In APQR, m/P = (x + 13)°, m/Q = (10x + 13)°, and
m/R = (2x − 2)°. Find m/Q.

From the given the vector function , T(t) = (2V2, ez, -2e-2t) N(t) = (2e-2t, -2V2, ez)(b) Use this formula to find , curvature. k(t) = (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)

(a) To find the unit tangent and unit normal vectors, we use the following formula:

T(t) = (1/|r'(t)|) * r'(t)

N(t) = (1/|r'(t)|) * (r'(t) x r"(t))

where r'(t) is the first derivative of the vector function and r"(t) is the second derivative of the vector function.

For the given vector function, r'(t) = (9, -4sin(t), 4cos(t)).

Therefore, |r'(t)| = sqrt(81 + 16sin2(t) + 16cos2(t))

To find r"(t), we take the derivative of r'(t), which is (0, -4cos(t), -4sin(t)).

Thus, T(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (9, -4sin(t), 4cos(t))

and N(t) = (1/sqrt(81 + 16sin2(t) + 16cos2(t))) * (0, -4cos(t), -4sin(t)).

(b) To find the curvature, we use the following formula:

k(t) = |r'(t) x r"(t)| / |r'(t)|3

For the given vector function, r'(t) = (2V2, ez, -2e-2t) and r"(t) = (0, -2V2, -ez).

Therefore, k(t) = |(2V2, ez, -2e-2t) x (0, -2V2, -ez)| / |(2V2, ez, -2e-2t)|3

= (2V2e-2t + 2ez) / (4V2 + e2z + 4e-4t2)

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63 degrees is the angle.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

The given triangle is a right angle triangle.

The opposite side length is 85 and the adjacent side is 38.

Opposite side=85

Adjacent side=38.

Calculate Opposite/Adjacent

= 85/38= 2.236

Which is tanθ=2.236

Now tan inverse on both the sides

θ=tan⁻¹2.236

θ=tan⁻¹2

θ=63 degrees.

Hence, the angle is 63 degrees.

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The factor of the expression 8w - 16 will be 8 and (w - 2).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

A frequency table displays a sequence of scores in either increasing or decreasing order together with their occurrences as a way to compactly organize raw data.

The expression is given below.

⇒ 8w - 16

The factor of each term in the expression, then we have

8w = 8 x w

16 = 8 x 2

Then the expression is written as,

⇒ 8w - 16

⇒ 8 × w - 8 × 2

⇒ 8 × (w - 2)

⇒ 8(w - 2)

The component of the articulation 8w - 16 will be 8 and (w - 2).

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Probability for the following events will be :-

The probability of an event E,P(E)=

 Number of favourable outcomes / Total number of outcomes

​ =  n(E) / n(S)

​

Applying the concept of probability as shown above, let's calculate all the probabilities one by one.

(i) Probability of getting a king of red colour:

We know that, there are 26 red cards, 13 each of hearts and diamonds. Hence, there will be 1 king each in hearts and diamonds.

∴  Number of kings of red colour, n(E)=2

Also, total number of cards, n(S)=52

∴  Probability of getting a king of red colour

= n(E) / n(S)

= 2 / 52

⇒ 1 / 26

Hence, the required probability is  1 / 26

​(ii) Probability of getting a face card:

We know that, each suit has 3 face cards (Jack, Queen and King). Hence, there will be 12 face cards in total.

∴  Number of face cards, n(E)=12

Also, total number of cards, n(S)=52

∴  Probability of getting a face card

= n(E) / n(S)

= 12 / 52

⇒ 3 / 13

Hence, the required probability is  3 / 13

(iii) Probability of getting the jack of hearts:

We know that, there is only one jack in hearts.

∴  Number of jack of hearts, n(E)=1

Also, total number of cards, n(S)=52

∴  Probability of getting the jack of hearts =

n(E) / n(S)= 1 / 52

Hence, the required probability is  1 / 52

(iv) Probability of getting a red face card:

We know that, there are 26 red cards, 13 each of hearts and diamonds. Both hearts and diamonds have 3 face cards each.

∴  Number of red face cards, n(E)=6

Also, total number of cards, n(S)=52

∴  Probability of getting a red face card =

n(E) / n(S) = 6 / 52

⇒ 3 / 26

Hence, the required probability is  3 / 26

​(v) Probability of getting a spade:

We know that, there are 13 cards of spades.

∴  Number of spades, n(E)=13

Also, total number of cards, n(S)=52

∴  Probability of getting a spade =

n(E) / n(S) = 13 / 52

⇒ 1 / 4

Hence, the required probability is  1 / 4

(vi) Probability of getting the queen of diamonds:

We know that, there are 13 cards of diamonds. There is 1 queen of diamonds.

∴  Number of queens in diamonds, n(E)=1

Also, total number of cards, n(S)=52

∴  Probability of getting the queen of diamonds =

n(E) / n(S) = 1 / 52

​Hence, the required probability is  1/52

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15% discount; 6% sales tax in-store. Online retailer: $5 discount; $8.99 for delivery.

$5 off offer that can only be used online and a physical shop. Only the actual store is subject to the 5% sales tax. The online retailer charges a fixed $6.99 shipping fee.

Let's say the entire amount spent was $100.

In a physical store, 100 times 15% equals 15 off.

100 - 15 = 85 is the item's reduced cost.

85 x 6% is 5.1 sales tax.

85 + 5.1 = 90.10 as a whole price

Internet shop:

Discounted cost of item: 100 - 5 = 95

95 plus 8.99 is 103.99 in total.

15% discount; 6% sales tax in-store.

Online retailer: $5 discount; $8.99 for delivery.

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The amount of money for selling 450 baked goods will be

Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.

Given that;

At a bake sale, the Math Club raised $225 by selling 300 baked goods.

And, The amount raised varies directly with the baked goods sold.

Now,

Let the amount of money for selling 450 baked goods = x

Since, At a bake sale, the Math Club raised $225 by selling 300 baked goods.

And, The amount raised varies directly with the baked goods sold.

Hence, By definition of proportion we get;

⇒ $225/300 = x / 450

⇒ x = 225 × 450 / 300

⇒ x = $337.5

Thus, The amount of money for selling 450 baked goods = $337.5

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Applying DeMorgan's theorem to the expression overbar(overbar((overbar(a) overbar(b))) (overbar(c d))) results in (a b) + (c + d).

DeMorgan's theorem states that when two terms are combined with an AND operator (such as overbar(a) overbar(b)), the result is the two terms combined with an OR operator (such as a + b).

Similarly, when two terms are combined with an OR operator (such as overbar(c d)), the result is the two terms combined with an AND operator (such as c overbar(d)). Applying this theorem to the expression above results in (a b) + (c + d).

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Answer:

0.0036

Step-by-step explanation:

Answer: 0.0036

Step by step explin

x(7 - x) > 8

First solve x(7 - x)  = 8

x^2 - 7x + 8 = 0

x = 5.56, 1.44

If we plug in these values into the original equation we can see that solution is

1.44 < x < 5.56

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Answer:

f - 36

-3f - 23

are your prime polynomials.

The constant variation and the value of x are (a) Constant variation -1/3, x= 63

From the question, we have the following parameters that can be used in our computation:

X varies directly with Y

X equals 29 when Y equals -87

This means that

Constant of variation = X/Y

Substitute the known values in the above equation, so, we have the following representation

Constant of variation = 29/-87

Evaluate

Constant of variation = -1/3

From the question, we have

y = -187

This means that

Constant of variation = X/-187

So, we have

X = -187 * Constant of variation

This gives

X = -187 * -1/3

Evaluate

X = 63

Hence, the solution is (a)

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Answer:

x = 4

Hope it helps.

The picture of the (5, -1) beneath the same translation, in accordance with the stated statement, is (9, 6).

Each point in a graphic is moved the same distance within the same direction using a sort of transformation known as translation.

Translation in mathematics is the movement of a form in any direction—left, right, up, or down—without turning. They are congruent if the translated forms appear to be of the same size as that of the original ones. They have only changed their direction or directions.

The image of the translation is (9,-2).

The point is given as: P = (-6, -4)

The image of the point is: P' = (-2, 3)

The translation rule is calculated as:

T = x - 2 - (-6), y+3-(-4)

so,  T = x + 4, y + 7

So, the image of (5, -1) is:

the Image of the translation = 5 + 4, -1 + 7

Hence, the image of the translation is (9, 6).

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Answer:

A. 110°

Step-by-step explanation:

according to the theorems,

m∠1=m∠6=m∠9=m∠14=110°;

m∠2=m∠5=m∠10=m∠13=70°;

m∠3=m∠8=m∠11=m∠16=70°;

m∠4=m∠7=m∠12=m∠15=110°.

all the details are in the attachment.

Answer:

Step-by-step explanation:

The domain and range of the provided function are (-infinite, 3/4) and (5, infinite) respectively.

A function is defined as a relationship between a group of inputs that each have one output. A function is a connection between inputs in which each input is associated to exactly one output. A function is an expression, rule, or law in mathematics that describes a connection between one variable (the independent variable) and another variable (the dependent variable).

The domain of a function is the set of values that may be plugged into it. This set contains the x values in a function like f. (x). A function's range is the set of values that the function can take. This is the collection of values that the function returns when we enter an x value. To acquire the domain and range, just solve the equation y = f(x) to discover the values of the independent variable x. To compute the function's range, just define x as x=g(y) and then discover the domain of g. (y).

Here,

f(x)=3/4x+5

Domain=(-infinite, 3/4)

Range=(5, infinite)

The domain for given function is (-infinite, 3/4) and range is (5, infinite).

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Answer:

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

The salary during the 7th year is:

Total compensation through full 7 years is base salary for 7 years and total of the annual increase:

Answer: -1 - (-0.25) = -0.75

Step-by-step explanation:

The way you would do that is by first pretending as the negative sign (-), isn't present.

Then do "1 - 0.25".

1.00 - 0.25 = 0.75

After you solved the equation, then we can add the negative sign (-), back into the equation = -1 - (-0.25) = -0.75 ✅

Answer:

[tex]\frac{x}{x+3}[/tex]

Step-by-step explanation:

[tex]\frac{x(x-3)}{(x+3)(x-3)}[/tex]

[tex]\frac{x}{x+3}[/tex]

We have drawn the graph, and point (-2, -1) satisfies both equations and lies on the graph of the system.

What is the system of equations?

A system of equations is a set of two or more equations that are solved simultaneously. In other words, a system of equations is a group of equations that are related to each other and must be considered together in order to find a solution.

The given equations are

y = -5/2x -6

x - y = 1

To find the points of these equations on the graph, we need to solve the system of equations formed by the two given equations.

After solving these equations, we get the point (-2, -1).

Hence, we have drawn the graph, and point (-2, -1) satisfies both equations and lies on the graph of the system.

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After solving the following sets in roster form  we get B' = {-8,-5,-4,0,1,2,4,5,6,7,8} and

A' U (B ^ C) =  {-8, -6, -5 , -4 , 0 , 2, 3, 5, 6 ,7 }

What are sets and roster form?

Either elements or members of a set are terms used to describe the objects that make up a set. A set's components are denoted by curly brackets enclosing them and commas separating them. The sign "" is used to indicate that an element is part of a set. 2 A in the previous illustration. The symbol "" is used to designate an element that is not a part of a set. Here, 3 ∉ A.

The roster notation, in which the components of the sets are contained in curly brackets and separated by commas, is the most popular way to express sets. Set B, for instance, which is made up of the first five even integers, is equal to 2, 4, 6, 8, and 10. The order of the set's components in a roster form is irrelevant; for instance, the first five even integers can equally be described as 2, 6, 8, 10, 4. Additionally, if a set has an infinite number of items, the endless list is defined by adding a string of dots to the end of the final element. For instance, the representation of infinite sets is X = 1, 2, 3, 4, 5,..., where X is the set of natural numbers.

Please see the examples below for a summary of the roster form's notation.

Set A = 1, 2, 3, 4, and 5 in the finite roster notation of sets (The first five natural numbers)

Sets in Infinite Roster Notation: Set B = {5, 10, 15, 20 ....} (The multiples of 5) (The multiples of 5)

a) B' = U - B = {-8,-5,-4,0,1,2,4,5,6,7,8}

b) A' U (B ^ C)

A' = U - A = {-8, -6, -5 , -4  , 0 , 2, 3, 5, 6 ,7 }

B intersection C = ∅

A' U (B ^ C) = A' =  {-8, -6, -5 , -4  , 0 , 2, 3, 5, 6 ,7 }

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The WW2 era helped tp deliver several prosperity to the whites in the forms of college education funding, It gave them unemployment insurances in the nation and also helped them with housing benefits.

This bill, commonly known as the G.I. Bill, was passed by President Franklin D. Roosevelt on June 22, 1944, and it gave World War II veterans money for housing, unemployment insurance, and college tuition. Millions of WWII and post-World War II military veterans now have access to higher education.

It made it possible for hundreds of thousands of men and women to pursue higher education, many of whom would not have been able to do so without its assistance. Although it left many minority veterans behind, the bill also contributed to the growth of the middle class in America.

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A number has the same digit in its hundreds place and in its hundreds place. 10,000

Generally, Given that a number's hundreds place and its hundredths place both have the same digit, we may assume that the number is perfect.

Let's say that the digit is a 1.

Therefore, the value of the hundreds position in a number is equal to 100.

The value of the hundredth position in a number is equal to 0.01%.

The following formula may be used to determine the number of instances in which the value of the digit in the hundreds place is higher than the value of the digit in the hundredths place:

As a result, the difference between the value of the digit in the hundreds place and the value of the digit in the hundredth place is 10,000 times bigger.

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CQ

A number has the same digit in its hundreds place and its hundredths place. How many times greater is is the value of the digit in the hundreds place than the value of the digit in the hundredths place?

A. 100,00

B. 100

C. 1,000

D. 10,000

Answer:

1. parallel

2. no solutions

Step-by-step explanation:

You can prove the lines are parallel because they never intersect, as they have the same slope.

Thus, parallel lines have no solutions.

* a solution is the point (x,y) where 2 or more functions intersect

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Step-by-step explanation:

checking the slope of both lines :

red goes through (2, 1) and (4, 5)

blue goes through (-2, 0) and (0, 4).

the slope is the ratio

(y coordinate difference / x coordinate difference)

when going from one point on the line to another.

for the red slope and the identified points

x changes by +2 (from 2 to 4).

y changes by +4 (from 1 to 5).

the slope is +4/+2 = 2

for the blue slope and the identified points

x changes by +2 (from -2 to 0).

y changes by +4 (from 0 to 4).

the slope is +4/+2 = 2.

so, both lines have the same slope and are therefore parallel.

parallel lines that are not identical have no solution, as they have no intersection point.

so,

parallel

no solution

Answer:

Point of intersection is (13.72, 660)

Step-by-step explanation:

You have to use your graphing tool to answer questions 2 and 3.

Then click on the point of intersection and note the coordinates.

That's it.

This can also be solved mathematically but since the question does not ask I have not given that solution process.

Graph attached

Answer:

Step-by-step explanation:

Given a total of 244 sodas and hot dogs sold, with sodas numbering 42 more than hot dogs, you want to know the number of each that were sold.

Let s represent the number of sodas sold. Then s-42 is the number of hot dogs sold, and the total sold is ...

  s +(s -42) = 244

Add 42 and simplify

  2s = 286

  s = 143 . . . . . divide by 2

  hot dogs = 143 -42 = 101 . . . . . figure the number of hot dogs

143 sodas and 101 hot dogs were sold.

The probability that a randomly selected customer who is on plan B uses the phone most often to text is; 13/23

We are given that;

The data by payment plans are;

Plan A: 27 texts, 21 Internet

Plan B: 13 texts, 10 Internet

Now, the probability is defined as the ratio of the sum of all observations and the total number of observations.

The total number of observations for plan B is; 13 +10 = 23

The number of customers that are on payment plan B = 23 customers are on payment plan B.

The number of customers that are on plan B text is; 13

Thus, the probability that a randomly selected customer who is on plan B uses the phone most often to text is;

Probability = 13/23

The probability that a randomly selected customer who is on plan B uses the phone most often to text is 13/23.

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By using the fact that the sum of the internal angles of a triangle is 180°, we will see that p = 80°

Notice that on the top vertex of the triangle we have a plane angle, then we can write:

p + 49° + A = 180°

So we can solve that really simple linear equation we can find the value of A, the top internal angle of the triangle:

A = 180° - 49° - p

A = 131° - p

Now remember that the sum of the 3 internal angles of a triangle is equal to 180°, so now we can write the equation:

131° - p + p - 16° + p- 15° = 180°

p = 180° - 131° + 16° + 15°

p = 80°

The value of p is 80°.

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