I would like to know what formula I would use to solve this questionCircle P has a radius of 5cm. Point Q lies on circle P, and the equation of PQ is y=2/5x+3. Which equation could be the equation of a line tangent to circle P at point Q?

Answer:both a and b are correct

Step-by-step explanation:

Answer:

611.73

Step-by-step explanation:

90 divided by 19 is 4.73 then add 607 which adds up to 611.73 then divide by 1 which is 611.73

Answer:

w = 3

Step-by-step explanation:

factoring x² + x - 12 you get (x + 4)(x - 3) = 0

x = -4 and x = 3

since you cannot have a negative width, we exclude that value and use the positive value of 3

Probability of (a) George winning is 0.1

                       (b) Julia winning is 0.05

Given in question,

Total ticket sold = 100

George bought tickets = 10

Julia bought tickets = 5

Winning ticket = 1

Selecting 1 ticket from 100 = \(\left[\begin{array}{ccc}100\\1\\\end{array}\right]\)

                                            = 100

Selecting 1 ticket from 10 = \(\left[\begin{array}{ccc}10\\1\\\end{array}\right]\)

                                         = 10

Selecting 1 ticket from 5 = \(\left[\begin{array}{ccc}5\\1\\\end{array}\right]\)

                                        = 5

Probability = favorable outcome/total outcome

Probability of George winning = \(\frac{10}{100}\)

                                                  = 0.1

Probability of Julia winning = \(\frac{5}{100}\)

                                             = 0.05

Hence, probabilities are 0.1 and 0.05 respectively.

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Answer:

Step-by-step explanation:

We can use the method of undetermined coefficients to solve this differential equation. First, we will need to find the solution to the homogeneous equation and the particular solution to the non-homogeneous equation.

For the homogeneous equation, we will use the form y"+ky=0, where k is a constant. We can find the solutions to this equation by letting y=e^mx,

y"=m^2e^mx -> (m^2)e^mx+k*e^mx=0, therefore (m^2+k)e^mx=0

(m^2+k) should equal 0 for the equation to have a non-trivial solution. Therefore, m=±i√(k), and the general solution to the homogenous equation is y=A*e^i√(k)x+Be^-i√(k)*x.

Now, we need to find the particular solution to the non-homogeneous equation. We can use the method of undetermined coefficients to find the particular solution. We will let yp=a0+a1x+a2x^2+.... As the derivative of a sum of functions is the sum of the derivatives, we get

yp″=a1+2a2x....yp‴=2a2+3a3x+....

Substituting the general solution into the non-homogeneous equation, we get

a0+a1x+a2x^2+...+2a2x+3a3x^2+...=Y(4)

So, the coefficient of each term in the expansion of the left hand side should equal the coefficient of each term in the expansion of the right hand side. Since there is only one term on the right hand side, we get the recurrence relation:

a(n+1)=Y(n-2)/n^2

From this relation, we can find all the coefficients in the expansion for the particular solution. Using this particular solution, we can find the total solution to the differential equation as the sum of the homogeneous solution and the particular solution.

"The correct option is C." The only expression that is equivalent to log 2 - log 4 is option C: log(2) + log(¹).

The expression "log 2 - log 4" can be simplified using                   logarithmic properties. Specifically, the property states that "log(a) - log(b) = log(a/b)." Applying this property to the given expression, we have "log 2 - log 4 = log(2/4) = log(1/2) = -log(2)."

The expression log 2 - log 4 can be simplified using logarithmic properties. Let's analyze each option:

A. log(¹): This expression is not equivalent to log 2 - log 4. The logarithm of 1 is 0, but it does not cancel out the terms log 2 and log 4.

B. log 1: This expression is equivalent to 0, but it does not cancel out the terms log 2 and log 4.

C. log(2) + log(¹): This expression is equivalent to log 2 + 0, which simplifies to just log 2. It is not equivalent to log 2 - log 4.

D. log 2: This expression is not equivalent to log 2 - log 4. It represents the logarithm of 2, but it does not account for the subtraction of log 4.

Option C, "log(2) + log(¹)," again uses an exponentiation notation without an exponent and is not a valid mathematical expression.

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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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Step-by-step explanation:

The equation 3x + y = 0 can be rearranged to y = -3x. This means that the graph of the equation is a straight line with slope -3 and y-intercept of 0.

The three points that are in the solution set are (-2,6), (-5,5), and (3,-9). Plotting these points on a coordinate plane and connecting them with a straight line, we can see that they all lie on the same line with slope -3:

[Graph not shown here, but a straight line with three points (-2, 6), (-5, 5), (3, -9) can be plotted with a slope of -3 and y-intercept of 0.]

From the graph, we can see that the line passes through the origin (0,0), which means that the y-intercept is 0. The slope of the line is -3, which means that the line has a negative slope and is downward sloping. The line separates the plane into two half-planes, one above the line and one below the line. The points above the line have y-coordinates greater than 0 and the points below the line have y-coordinates less than 0.

The graph of h(x) = (x-1)^2 - 9 is a U-shaped parabola that opens upwards, with the vertex at (1, -9), and it extends indefinitely in both directions.

The function h(x) = (x-1)^2 - 9 represents a quadratic equation. Let's analyze the different components of the equation to understand the behavior of the graph.

The term (x-1)^2 represents a quadratic term. It indicates that the graph will have a parabolic shape. The coefficient in front of the quadratic term (1) implies that the parabola opens upwards.

The constant term -9 shifts the graph downward by 9 units. This means the vertex of the parabola will be at the point (1, -9).

Based on this information, we can draw the following conclusions:

The graph will be a U-shaped curve with the vertex at (1, -9).

The vertex represents the minimum point of the parabola since it opens upward.

The parabola will be symmetric with respect to the vertical line x = 1 since the coefficient of the quadratic term is positive.

The graph will extend indefinitely in both directions.

To accurately plot the graph, you can choose several x-values, substitute them into the equation to find the corresponding y-values, and then plot the points on the graph. Alternatively, you can use graphing software or calculators that can plot the graph of the equation for you.

Remember to label the axes and indicate the vertex at (1, -9) to provide a complete representation of the graph of h(x) = (x-1)^2 - 9.

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Answer:

x=23

Step-by-step explanation:

\((x-5)/2=9\)

Multiply both sides of the equation by 2

x-5=18

move constant to the right-hand side and change its sign

x=18+5

add the number

x=23

Entry ticket = $7

Gift shop money = $g

Maximum to spend = $30

Inequality => 7+g ≤ 30

Hope it helps!

The statement about the unit prices which is true is Kitty Kibbles has a lower unit price of $1.30/pound.

The correct answer choice is option D.

Cost of 16-pound bag of Kitty Kibbles = $20.80

Unit price of kitty kibbles = Price / number of pounds

= $20.80 / 16

= $1.30 per pound.

Cost of 8-pound bag of Feline flavor = $11.20

Unit price of feline flavor = Price / number of pounds

= $11.20 / 8

= $1.40 per pound

Ultimately, the unit price of kitty kibbles and feline flavor is $1.30 and $1.40 respectively.

Complete question:

A 16-pound bag of Kitty Kibbles is $20.80. An 8-pound bag of Feline Flavor is $11.20. Which statement about the unit prices is true?

A. Feline Flavor has a lower unit price of $1.40/pound.

B. Feline Flavor has a lower unit price of $1.30/pound.

C. Kitty Kibbles has a lower unit price of $1.40/pound.

D. Kitty Kibbles has a lower unit price of $1.30/pound.

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Answer:

\(d^{2}\) - 16.

Step-by-step explanation:

To solve for the product of (d + 4) and (d - 4), we can use the FOIL method.

This means we multiply the first terms, then the outer, then the inner, and finally the last terms, then we add all the products together.

So, (d + 4) (d - 4) can be expanded like this:

Adding all of them together, we get: \(d^{2}\) - 4d + 4d - 16, which simplifies to \(d^{2}\) - 16.

Therefore, (d + 4)(d - 4) = \(d^{2}\) - 16.

Answer:

given diameter travels for a given number of wheel revolutions. ... relationship between wheel size, revolutions and distance, and may be completed by students with little ... The answers assume rounding to 2 digits beyond the decimal ... a mile); in the metric system, there are 100 centimeters in a meter and 1000 meters in a.

i think if its not right then my bad

Step-by-step explanation:

The diameter of the wheel is  36.23 centimeters

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

The wheel on a car completes 25 revolutions and travels about 35.325 meters

We can use the formula C = πd to relate the circumference of the wheel to its diameter.

Since the wheel completes 25 revolutions, it travels a distance of 25 times its circumference.

Therefore, we can write 25C = 35.325 meters.

Solving for the diameter, we get

d = C/π

= 36.23 centimeters

Hence, the diameter of the wheel is  36.23 centimeters

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The factοrs οf the expressiοn is 4x(2xy+3y-4z).

Tο factοrise an algebraic statement, we first identify the terms' highest cοmmοn factοrs and then arrange the terms intο grοups in accοrdance with thοse grοups. In plain English, factοrizatiοn is the prοcess thrοugh which an algebraic expressiοn gets expanded in the οppοsite directiοn.

Here the given expressiοn is ,

=> \(8x^2y+12xy-16xz\)

Nοw factοrizing the given expressiοn then,

=> 4×2×x×x×y+4×3×x×y-4×4×x×z

=> 4x(2xy+3y-4z)

Hence the factοrs οf the expressiοn is 4x(2xy+3y-4z).

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Answer:

x > -5, so the correct answer is C.

Suppose 1 - |x| ≤ f(x) ≤ cos(x) for all values of x. Since the function f(x) is defined for all values of x, the limit at x = 0 must exist. Therefore, statements a and c  are true.

To determine whether b and c are true, we need to consider the bounds on f(x):

1 - |x| ≤ f(x) ≤ cos(x)

When x = 0, the bounds become:

1 - |0| = 1 ≤ f(0) ≤ cos(0) = 1

So f(0) must be equal to 1, and statement c is true:

c. f(0) = 1

However, statement b is not necessarily true. The limit of f(x) as x approaches 0 is equal to the value that f(x) approaches as x gets arbitrarily close to 0, but it does not have to be equal to the value of f(0).

To determine whether d is true, we need to consider the limit of f(x) as x approaches 1. To do this, we will use the bounds on f(x):

1 - |x| ≤ f(x) ≤ cos(x)

As x approaches 1 from the left, the lower bound approaches 0, and as x approaches 1 from the right, the upper bound approaches cos(1).

Since 0 ≤ f(x) ≤ cos(1) for all values of x near 1, it is possible that the limit of f(x) as x approaches 1 is any value between 0 and cos(1). Therefore, statement d is not necessarily true:

d. lim x→1 f(x) = 0

The correct answer choices are:

a. lim x→0 f(x) exists.

c. f(0) = 1

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In response to the stated question, we may state that As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.

A cylinder seems to be a three-dimensional geometric shape made up of two parallel congruent circular bottoms and a curving surface linking the two bases. The bases of a cylinder are always perpendicular from its axis, which is an artificial straight line passing through the centre both of bases. The volume of a cylinder is equal to the product among its base area and height. A cylinder's volume is computed as V = r2h, within which "V" represents the volume, "r" represent the circle of the base, and "h" represents the height of the cylinder.

The volume of a cylinder is determined by the formula V = r2h, where r is the radius of the base, h is the cylinder's height, and is a mathematical constant close to 3.14.

In this situation, the radius is 2.5 cm since the base is 5 cm in diameter. The cylinder stands 10 cm tall. As a result, the volume of the cylinder is:

\(V = \pi(2.5 cm)^2(10 cm) (10 cm)\\V = 196.35 cm^3\)

As a result, the cylindrical container can carry around 196.35 cm3 of water. As a result, (a) 196.35 cm cubic is the right answer.

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Answer: 6.6 m

Add known sides and subtract the sum from the given perimeter.

Answer:

6.6 m

Step-by-step explanation:

33.8 + 2(14.1) + 3(9.1) + 16.9 = 106.2

112.8 - 106.2 = 6.6

The time taken by Amy to travel to the place was t = 4 hours.

A measure of average speed is the amount of distance travelled in a given amount of time. It is determined by dividing the overall mileage by the overall time required to cover that mileage.

In physics and other sciences, average speed is frequently employed to describe how objects move. For instance, it is possible to estimate how long it will take to go a certain distance or assess a car's fuel economy by looking at its average speed over a given distance. By dividing the whole distance travelled by the total time required, average speed may also be used to characterise the speed of an object that is moving at various speeds at different points along its path.

Let the time taken to get back = t + 1.

Now, it took one hour less time to get there thus time = t.

Now, average speed is given as:

average speed = total distance / total time

Substituting the values:

50 km/h = d / t

d = 50t  .........(1)

40 km/h = d / (t + 1)

d = 40(t + 1)......(2)

Setting the value of d as equal we have:

50t = 40(t + 1)

50t = 40t + 40

10t = 40

t = 4

Hence, the time taken by Amy to travel to the place was t = 4 hours.

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The equivalent expression of 14r^4y^6/7r^8y^2 is 2y^4/r^4

The expression is given as:

14r^4y^6/7r^8y^2

Start by dividing 14 by 7

2r^4y^6/r^8y^2

Next divide y^6 by y^2

2r^4y^4/r^8

Lastly divide r^4 by r^8

2y^4/r^4

Hence, the equivalent expression of 14r^4y^6/7r^8y^2 is 2y^4/r^4

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Answer:

27

Step-by-step explanation:

compitative property

Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.

To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.

The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.

Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.

To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:

£72 / 5 = £14.40

Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.

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The kinetic energy possessed by the skydiver is 14, 062. 5 Joules

Kinetic energy of an object is defined as the energy possessed by an object due to its motion.

It is also described as the work that is required to accelerate a body of mass from rest to its given velocity.

The formula for calculating kinetic energy is expressed as;

Kinetic energy = 1/2 mv²

Where;

Now, substitute the values

Kinetic energy = 1/2 (45)(25)²

Find the square

Kinetic energy = 1/2 (45)(625)

Find the product

Kinetic energy = 1/2(28125)

Find the quotient

Kinetic energy = 14, 062. 5 Joules

Hence, the value is  14, 062. 5 Joules

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Answer:

AB

Step-by-step explanation:

Using FOIL (first outer inner last) u can determine that the final term will be produced by multiplying the last terms in each bracket. These are A and B, so the final term of the resulting trinomial is AB.

You can check this by fully expanding (x + A)(x + B):

\((x + A)(x + B)\\= x^{2} + Bx + Ax + AB\)

the terms B and A are usually numbers, so Bx and Ax tend to get added together to form a middle term. hope this helps!

this is soo funny

haha thanks for the points

By using derivatives of rational functions, we find the following results:

Case 7: y' = [8 · (7 - tan x) - (8 · x) · (- sec² x)] / (7 - tan² x)

Case 8: y' = [(- sec x · tan x) · tan x - (8 - sec x) · sec² x] / tan² x

Case 9: y = 0

In this problem we find three cases of rational functions, whose derivatives must be found. The third case (point 9) asks us to find the equation of the tangent line. The derivative of a rational function requires to combine derivative rule for a division of functions and chain rule.

Division of functions

y = f(x) / g(x)

y' = [f'(x) · g(x) - f(x) · g'(x)] / [g(x)]²

Chain rule

y = f[u(x)]

y = f'[u(x)] · u'(x)

With respect to tangent lines, the derivative represents the slope of the line, whose definition is now shown:

y = m · x + b

Where:

Case 7

y = (8 · x) / (7 - tan x)

y' = [8 · (7 - tan x) - (8 · x) · (- sec² x)] / (7 - tan² x)

Case 8

y = (8 - sec x) / tan x

y' = [(- sec x · tan x) · tan x - (8 - sec x) · sec² x] / tan² x

Case 9

First, determine the slope of the line:

m = [2 · x · (x² + 2 · x + 1) - (x² + 1) · (2 · x + 2)] / (x² + 2 · x + 1)²

m = [2 · 1 · (1² + 2 · 1 + 1) - (1² + 1) · (2 · 1 + 2)] / (1² + 2 · 1 + 1)²

m = (2 · 1 · 4 - 2 · 4) / 4²

m = (8 - 8) / 16

m = 0

Second, find the intercept of the line:

0 = 0 · 1 + b

b = 0

Third, write the equation of the line:

y = 0

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Answer:

rectangle above = 3 x 5 = 15 cm²

rectangle below = 8 x 5 = 40 cm²