The point P = (x, 1/3) lies on the unit circle shown below. What is the value of x in simplest form?

When creating a confidence interval for the mean in a (B) t-distribution, the number of standard deviations needed is determined using the following distribution.

Any member of the family of continuous probability distributions known as the Student's t-distribution (or simply the t-distribution) in probability and statistics is used to estimate the mean of a normally distributed population when the sample size is small and the population's standard deviation is unknown.

The following distribution is used to calculate the number of standard deviations required for our confidence interval when doing a confidence interval for the mean in a t-distribution.

The Student's t-test for determining the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and linear regression analysis are just a few commonly used statistical analyses that make use of the t-distribution.

Therefore, when creating a confidence interval for the mean in a (B) t-distribution, the number of standard deviations needed is determined using the following distribution.

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Correct question:
When we do a confidence interval for the mean, we use the following distribution to determine the number of standard deviations needed for our confidence:

a. z-distribution

b. t-distribution

c. Chi-Square distribution

d. skewed distribution

Answer:

142 506

Step-by-step explanation:

here the order does not matter

Then

we the number of sets is equal to the number of combinations.

Using the formula :

the number of sets is 30C5

\(C{}^{5}_{30}=\frac{30!}{5!\left( 30-5\right) !}\)

      \(=142506\)

There are 142506 ways in which 5 students can be selected out of 30 students.

The selection of 5 students out of 30 students can be achieved with the use of combination since the order of selection is not required to be put into consideration.

By using the formula:

\(\mathbf{^nC_r = \dfrac{n!}{r!(n-r)!}}\)

where;

\(\mathbf{^nC_r = \dfrac{30!}{5!(30-5)!}}\)

\(\mathbf{^nC_r = \dfrac{30!}{5!(25)!}}\)

\(\mathbf{^nC_r = 142506}\)

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The Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Here, we have,

The Taylor series at x=0 for cos(x) is given by:

cos(x) = ∑(n=0 to infinity) (-1)ⁿ * (x²ⁿ)) / (2n)!

Now, let's find the Taylor series at x=0 for the given function x * cos²((3πx)/2):

To find the Taylor series for the given function, we'll use power series operations.

We'll substitute the Taylor series expansion for cos(x) into the given function and then perform the necessary operations.

Let's start with cos²((3πx)/2):

cos²((3πx)/2) = (cos((3πx)/2))²

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!)²

Expanding the square of the series, we get:

cos²((3πx)/2)

= (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Now, we'll multiply the x term to obtain the Taylor series for the given function:

x * cos²((3πx)/2) = x * (∑(n=0 to infinity) (-1)ⁿ * (((3πx)/2)²ⁿ) / (2n)!) * (∑(m=0 to infinity) (-1)^m * (((3πx)/2)^(2m)) / (2m)!)

Expanding the multiplication and rearranging the terms, we have:

x * cos²((3πx)/2) = ∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

Therefore, the Taylor series at x=0 for the given function x * cos²((3πx)/2) is:

∑(n=0 to infinity) ∑(m=0 to infinity) (-1)^(n+m) * (x²ⁿ⁺¹) * ((((3π)/2)^(2n+2m)) / ((2n)!(2m)!))

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Answer: \(x=5\)

Step-by-step explanation:

Because the \(x\) coordinate of both of the points is 5, the equation is \(x=5\).

Answer:

50°

Step-by-step explanation:

angle 5 = angle 4 ( Alternative Interior Angles are equal )

But angle 3 & angle 4 are linear pairs. So,

angle 3 + angle 4 = 180°

=> angle 3 + angle 5 = 180° (angle 5 = angle 4)

=> angle 3 + 130° = 180°

=> angle 3 = 180° - 130° = 50°

Answer:

x = -5.39

Step-by-step explanation:

x + (−2.4) = −7.79

x =  −7.79 + 2.4

x  =  -5.39

Answer:

-5.39

Step-by-step explanation:

The probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.

We need to calculate the probability that exactly 8 of the 19 people in the random sample are employed. The probability of a single person being employed is 4%, or 0.04.

To calculate the probability of 8 people being employed out of the 19, we can use the binomial distribution formula:

P(X=8) = nCx * (p^x) * (1-p)^(n-x) Where n = 19, x = 8, p = 0.04, and 1-p = 0.96

So, P(X=8) = 19C8 * (0.04^8) * (0.96^11) = 0.2793 or 27.93%.

Therefore, the probability that exactly 8 of the 19 people in the random sample are employed is 27.93%.

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The length of this cable to the nearest tenth of a block will be 6.3 blocks. Then the correct option is C.

Let one point be (x, y) and another point be (h, k). Then the distance between the points will be

D² = (x - h)² + (y - k)²

A map of a small town identifies the town square as the origin (0,0). Each block along a street is represented by one unit along the x- or y-axis. The ice cream shop is at (5. 4) and the grocery store is at (3.-2).

To speed up deliveries, the grocer plans to set up an overhead delivery wire that runs directly between the grocery store and the ice cream parlor.

The length of this cable to the nearest tenth of a block will be

D² = (5 - 3)² + (4 + 2)²

D² = 2² + 6²

D² = 4 + 36

D² = 40

D = 6.3 blocks

The length of this cable to the nearest tenth of a block will be 6.3 blocks. Then the correct option is C.

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Answer:

A one-sample t-test for a population mean is the appropriate test for the researchers' hypothesis. In this case, they want to test the hypothesis that the mean battery life of their new battery is greater than a known mean battery life of their older version. The one-sample t-test allows them to compare the mean of a sample to a known population mean and determine if the difference between them is statistically significant.

Answer:

5. ∠BOC = 101°

6. ∠AOD = 160°

Step-by-step explanation:

5) 1) cari nilai x

\(150=(4x-7)+(2x-5)\\150=4x-7+2x-5\\150=6x-12\\6x=150+12\\6x=162\\x=\frac{162}{6}\\x=27\)

2) masukkan nilai x dalam (4x-7)

\((4x-7)\\=4(27)-7\\=108-7\\=101\)

6) 1) cari nilai x

\(180=x+(7x+20)\\180=x+7x+20\\180=8x+20\\8x=180-20\\8x=160\\x=\frac{160}{8}\\x=20\)

2) tolak 180° dengan nilai x

\(180-20=160\)

ataupun masukkan nilai x dalam (7x+20)

\((7x+20)\\=7(20)+20\\=140+20\\=160\)

Answer:

3 a 2 − a + 10

Step-by-step explanation:

like and 5 star

Answer:

3a^2-a+10

Step-by-step explanation:

...

Simplification of Complex Rational Functions: Partial Fractions Expansion helps to break down complex rational functions into simpler, more manageable fractions.

Integration: Partial Fractions Expansion is often used in calculus to simplify the integration of rational functions. By breaking down the function into simpler fractions, it becomes easier to integrate each fraction separately.

Solving Linear Differential Equations: Partial Fractions Expansion can be used to solve linear differential equations involving rational functions. By decomposing the function into partial fractions, it becomes possible to find the solution to the differential equation.

As for the third part of your question, to solve the differential equation dt2d2x​+2dtdx​+10x=t2, you can use the method of undetermined coefficients. Assume a solution of the form

x(t)=At2+Bt+C, where A, B, and C are constants.

Differentiate this equation twice and substitute it back into the original differential equation. Equate the coefficients of each power of t and solve the resulting system of equations to find the values of A, B, and C.

Finally, substitute the values back into the assumed solution to obtain the specific solution to the differential equation.

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Partial fraction expansion is advantageous in simplifying algebraic expressions and facilitating integration and inverse Laplace transform calculations. To solve the given differential equation, various techniques such as the method of undetermined coefficients or variation of parameters can be used to obtain the particular and complementary solutions.

Partial fraction expansion is a useful technique in mathematics, particularly in the field of algebra and calculus, for simplifying and solving problems involving rational functions. It involves decomposing a complex rational function into simpler fractions called partial fractions. Here are some advantages of partial fraction expansion:

1. Simplification: By decomposing a complex rational function into partial fractions, it becomes easier to manipulate and analyze. It allows for simplification of algebraic expressions, making calculations more manageable.

2. Integration: Partial fraction expansion is commonly used in calculus for integrating rational functions. By decomposing a rational function into partial fractions, the integration process becomes simpler and can be performed term by term.

3. Inverse Laplace Transform: Partial fraction expansion is essential in finding the inverse Laplace transform of a given function. By decomposing the function into partial fractions, the inverse transform can be applied to each term individually, leading to a solution in the time domain.

Now, let's move on to the second part of your question:

To obtain the inverse Laplace transform of the given function F(s) = s^3 + 6s^2 + 8s/(s^5 + 8s^4 + 23s^3 + 35s^2 + 28s + 3), we need to perform partial fraction expansion. By factoring the denominator, we find that it can be expressed as (s + 1)(s + 3)(s^3 + 4s + 1).

By applying partial fraction decomposition and solving for the unknown coefficients, the function F(s) can be expressed as F(s) = A/(s + 1) + B/(s + 3) + (Cs^2 + Ds + E)/(s^3 + 4s + 1).

Next, we can use the method of inverse Laplace transforms to find the inverse transform of each term separately. This involves consulting Laplace transform tables or using known Laplace transform properties to obtain the final solution in the time domain.

Now, let's move on to the third part of your question:

The given differential equation is d^2x/dt^2 + 2(dx/dt) + 10x = t^2, with initial conditions x(0) = dx/dt(0) = 0.

To solve this differential equation, we can use various techniques such as the method of undetermined coefficients or variation of parameters. These methods involve assuming a particular form for the solution and determining the coefficients or functions that satisfy the given equation and initial conditions.

Once the particular solution is found, we add it to the complementary solution obtained by solving the associated homogeneous equation, which is obtained by setting the right-hand side of the differential equation to zero.

By applying the appropriate method, the solution to the given differential equation can be obtained. It is important to note that without specific initial conditions or further constraints, the solution may not be unique.

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Answer: Each side of the original square paper was 42 inches long.

Step-by-step explanation:

Let's start by using algebra to solve the problem.

Let x be the length of a side of the original square paper, in inches.

When Juan cut the paper vertically to make two rectangle pieces, he created two rectangles with different dimensions. However, we know that the perimeter of each rectangle is 63 inches.

The formula for the perimeter of a rectangle is:

Perimeter = 2 x Length + 2 x Width

We can use this formula to create two equations, one for each rectangle:

63 = 2L1 + 2W1

63 = 2L2 + 2W2

Since the original square paper was cut vertically, we know that the length and width of each rectangle must add up to x.

We can use this information to write two more equations:

L1 + W1 = x

L2 + W2 = x

Now we have four equations:

63 = 2L1 + 2W1

63 = 2L2 + 2W2

L1 + W1 = x

L2 + W2 = x

We have four equations and four unknowns (L1, W1, L2, W2), so we can solve for x.

First, let's simplify the equations by solving for one of the variables in terms of the others. We can solve the equations for L1 and L2:

L1 = x - W1

L2 = x - W2

Now we can substitute these expressions into the perimeter equations:

63 = 2(x - W1) + 2W1

63 = 2(x - W2) + 2W2

Simplifying, we get:

63 = 2x + 2W1

63 = 2x + 2W2

Subtracting 2x from both sides of each equation, we get:

2W1 = 63 - 2x

2W2 = 63 - 2x

Dividing both sides of each equation by 2, we get:

W1 = (63 - 2x)/2

W2 = (63 - 2x)/2

Now we can substitute these expressions into the equations for L1 and L2:

L1 = x - (63 - 2x)/2

L2 = x - (63 - 2x)/2

Simplifying, we get:

L1 = (3x - 63)/2

L2 = (3x - 63)/2

Now we can use the fact that the perimeter of each rectangle is 63 inches to create one more equation:

2L1 + 2W1 = 63

Substituting in the expressions for L1 and W1, we get:

2[(3x - 63)/2] + [(63 - 2x)/2] = 63

Simplifying, we get:

3x = 126

Dividing both sides by 3, we get:

x = 42

Therefore, each side of the original square paper was 42 inches long.

Answer:

give clear image is next question

Step-by-step explanation:

i will give you the answer

On solving the system of equations 1x + 4y = 73 and 9x + 5y = 192, the value for one plain and one shiny wrapping paper is obtained as $13 and $15 respectively.

What is an equation?

A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").

Let the cost of plain wrapping paper be x.

Let the cost of shiny wrapping paper be y.

Stephanie sold 1 roll of plain wrapping paper and 4 rolls of shiny wrapping paper for a total of $73.

The equation for Stephanie is -

1x + 4y = 73 ..... (1)

Aliyah sold 9 rolls of plain wrapping paper and 5 rolls of shiny wrapping paper for a total of $192.

The equation for Aliyah is -

9x + 5y = 192 ....... (2)

Multiply equation (1) by 9 -

9x + 36y = 657 ....... (3)

Subtract equation (2) form (3) -

9x + 36y - (9x + 5y) = 657 - 192

9x + 36y - 9x - 5y = 465

31y = 465

y = 465 / 31

y = 15

Therefore, the cost of one shiny wrapping paper is $15.

Substitute the value of y in equation (1) -

1x + 4(15) = 73

x = 73 - 60

x = 13

Therefore, the cost of one plain wrapping paper is $13.

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the statement is true.the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.

Simple random sampling is a type of probability sampling technique wherein every member of the population has an equal and independent chance of being selected. Independence means that the selection of one unit does not affect the selection of any other unit. The success-failure condition is an important condition of simple random sampling, which states that the size of each of the two groups (i.e., success and failure) should be at least 10. In this case, the two groups are 289 and 111, which are both greater than 10. Therefore, the success-failure condition is satisfied and we can conclude that simple random sample gets us independence.

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Answer:

y = 15x

Step-by-step explanation:

Given x and y are in direct variation then the equation relating them is

y = kx ← k is the constant of variation

To find k use the condition x = 2, y = 30, then

30 = 2k ( divide both sides by 2 )

15 = k

y = 15x ← equation of variation

Answer:

6h+14k

Step-by-step explanation:

Multiply 2by 3h which gives 6h then multiply 7k by 2 which gives 14k.

Since 6h and 14k are not like terms u cannot add so your answer will be 6h + 14k.

Answer:

9h² + 42hk + 49k²

Step-by-step explanation:

Given

(3h + 7k)²

= (3h + 7k)(3h + 7k)

Each term in the second factor is multiplied by each term in the first factor, that is

3h(3h + 7k) + 7k(3h + 7k) ← distribute both parenthesis

= 9h² + 21hk + 21hk + 49k² ← collect like terms

= 9h² + 42hk + 49k²

Between Method A with a MAD(Mean Absolute Deviation) of 1.4 and Method B with a MAD (Mean Absolute Deviation) of 1.8, Method A performed better as it has a smaller MAD value.

To decide which estimating strategy performed the leading, we got to compare their Mean Absolute Deviation (Mad) values. Mad may be a degree of the average outright contrast between the genuine values and the forecasted values.

A little Mad esteem shows distant better; a much better; a higher; stronger; an improved" an improved forecasting accuracy, because it implies the forecasted values are closer to the real values.

Hence, between Strategy A with a Mad of 1.4 and Strategy B with a Mad of 1.8, Strategy A performed way better because it incorporates littler Mad esteem.

Be that as it may, it's vital to note that Mad alone does not allow a total picture of the determining execution. Other measurements, such as Mean Squared Blunder (MSE) or Mean Supreme Rate Blunder (MAPE) ought to too be considered to assess the exactness of the estimating strategies.

Furthermore, the setting and reason for the determining ought to too be taken under consideration when choosing the fitting estimating strategy. 

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Answer:

Paul had  5 sweets  in the first place ( Now he has 15)

Step-by-step explanation:

p= Paul   Sally = 5p

5p -10 = p+10

4p =  20

p = 5

Now Paul has 15 and Sally has 15 too

The average number of toys per person is 8 (option C).

let's calculate the average number of toys per person. We know that five people are working 8 hours a day for 5 days, so the total work hours for the week is 5 × 8 × 5 = 200 hours.

Since these five people can assemble 400 toys in that time, the average number of toys assembled per hour is 400 / 200 = 2 toys per hour.

Now, since each person works for 8 hours a day, the average number of toys assembled per person per day is 2 × 8 = 16 toys.

Since there are 5 working days in a week, the average number of toys assembled per person per week is 16 × 5 = 80 toys.

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When the above is simplified using Boolean Algebra, we have F = x' + y' + w'xy.

We can simplify  the Boolean function F = xy'z' + xy'z+ w'xy +   w'x'y' + w'xy using the following Boolean Algebra rules.

Absorption - x + xy = x

Commutativity -  xy = yx

Associativity - x(yz) = (xy)z

Distributivity - x(y + z) = xy + xz

Using the above , we   have

F = xy'z' + xy'z+ w'xy + w'x'y' +   w'xy

= xy'(z + z') + w'xy(x + x')

= xy' +  w'xy

= (x' + y)(x' + y')  + w'xy

= x' + y' + w'xy

This means that the simplified expression is F = x' + y' + w'xy.

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Based on the given clues, we can determine the person, drink, and price paid for each individual:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

From clue 1, we know that either Calvin or the person who got the Root Beer paid $4.99. Since Calvin paid more than Lee according to clue 4, Calvin cannot be the one who got the Root Beer. Therefore, Calvin paid $4.99.

From clue 2, Kelli paid $6.99.

From clue 3, the person who got the water paid $1 less than Dean. Since Dean paid the highest price, the person who got the water paid $1 less, which means Lee paid $5.99.

From clue 5, the person who got the Root Beer paid $1 less than the person who got the Iced Tea. Since Calvin got the Root Beer, Lee must have gotten the Iced Tea.

Therefore, the final assignments are:

Calvin: Root Beer, $4.99

Dean: Lemonade, $7.99

Kelli: Water, $6.99

Lee: Iced Tea, $5.99

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A) To find \(\( f'(t) \) for \( f(t) = \left(\frac{{6t - 6}}{{t}}\right)^2/9 \)\), we can use the chain rule. First, let's simplify the expression:

\(\[ f(t) = \left(\frac{{(6t - 6)^2}}{{t^2}}\right)/9 \]\)

Applying the chain rule, we differentiate the numerator and denominator separately:

\(\[ f'(t) = \frac{{2(6t - 6)(6) \cdot t^2 - (6t - 6)^2(2t)}}{{9t^4}} \]\)

Simplifying further:

\(\[ f'(t) = \frac{{72t^3 - 72t^2 - 12t(6t - 6)^2}}{{9t^4}} \]\)

B) To find \(\( f'(x) \) for \( f(x) = e^{\sqrt{5x + 2}} \)\), we can use the chain rule.

The derivative of the exponential function \(\( e^u \) with respect to \( u \) is \( e^u \cdot u' \).\)

In this case, \(\( u = \sqrt{5x + 2} \), so \( u' = \frac{d}{dx}(\sqrt{5x + 2}) \).\)

Applying the chain rule:

\(\[ u' = \frac{1}{2\sqrt{5x + 2}} \cdot \frac{d}{dx}(5x + 2) = \frac{1}{2\sqrt{5x + 2}} \cdot 5 = \frac{5}{2\sqrt{5x + 2}} \]\)

Now, we can apply the chain rule to find \(\( f'(x) \):\)

\(\[ f'(x) = e^{\sqrt{5x + 2}} \cdot \frac{5}{2\sqrt{5x + 2}} \]\)

C) To find the derivative of \(\( f(x) = x^3 \cos(x) \)\), we can apply the product rule. The derivative of the product of two functions \(\( u \) and \( v \)\) is given by \(\( (uv)' = u'v + uv' \).\) In this case, \(\( u = x^3 \) and \( v = \cos(x) \).\) Differentiating \(\( u \) and \( v \):\)

\(\[ u' = 3x^2 \quad \text{and} \quad v' = -\sin(x) \]\)

Applying the product rule:

\(\[ f'(x) = (x^3 \cdot \cos(x))' = 3x^2 \cdot \cos(x) + x^3 \cdot (-\sin(x)) \]\)

Simplifying further:

\(\[ f'(x) = 3x^2 \cos(x) - x^3 \sin(x) \]\)

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Answer:

4+8-4=8

Step-by-step explanation:

2^3 simplified is 8

The absolute value of -4 is 4

Therefore you get 4+8-4

4+8=12-4=8

Answer:

d

Step-by-step explanation:

beacusee its wiill will be resonable

The inverse of function of f(x) will be p(x) = 7x – 2. Then the correct option is B.

A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.

Let the function will be

f: X → Y

Then the inverse function will be

f⁻¹: Y → X

The function is given below.

f(x) = (x + 2) / 7

Substitute p(x) in place of x and x in place of f(x). Then the equation of the inverse function will be

x = [p(x) + 2] / 7

Solve the equation for p(x), then the equation of the inverse function will be

p(x) + 2 = 7x

     p(x) = 7x – 2

Thus, the inverse of function of f(x) will be p(x) = 7x – 2.

Then the correct option is B.

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Answer:

x = 120

Step-by-step explanation:

Given

0.25(x + 4) - 3 = 28 ( add 3 to both sides )

0.25(x + 4) = 31 ( divide both sides by 0.25 )

x + 4 = 124 ( subtract 4 from both sides )

x = 120

The value of x that satisfies the equation 0.25(x + 4) - 3 = 28 is x = 120.

Here, we have,

To solve the equation 0.25(x + 4) - 3 = 28, we will follow these steps:

Let's go through each step in detail:

Step 1: Distribute the 0.25 to the terms inside the parentheses.

0.25(x + 4) - 3 = 28

Distribute 0.25 to (x + 4):

0.25x + 0.25 * 4 - 3 = 28

Step 2: Simplify the equation by combining like terms.

0.25x + 1 - 3 = 28

Simplify 0.25 * 4:

0.25x + 1 - 3 = 28

0.25x - 2 = 28

Step 3: Isolate the variable x on one side of the equation.

To isolate the variable x, we want to get rid of the constant term -2 on the left side.

We can do this by adding 2 to both sides:

0.25x - 2 + 2 = 28 + 2

Simplifying:

0.25x = 30

Step 4: Solve for x.

To find the value of x, divide both sides by 0.25:

0.25x / 0.25 = 30 / 0.25

Simplifying:

x = 120

So, the value of x that satisfies the equation 0.25(x + 4) - 3 = 28 is x = 120.

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Answer:

1

Step-by-step explanation:

\( {8}^{0} = 1 \\ \)

Any number raised to zero is always equal to one.

The coordinates of the triangle S'T'U' is (2, -1), (5,3), (1, -4) and the triangle S"T"U" is (1,3), (4,5),(0,-2)

Coordinates:

Basically, the pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes is known as coordinates.

Given,

The triangle STU is graphed at S(2,-1) T(5,-3) U(1,4). Triangle STU is reflected over the x-axis to create triangle S'T'U' and then translated by the rule (x,y) ->(x-1,y+2) to create S"T"U".

Here we need to find the coordinates for triangle S'T'U' and S"T"U".

In order to find the correct transformation for this triangle, we have to do the following,

The formula that is used to reflect a coordinate point about the x-axis.

(X2,Y2) = (X1,Y1) * (1,-1)

So, based on this rule, the coordinates of S'T'U' is,

S(2,-1) => S'((2 x 1), (-1 x -1)) = > S'(2,-1)

T(5,-3) => T'((5 x 1), (-3 x -1)) => T'(5, 3)

U(1,4) => U'((1 x 1), (4 x -1)) => U'(1, -4)

Now we have to apply the next rule,

=> (x, y) -> (x-1, y+2)

S'(2,1) => S'((2 - 1), (1 + 2)) = > S'(1, 3)

T'(5,3) => T'((5 - 1), (3 + 2)) => T'(4, 5)

U'(1,-4) => U'((1 - 1), (-4 + 2)) => U'(0, -2)

Therefore, the coordinates of S'T'U' is (2, -1), (5,3), (1, -4) and the coordinates of S"T"U" is (1,3), (4,5),(0,-2)

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Answer:

4

Step-by-step explanation: