solve y-3x=13 for y

Answer: \(\frac{1}{x^{4} }\)

The h the price of a hamburger and f the price of an order of french fries is h = (11/2) - (f/2) and f = 11 − 2h.

Let h be the price of a hamburger and f be the price of an order of french fries.

        3h + 4f = 22.75

        2h + 1f = 11

Therefore, the system of equations that can be used to find the prices of a hamburger and an order of french fries are:

3h + 4f = 22.75

2h + 1f = 11

The specific equations I provided are only applicable to the problem of finding the prices of hamburgers and french fries at Hamberger Hut based on the given information.

For other problems, different equations may be needed to model the situation and solve for the unknown variables.

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Answer:

Line a has a slope of undefined as its a vertical line.

Line B has a slope of 4/3

line c has a slope of 3/4

and line d has a slope of 0 as its a horizontal line

Step-by-step explanation:

Answer:4/3 is B goes up 4 units then over 3

3/4 is C goes up 3 units and over 4

1-9/16 :) good luck my friend

The total amount of the checks listed on the opposite site of the deposit slip​ was $ 548.65. The correct option is (B).

When a bank customer deposits money into an account, they typically add a little paper form called a deposit slip.

The account may belong to the user personally or it may belong to another else. A deposit slip functions as a sort of insurance for the customer and the bank.

A deposit slip is a document that by definition includes the date, the depositor's name, account information, and the sums being deposited.

Here,

Calculation of total amount of the checks:

Total amount = 123.51 + 211.00 + 214.14

Total amount = 548.65

Therefore, the total amount of the checks listed on the opposite site of the deposit slip​ was $ 548.65.

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Answer:

The other two angles are 22° , 22°

Step-by-step explanation:

To find the other angles, we can use angle sum property of triangle.

      The given angle 136° cannot be base angles. Let the base angles be x.

x + x + 136 = 180°

   2x + 136 = 180°

Subtract 136 from both sides,

            2x = 180 - 136

            2x = 44°

Divide both sides by 2,

              x = 44 ÷ 2

                \(\sf \boxed{x = 22^\circ}\)

Answer:42

Step-by-step explanation:

hello

the current population is 28,000 and it increases by a factor of 750 annually .

to write a function to express this relationship

from the calculation above, it's evident that the answer corresponds to option A in the given options

Answer:

the number of white cars vs the number of white trucks

C: The total number of planes landing at O’Hare Airport categorized by type is the answer

the dataset is a collection of numbers connected by theme. There are three ways to work with datasets: mean, median, and mode. The mean is the average of the dataset, the median is the median of the dataset, and the mode is the number or value that occurs most often in the dataset.

Standard deviation of a data set is the square root of the calculated variance of a set of data. The formula for variance (s2) is the sum of the squared differences between each data point and the mean, divided by the number of data points.

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Answer:

Yes

Step-by-step explanation:

It is a function look at the numbers

BC is tangent to circle A, and the value of r is 10.

Given,

BC=24

CD=16

AD=AB=r

To find the value of r, we can use the fact that a tangent line to a circle is perpendicular to the radius at the point of tangency. So we know that angle ABD is a right angle, and we can use the Pythagorean theorem

The Pythagorean theorem can be used to calculate the value of r:

\(AB^2+BC^2=AC^2\)

\(r^2+24^2=(r+16)^2\)

\(r^2= (r+16)^2-24^2\)

\(r^2\)= \(r^2\)+256+32r-576

\(r^2\)=\(r^2\)+32r-320

\(r^2-r^2\)-32r=-320

-32r=-320

r=320/32

r=10

Therefore the correct answer is r=10.

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1.Bricks and timber purchased for construction. (Debit: Bricks - Rs 60,000, Debit: Timber - Rs 35,000, Credit: Bank - Rs 95,000)

2.Transfer of Rs 13,000 to fixed deposit account. (Debit: Fixed Deposit - Rs 13,000, Credit: Current Account - Rs 13,000)

3.Appointment of Mr. S.N. Rao as Accountant. (Debit: Salary Expense - Rs 300, Debit: Security Deposit - Rs 1,000, Credit: Accountant - Rs 300)

4.Goods sold to Shruti with discounts. (Debit: Accounts Receivable - Shruti - Rs 80,000, Credit: Sales - Rs 80,000)

5.Goods purchased from Richa with discounts. (Debit: Purchases - Rs 60,000, Credit: Accounts Payable - Richa - Rs 60,000)

6.Goods sold to Shilpa with discounts and received payment. (Debit: Accounts Receivable - Shilpa - Rs 50,000, Credit: Sales - Rs 50,000)

7.Goods sold to Garima with discounts and received partial payment. (Debit: Accounts Receivable - Garima - Rs 1,00,000, Credit: Sales - Rs 1,00,000)

8.Purchase of land with additional charges. (Debit: Land - Rs 2,00,000, Debit: Brokerage Expense - Rs 2,000, Debit: Registration Charges - Rs 15,000, Credit: Bank - Rs 2,17,000)

9.Proprietor took goods and cash for personal use. (Debit: Proprietor's Drawings - Rs 65,000, Credit: Goods - Rs 25,000, Credit: Cash - Rs 40,000)

10.Goods sold to Charu with profit and discount. (Debit: Accounts Receivable - Charu - Rs 1,20,000, Credit: Sales - Rs 1,20,000)

11.Rent paid for the building. (Debit: Rent Expense - Rs 60,000, Credit: Bank - Rs 60,000)

12.Goods sold to Sunil with profit and discount. (Debit: Accounts Receivable - Sunil - Rs 24,000, Credit: Sales - Rs 24,000)

13.Purchased goods from Nanda and supplied to Helen. (Debit: Purchases - Rs 1,000, Debit: Accounts Payable - Nanda - Rs 1,000, Credit: Accounts Receivable - Helen - Rs 1,300, Credit: Sales - Rs 1,300)

14.Purchased goods from Rohit and Sons and supplied to Madan. (Debit: Purchases - Rs 2,700, Credit: Accounts Payable - Rohit and Sons - Rs 2,700, Debit: Accounts Receivable - Madan - Rs 3,000, Credit: Sales - Rs 3,000)

Here are the journal entries for the given transactions:

1. Bricks and timber purchased for construction:

Debit: Bricks (Asset) - Rs 60,000

Debit: Timber (Asset) - Rs 35,000

Credit: Bank (Liability) - Rs 95,000

2. Transfer to fixed deposit account:

Debit: Fixed Deposit (Asset) - Rs 13,000

Credit: Current Account (Asset) - Rs 13,000

3. Appointment of Mr. S.N. Rao as Accountant:

Debit: Salary Expense (Expense) - Rs 300

Debit: Security Deposit (Asset) - Rs 1,000

Credit: Accountant (Liability) - Rs 300

4. Goods sold to Shruti:

Debit: Accounts Receivable - Shruti (Asset) - Rs 80,000

Credit: Sales (Income) - Rs 80,000

5. Goods purchased from Richa:

Debit: Purchases (Expense) - Rs 60,000

Credit: Accounts Payable - Richa (Liability) - Rs 60,000

6. Goods sold to Shilpa:

Debit: Accounts Receivable - Shilpa (Asset) - Rs 50,000

Credit: Sales (Income) - Rs 50,000

7. Goods sold to Garima:

Debit: Accounts Receivable - Garima (Asset) - Rs 1,00,000

Credit: Sales (Income) - Rs 1,00,000

8.Purchase of land:

Debit: Land (Asset) - Rs 2,00,000

Debit: Brokerage Expense (Expense) - Rs 2,000

Debit: Registration Charges (Expense) - Rs 15,000

Credit: Bank (Liability) - Rs 2,17,000

9. Goods and cash taken away by proprietor:

Debit: Proprietor's Drawings (Equity) - Rs 65,000

Credit: Goods (Asset) - Rs 25,000

Credit: Cash (Asset) - Rs 40,000

10. Goods sold to Charu:

Debit: Accounts Receivable - Charu (Asset) - Rs 1,20,000

Credit: Sales (Income) - Rs 1,20,000

Credit: Cost of Goods Sold (Expense) - Rs 80,000

Credit: Profit on Sales (Income) - Rs 40,000

11. Rent paid for the building:

Debit: Rent Expense (Expense) - Rs 60,000

Credit: Bank (Liability) - Rs 60,000

12. Goods sold to Sunil:

Debit: Accounts Receivable - Sunil (Asset) - Rs 24,000

Credit: Sales (Income) - Rs 24,000

Credit: Cost of Goods Sold (Expense) - Rs 20,000

Credit: Profit on Sales (Income) - Rs 4,000

13. Goods purchased from Nanda and supplied to Helen:

Debit: Purchases (Expense) - Rs 1,000

Debit: Accounts Payable - Nanda (Liability) - Rs 1,000

Credit: Accounts Receivable - Helen (Asset) - Rs 1,300

Credit: Sales (Income) - Rs 1,300

14. Goods received from Rohit and Sons and supplied to Madan:

Debit: Purchases (Expense) - Rs 2,700 (after 10% trade discount)

Credit: Accounts Payable - Rohit and Sons (Liability) - Rs 2,700

Debit: Accounts Receivable - Madan (Asset) - Rs 3,000

Credit: Sales (Income) - Rs 3,000

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Answer:

We are aware of the equation.

Equation 1 reads (fg)(x) = f(x) * g(x).

Hence, we can resolve it as follows:

Given equation: equation 2 (fg)(x) = 3x (x2 + 5)

Equation 3 is obtained by comparing equations 1 and 2, as follows:

"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5

When we change equation 3 to read f(x) = x2 + 5, we get:

(x2 + 5) * g(x) = 3x (x2 + 5)

See what both equations have in common; it is (x2 + 5)

The result of dividing both sides by x2 + 5 is:

g(x) = 3x

G(x) will therefore have a value of 3x.

From the above equation given in the question , we get that g(x)  have a value of 3x.

We are aware of the equation.

Equation 1 reads (fg)(x) = f(x) * g(x).

Hence, we can resolve it as follows:

Given equation: equation 2 (fg)(x) = 3x (x2 + 5)

Equation 3 is obtained by comparing equations 1 and 2, as follows:

"f(x)*g(x)" equals "3x (x2 + 5" - The equation 3 that is provided: f(x) = x2 + 5

When we change equation 3 to read f(x) = x2 + 5, we get:

(x2 + 5) * g(x) = 3x (x2 + 5)

See what both equations have in common; it is (x2 + 5)

The result of dividing both sides by x2 + 5 is:

g(x) = 3x

G(x) will therefore have a value of 3x.

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The values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

What is a linear factor?

A linear factor is a polynomial of degree one, which means it has one variable raised to the first power and a constant coefficient. In other words, it is an expression of the form ax + b, where a and b are constants and x is the variable.

We can factor the quadratic 2x² + kx - 5 into the product of two linear factors with integer coefficients if and only if its discriminant is a perfect square.

The discriminant of the quadratic equation ax² + bx + c = 0 is given by the expression b² - 4ac. In this case, a = 2, b = k, and c = -5. Therefore, the discriminant is:

b² - 4ac = k² - 4(2)(-5) = k² + 40

For the quadratic to be factored into two linear factors with integer coefficients, k² + 40 must be a perfect square.

One way to proceed is to list the perfect squares that are 40 greater than a square, and see if k is one of the corresponding values. We can do this by solving the equation:

k² + 40 = m²

where m is an integer. Rearranging, we get:

k² - m² = -40

This is a difference of squares, so we can factor it:

(k + m)(k - m) = -40

We now need to find integer values of k and m that satisfy this equation. We can do this by considering all possible pairs of factors of -40 and solving for k and m.

The pairs of factors of -40 are:

(-1, 40), (-2, 20), (-4, 10), (-5, 8)

For each pair, we can solve the system of equations:

k + m = a

k - m = b

where a and b are the two factors in the pair. Adding these equations, we get:

2k = a + b

Subtracting them, we get:

2m = a - b

Solving for k and m, we obtain:

k = (a + b)/2

m = (a - b)/2

We can now check if the values of k and m are integers and if they satisfy the original equation.

For example, if we take the pair (-1, 40), we get:

k + m = -1

k - m = 40

Adding these equations, we get:

2k = 39

This implies that k = 39/2, which is not an integer, so this pair does not work.

Trying the other pairs, we find that:

(-2, 20) gives k = 9 and m = 11, which works

(-4, 10) gives k = 3 and m = 7, which works

(-5, 8) gives k = 1 and m = 3, which works

Therefore, the values of k for which 2x² + kx - 5 can be factored as the product of two linear factors with integer coefficients are k = 3, 1, and 9.

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To find the values of x for which the gradient function of the curve is zero, we need to find the values of x that make the derivative of the curve equal to zero.

The given function is: \(\displaystyle\sf f(x)=23x^{3}+2x^{2}-12x+3\).

To find the derivative of the function, we differentiate each term with respect to x:

\(\displaystyle\sf f'(x)=69x^{2}+4x-12\).

Now we set the derivative equal to zero and solve for x:

\(\displaystyle\sf 69x^{2}+4x-12=0\).

We can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula to find the values of x:

\(\displaystyle\sf x=\frac{-b\pm \sqrt{b^{2}-4ac}}{2a}\).

Plugging in the values a=69, b=4, and c=-12, we get:

\(\displaystyle\sf x=\frac{-4\pm \sqrt{(4)^{2}-4(69)(-12)}}{2(69)}\).

Simplifying further, we have:

\(\displaystyle\sf x=\frac{-4\pm \sqrt{16+3312}}{138}\).

\(\displaystyle\sf x=\frac{-4\pm \sqrt{3328}}{138}\).

\(\displaystyle\sf x=\frac{-4\pm 8\sqrt{13}}{138}\).

Therefore, the values of x for which the gradient function of the curve is zero are given by \(\displaystyle\sf x=\frac{-4+8\sqrt{13}}{138}\) and \(\displaystyle\sf x=\frac{-4-8\sqrt{13}}{138}\).

To find the equations of the tangents to the curve that are parallel to the x-axis (horizontal tangents), we substitute these x-values into the original function \(\displaystyle\sf f(x)\). The resulting y-values will give the equations of the tangents.

For \(\displaystyle\sf x=\frac{-4+8\sqrt{13}}{138}\):

\(\displaystyle\sf y=f\left(\frac{-4+8\sqrt{13}}{138}\right)=23\left(\frac{-4+8\sqrt{13}}{138}\right)^{3}+2\left(\frac{-4+8\sqrt{13}}{138}\right)^{2}-12\left(\frac{-4+8\sqrt{13}}{138}\right)+3\).

For \(\displaystyle\sf x=\frac{-4-8\sqrt{13}}{138}\):

\(\displaystyle\sf y=f\left(\frac{-4-8\sqrt{13}}{138}\right)=23\left(\frac{-4-8\sqrt{13}}{138}\right)^{3}+2\left(\frac{-4-8\sqrt{13}}{138}\right)^{2}-12\left(\frac{-4-8\sqrt{13}}{138}\right)+3\).

These two equations represent the equations of the tangents to the curve that are parallel to the x-axis.

Using the t-distribution, it is found that the margin of error for the 95% confidence interval is of $336.

The confidence interval is:

\(\overline{x} \pm t\frac{s}{\sqrt{n}}\)

In which:

The margin of error is given by:

\(M = t\frac{s}{\sqrt{n}}\)

The critical value, using a t-distribution calculator, for a two-tailed 95% confidence interval, with 69 - 1 = 68 df, is t = 1.9955.

The standard deviation and sample size are given, respectively, by:

s = 1400, n = 69.

Hence, the margin of error in dollars is given by:

\(M = t\frac{s}{\sqrt{n}}\)

\(M = 1.9955\frac{1400}{\sqrt{69}}\)

M = 336.

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Answer:

x = 65.26 degrees or x = 245.26 degrees.

Step-by-step explanation:

To solve the equation 4tan(x)-7=0 for 0<=x<360, we can first isolate the tangent term by adding 7 to both sides:

4tan(x) = 7

Then, we can divide both sides by 4 to get:

tan(x) = 7/4

Now, we need to find the values of x that satisfy this equation. We can use the inverse tangent function (also known as arctan or tan^-1) to do this. Taking the inverse tangent of both sides, we get:

x = tan^-1(7/4)

Using a calculator or a table of trigonometric values, we can find the value of arctan(7/4) to be approximately 65.26 degrees (remember to use the appropriate units, either degrees or radians).

However, we need to be careful here, because the tangent function has a period of 180 degrees (or pi radians), which means that it repeats every 180 degrees. Therefore, there are actually two solutions to this equation in the given domain of 0<=x<360: one in the first quadrant (0 to 90 degrees) and one in the third quadrant (180 to 270 degrees).

To find the solution in the first quadrant, we can simply use the value we just calculated:

x = 65.26 degrees (rounded to two decimal places)

To find the solution in the third quadrant, we can add 180 degrees to the first quadrant solution:

x = 65.26 + 180 = 245.26 degrees (rounded to two decimal places)

So the solutions to the equation 4tan(x)-7=0 for 0<=x<360 are:

x = 65.26 degrees or x = 245.26 degrees.

Answer:

20000

Step-by-step explanation:

because the x =1 and X=2 so is 1x2=2

Answer:

Between 19.3 and 55.9 animals.

Step-by-step explanation:

Chebyshev Theorem

The Chebyshev Theorem can also be applied to non-normal distribution. It states that:

At least 75% of the measures are within 2 standard deviations of the mean.

At least 89% of the measures are within 3 standard deviations of the mean.

An in general terms, the percentage of measures within k standard deviations of the mean is given by \(100(1 - \frac{1}{k^{2}})\).

In this question:

Mean of 37.6, standard deviation of 6.1.

Between what two numbers of animals does Chebyshev's Theorem guarantees that we will find at least 89% of the days?

Within 3 standard deviations of the mean, so:

37.6 - 3*6.1 = 19.3

37.6 + 3*6.1 = 55.9

Between 19.3 and 55.9 animals.

The total area of the composite figure which has triangle and rectangle is  24.41 square inches

The given composite figure has two triangles and one rectangle

Area of rectangle =length × width

=4.6×3.15

=14.49 square inches

Area of left side triangle, it has base of 3.3 in and height 3.15 inches

Area of triangle = 1/2×3.3×3.15

=5.1975 square inches

Area of triangle on right side

Base = 3 in

Height = 6.3-3.15=3.15 in

Area of triangle = 1/2×3×3.15

=4.725 square inches

Total area = 14.49 + 5.1975  + 4.725

=24.41 square inches

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a. The chart is prepared below.

b. At the end of 4 years, Ross still owes his parents $1,576.92.

To solve this problem, we need to calculate the balance of Ross's loan at the end of each year.

The balance for each year can be calculated by subtracting the yearly payment from the balance at the beginning of the year and adding the interest earned for the year.

The interest for each year is calculated by multiplying the balance at the beginning of the year by the annual interest rate of 3.2%.

Here are the steps for calculating the balance for each year:

Year 1:

Beginning balance = $2,500.00

Interest for the year = $2,500.00 x 0.032 = $80.00

Ending balance = $2,500.00 + $80.00 - $300.00 = $2,280.00

Year 2:

Beginning balance = $2,280.00

Interest for the year = $2,280.00 x 0.032 = $72.96

Ending balance = $2,280.00 + $72.96 - $300.00 = $2,052.96

Year 3:

Beginning balance = $2,052.96

Interest for the year = $2,052.96 x 0.032 = $65.76

Ending balance = $2,052.96 + $65.76 - $300.00 = $1,818.72

Year 4:

Beginning balance = $1,818.72

Interest for the year = $1,818.72 x 0.032 = $58.20

Ending balance = $1,818.72 + $58.20 - $300.00 = $1,576.92

Here's a table that shows the details:

Year ,principal ,Interest rate, interest, Payment ,annual owing

1 $2,500.00 $80.00 $300.00              $2,280.00

2 $2,280.00 $72.96 $300.00              $2,052.96

3 $2,052.96 $65.76 $300.00               $1,818.72

4 $1,818.72         $58.20  $300.00       $1,576.92

b. At the end of 4 years, Ross still owes his parents $1,576.92.

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A set of numbers that can represent the side lengths, in centimeters, of a right triangle is any set that satisfies the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

A right triangle is a type of triangle that contains a 90-degree angle. According to the Pythagorean theorem, in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's consider a set of numbers that could represent the side lengths of a right triangle in centimeters.

One possible set could be 3 cm, 4 cm, and 5 cm.

To verify if this set forms a right triangle, we can apply the Pythagorean theorem.

Squaring the length of the shortest side, 3 cm, gives us 9. Squaring the length of the other side, 4 cm, gives us 16.

Adding these two values together gives us 25.

Finally, squaring the length of the hypotenuse, 5 cm, also gives us 25. Since both values are equal, this set of side lengths satisfies the Pythagorean theorem, and hence forms a right triangle.

It's worth mentioning that the set of side lengths forming a right triangle is not limited to just 3 cm, 4 cm, and 5 cm.

There are infinitely many such sets that can be generated by using different combinations of positive integers that satisfy the Pythagorean theorem.

These sets are known as Pythagorean triples.

Some other examples include 5 cm, 12 cm, and 13 cm, or 8 cm, 15 cm, and 17 cm.

In summary, a right triangle can have various sets of side lengths in centimeters, as long as they satisfy the Pythagorean theorem, where the square of the hypotenuse's length is equal to the sum of the squares of the other two sides.

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The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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After considering the given data we come to the conclusion that the length of AB is 12.124 units, under the condition that A (-3, 5) and B (4, -2) are the given coordinates.

The distance between two points in a plane can be found using the distance formula which is an application of the Pythagorean theorem. The formula is given by d=√ ( ((x₂ – x₁ )² + (y₂ – y₁ )²)

Here (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.

Applying the given coordinates of A (-3, 5) and B (4, -2), we can evaluate the distance between them as follows:

d = √( (4 - (-3))² + (-2 - 5)² )

 = √(7² + (-7)²)

 = √(98 + 49)

 = √147

 = 12.124

Therefore, the length of AB is approximately 12.124 units.

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Answer:

(2, 1)

Step-by-step explanation:

In a reflection across the x-axis, the x coordinate will stay the same but the y coordinate will be the negative version of the original number.

This means (2, -1) will change to (2, 1)

Answer:

2,1

Step-by-step explanation:

The mean of the given data is 1744 days, median of the given data is 1460.5 days, mode of the given data is 1461 days & 4422 days.

To find the mean, median, and mode of the lengths of terms of the US Presidents that preceded Joe Biden:

Mean:

To find the mean, we add up all of the term lengths and divide by the total number of terms:

Mean = (4422 + 2922 + 2865 + 2840 + 2728 + 2041 + 2027 + 1886 + 1654 + 1503 + 1461 + 1460 + 1430 + 1419 + 1262 + 1036 + 969 + 895 + 881 + 492 + 199 + 31) / 44

Mean = 1743.77 days

Median:

To find the median, we need to arrange the term lengths in order from smallest to largest, and then find the middle term. In this case, since we have an even number of terms, we will take the average of the two middle terms:

31 199 492 881 895 969 1036 1262 1419 1430 1460 1461 1503 1654 1886 2027 2041 2728 2840 2865 2922 4422

Median = (1460 + 1461) / 2

Median = 1460.5 days

Mode:

The mode is the most frequently occurring term length. In this case, there are two modes: 1,461 days and 4,422 days.

Since the term length of FDR is much higher than all the other term lengths, it has pulled up the mean to a higher value than the other measures of central tendency. Additionally, the mode being a high value is likely due to the fact that FDR served for more than three terms, which is an outlier in the data set.

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,By following these steps, we can find the value of this expression:

first we multiply both -2 and 3 by their corresponding fractions, we do this by just multiplying the numbers with the numerator of the fraction, like this:

Now simplify the fractions:

To sum fractions, we have to make sure that the denominators are the same, this is not the case, we can make their denominators the same by dividing and multiplying the two by two, like this:

Now, we just have to sum up the numerators, like this:

Then, the value of this expression is:

If \($&f(x)=\frac{19}{x^{2}} \\\) then the inverse function exists  \($&f^{-1}(x)=\sqrt{\frac{19}{x}}\).

An inverse function in mathematics exists function which "reverses" the another function.

Let f(x) = y, then the inverse function, \($x=f^{-1}(y)$\)

\($&f(x)=\frac{19}{x^{2}} \\\)

\($&y=\frac{19}{x^{2}} \\\)

\($&x^{2}=\frac{19}{y} \\\)

simplifying the equation, we get

\($&x=\sqrt{\frac{19}{y}} \\\)

\($&x^{-1}=f^{-1}(y)=\sqrt{\frac{19}{y}} \\\)

\($&f^{-1}(y)=\sqrt{\frac{19}{y}},\)  then \($&f^{-1}(x)=\sqrt{\frac{19}{x}}\).

If \($&f(x)=\frac{19}{x^{2}} \\\) then the inverse function exists  \($&f^{-1}(x)=\sqrt{\frac{19}{x}}\).

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