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BA

The measure of angle x of the quadrilateral inscribed in a circle is x = 31°

Given data ,

Let the quadrilateral be ABCD inscribed in a circle

Now , the measure of angles of the quadrilateral are

Opposite angles are supplementary: A + C = 180° and B + D = 180°.

Adjacent angles are supplementary: A + B = 180°, B + C = 180°, C + D = 180°, and D + A = 180°

And , the sum of opposite angles is always equal to 180°

So , the measure of 118° + 2x° = 180°

On simplifying , we get

2x = 62

Divide by 2 on both sides , we get

x = 31

Hence , the angle is solved and x = 31

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Answer:

2

Step-by-step explanation:

This is because if you draw an imaginary line between them you can see that they can fold horizontally and vertically and thats it.

There are 1.92 x 10²⁷ pennies weigh as much as the earth is,

We have to given that;

The Earth Weights 5.972 x 10²⁴ kilograms.

And, A penny weighs 3.1 x 10⁻³ kilograms.

Hence, Number of pennies weigh as much as the earth is,

⇒ 5.972 x 10²⁴ / 3.1 x 10⁻³

⇒ 1.92 x 10²⁷

Thus, There are 1.92 x 10²⁷ pennies weigh as much as the earth is,

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Answer:

y=1

Step-by-step explanation:

Because the answer to y is always 1.

Answer:

403970 Is the answer

Step-by-step explanation:

first:

2 × 5 = 10

Next:

10 × 40397 = 403970

Easy. As. That.

403970 Being the answer

Answer:403970

Step-by-step explanation: i think

The probability of tossing tails and rolling a multiple of 2 is 1/4.

Probability is measuring the likelihood of an event occurring, based on the available information.

According to the multiplication rule, the probability of two independent events happening together is equal to the product of their individual probabilities.

Here we have

A fair coin and a fair six-sided number cube

The probability of tossing tails with a fair coin is 1/2, and the probability of rolling a multiple of 2 on a fair six-sided number cube is 3/6.

To find the probability of both events happening, we multiply the probabilities:

P(tails and a multiple of 2) = P(tails) x P(multiple of 2)

P(tails and a multiple of 2) = (1/2) x (1/2)

P(tails and a multiple of 2) = 1/4

Therefore,

The probability of tossing tails and rolling a multiple of 2 is 1/4.

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The function is a logarithmic function

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = { 2 , 5 , 8 , 11 , 14 }

Now , the values of x of the function are

x = { 2 , 6 , 18 , 54 , 162 }

Plotting the points on the graph , we get a logarithmic equation

Hence , the function is logarithmic

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Answer:

  1, 4

Step-by-step explanation:

You want to know which of these statements is true:

The relationship between the various liquid measures is ...

  1 gallon = 4 quarts = 8 pints = 16 cups = 128 fl oz

  2 quarts = 4 pints, so the relation ...

  7 pints > 2 quarts is TRUE . . . . . . 7 pints > 4 pints

  4 pints = 8 cups, so the relation ...

  4 pints 1 cup > 10 cups is false . . . . . . 9 cups is not greater than 10 cups

  1 quart = 32 fl oz, so the relation ...

  1 quart > 40 fl oz is false . . . . . . 32 fl oz is not greater than 40 fl oz

  1 gallon = 8 pints, so the relation ...

  1 gallon < 8 pints 1 cup is TRUE . . . . . . 16 cups < 17 cups

  8 quarts = 2 gallons, so the relation ...

  8 quarts = 32 gallons is false

__

Additional comment

It is true that 32 quarts = 8 gallons.

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The total surface area of the figure will be 1968.85 square meters.

To determine  the surface area of the figure, we need to find the area of each face and then add them together.

Surface Area of the rectangular prism = 2(lb + bh + hl)

= 2(16 × 9.5) + 2(9.5 × 14) + 2(16 × 14)

= 2(152 + 133 + 224) = 2(509)

= 1018 m²

Next, we need to find the area of the triangular prism on the front with dimensions 11 m, 12.7 m, and 14 m:

Surface Area of the triangular prism;

= (11 × 14) + 2(0.5 × 11 × 12.7) + 2(0.5 × 12.7 × 14)

= (154 + 350.35 + 445.5)

= 950.85 m²

Therefore, the total surface area of the figure will be;

Total Surface Area = Surface Area of rectangular prism + Surface Area of triangular prism

= 1018 m² + 950.85 m²

= 1968.85 m²

So, the surface area of the figure is 1968.85 square meters.

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The value of c is 12 for the given expression c = (2)(1) + (-1)(-1) + (3)(3)

To find the value of c, we need to perform the calculation

c = (2)(1) + (-1)(-1) + (3)(3)

Expanding the products, we get:

c = 2 + 1 + 9

Simplifying, we get:

c = 12

So the value of c is 12.

However, no information is given about d or any other values, so we cannot calculate the value of d or any other variables with the given information.

Overall, the calculation to find c is (2)(1) + (-1)(-1) + (3)(3) = 12.

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-- The given question is incomplete, the complete question is

"Find the value of c for the given expression c = (2)(1)+(-1)(-1)+(3)(3)" --

Answer and Step-by-step explanation:

To solve this problem, we can use the formula for compound interest:

A = P(1 + r/n)^(nt)

where:

A = the future value of the investment

P = the initial principal ($8,000.00 in this case)

r = the annual interest rate (10% in this case)

n = the number of times the interest is compounded per year (since interest is compounded quarterly, n = 4)

t = the number of years (17 - 3 = 14 years in this case)

We want to find the future value of the investment on Courtney's 17th birthday, so t = 14 years. Substituting the values into the formula:

A = $8,000.00(1 + 0.10/4)^(4*14)

A = $8,000.00(1.025)^56

Using a calculator:

A ≈ $44,322.42

Therefore, the certificate will be worth approximately $44,322.42 on Courtney's 17th birthday, assuming a 10% annual interest rate compounded quarterly.

The certificate will be worth $23,683.96 on Courtney's 17th birthday.

It is the interest we earned on the interest.

The formula for the amount earned with compound interest after n years is given as:

A = P [tex](1 + r/n)^{nt}[/tex]

P = principal

R = rate

t = time in years

n = number of times compounded in a year.

We have,

To find the value of the certificate on Courtney's 17th birthday, we need to use the formula for compound interest:

[tex]A = P(1 + r/n)^{nt}[/tex]

where:

A = the amount at the end of the investment period

P = the principal investment amount

r = the annual interest rate (as a decimal)

n = the number of times the interest is compounded per year

t = the number of years

In this case,

The principal (P) is $8,000.

The annual interest rate (r) is 10%, or 0.1 as a decimal.

The interest is compounded quarterly, so n = 4.

The investment period is 14 years, so t = 14.

Plugging these values into the formula, we get:

A = 8000(1 + 0.1/4)^(4 x 14)

A = 8000(1 + 0.025)^56

A = 8000(1.025)^56

A = 8000(2.960496)

A = $23,683.96

Therefore,

The certificate will be worth $23,683.96 on Courtney's 17th birthday.

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Answer:

Step-by-step explanation:

Triangle UVW has vertices at U(−1, 0), V(−4, 1), W(−4, 4). Determine the vertices of image U′V′W′, if the preimage is rotated 90° counterclockwise.

U′(0, −1), V′(−1, −4), W′(−4, −4)

U′(0, −1), V′(1, −4), W′(4, −4)

U′(1, 0), V′(4, −1), W′(4, −4)

U′(−1, 0), V′(−4, 0), W′(4, −4)

The system of equations has two solutions: (7, 8) and (9, 6). We have solved question by using substitution method.

Define substitution method ?

Substitution method is a way of solving a system of linear equations in which one variable in one of the equations is solved for, and then substituted into the other equation to eliminate that variable.

To solve the system of equations:

[tex]y = x^2 - 12x + 33[/tex] ...(1)

[tex]y = 4x - 30[/tex] ...(2)

We can substitute (2) into (1) and solve for x:

[tex]4x - 30 = x^2 - 12x + 33[/tex]

Rearranging the terms, we get:

[tex]x^2 - 16x + 63 = 0[/tex]

We can factor this quadratic equation as:

(x - 7)(x - 9) = 0

So the solutions for x are:

x = 7 or x = 9

To find the corresponding values of y, we can substitute these values of x into either (1) or (2). Let's use (2):

For x = 7:

y = 4x - 30 = 4(7) - 30 = 8

So the solution is (x, y) = (7, 8)

For x = 9:

y = 4x - 30 = 4(9) - 30 = 6

So the solution is (x, y) = (9, 6)

Therefore, the system of equations has two solutions: (7, 8) and (9, 6).

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Answer:

27

Step-by-step explanation:

Answer:

To find the standard form of the equation of a quadratic function with roots of 4 and −1 that passes through (1, −9), we can start by using the fact that if a quadratic function has roots at r1 and r2, its standard form is:

y = a(x - r1)(x - r2)

where "a" is a constant that depends on the function, and (x - r1) and (x - r2) are the factors of the quadratic function.

So, in this case, we have:

r1 = 4

r2 = -1

Passes through (1, -9)

To find "a," we can use the fact that the function passes through (1, -9). Substituting x=1 and y=-9 into the standard form, we get:

-9 = a(1 - 4)(1 - (-1))

-9 = a(-3)(2)

-9 = -6a

a = 1.5

So, the equation of the quadratic function in standard form is:

y = 1.5(x - 4)(x - (-1))

y = 1.5(x - 4)(x + 1)

y = 1.5(x^2 - 3x - 4)

y = 1.5x^2 - 4.5x - 6

Therefore, the answer is y = 1.5x^2 - 4.5x - 6. Option A.

Step-by-step explanation:

dont ask me to huirry

There are 10 tables and 26 chairs in the classroom.

We have,

Let's call the number of tables "t" and the number of chairs "c".

According to the problem,

Two equations are:

c = 2t + 6 (the number of chairs is twice the number of tables plus six)

c + t = 36 (the total number of chairs and tables is 36)

We can use substitution to solve for one of the variables.

Substitute c = 2t + 6 into the second equation:

(2t + 6) + t = 36

Simplify and solve for t:

3t + 6 = 36

3t = 30

t = 10

Now that we know there are 10 tables, we can use the first equation to find the number of chairs:

c = 2t + 6 = 2(10) + 6 = 26

Therefore,

There are 10 tables and 26 chairs in the classroom.

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The complete question.

The number of chairs in the classroom is twice the number of tables plus six. If there are thirty-six pieces of furniture in the classroom between chairs and tables, how many chairs and tables are there?

Answer:

[tex]P = 48 in[/tex],[tex]A= 120in^2[/tex]

Step-by-step explanation:

Again we can use Pythagorean theorem to find the missing side

x^2 + 15^2 = 17^2

x^2 + 225 = 289

Subtract 225 from both sides

x^2 = 64

Find the square root of both sides

√x^2 = √64

x = 8

So

l = 15in, w = 8in

P=2(15) + 2(8)

P = 30 + 18

P = 48 in

A= 15(8)

A= 120in^2

The temperature increases by 0.2245 °C.

We have,

Heat = 0.418 J

Mass= 0.4453 g

and, The specific heat capacity of water is 4.18 J/g/°C.

Using the equation

q = m c ΔT

0.418 = 0.4453 x 4.18 x ΔT

0.418 = 1.861354 x ΔT

ΔT= 0.2245 °C

Thus, the temperature increases by 0.2245 °C.

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the solution is [tex]x = \pi /3, 2\pi /3[/tex].

the equation's solutions in the range [0,21) are π/3 and 2π/3. Because it is already included in the solutions to the first equation.

A mathematical statement that declares two expressions to be equal is known as an equation. In most cases, it is made up of variables, constants, and mathematical operations like addition, subtraction, multiplication, and division. The two expressions on either side of the equal symbol "=" are considered to be equivalent. Equations are used to explain how variables relate to one another and to solve issues by identifying the values of the variables that satisfy the equation. Equations are essentially instruments that allow us to communicate and work with mathematical ideas and concepts in a clear, accurate, and succinct way.

Setting each element to zero and figuring out x will allow us to solve the equation:

As much as

[tex]2 cos x + 1 = 0, 2 sin x - 3 = 0[/tex]

When we solve the first equation, we obtain:

[tex]2 sin x = \sqrt3\\sin x = \sqrt3/2[/tex]

In the range [0,21], there are two solutions to this equation: π/3 and 2π/3.

When we solve the second equation, we obtain:

[tex]2 cos x = -1\\cos x = -1/2[/tex]

There is just one answer to this equation in the range [0,21): 2π/3.

As a result, the equation's solutions in the range [0,21) are π/3 and 2π/3. Because it is already included in the solutions to the first equation, we have omitted the solution from the second equation, 2π/3 .

Thus, the solution is

[tex]x = \pi /3, 2\pi /3.[/tex]

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There are 42 ways to seat the group in the given manner.

There are two specific seats that must be occupied: the sixth seat, which must be occupied by the counselor, and the seventh seat, which must be occupied by the camper who engages in food fights.

We can first consider the number of ways to arrange the remaining seven people in the first five seats and the last two seats, which is 7!/(5!2!) = 21. This is the number of ways to choose any five of the seven remaining people to sit in the first five seats, and then assign the remaining two people to the last two seats.

Now we must consider the two specific seats that must be occupied by the counselor and the food fight-prone camper. Since the counselor is already in the sixth seat, there are only two choices for the food fight-prone camper: they must sit in the seventh seat.

Therefore, the total number of ways to seat the counselor and eight campers along the picnic bench, with the counselor in the sixth seat and the food fight-prone camper in the seventh seat, is:

21 x 2 = 42

So there are 42 ways to seat the group in the given manner.

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Approximately 17.95% of the people over the age of 55 prefer other sports and/or hate sports.

The number of people in the "55 and older" age group who prefer other sports or hate sports is 7.

Now we need to find the total number of people in the "55 and older" age group, which is 39.

To find the percentage, we'll use the following formula:

Percentage = (Number of people in the category / Total number of people in the age group) * 100

Percentage = (7 / 39) * 100

Percentage ≈ 17.95%

So, approximately 17.95% of the people over the age of 55 prefer other sports and/or hate sports.

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Answer:

Let d be the distance from home to the library.

(3/4)d - (1/4)d + 3.2 = d

(1/2)d + 3.2 = d

d + 6.4 = 2d

d = 6.4 miles

If the point (2 + d, y) is on the graph of the function, it is true that the point (2 - d, y) is also on the graph.

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

(x, y) = (2 + d, y) and (2 - d, y)

And the function is given as

f(x) = x(x - 4)

Substituting the points in the equation, we have

f(2 + d) = (2 + d)(2 + d - 4)

f(2 - d) = (2 - d)(2 - d - 4)

Evaluate the sum and the difference

So, we have

f(2 + d) = (2 + d)(d - 2)

f(2 - d) = (2 - d)(- d - 2)

Rewrite the second equation as follows

f(2 + d) = (2 + d)(d - 2)

f(2 - d) = (-2 + d)(d + 2)

So, we have

f(2 + d) = (2 + d)(d - 2)

f(2 - d) = (2 + d)(d - 2)

See that

f(2 - d) = f(2 + d) = (2 + d)(d - 2)

Hence, the claim is true

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Complete question

Consider the following claim: if the point (2 + d, y) is on the graph of the function

f(x) = x(x-4), then the point (2 - d, y) is also on the graph.

Use algebra to show that the claim is true

Null hypothesis: The variance of the heights of major-league baseball players is equal to or surpasses 2.6 inches.

Alternative hypothesis: The standard deviation of heights of major-league baseball players is slighter than 2.6 inches.

With the figures placed into the formula for t, we attain:

t = (2.573 - 2.6) / (2.573 / sqrt(20)) = -0.56

The calculated test statistic is consequently a negative 0.56.

Considering our alternative hypothesis posits that the variation of heights is underneath 2.6 inchses, we are conducting a one-tailed trial with the decisive value at the 0.05 level of significance = -1.729.

Since the resulting test statistic (-0.56) is superior to the vital value (-1.729), we are unable to reject the null assumption. Thus, we lack ample proof to determine that the divergence of heights of major-league baseball players is smaller than 2.6 inches at the 0.05 level of importance.

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Answer:

Step-by-step explanation:

Describe a functiDescribe a function that takes an input, adds 2, and then multiplies by 4on that takes aDescribe a function that takes an input, adds 2, and then multiplies by 4n inpDescribe a function that takes an input, adds 2, and then multiplies by 4ut, adds 2, and then multiplies by 4

Answer: f(θ)=5sin(π/4θ)

Step-by-step explanation:

A=5

B=(2π)/8π= (1)/4π

The equation of a sine function with an amplitude of 5 and a period of 8π is y = 5 sin((1/4)x). The amplitude and period in the question have been used to derive values for the constants in the general sine function equation.

The equation of a sine function in general is given by y = A sin(B(x - C)) + D where A represents the amplitude of the function, B represents the period, C represents the horizontal shift, and D represents the vertical shift.

Since the amplitude is 5 and the period is 8π, these will take the place of A and B in the equation. Given that there are no shifts indicated, C and D are both 0.

However, we need to remember that the value B in the equation is actually found using the formula B = 2π / period.

So, B will become 2π/8π = 1/4. Thus, the final equation of a sine function for the given conditions is y = 5 sin((1/4)x).

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The  triangles are:

For a person to be able to know the different types of triangles, one need to know the attributes that tells one type of triangle from others such as.

Equilateral triangle is seen as  kind of a triangle that has all three sides to be of equal length as well as all three angles of equal measure (60 degrees).

Note also that an Isosceles triangle is one that is known to be seen as a kind of a triangle that has two sides of equal length as well as two angles of equal measure.

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The Area of figure, having base as 3 inches and height as 6 inches is 9 square inches.

We know that, the Area of triangle denoted by letter "A" which is having height as "h" units, and base as "b" units, is : (1/2)×b×h,

In the given figure, the "base" length is : (b) = 3 inch,

The height of the triangle in figure is : h = 6 inches,

Substituting the values,

We get,

Area of figure = (1/2) × 3 × 6,

Area of figure = 3 × 3,

Area of figure = 9 square inches,

Therefore, the required area is 9 square inches.

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The value of distance between two points (2‚5) and (6‚8) is,

⇒ d = 5

We have to given that;

To find the distance between two points (2‚5) and (6‚8).

Since, We know that;

The distance between two points (x₁ , y₁) and (x₂, y₂) is,

⇒ d = √ (x₂ - x₁)² + (y₂ - y₁)²

Hence, We get;

The value of distance between two points (2‚5) and (6‚8) is,

⇒ d = √ (6 - 2)² + (8 - 5)²

⇒ d = √ 16 + 9

⇒ d = √25

⇒ d = 5 units

Thus, The value of distance between two points (2‚5) and (6‚8) is,

⇒ d = 5

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