is (x + 4)2 + (y + 2)2 = 25.

B) The general formula for the equation of a circle is (x - h)2 + (y - k)2 = r2, where (h,k) is the center of the circle and r is the radius.

Answer:

(g+f)(x/4) = x^2/16 + 3x/4

Step-by-step explanation:

To find (g+f)(x/4), we must first find the expressions for g(x) and f(x) and then add them together.

g(x) = x^2 + 4

f(x) = 3x - 4

So (g+f)(x) = g(x) + f(x) = x^2 + 4 + 3x - 4 = x^2 + 3x + 0

Now we can substitute x/4 for x in the expression:

(g+f)(x/4) = (x/4)^2 + 3(x/4) + 0

Multiplying it out

(g+f)(x/4) = (x^2/16) + (3x/4) + 0

so (g+f)(x/4) = x^2/16 + 3x/4

Answer:

To complete the transactions in your register:

Beginning balance on October 1: $542.89

On October 7, you pay Land Electric $43.90. This is a check transaction and the check number is 400. To record this in your register, you would subtract $43.90 from your current balance, which would bring your new balance to $498.99.

On October 23, you deposit your paycheck. To calculate your paycheck, you would multiply your hourly wage ($7.25) by the number of hours worked (40) by the number of weeks (2). This would give you a gross pay of $1140. Then, you would calculate the deductions: FICA (7.65%), federal withholding (12%), and state withholding (8.75%). To do this, you would multiply your gross pay by the percentage for each deduction and then subtract that amount from the gross pay. Your final paycheck would be $1140 - $87.41 (FICA) - $136.8 (federal withholding) - $100.65 (state withholding) = $815.34. To record this in your register, you would add $815.34 to your current balance, which would bring your new balance to $1314.33

On October 24, you buy $78.54 in clothes from FitRight and pay 6% sales tax. To calculate the sales tax, you would multiply $78.54 by 0.06 and add that amount to the total cost of the clothes. The total cost of the purchase including sales tax would be $78.54 + $4.71 = $83.25. To record this in your register, you would subtract $83.25 from your current balance, which would bring your new balance to $1231.08

The balance as of October 24 would be $1231.08

In the register

10/1 Beginning balance $542.89

10/7 Check #400 Land Electric -$43.90

10/23 Paycheck $815.34

10/24 Debit FitRight -$83.25

Ending balance $1231.08

Step-by-step explanation:

ABOVE

Answer:

Step-by-step explanation:

Sanjay is making two pumpkin pies for Thanksgiving, one to share with his family and one to share with his friends. He adds the same amount of cinnamon to both pies, but he adds more pumpkin puree to the pie he will share with his friends. Which pie will have a stronger cinnamon flavor?

"The pie he will give to his parents"

More pumpkin flavor less cinnamon flavor

The given expression can be as 2 + i as a complex number standard form.

The combination of a number and an imaginary number is a complex number. Complex numbers are symbolized by the symbol z and have the form a + ib. a and b are said to be real numbers.

The imaginary portion of the complex number can be represented by the letter i called the iota.  

Here i² = -1

Here we have

 [tex]\frac{4 +\sqrt{16 - 4(5)}}{2}[/tex]    

The above expression can be simplified as follows

=>  [tex]\frac{4 +\sqrt{16 - 20}}{2}[/tex]  

=>  [tex]\frac{4 +\sqrt{- 4}}{2}[/tex]    

As we know, [tex]i^{2} = -1[/tex]  

=>  [tex]\frac{4 +\sqrt{i^{2} (2)^{2} }}{2}[/tex]  

=> [tex]\frac{4+2i}{2}[/tex]  

=> [tex]\frac{2(2+i)}{2}[/tex]  

= 2 + i  

Therefore,

The given expression can be as 2 + i as a complex number standard form.

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Answer: Timespan is 410 minute(s).

Step-by-step explanation:

The standard deviation of the number of restaurants that failed within a year is 3.46.

The normal distribution, also known as the Gaussian distribution, is a symmetric probability distribution about the mean, indicating that data near the mean occur more frequently than data distant from the mean. The normal distribution will show as a bell curve on a graph.

Given that the probability that an independent restaurant will fail in the first year is 48%. Therefore, the probability can be written as,

p = 48% = 0.48

q = 1-p = 1-0.48 = 0.52

Also, Kristen obtains a random sample of 66 independent restaurants that opened in her city more than one year ago and determines if each one had closed within a year. Therefore, the sample size is 53.

n = 53

Now, the standard deviation can be calculated as,

Standard deviation, σ = √(npq)

                                    = √(53 × 0.48 × 0.52)

                                    = √11.9808

                                    = 3.46

Hence, the standard deviation is 3.46.

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The function that is positive for the entire interval [-3, -2] is given as follows:

On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0).

A function is positive over an interval if the values of y of the function are above zero for the entire interval.

A function is negative over an interval if the values of y of the function are below zero for the entire interval.

For the function in this problem, we have that:

As the function is concave up, it is positive to the left of the smaller root at x = -1, that is, positive for all x < -1, hence the correct option.

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Answer:

x=3

Step-by-step explanation: I'm not 100% if this is it because it's been awhile but I believe that you write 2x+2=4x-4 to solve for x since they're both y=mx+b equations. After solving it you would get 3

The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) ,

B ' ( 28, 14 ) and C ' ( -7, -7 ) .

What is a graph ?

Graph can be defined as the visual representation which is used to represent the data.

The scale factor is k = 7. This tells us to multiply each coordinate, of each point, by the scale factor to get the dilated points.

For example, point A is at (-3, 2) and moves to A ' (-21, 14) after multiplying the x,y coordinates by 7. The same applies for points B and C as well.

The dilation rule can be written as (x, y) -> (7x, 7y)

As a result of the dilation, triangle A'B'C' has sides that are 7 times longer compared to the corresponding sides of triangle ABC.

Example: side AB = 7 units, side A'B' = 49 units

Hence, The new coordinates after dialting using scale factor are , A ' ( -21, 14 ) , B ' ( 28, 14 ) and C ' ( -7, -7 ) .

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The required transformations are

A function is a mathematical equation which shows the relationship between two variables.

Transformation is the performing of the mathematical operations of dilation, translation, relection and rotation on a function.

Given the function [tex]f(x) = 2^{3\sqrt{x} }[/tex] which is transformed into the function [tex]g(x) = 2^{3\sqrt{x - 4}} + 5[/tex], we describe the transformations as follows.

First Since we have x - 4,  [tex]f(x) = 2^{3\sqrt{x} }[/tex] is shifted four units to the right. So, we have , [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex].

Also, since 5 is added  to [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex].   [tex]g(x) = 2^{3\sqrt{x - 4}}[/tex]. is shifted 5 units up to get    [tex]g(x) = 2^{3\sqrt{x - 4}} + 5[/tex],

So, the required transformations are

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Answer:

B. -0.45

Step-by-step explanation:

I'm assuming the values you have provided are pertaining to the correlation coefficient.

The correlation coefficient (r) is used to describe how strongly points are correlated and in which direction they are correlated. This correlation coefficient ranges between -1 and 1: [tex]-1\le r\le1[/tex]

If the correlation coefficient is negative, the correlation is down-sloped or in other words as the variable on the x-axis increases, the variable on the y-axis decreases.

If the correlation coefficient is positive, the correlation is upward-sloped or in other words as the variable on the x-axis increases, the variable on the y-axis also increases.

The strength of the correlation can be analyzed by the absolute value of the correlation coefficient (r). So if you want to compare two correlation coefficients and say which has a stronger correlation, you would first take the absolute value and then compare which is larger as such: [tex]|r|[/tex]

In this case the -0.45 is technically less than the 0.34, although the absolute value indicates it is a stronger correlation, just in a different direction. You can compare all the other options and -0.45 has the largest absolute value.

The value 2(-7) is interpreted that a location that is twice as far below sea level as the dolphin. Option A is the correct option.

What is the meaning of interpretation?

Elucidate, explain, explicate, and expound are some synonyms for interpret. While all of these words mean "to make something clear or understandable," interpretation adds to explain why dealing with something requires imagination, sympathy, or special knowledge.

Given that sea level is defined as having an elevation of 0. A dolphin is 7 meters below sea level.

If the level is below sea level, then it can represent by a negative number.

The statement "A dolphin is 7 meters below sea level." can be written as:

A dolphin is -7 meters far from sea level.

Thus 2(-7) represents a location that is 7 meters below the dolphin's position.

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The factors of a fraction 3 1/2 is 3/2.

Generally, A divisor of an integer n, also known as a factor of n, is an integer m that can be multiplied by another number to generate n. Another name for this concept is a factor of n. One may also state that n is a multiple of m in this particular scenario.

Since 3/2 is a fraction, it does not have any factors since factors are integers that may evenly divide a number. Since 3/2 is a fraction, it does not have any factors. Only integers are capable of having factors; fractions are unable to do so.

To find the factors of a fraction, you can factor the numerator and denominator separately.

In the case of 3 1/2, the numerator 3 is a prime number and cannot be factored further.

However, the denominator 2 can be factored as 2 x 1.

Therefore, the factors of 3 1/2 are: (3 x 1) / (2 x 1),

which can be simplified to 3/2.

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From the coordinates we can see the rule for this transformation is:

It is a dilation by a scale factor of 2 and reflection in the y-axis.

It means this is a similarity transformation, since the figure has changed its size.

Answer:

Dilation of scale factor 2 centered at the origin, followed by a reflection in the y-axis.

Similarity transformation.

Step-by-step explanation:

Given vertices of ΔABC:

Given vertices of ΔA'B'C':

From observation, the series of transformations the transforms ΔABC to ΔA'B'C' are:

This is a similarity transformation as the two triangles have the same shape but different sizes.

The simplified expression of -7(3z + 5t - 3g) is  -21z - 35t + 21g.

An algebraic expression consists of unknown variables, numbers and arithmetic operators such as addition, subtraction, multiplication etc.

To simplify an expression means to write an equivalent expression which contains no similar terms.

Therefore, let's simplify the expression as follows:

-7(3z + 5t - 3g)

Hence, open the brackets

-7(3z + 5t - 3g) = -21z - 35t + 21g

Therefore, the simplified expression is -21z - 35t + 21g.

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Resizing or changing an object is the process of dilation. Through the use of the specified scale factor, it is a transformation that reduces or enlarges the objects.

P(1,3) → P' (3,9) (3,9)

Q(3,1) → Q' (9,3) (9,3)

R(1,1) → R' (3,3) (3,3).

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Answer:

162 miles.

Step-by-step explanation:

To find the total distance Nicole cycled, we can multiply the number of laps by the length of each lap.

The total distance Nicole cycled is:

9 laps * 9540 ft/lap = 858,600 ft

To convert this distance to miles, we can use the conversion factor that there are 5280 feet in a mile.

858,600 ft / 5280 ft/mile = 162 miles

So the total distance Nicole cycled is 162 miles.

Answer:

A way for one of the toddler triplets to end up with their coat is if the other two toddler triplets each get one another coat.

making it a 33% chance of one of the toddler triplets to end up with their own coat.

100% divided by 3 = 0.33

The p-value for right tailed test based on the information will be 0.2147.

The p-value, under the assumption that the null hypothesis is true, is the likelihood of obtaining results from a statistical hypothesis test that are at least as extreme as the observed results. The p-value provides the smallest level of significance at which the null hypothesis would be rejected as an alternative to rejection points. The alternative hypothesis is more likely to be supported by stronger evidence when the p-value is lower.

In this case, the survey was done to test the claim that 20% of adult Americans believe that the lottery is the path to riches. The hypothesis test of H0: p=.2 versus Ha: p>.2 resulted in 0.79 for a right-tailed test

The Z statistic given to be =0.79 for a right tailed test. Here, by looking aththe distribution table, the p value for Z=0.79 for one tail test is 0.2147.

So, we do not reject null hypothesis and then conclude that data does not provide sufficient evidence that the proportion of Americans who believe path to riches is the lottery is greater than 0.2

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Answer:

Step-by-step explanation:

a. 47 men

b. 24 men like soda

c. 23 men do not like soda

d. 61 women

e. 26 women like soda

f. 35 women do not like soda

After transformation, the point (-1,2) in the image would be (-1,-2)

Each transformation applied to the prior image is combined into a composition of transformations. The result of a translation is identical to a composition of reflections across parallel lines (twice the distance between the parallel lines). The composite transformation is carried out by multiplying the matrix in order from the right to the left side if it is represented as a column. The output from the preceding matrix is multiplied by the new matrix that will follow.

First, we must mirror the point (-1, 2) around the line y=-x.

(X, Y) is the rule (-y,-x)

you obtain (-1,2)—>(-2,1) (-2,1)

At this point, you must rotate (-2,1) by 90 degrees.

(X, Y) is the rule ( -y,x)

so (-2,1)—> (-1,-2) (-1,-2)

After transformation, the point (-1,2) in the image would be (-1,-2)

The complete question is,

What is the image point of (-1,2) after the transformation R 90° ry=-x

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A system of inequalities that can be used to model the scenario is d + a ≤ 300 and 10d ≥ 1,200.

A system of inequalities is two or more inequalities that must be proved simultaneously.

A system of inequalities contains at least two linear inequalities in the same variables.

Systems of inequalities are applied when there are a range of solutions and more than one constraint.

Inequalities may include greater than, less than, not equal to, equal to but less than, and equal to but greater than.

The total capacity of people the auditorium can hold = 300

The cost per ticket at the door = $10

The cost per ticket in advance = $7.50

Tickets cannot exceed 300

Door tickets must generate at least $1,200

Let the number of tickets sold at the door = d

Let the number of tickets sold in advance = a

10d + 7.5a ≤ 300

10d ≥ 1,200

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Answer:

Let's use the same information as above to show how a formula can be used to quickly calculate the break-even output.

Remember contribution per unit? Here is a reminder of this crucial and really useful formula:

Contribution per unit = selling price per unit less variable cost per unit

In our example, contribution per unit = £10 less £4 = £6 per unit

Now apply the classic formula for calculating breakeven output:

Break-even output (units) = Fixed costs (£) / Contribution per unit (£)

So, break-even output = £40,000 divided by £6 = 6,666 units

Note: break-even output is always expressed in terms of units

So break-even output = 6,666 units

If the information is available, it is always quicker and easier to use this formula rather than use a table or draw a chart.

The average pay for an entry-level technician position is $15.6375.

The arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean

The formula for the mean of a given set of data is as follows:

Average = Sum of Observations/Total number of observations

Σx = 15.50 + 16.85 + 14.25 + 15.95 = 62.55

Here n = 4

⇒ Average = Σx/n

⇒ Average = 62.55/4

Apply the division operation, and we get

⇒ Average = 15.6375

Thus, the average pay is $15.6375.

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Answer: $34.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula for calculating the time it takes to reach a target amount with a constant periodic deposit is given by

Time = ln(Target Amount / (Periodic Deposit x (1 + Interest Rate)^0)) / ln(1 + Interest Rate)

In this case, we have Target Amount = 500,000, Periodic Deposit = 500, and Interest rate = 7.8%. Plugging the values into the formula gives

Time = ln(500,000 / (500 x (1 + 0.078)^0)) / ln(1 + 0.078)

Time = ln(500,000 / 500) / ln(1.078)

Time = ln(1,000) / ln(1.078)

Time = 8.98 years

Rounding to the nearest tenth of a year, the answer is 8.9 years.

The annual salary of the man is Rs 780,000 and his total taxes is given by the relation T = Rs 9,000

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Since the man's monthly salary is Rs 65,000, his annual salary would be:

Annual salary = Monthly salary x 12

Annual salary = 65,000 x 12

Annual salary = 780,000

His annual salary of Rs 780,000 falls in the third tax bracket which is from 750,001 to 2,000,000.

So, the tax rate applicable to him would be 30%.

To calculate the amount of tax he would have to pay, we can use the formula:

Tax amount = Tax rate x Taxable income

where taxable income is the income above the lower limit of the tax bracket.

In this case, the taxable income would be:

Taxable income = Annual income - Lower limit of tax bracket

Taxable income = 780,000 - 750,001

Taxable income = 29,999

So, the amount of tax he would have to pay would be:

Tax amount = 30% x 29,999

Tax amount = 8,999.7

Rounding this to the nearest rupee gives us:

Tax amount = Rs 9,000

Hence , the man would have to pay Rs 9,000 in taxes on his annual salary of Rs 780,000.

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Answer:

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

According to the given we can state:

Find arc AB, it is a semicircle of 1 cm radius:

ΔAEO and ΔBEO are both isosceles, hence ∠A and ∠B are both 45°.

Find arcs ABD and BAC:

∠AEB is a right angle since ∠AEO and ∠BEO are both 45°.

Hence ∠CED is also right angle as vertical angle with ∠AEB.

Find the length of EC and ED.

We know AD = BC = 2 cm and ΔAEO is 45° right triangle.

It gives us:

Then:

Find arc ECD:

The perimeter is the sum of all the arc measures:

Answer:

[tex]\textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}=7.20333649...\; \sf cm[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{6.4 cm}\underline{Arc length}\\\\Arc length $=r \theta$\\\\where:\\ \phantom{ww}$\bullet$ $r$ is the radius. \\ \phantom{ww}$\bullet$ $\theta$ is the angle measured in radians.\\\end{minipage}}[/tex]

To convert degrees to radians, multiply the angle in degrees by π/180°.

Arc AB

As arc AB has center O, the radius of arc AB is OA = 1 cm.

As AB is a straight line, ∠AOB is 180° = π.

Therefore, the length of arc AB is:

[tex]\implies AB=r \:\theta=1 \cdot \pi = \pi[/tex]

Arc AC

Triangle BOE is a right triangle with base of 1 cm and height of 1 cm.

Therefore, ∠OBE is 45° = π/4

If arc AC has center B, then the radius is AB = 2 cm.

Therefore, the length of arc AC is:

[tex]\implies AC=r \:\theta=2 \cdot \dfrac{\pi}{4} = \dfrac{\pi}{2}[/tex]

Arc BD

Arc BD is the same as arc AC.

[tex]\implies BC= \dfrac{\pi}{2}[/tex]

Arc CD

As triangle BOE is a right triangle with base of 1 cm and height of 1 cm, the length of its hypotenuse BE is:

[tex]\implies BE=\sqrt{1^2+1^2}=\sqrt{2}[/tex]

As arc AC has center B and radius of AB = 2 cm, then BC is also its radius and therefore BC = 2 cm

Therefore:

[tex]\implies CE=BC-BE[/tex]

[tex]\implies CE=2-\sqrt{2}[/tex]

The arc CD has center E so its radius is CE = 2-√2.

As ∠BEO and ∠AEO are both 45° then ∠AEB is 90°.

According to the vertical angle theorem, ∠CED is also 90° = π/2.

Therefore, the length of arc CD is:

[tex]\implies CD=r \:\theta=(2-\sqrt{2}) \cdot \dfrac{\pi}{2} = \dfrac{(2-\sqrt{2})\pi}{2}[/tex]

Perimeter of the egg

The perimeter of the egg is the sum of the found arcs:

[tex]\implies \textsf{Perimeter}=AB+AC+BD+CD[/tex]

[tex]\implies \textsf{Perimeter}=\pi+\dfrac{\pi}{2}+\dfrac{\pi}{2}+\dfrac{(2-\sqrt{2})\pi}{2}[/tex]

[tex]\implies \textsf{Perimeter}=2\pi+\dfrac{(2-\sqrt{2})\pi}{2}[/tex]

[tex]\implies \textsf{Perimeter}=2\pi+\dfrac{2 \pi}{2}-\dfrac{\sqrt{2}\:\pi}{2}[/tex]

[tex]\implies \textsf{Perimeter}=3\pi-\dfrac{\sqrt{2}\:\pi}{2}[/tex]

[tex]\implies \textsf{Perimeter}=3\pi-\dfrac{\pi}{\sqrt{2}}[/tex]

[tex]\implies \textsf{Perimeter}=7.20333649...\; \sf cm[/tex]