Quadrilateral ABCD is inscribed in a circle.
What is the measure of angle A?
Enter your answer in the box.
m/A=

Answer:

r=7

Step-by-step explanation:

Cylinder Area

= πr² x h

1078 = 22/7 x r² x 7

1078/22 = r²

49=r²

r=7

The next time when a train and a bus leave the station together is 4:30pm.

The next time when a train and a bus leave the station together will be the least common multiple (LCM) of the two intervals, 8 minutes and 10 minutes.

To find the LCM of 8 and 10, we can list the multiples of each number until we find a common multiple:
8: 8, 16, 24, 32, 40
10: 10, 20, 30, 40

The LCM of 8 and 10 is 40. This means that a train and a bus will leave the station together every 40 minutes.

Since the train and bus both leave the station at 3:50pm, the next time they will leave together will be 40 minutes later, at 4:30pm.

Therefore, the next time when a train and a bus leave the station together is 4:30pm.

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The correct classification for 11+8i is a complex number.√−81 can be expressed as the complex number 9i.

The number 11+8i is a complex number. This is because it has both a real part (11) and an imaginary part (8i). A complex number is any number that can be expressed in the form a+bi, where a and b are real numbers and i is the imaginary unit. Therefore, the correct classification for 11+8i is a complex number.

To express √−81 as a complex number, we can use the fact that √−1 = i. So, √−81 = √(81)*√(−1) = 9*i = 9i. Therefore, √−81 can be expressed as the complex number 9i.

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Therefore, Roberto needs 26 more inches of lumber. Answer: 26 inches.

an explanation of the relationship between the two phrases on either side of a sign. A single variable and an equal sign are typically present. It is equivalent to this 2. 2x - 4 Equals 2. The variable x is present in the earlier instance.

To solve this problem, we need to convert all the measurements to the same units. Let's convert 6 feet and 8 inches to inches:

6 feet = 6 x 12 inches = 72 inches

6 feet and 8 inches = 72 + 8 = 80 inches

So Roberto needs 80 inches of lumber to repair the deck.

He has 54 inches of lumber, so he needs:

80 - 54 = 26 inches

Therefore, Roberto needs 26 more inches of lumber. Answer: 26 inches.

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The sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians.

When \( n \) is a positive integer, we can use mathematical induction to prove that \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \) is also a positive integer.

Base case: \( n = 1 \), then \( \left(1^{3}+6 \cdot 1^{2}+2 \cdot 1\right) / 3 = \frac{9}{3} = 3 \) which is a positive integer.

Induction step: Assume \( \left(k^{3}+6 k^{2}+2 k\right) / 3 \) is a positive integer for some positive integer \( k \). Then:

\[ \left( \left(k+1\right)^{3}+6 \left(k+1\right)^{2}+2 \left(k+1\right)\right) / 3 = \frac{k^{3}+18 k^{2}+22 k+9}{3} \]

\[ = \frac{k^{3}+6 k^{2}+2 k + 6 k^{2}+16 k + 9}{3} \]

\[ = \frac{k^{3}+6 k^{2}+2 k}{3} + \frac{6 k^{2}+16 k + 9}{3} \]

\[ = \frac{\left(k^{3}+6 k^{2}+2 k\right)}{3} + \frac{\left(6 k^{2}+16 k + 9\right)}{3} \]

\[ = \frac{\left(k^{3}+6 k^{2}+2 k\right)}{3} + \left(2 k + 3\right) \]

Since the first term is a positive integer and the second term is a positive integer, it follows that \( \left(\left(k+1\right)^{3}+6 \left(k+1\right)^{2}+2 \left(k+1\right)\right) / 3 \) is a positive integer as well.

Therefore, it has been shown that when \( n \) is a positive integer, so also is \( \left(n^{3}+6 n^{2}+2 n\right) / 3 \).

To verify that the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians, consider the following: the sum of the interior angles of any polygon is equal to \( (n-2) \pi \) radians, where \( n \) is the number of sides in the polygon. This is true for any type of polygon, whether it is a triangle, quadrilateral, pentagon, etc.

Therefore, the sum of the interior angles of a polygon with \( n \) sides is \( (n-2) \pi \) radians.

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Answer:

Without a diagram or additional context, it's difficult to determine the values of x and y precisely. However, we can use the given information to set up some equations and solve for x and y in terms of each other.

First, since m is parallel to n, we know that angles 4 and 9 are alternate interior angles and angles 10 and 9 are corresponding angles. Therefore:

angle 4 = angle 9 (alternate interior angles)

angle 9 + angle 10 = 180 degrees (interior angles on the same side of the transversal)

angle 4 + angle 10 = 180 degrees (corresponding angles)

Substituting the given expressions for each angle, we have:

6x - 5 = 3y - 10

5x + 8 + 3y - 10 = 180

6x - 5 + 5x + 8 = 180

Simplifying the second equation by combining like terms, we get:

8x + 3y - 2 = 0

We can now solve for one variable in terms of the other. From the first equation, we have:

6x = 3y + 5

x = (3/2)y + (5/6)

Substituting this expression for x into the third equation, we get:

6((3/2)y + (5/6)) - 5 + 5((3/2)y + (5/6)) + 8 = 180

Simplifying and solving for y, we get:

y = 29/9

Substituting this value for y back into the expression we found for x, we get:

x = (3/2)(29/9) + (5/6) = 59/6

Therefore, the values of x and y that satisfy the given conditions are x = 59/6 and y = 29/9.

Answer:

Direct proportion and inverse proportion are two types of relationships between two variables.

Direct proportion is a relationship in which two variables increase or decrease together at the same rate. In other words, if one variable increases, the other variable also increases, and if one variable decreases, the other variable also decreases. The mathematical expression for direct proportion is:

y = kx

where y is the dependent variable, x is the independent variable, and k is a constant of proportionality.

On the other hand, inverse proportion is a relationship in which two variables change in opposite directions. In other words, if one variable increases, the other variable decreases, and if one variable decreases, the other variable increases. The mathematical expression for inverse proportion is:

y = k/x

where y is the dependent variable, x is the independent variable, and k is a constant of proportionality.

So, the main difference between inverse proportion and direct proportion is the direction of change between the two variables. In direct proportion, the two variables change in the same direction, while in inverse proportion, the two variables change in opposite directions.

I may be wrong but, i think it may be C. due to how the question  states the answers and questions, Although it may also be B.

The solution to the equation is (5, -1)

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

2x + 3y = 7

-2x + 1y = -11

Add to eliminate x

So, we have

4y = -4

Divide both sides by 4

y = -1

Recall that 2x + 3y = 7

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

2x - 3 = 7

So, we have

2x = 10

Divide

x = 5

For the substitution method, we have

2x + 3y = 7

-2x + y = -11

The second equation becomes

y = 2x - 11

By substitution, we have

2x + 6x - 33 = 7

So, we have

8x = 40

x = 5

Recall that

y = 2x - 11

So, we have

y = 2 * 5 - 11

y = -1

Hence, the solution is (5, 2)

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The Demand function D(x) = -0.00094x + 4.54

Step 1: To find the equation for D(x), we need to find the slope and the y-intercept of the demand function. The slope can be found using the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Step 2: We can use the given information to find the slope. The first point is (1919, 2.74) and the second point is (3131, 1.60). Plugging these values into the formula, we get:

m = (1.60 - 2.74)/(3131 - 1919)
m = -1.14/1212
m = -0.00094

Step 3: Now we need to find the y-intercept, b. We can use the point-slope form of a line, y - y1 = m(x - x1), and plug in one of the points and the slope to find b.

y - 2.74 = -0.00094(x - 1919)
y = -0.00094x + 2.74 + 0.00094(1919)
y = -0.00094x + 4.54

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The expression equivalent to 2(2x + 2y) are,

⇒ 4 (x + y)

Or, (4x + 4y)

An expression which is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division is called an mathematical expression.

Given that;

The expression is,

⇒ 2 (2x + 2y)

Since, Natalie and Johnathan are asked to write an expression equivalent to 2(2x + 2y).

Hence, We get;

⇒ 2 (2x + 2y)

Take 2 as common;

⇒ 2 × 2 (x + y)

⇒ 4 (x + y)

⇒ 4x + 4y

Thus, The expression equivalent to 2(2x + 2y) are,

⇒ 4 (x + y)

Or, (4x + 4y)

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The final answer is:
First Triangle:
B = NONE
C = NONE
c = NONE

Second Triangle:
B' = NONE
C' = NONE
c' = NONE

Using the Law of Sines, we can find the missing angles and sides of the triangles.

First Triangle:
Since A = 147°, b = 2.9 yd, and a = 1.4 yd, we can use the Law of Sines to find angle B.
sin B / 2.9 yd = sin 147° / 1.4 yd
sin B = (2.9 yd)(sin 147°) / 1.4 yd
sin B = 1.97
Since sin B is greater than 1, there is no solution for angle B. Therefore, the first triangle is not possible and we can enter NONE in each corresponding answer blank.

B = NONE
C = NONE
c = NONE

Second Triangle:
Since A = 147°, b = 2.9 yd, and a = 1.4 yd, we can use the Law of Sines to find angle B'.
sin B' / 2.9 yd = sin 147° / 1.4 yd
sin B' = (2.9 yd)(sin 147°) / 1.4 yd
sin B' = 1.97
Since sin B' is greater than 1, there is no solution for angle B'. Therefore, the second triangle is not possible and we can enter NONE in each corresponding answer blank.

B' = NONE
C' = NONE
c' = NONE

So, the final answer is:
First Triangle:
B = NONE
C = NONE
c = NONE

Second Triangle:
B' = NONE
C' = NONE
c' = NONE

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The correct answer is O for some discrete probability distributions but not all.

This is because the probability of a random variable X being less than 8 can vary depending on the type of distribution it follows. For some discrete distributions, such as a binomial distribution, the probability of X < 8 can be calculated by summing the probabilities of all possible values of X that are less than 8. However, for other discrete distributions, such as a Poisson distribution, the probability of X < 8 may not be as straightforward to calculate. Therefore, the statement that P(X < 8) = P(X < 8) is true for some discrete distributions but not all.

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a)f(x) = { 0, if x < 0 \\ 4x, if 0 ≤ x < 4 \\ 0, if x ≥ 4 }

b)P(X=-1) = 0

c)P(X ≤ 3) = 4 * 3 = 12

a) The pdf (probability density function) of the variable X is given by
f(x) =
{
   0, if x < 0 \\
   4x, if 0 ≤ x < 4 \\
   0, if x ≥ 4
}

b) P(X=-1) = 0, since x < 0

c) P(X ≤ 3) = 4 * 3 = 12

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The sets of points that have a distance of 4 units between them are:

Point X and Point W

Point T and Point S

To find the distance between two points, we use the distance formula:

distance = √ (x₂ – x₁)² + (y₂ – y₁) ²

We can calculate the distances between each pair of points and check if any of them are equal to 4.

The distances between the following pairs of points are 4 units:

Point X (3,9) and Point W (5,0): distance = √((5 - 3)² + (0 - 9)²) = √52 = 4.12

Point T (5,0) and Point S (-1,0): distance = √((-1 - 5)² + (0 - 0)²) = √36 = 6

Point T (5,0) and Point S (-3,0): distance = √((-3 - 5)² + (0 - 0)²) = √64 = 8

Point R (1,6) and Point Q (-1,2): distance = √((-1 - 1)² + (2 - 6)²) = √20 = 4.47

Point P (-1,0) and Point O (0,9): distance = √((0 - (-1))² + (9 - 0)²) = √82 = 9.06

Therefore, the only sets of points that have a distance of exactly 4 units between them are Point X and Point W, and Point T and Point S.

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Answer:

Step-by-step explanation:

Pages Alana writes = m+4

to fill in the blanks add 4 to 5, 7, and 9 because of the 4 extra pages Alana writes.

That will give you: 9, 11, and 13 as your answers

A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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Answer:

75%

Step-by-step explanation:

Starting value: 12

Final Value: 21

Subtract final value minus starting value

Divide that amount by the absolute value of the starting value

Multiply by 100 to get percent increase

If the percentage is negative, it means there was a decrease and not an increase.

The area of the figure composed of a rectnagle and a triangle is 128in².

The figure in the the image is composed of rectangle and a triangle.

The area of a rectangle = length × width

Area of a triangle = 1/2 × base × height

Hence;

Area of the composite figure will be;

A = area of a rectangle + area of a triangle

From the image;

Now, we solve for thr area of the composite figure.

A = area of a rectangle + area of a triangle

A = ( 12in × 9in ) + ( 1/2 × 5in × 8in )

A = ( 108in² ) + ( 20in² )

A = 128in²

Therefore, the total area of the figure id 128 squared inch.

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To factor a trinomial, you need to find two binomials that, when multiplied together, give you the original trinomial.

The key to finding binomials is to identify the factors of the quadratic term and the constant term, and then use those factors to construct the binomials.

Here's a step-by-step process for factoring a trinomial:

It's important to note that not all trinomials can be factored using this method.

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Answer: Roshan: 250/5 = 50 Rs.

Isha: 250 - 50 = 200 Rs.

Step-by-step explanation:

The final answer is 3

The calculation you are looking to solve is 2.2 + (3)/(5). To solve this, we first need to convert the improper number 2.2 to a fraction. We can do this by multiplying the whole number by the denominator of the fraction and then adding the numerator. In this case, we would multiply 2 by 5 and then add 2, giving us 12/5. Now, we can add this fraction to the other fraction:

12/5 + 3/5 = 15/5

Next, we can simplify the fraction by dividing both the numerator and denominator by the greatest common factor. In this case, the greatest common factor is 5, so we can divide both the numerator and denominator by 5:

15/5 = 3

Therefore, the final answer is 3.

In summary, 2.2 + (3)/(5) = 3.

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Answer:

5/8

Step-by-step explanation:

GCF:

5/8 = 25/40 ( multiply both sides by 5)

11/20 = 22/40 ( multiply both sides by 2)

Based on the calculation we know that

The value of x as 7− is 35.

The value of x as 7+ is 35.

Suppose that f( x ) = 7 x − 7. We can complete the following statements by plugging in the values of x and evaluating the function.

As x → 7 − , f ( x ) → 42 − 7 = 35
As x approaches 7 from the left, the function f(x) approaches 35.

As x → 7 + , f ( x ) → 42 − 7 = 35
As x approaches 7 from the right, the function f(x) also approaches 35.

Therefore, the function f(x) = 7x - 7 has a horizontal asymptote at y = 35 as x approaches 7 from both the left and the right.

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We can see here that the experimental probability that it will snow in March is:

Experimental probability is the probability that an event will occur based on actual experiments or observations.

It is calculated by performing an experiment or conducting observations, counting the number of times the event of interest occurs, and dividing that count by the total number of trials or observations.

Mathematically, the formula for the experimental probability is defined by:

Probability of an Event P(E) = Number of times an event occurs / Total number of trials.

Number of times it snowed = 2

Total number of trials = 5.

Thus, the experimental probability will be: 2/5.

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Missing number to make the binomial 9x² + X + 25 a perfect square is 30x.

Quadratic equations are the polynomial equations of degree 2 in one variable of type f(x) = ax² + bx + c = 0 where a, b, c, ∈ R and a ≠ 0. It is the general form of a quadratic equation where 'a' is called the leading coefficient and 'c' is called the absolute term of f (x).

Given expression

9x² + X + 25

It can be written as

(3x)² + X + 5²

Comparing with a² + 2ab + b²

a = 3x

b = 5

X = 2ab

X = 2(3x)(5)
X = 30x

Hence, 30x is the missing number  to create a perfect-square binomial.

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The values of a and b that make the function both continuous and differentiable everywhere are a=-13/3 and b=11.

To make the function both continuous and differentiable everywhere, we need to find the values of a and b that make the two parts of the piecewise function equal at x=-1. This will ensure that there are no jumps or breaks in the function at x=-1, making it continuous and differentiable.

First, we plug in x=-1 into both parts of the function and set them equal to each other:

3−3(-1) = -2/3(-1)^2 + a(-1) + b

Simplifying both sides gives us:

6 = -2/3 + a + b

Next, we can rearrange the equation to solve for one of the variables in terms of the other. Let's solve for b in terms of a:

b = 20/3 - a

Now we can take the derivative of both parts of the piecewise function and set them equal to each other at x=-1 to ensure that the function is differentiable:

-3 = -4/3x + a

Plugging in x=-1 gives us:

-3 = 4/3 + a

Rearranging to solve for a gives us:

a = -13/3

Finally, we can plug this value of a back into the equation for b to find the value of b:

b = 20/3 - (-13/3) = 33/3 = 11

So the values of a and b that make the function both continuous and differentiable everywhere are a=-13/3 and b=11.

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The minimum value of the objective function is 16 and it occurs at x = 1 and y = 5.

The given objective function is 9x+3y. The given constraints are y≥−2x+11, y≤−x+10, y≤−3, x+6y≥−4, and x+4.

To minimize this objective function, we need to set up the Lagrangian function:

L(x,y,λ1,λ2,λ3) = 9x+3y - λ1(y+2x-11) - λ2(y-x+10) - λ3(y+3) - λ4(x+6y-4) - λ5(x+4)

We can then find the critical points of this function by taking the partial derivatives of the Lagrangian with respect to x, y, λ1, λ2, and λ3, and setting them equal to zero:

∂L/∂x = 9 - λ2 + 6λ4 = 0
∂L/∂y = 3 - λ1 - λ2 - λ3 - 6λ4 = 0
∂L/∂λ1 = -(y+2x-11) = 0
∂L/∂λ2 = -(y-x+10) = 0
∂L/∂λ3 = -(y+3) = 0
∂L/∂λ4 = -(x+6y-4) = 0
∂L/∂λ5 = -(x+4) = 0

Solving these equations, we get the solution x = 1, y = 5, λ1 = 4, λ2 = -3, λ3 = 8, λ4 = -3, and λ5 = -1.

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The two functions with the end behavior x→+∞ , f(x) →+∞ are:

f(x) = (1/4)*x + 3

h(x) = 2x - 1

The end behavior of a function studies how the function behaves as x tends to infinity or negative infinity.

The function will tend to positive infinity as x tends to positive infinity if the function increases for x > 0.

Then we need to identifty which of these two functions are increasing, the two increasing ones are:

f(x) = (1/4)*x + 3

h(x) = 2x - 1

These two are linear equations with positive solpes, so these are increasing functions, and as x→+∞ , f(x) →+∞

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