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The equation of the circle with center (0, 5) and a point on the circle (2, 4) is x² + (y - 5)² = 5

In geometry, a circle is a closed two-dimensional shape that is formed by a set of points that are equidistant from a fixed point called the center. The distance between any point on the circle and the center is called the radius.

The equation of a circle with center (h, k) and radius r is given by:

 r²=(x - h)² + (y - k)²  

In this case, the center of the circle is (0, 5) and a point on the circle is (2, 4). The radius of a circle, which is the separation between its centre and any point on the surface, may be calculated using the following formula:

r = √((2 - 0)² + (4 - 5)²) = √(5)

Now we can substitute the values of the center and the radius into the equation of the circle:

(x - 0)² + (y - 5)² = (√(5))²

Simplifying, we get:

x²+ (y - 5)² = 5

As a result, the circle's equation with its centre (0, 5) and a point on it (2, 4) is:

x² + (y - 5)² = 5

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Answer: 2x^2-1/2

Step-by-step explanation:

mulityply this by the given lenght

From given quadratic function we get that the rocket will hit the ground after 4.75 seconds and the rocket will be 70 feet above the ground after 7/2 or 3.5 seconds.

What is quadratic function?

A quadratic function is defined as f(x) = ax² + bx + c, where a, b, and c are constants and x is the independent variable. This function is a second-degree polynomial, which means it has a degree of two.

Now,

To find out when the rocket will hit the ground, we need to find the value of t when h(t) = 0:

-16t² + 76t = 0

Factor out -16t:

-16t(t - 4.75) = 0

So either t = 0 or t = 4.75 seconds. However, we can discard t = 0 because it represents the initial launch and not the impact with the ground. Therefore, the rocket will hit the ground after 4.75 seconds.

To find out when the rocket will be 70 feet above the ground, we need to solve the following equation:

-16t² + 76t = 70

-16t² + 76t - 70 = 0

Dividing both side

8t² - 38t + 35 = 0

Factor the equation:

(4t - 5)(2t - 7) = 0

So either t = 5/4 or t = 7/2. However, we can discard t = 5/4 because it represents a time before the rocket reaches 70 feet. Therefore, the rocket will be 70 feet above the ground after 7/2 or 3.5 seconds.

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The area of the  ABCD is 30 square units.

A quadrilateral which have opposite side are parallel and equal to each other.

area of the parallelogram ABCD,

Area = base × height

find the equations of the lines AB and BC:

Line AB passes through the points A(-4,2) and B(-4,-3):

slope = (y2 - y1)/(x2 - x1) = (-3 - 2)/(-4 - (-4)) = -5/0 = undefined

Since the slope is undefined, the line is vertical and has the equation x = -4.

Line BC passes through the points B(-4,-3) and C(2,-3):

slope = [tex]\frac{(y2 - y1)}{(x2 - x1)}[/tex] = [tex]\frac{-3 - (-3)}{(2 - (-4)}[/tex]) = 0

Since the slope is 0, the line is horizontal and has the equation y = -3.

The height corresponding to AB is the perpendicular distance between AB and CD, which is the vertical distance between the lines x = -4 and x = 2. This distance is 6 units.

The height corresponding to BC is the perpendicular distance between BC and AD, which is the horizontal distance between the lines y = -3 and y = 2. This distance is 5 units.

Since the height corresponding to BC is shorter, we use it as the height of the parallelogram. The base is BC, which has a length of 6 units. Therefore, the area of the parallelogram is:

Area = base × height = 6 × 5 = 30 square units.

Therefore, the area of the  ABCD is 30 square units.

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the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.

what is right-angled triangle  ?

A right-angled triangle is a type of triangle that has one angle measuring exactly 90 degrees (a right angle). This angle is formed by the intersection of two sides of the triangle, which are called the legs or catheti, and it is opposite to the longest side of the triangle, which is called the hypotenuse. The hypotenuse is always opposite the right angle.

In the given question,

The area of a right-angled triangle is given by the formula:

Area = 1/2 x base x height

where the base and height are the two perpendicular sides of the triangle.

In this case, the adjacent side and opposite side of the right-angled triangle are both 2 units.

Let's call the hypotenuse of the triangle 'c'. Then, by the Pythagorean theorem, we have:

c² = 2² + 2²

c² = 8

c = √(8) = 2.8284 (rounded to 4 decimal places)

Now, we can use the trigonometric ratios to find the base and height of the triangle. In this case, we can use the tangent ratio:

tan(theta) = opposite/adjacent

tan(theta) = 2/2

tan(theta) = 1

theta = tan⁻¹(1) = 45 degrees

Therefore, the base and height of the triangle are:

base = adjacent x tan(theta) = 2 x tan(45) = 2 x 1 = 2

height = opposite x tan(theta) = 2 x tan(45) = 2 x 1 = 2

Now we can use the area formula to find the area of the triangle:

Area = 1/2 x base x height

Area = 1/2 x 2 x 2

Area = 2 square units

Therefore, the area of the right-angled triangle with adjacent and opposite sides of 2 units is 2 square units.

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Answer: not factorable with rational numbers.

Step-by-step explanation: No explanation because it is not factorable.

Answer:

To find the estimated standard error for the sample mean, we need to use the formula:

SE = s/√n

where s is the sample standard deviation and n is the sample size.

However, we are not given the sample standard deviation, but we are given the sum of squares (SS). We can use this to find the sample variance (s^2) and then take the square root to find the sample standard deviation.

For a sample size of n = 9, the degrees of freedom (df) are:

df = n - 1 = 9 - 1 = 8

Using the formula for the sample variance:

s^2 = SS/df = 1152/8 = 144

Taking the square root, we find the sample standard deviation:

s = √144 = 12

Now we can find the estimated standard error:

SE = s/√n = 12/√9 = 4

Therefore, the estimated standard error for the sample mean is 4.

Answer:

To find the estimated standard error for the sample mean, we need to divide the sample standard deviation by the square root of the sample size. However, we are given the sum of squares (SS), not the sample standard deviation, so we first need to calculate the sample variance. The formula for the sample variance is: s^2 = SS / (n - 1) where s^2 is the sample variance, SS is the sum of squares, and n is the sample size. Using the given values, we have: s^2 = 1152 / (9 - 1) = 144 Now we can find the estimated standard error: SE = s / sqrt(n) where SE is the estimated standard error, s is the sample standard deviation, and n is the sample size. Since s = sqrt(s^2), we have: SE = sqrt(s^2

The value of

1. v = 40cm

2. w= 126°

3. x = 30°

4. y = 63cm

Similar triangles are triangles that have the same shape, but their sizes may vary.

The ratio of corresponding sides of similar triangles are equal.

Therefore ;

60/v = 72/48

48 × 60 = 72v

2880 = 72v

divide both sides by 72

v = 2880/72

v = 40cm

since the two triangles are similar w = 126°

x = 180-(126+24)

x = 180- 150

x = 30°

then;

y/42 = 72/48

48y = 42 × 72

48y = 3024

y = 3024/48

y = 63 cm

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The value of x in the given figure, rounding the length to the nearest tenth is 2879.4 meters.

Pythagoras' theorem says that the hypotenuse's square equals the square of the other two sides.

The value of x in the triangle using the principle of Pythagoras is 2879.4 meters

Given the right angle triangle :

The angle of elevation = 10°

Opposite side = 500 m

x = hypotenuse

Using the relation :

Sin θ = opposite / hypotenus

Sin 10° = 500 / x

Cross multiply :

x(sin 10°) = 500

0.1736481x = 500

x = 500 / 0.1736481

x = 2879.39 meters

Therefore, the value of x in the triangle is 2879.4 meters.

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Step-by-step explanation:

using Pythagoras theorem

Answer:

4² + r² = (2+ r)²

16 + r² = 4 + 4r + r²

12 = 4r

r = 3

(A) Between 1995 and 2003, there was a change at an annual rate of -0.1463

(B) Between 1995 and 2003, a change occurred at a rate of -14.63% per year.

(C) The automobile would be worth $5,844.24 in 2007.

Depreciation is an annual income tax deduction that enables you to recoup the purchase price or other basis of a specific item over the course of its use.

It is a provision for the property's normal wear and tear, degeneration, or obsolescence.

As the years pass, the car's value drops.

This process is known as depreciation.

Depreciation is the decrease in asset value brought on by normal wear and tear.

Use this formula to calculate the annual rate of change:

g = (FV/PV)¹⁾ⁿ - 1

Now, using the formula calculate as follows:

(11000/3900)¹⁾⁸ - 1

-0.1463 = -14.63%

The following formula can be used to estimate a car's worth in 7 years:

FV = P (1 + g)ⁿ

$39,000 x (1 - 0.1463)¹²

$39,000 x 0.8537¹² = $5,844.24

Therefore, (A) between 1995 and 2003, there was a change at an annual rate of -0.1463

(B) Between 1995 and 2003, a change occurred at a rate of -14.63% per year.

(C) The automobile would be worth $5,844.24 in 2007.

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Correct question:

A car was valued at $39,000 in the year 1995. The value depreciated to $11,000 by the year 2003.

A)What was the annual rate of change between 1995 and 2003? (Round to 4 decimal places)

B)What is the correct answer to part A written in percentage form?

C)Assume that the car value continues to drop by the same percentage. What will the value be in the year 2007?

As a result, the cylinder's lateral surface area is about 59.69 cm²to the nearest tenth.

The three-dimensional shape of a cylinder consists of two parallel circular bases joined by a curving surface. It is comparable to a prism with an endless number of sides.

Side Surface Area = 2 ×πrh

where h is the cylinder's height and r is its radius.

The result of entering the specified values into this formula is:

Surface Area Lateral = 2π(2) (9.5)

π = 3.141 , 6.282 ×19

= 119.32 cm

So , 59.69 cm² is the lateral surface area.

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The complete question is : Find the lateral surface area of the cylinder to the nearest hundredth. where radius is 2cm and height is 9.5 cm

1. H × (3/7) and 2. H - (4/7)H are two different numerical expressions to model the height of the British telecom tower.

What are the expressions?

Let H be the height of the Empire State Building. Then, the height of the British Telecom Tower can be modeled using the following expressions:

1. H × (3/7)

This expression finds 3/7 of the height of the Empire State Building, which represents the height of the British Telecom Tower.

2. H - (4/7)H

This expression finds the remaining height after taking away 3/7 of the height of the Empire State Building.

Simplifying, we get (3/7)H, so subtracting this from H gives (4/7)H, which represents the height of the Empire State Building above the height of the British Telecom Tower.

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1. The picture depicts the circle theorem

2. I wonder how the circle theorem fully apply to the image

3. The informed is that the angle between a radius and a tangent at the point of contact is a right angle.

The angle between a radius and a tangent at the point of contact is a right angle.

Suppose FGC

Then FC is the hypothenuse of triangle FGC

So, FC greater than FG

FC greater than FB+BG

FC greater than FC+BG (impossible)

This is the case on either side of C along the tangent

So, the shortest distance between F and the tangent is FC

When the distance between a point and a line is minimum, the angle between them is right angled.

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The measure of the angle ADC in circle B is 23 degrees.

A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also known as the location of points that are evenly spaced apart from the centre. The radius of a circle is measured from the centre to the edge. The line that splits a circle into two identical halves is its diameter, which is also twice as wide as its radius.

A circle is a fundamental 2D form whose radius is quantified. The interior and exterior parts of the aircraft are separated by the circles. It resembles a line segment in several ways.

For the given circle B, the measure of angle ABC is 46 degrees.

Now, the angle subtended by the circle is half the angle subtended at the center.

Angle ADC = 1/2(angle ABC)

Angle ADC = 1/2(46)

Angle ADC = 23 degrees.

Hence, the measure of the angle ADC in circle B is 23 degrees.

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By paying off the higher interest card first, we save $1932 - $1579 = $353 in interest charges over the course of 56 months.

The conventional method is to pay off the credit card with the highest interest rate first if we have two credit cards with differing interest rates. We can figure out how much money we save by reworking the issue to pay off the card with the lowest interest rate first.

Consider that we have two credit cards: Card A, which has a $5,000 debt and a 15% interest rate, and Card B, which has a balance of $3,000 and a 10% interest rate. We can save money by lowering the interest paid on Card B while still making minimum payments on Card A if we pay that card off first.

It would take us around 22 months to pay off Card B and 36 months to pay off Card A if we made the minimum payments of $300 on Card B and $150 on Card A each month. We would pay interest on Card A in total of $1932 and Card B in total of $386 throughout this time.

Instead, if we pay off Card A first, we would devote the remaining $300 to Card A until it is completely paid off while continuing to make the minimum payments on Card B. We would need around 24 and 32 months, respectively, to pay off Card A and Card B. We would pay interest on Card A for a total of $1579 and Card B for a total of $282 during this time.

We therefore save $1932 - $1579 = $353 in interest fees over the course of 56 months by paying off the higher rate card sooner.

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Answer:

Range = [-129, 136]

Step-by-step explanation:

If this is not the answer you are looking for, please comment

Answer:

265°

Step-by-step explanation:

from -129° to 0° is 129°

from 0° to 136° there is 136°

you add this numbers together and get an answer, so 129°+136°= 265°

Answer: To find the value of f(x) for a given value of x, you need to substitute that value of x into the equation and simplify.

For example, if you want to find f(2), you would substitute x=2 into the equation:

f(x) = 6 + 3x

f(2) = 6 + 3(2)

f(2) = 6 + 6

f(2) = 12

Therefore, f(2) = 12.

Step-by-step explanation:

The value of f(x) is 18 given that the value of x is substituted as 4. The expression is usually solved with substitution method.

To find the value of f(x) for a given value of x, you need to substitute that value of x into the equation for f(x) and solve for f(x).

For example, if you want to find the value of f(x) when x = 4, you would substitute x = 4 into the equation for f(x) as follows:

f(4) = 6 + 3(4)

Simplifying the expression on the right-hand side:

f(4) = 6 + 12

f(4) = 18

Therefore, the value of f(x) when x = 4 is 18.

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Answer:

The answer is the first graph.

Step-by-step explanation:

f(0) = l0-2l + 1

f(0) =2 + 1

f(0) = 3

(0,3)

f(1) = l1-2l + 1

f(1) = 1 + 1

f(1) = 2

(1,2)

f(2) = l2 -2 l + 1

f(2) = 0 + 1

f(2) = 1

(2,1)

f(3) = l3-2l + 1

f(3) = 1 = 1

f(3)

2

(3,2)

f(4) = l4-2l + 1

f(4) = 2 + 1

f(4) = 3

(4,3)

If you graph each of the ordered pairs that are in bold, you will see that it matches the first graph.

Helping in the name of Jesus.

Answer:

a

Step-by-step explanation:

the option that is not a way for Isabelle to get a representative sample of the most popular music group of students in her community is D. ask every student at a local movie theater.

The reason is that asking every student at a local movie theater is a form of convenience sampling, where the sample is chosen based on convenience and accessibility, rather than being selected randomly from the entire population of interest. It may not provide a representative sample of the community's music preferences since the population of students who attend a movie theater may not be the same as the general population of students in the community. In contrast, options A, B, and C suggest a form of systematic sampling, where every nth student is selected from a randomly chosen starting point, which can help to ensure that the sample is more representative of the general population of students in the community.

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The probabilities for the given events will be a) 1/13 b) 3/13 c) 10/13.

What exactly is probability?

Probability is a measure of the possibility of an event to be occurred. In mathematics, it is defined as a number between 0 and 1, where 0 means that the event is impossible and 1 means that the event is certain to occur.

Now,

(a) The probability of drawing a 7 from a standard 52-card deck is 4/52 or 1/13. This is because there are 4 7s in the deck (one in each suit) and a total of 52 cards.

(b) The probability of drawing a face card from a standard 52-card deck is 12/52 or 3/13. This is because there are 12 face cards in the deck (4 jacks, 4 queens, and 4 kings) and a total of 52 cards.

(c) The probability of drawing a non-face card from a standard 52-card deck is 40/52 or 10/13. This is because there are 40 non-face cards in the deck (the 2s through 10s and the aces) and a total of 52 cards.

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We have shown that P(F) is the direct sum of W1 and W2.

What is a polynomial?

a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables.

To prove that P(F) is the direct sum of W1 and W2, we need to show two things: first, that every polynomial in P(F) can be written as a sum of a polynomial in W1 and a polynomial in W2, and second, that this decomposition is unique.

Let's begin by showing that P(F) can be written as the direct sum of W1 and W2. Consider an arbitrary polynomial f(x) in P(F). We can write it as a sum of even and odd terms as follows:

f(x) = [f(x) + f(-x)]/2 + [f(x) - f(-x)]/2

The first term on the right-hand side is even, while the second term is odd. Let's define g(x) = [f(x) - f(-x)]/2 and h(x) = [f(x) + f(-x)]/2. Note that g(x) is odd and h(x) is even. Thus, we have expressed f(x) as a sum of an even polynomial h(x) and an odd polynomial g(x).

To show that this decomposition is unique, suppose that f(x) can be written in two ways as a sum of an even polynomial and an odd polynomial:

f(x) = h1(x) + g1(x) = h2(x) + g2(x)

where h1(x) and h2(x) are even polynomials, and g1(x) and g2(x) are odd polynomials. Then we have:

[h1(x) - h2(x)] = [g2(x) - g1(x)]

Since h1(x) - h2(x) is even, and g2(x) - g1(x) is odd, we have:

[h1(x) - h2(x)] = 0 and [g2(x) - g1(x)] = 0

This implies that h1(x) = h2(x) and g1(x) = g2(x), so the decomposition is unique.

Therefore, we have shown that P(F) is the direct sum of W1 and W2.

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0.43 Option (B) is the correct answer.

The probability of a customer ordering both marinara and pesto sauces is 0.43.

We can use the inclusion-exclusion principle to find P(marinara and pesto):

P(marinara or pesto) = P(marinara) + P(pesto) - P(marinara and pesto)

We know that P(marinara or pesto) = 0.93 and P(marinara) = 0.74, and P(pesto) = 0.62. Substituting these values in the above equation, we get:

0.93 = 0.74 + 0.62 - P(marinara and pesto)

P(marinara and pesto) = 0.74 + 0.62 - 0.93

P(marinara and pesto) = 0.43

Probability is the measure of the likelihood or chance of an event occurring. It ranges from 0 (impossible) to 1 (certain). It is used to make predictions and decisions in various fields, including mathematics, statistics, physics, finance, and more.

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Answer: 44.64ft^2

Step-by-step explanation:

Triangle 1:
A = 1/2 x 5.3 x 7.2
A = 19.08

Triangle 2:
A = 1/2 x 7.1 x 7.2
A = 25.56

25.56 + 19.08 = 44.64
Total area of triangles = 44.64ft^2

Answer:

it was c

Step-by-step explanation:

because on my fraction test I got the same answer and it was right

Answer:

C

Step-by-step explanation:

because it

When diagonalizing Matrix A = PDP^(-1) and λ1 = (1 + √5)/2 and λ2 = (1 - √5)/2 are the eigenvalues of A, and [0 1] is an eigenvector associated with both λ1 and λ2.

To diagonalize a matrix, we need to find its eigenvalues and eigenvectors. Let's begin by finding the eigenvalues of A.

The characteristic equation is given by:

det(A - λI) = 0

where I is the identity matrix and λ is the eigenvalue.

For matrix A, we have:

A - λI = [1 - λ 0 ]

[6 -1 - λ]

det(A - λI) = (1 - λ)(-1 - λ) - 6(0) = λ^2 - λ - 1 = 0

Using the quadratic formula, we find that the eigenvalues are:

λ1 = (1 + √5)/2

λ2 = (1 - √5)/2

Now let's find the eigenvectors associated with each eigenvalue. For λ1 = (1 + √5)/2, we have:

(A - λ1I)x = 0

[1 - λ1 0] [x1] = [0]

[6 -1 - λ1] [x2] [0]

which simplifies to:

[-(√5-1)/2 0] [x1] = [0]

[6 -√5-1] [x2] [0]

From the first row, we have x1 = 0. Substituting this into the second row, we get:

(√5+1)x2 = 0

Since x2 cannot be zero (otherwise the eigenvector would be the zero vector), we have:

x2 = 1

Therefore, the eigenvector associated with λ1 is:

v1 = [0 1]

Similarly, for λ2 = (1 - √5)/2, we have:

(A - λ2I)x = 0

[1 - λ2 0] [x1] = [0]

[6 -1 - λ2] [x2] [0]

which simplifies to:

[-(√5+1)/2 0] [x1] = [0]

[6 -√5+1] [x2] [0]

From the first row, we have x1 = 0. Substituting this into the second row, we get:

(√5-1)x2 = 0

Again, since x2 cannot be zero, we have:

x2 = 1

Therefore, the eigenvector associated with λ2 is:

v2 = [0 1]

Now we can use the eigenvectors to diagonalize the matrix. The diagonal matrix D will have the eigenvalues on the diagonal and zeros elsewhere. The matrix P will have the eigenvectors as columns.

D = [λ1 0]

[0 λ2]

P = [v1 v2] = [0 0]

[1 1]

To check that this is the correct diagonalization, we can verify that:

A = PDP^(-1)

where P^(-1) is the inverse of P. Since P is not invertible (the columns are linearly dependent), we can use the pseudoinverse instead:

A = PD†P

where D† is the pseudoinverse of D. We have:

we have diagonalized A as:

A = PDP^(-1)

where:

D = [λ1 0]

[0 λ2]

P = [v1 v2] = [0 0]

[1 1]

and λ1 = (1 + √5)/2 and λ2 = (1 - √5)/2 are the eigenvalues of A, and [0 1] is an eigenvector associated with both λ1 and λ2.

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The circumference of the circle is 340 units.

What is circle ?

In geometry, a circle is a two-dimensional shape consisting of all points that are a fixed distance (called the radius) from a given point (called the center). A circle is a set of points that are equidistant from the center.

Let's use the formula relating the length of an arc to the circumference of a circle:

Length of arc = (central angle / 360) x circumference

Plugging in the given values, we get:

17 = (18/360) x circumference

Simplifying and solving for the circumference, we get:

circumference = 17 x (360/18) = 17 x 20 = 340

Therefore, the circumference of the circle is 340 units.

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