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The equation is written as z = 7 + (20 -4x²/2)

From the information given, we have that the equations as;

x²-2y=5   ( 1)

4y+z=7     (2)

From equation (1), make y the subject of formula, we have;

-2y= 5 - x²

Divide both sides by the coefficient of the variables, we have;

y = 5 - x²/-2

y = -5 + x²/2

Now, substitute the value of y in (2), we have;

4 (-5 + x²/2) + z = 7

expand the bracket

-20 + 4x²/2 + z = 7

collect the like terms, we have;

z = 7 + (20 -4x²/2)

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The equation for the function shown is f(x) = (x + 1)² - 2. Option B

From the information given, we have the deductions;

The vertex of the parabola is given as (-1, -2)

Using the form;

f(x) = a(x - h)^2 + k

Such that (h, k) represents the vertex coordinates.

Substitute the vertex coordinates into formula, we get;

f(x) = a(x - (-1))² + (-2)

= a(x + 1)² - 2

Now, substitute the value for a, we get;

2 = a(-3 + 1)² - 2

find the square and collect like terms

4 = a(4)

a = 1

Put value back into the equation

f(x) = 1(x + 1)² - 2

Multiply the value, we get;

f(x) = (x + 1)² - 2

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Explanation:

The formula to use is n*(n-1)/2

Plug in n = 12 to get 12*(12-1)/2 = 12*11/2 = 132/2 = 66

That formula is from the nCr combination formula when r = 2.

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

Here's a visual way to see why that rule works.

Imagine there are only 4 teams. We'll make a table that has 4 rows and 4 columns. The team names are A,B,C,D.

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & & & & \\\cline{1-5}B & & & & \\\cline{1-5}C & & & & \\\cline{1-5}D & & & & \\\cline{1-5}\end{array}[/tex]

In the table, cross out the cells where one team pairs up with itself. That's along the main diagonal pointing to the northwest (or southeast).

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & & X & & \\\cline{1-5}C & & & X & \\\cline{1-5}D & & & & X\\\cline{1-5}\end{array}[/tex]

Let's also cross out any cell below the main diagonal.

[tex]\begin{array}{|c|c|c|c|c|} \cline{1-5} & A & B & C & D\\\cline{1-5}A & X & & & \\\cline{1-5}B & X & X & & \\\cline{1-5}C & X & X & X & \\\cline{1-5}D & X & X & X & X\\\cline{1-5}\end{array}[/tex]

We do this because a mirrored copy is found above the diagonal.

We started with 4*4 = 16 cells. Then subtracted off the diagonal to get 16-4 = 12 cells left over. Then divide in half because we crossed off the lower half to get 12/2 = 6 different matchups among the 4 teams.

Those 6 matchups are:

The order doesn't matter. A matchup like "A vs B" is the same as "B vs A".

We'll take this concept to extend it to n teams. We have n*n = n^2 cells to start with. Subtract off the n cells along the diagonal to get n^2-n = n(n-1) cells remaining.

Then we split that in half to get the formula n(n-1)/2.

The Burj Khalifa, located in Dubai in the United Arab Emirates, is the tallest building in the world as of 2022, there are approximately 148 floors in the Burj Khalifa.

We can make use of the data given to determine the Burj Khalifa's floor count.

Andre is known to have stood 1,000 metres away from the structure and turned his head to look up at a 39.62 degree angle.

Let's write "h" for the Burj Khalifa's height and "d" for Andre's distance from the building's base.

tan(39.62°) = h / d

h = d * tan(39.62°)

h = 1000 * tan(39.62°) ≈ 753.7 meters

So, as per this, Number of floors = h / floor height

Number of floors = 753.7 meters / 5.079 meters

Number of floors ≈ 148.4 floors or 148 floors.

Thus, 148 floors are there in Burj Khalifa.

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The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.

Here, we have,

given that,

the product of two number in scientific notation is: 0.0258 × 10⁻⁸

now, let the two numbers be:

0.43× 10⁻⁵ and, 0.06× 10⁻³

we get,

 0.43× 10⁻⁵ × 0.06× 10⁻³

= 0.43 × 0.06× 10⁻⁵ × 10⁻³

= 0.43 × 0.06 × 10⁻⁵⁻³

=0.43 × 0.06× 10⁻⁸

=0.0258 × 10⁻⁸

Hence, The two numbers could be 0.43× 10⁻⁵ and, 0.06× 10⁻³.

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The order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:

Situation 1: Derrick rolls the die 10 times.

Situation 2: Derrick rolls the die 100 times.

Situation 3: Derrick rolls the die 1,000 times.

Situation 4: Derrick rolls the die 10,000 times.

Situation 5: Derrick rolls the die 1,000,000 times.

To determine the order of situations from the largest difference between relative frequency and actual probability to the smallest difference, we need to consider the concept of relative frequency and actual probability.

Relative frequency refers to the observed proportion of an event occurring in an experiment or trial, while actual probability represents the theoretical or expected probability of that event occurring.

Situation 1: Derrick rolls the die 10 times.

In this situation, the relative frequency of rolling a three can vary, but with a limited number of trials, the relative frequency might not accurately reflect the actual probability. Therefore, the difference between relative frequency and actual probability is likely to be larger compared to situations with more trials.

Situation 2: Derrick rolls the die 100 times.

With a larger number of trials, the relative frequency is expected to converge towards the actual probability. The difference between relative frequency and actual probability would likely be smaller compared to the previous situation.

Situation 3: Derrick rolls the die 1,000 times.

Increasing the number of trials further enhances the convergence of relative frequency to the actual probability. The difference between relative frequency and actual probability would be smaller than in the previous two situations.

Situation 4: Derrick rolls the die 10,000 times.

With an even larger number of trials, the relative frequency becomes more reliable and closely approximates the actual probability. The difference between relative frequency and actual probability would be smaller compared to the previous situations.

Situation 5: Derrick rolls the die 1,000,000 times.

In this situation, the large number of trials greatly increases the reliability and accuracy of the relative frequency. The observed relative frequency is expected to be very close to the actual probability, resulting in the smallest difference between the two.

Therefore, the order from the situation with the largest difference between relative frequency and actual probability to the situation with the smallest difference would be:

Situation 1: Derrick rolls the die 10 times.

Situation 2: Derrick rolls the die 100 times.

Situation 3: Derrick rolls the die 1,000 times.

Situation 4: Derrick rolls the die 10,000 times.

Situation 5: Derrick rolls the die 1,000,000 times.

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The equation of the circle is (x + 4)² + (y - 1)² = 81

Given is an equation of a circle we need to convert it in standard form,

x² + y² + 8x - 2y = 64,

To convert the equation of a circle to standard form, you need to complete the square for both the x and y variables.

The standard form of a circle equation is:

(x - h)² + (y - k)² = r²

where (h, k) represents the center of the circle, and r represents the radius.

Let's convert the given equation to standard form step by step:

x² + y² + 8x - 2y = 64

Rearrange the equation to group the x-terms and y-terms:

x² + 8x + y² - 2y = 64

Now, complete the square for the x-terms.

Take half of the coefficient of x (which is 8 in this case), square it, and add it to both sides of the equation:

x² + 8x + 16 + y² - 2y = 64 + 16

Simplify:

(x + 4)² + y² - 2y = 80

Complete the square for the y-terms.

Take half of the coefficient of y (which is -2 in this case), square it, and add it to both sides of the equation:

(x + 4)² + y² - 2y + 1 = 80 + 1

Simplify:

(x + 4)² + (y - 1)² = 81

Now, the equation is in standard form, with the center at (-4, 1) and a radius of √81 = 9.

Hence the equation of the circle is (x + 4)² + (y - 1)² = 81

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The 77th term of the given Sequence is 244.

The given sequence is an arithmetic progression with a common difference of 3. To find the 77th term of the sequence, we can use the formula for the nth term of an arithmetic progression.

The formula for the nth term of an arithmetic progression is:

_ = _1 + ( − 1),

where _ is the nth term, _1 is the first term, is the position of the term in the sequence, and is the common difference.

In this case, _1 = 16 and = 3. Plugging in these values into the formula, we get:

_77 = 16 + (77 − 1) × 3.

_77 = 16 + 76 × 3.

_77 = 16 + 228.

_77 = 244.

Therefore, the 77th term of the given sequence is 244.

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The maximum number of CYN Dewi can buy is 4268.8 CYN and cost in pounds is  £453.20.

Maximum number of CYN Dewi can buy:

Since £1 buys 9.28 CYN, Dewi's £460 can be converted to Chinese yuan by multiplying it by the exchange rate:

Maximum CYN = £460 × 9.28 CYN/£1

To calculate this, we multiply the pound amount by the exchange rate:

Maximum CYN = £460 × 9.28 CYN/£1 ≈ 4268.8 CYN

Cost in pounds to the nearest penny:

To calculate the cost in pounds, we divide the desired amount of Chinese yuan by the exchange rate:

Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1

To calculate this, we divide the Chinese yuan amount by the exchange rate:

Cost in pounds = 4268.8 CYN ÷ 9.42 CYN/£1

= £453.20

Therefore, the cost in pounds, to the nearest penny, will be £453.20.

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Complete question

Buying chinese yuan (CYN)             £1 buys 9.28 CYN

Selling chinese yuan (CYN)           9.42 CYN buys  £1

(a) Dewi has £460 to buy Chinese yuan.

Calculate the maximum number of CYN Dewi can buy, and

how much, to the nearest penny, this will cost him.

Answer:

C. y + 4 = 4(x+3)

Step-by-step explanation:

Point slope form: y-y1 = m(x-x1)

Substitute the given slope 4 and point (-3, -4)

y-(-4) = 4(x - (-3))

Simplify

y + 4 = 4 (x+3)

Answer: B

Step-by-step explanation: 63.3 in^2

The value of the angle csc θ of the given problem is: 5/4

There are different trigonometric ratios such as:

sin x = opposite/hypotenuse

cos x = adjacent/hypotenuse

tan x = opposite/adjacent

Now, we are given that:

cot θ = 4/3

We know that cot θ = 1/tan θ

Thus:

tan θ = 3/4

Since θ is an acute angle, it means it is less than 90 degrees. Thus, using Pythagoras theorem, we can find the third side which is the hypotenuse to be 5

Now, csc θ = 1/sin θ

Thus: sin θ = 4/5

csc θ = 5/4

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Answer:  A.   x=3     y= -1         z=4

Step-by-step explanation:

I plugged it into my graphing calculator.

>2nd Matrix

>Edit >A

>choose 3x3

>Enter all coefficients as they look

>2nd Matrix

>Edit >B

>Choose 3x1

>Enter answers as they look

Go to main page

[tex][A]^{-1} [B]\\[/tex]

Answers end up being 3, -1,  4

The surface area of the rectangular prism is 318 square mm

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

9 mm by 6 mm by 7 mm

The surface area of the rectangular prism is calculated as

Surface area = 2 * (Length * Width + Length * Height + Width * Height)

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

Area = 2 * (9 * 6 + 9 * 7 + 6 *7)

Evaluate

Area = 318

Hence, the area is 318 square mm

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Question

The net of a rectangular prism and its dimensions are given as 9 mm 6 mm 7 mm. What is the total surface area of the rectangular prism in square inches?

1. The area of composed figure is 52.26 cm².

2. The area of composed figure is 74 ft².

1. Area if Triangle

= 1/2 x b x h

= 1/2 x 6 x 8

= 24 cm²

Area of semicircle

= πr²/2

= 3.14 x 3 x 3

= 28.26 cm²

So, area of composed figure

= 28.26 + 24

= 52.26 cm²

2. Area of Trapezium

= 1/2 (7 + 13) x 5

= 1/2 x 20 x 5

= 50 ft²

Area of Triangle

= 1/2 x b x h

= 1/2 x 8 x 6

= 24 ft²

So, area of composed figure

= 24 + 50

= 74 ft²

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Answer:

a set of numbers in order of least to greatest

The solution is the multiplication is: 5x × (3x-2)  = 15x² - 10x.

Here, we have,

given that,

the expression is:

5x(3x-2)

now, we have to Multiply out

so, we have,

5x × (3x-2)

= 5x×3x - 5x×2

=15x² - 10x

Hence, The solution is the multiplication is: 5x × (3x-2)  = 15x² - 10x.

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Examining the word problem we can say that, Molly used 160 beads to make the necklace.

Let's assume the number of beads used to make the bracelet is x.

We also know that Molly used a total of 192 beads for both the necklace and the bracelet. and It takes 5 times as many beads to make a necklace as it does a bracelet, So,

x + 5x = 192

6x = 192

solve for x

x = 192 / 6

x = 32

Molly used 32 beads to make the bracelet.

number of beads used to make the necklace

Number of beads used for the necklace = 5 * 32

Number of beads used for the necklace = 160

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The surface area of the triangular prism is 193.05 cm².

We have,

The figure is a triangular prism.

Now,

There are 4 triangular surfaces.

Each surface area is the same except the base surface.

So,

3 surface area.

= 3 x (1/2 x 9 x 11.3)

= 3 x 50.85

= 152.55 cm²

And,

Base surface area.

= 1/2 x 9 x 9

= 40.5 cm²

Now,

The surface area of the triangular prism.

= 152.55 + 40.5

= 193.05 cm²

Thus,

The surface area of the triangular prism is 193.05 cm².

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The Percentage of people from the 46-55 age group preferring Plan II is 42%.

The percentages, we need to calculate the ratio of people preferring Plan I in the 36-45 age group and the ratio of people preferring Plan II in the 46-55 age group.

Let's start with the first part of the question:

Percentage of people preferring Plan I from the 36-45 age group:

To calculate this percentage, we need to divide the number of people preferring Plan I in the 36-45 age group by the total number of people preferring Plan I, and then multiply by 100 to express it as a percentage.

Number of people preferring Plan I in the 36-45 age group = 14

Total number of people preferring Plan I = 14 + 28 + 21 = 63

Percentage = (14 / 63) * 100 ≈ 22.22 ≈ 22% (rounded to the nearest whole number)

So, the percentage of people preferring Plan I from the 36-45 age group is approximately 22%.

Now, let's move on to the second part of the question:

Percentage of people from the 46-55 age group preferring Plan II:

To calculate this percentage, we need to divide the number of people preferring Plan II in the 46-55 age group by the total number of people from the 46-55 age group, and then multiply by 100 to express it as a percentage.

Number of people preferring Plan II in the 46-55 age group = 21

Total number of people in the 46-55 age group = 27 + 21 + 2 = 50

Percentage = (21 / 50) * 100 = 42%

So, the percentage of people from the 46-55 age group preferring Plan II is 42%.

Based on the calculations, the correct answer is:

A. 23% of people who prefer Plan I are from the 36-45 age group, and 42% of people from the 46-55 age group prefer Plan II.

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The hands of an analog clock point at 1:27 is at 1o'clock position

At 1:27 on an analog clock, the hour hand focuses straightforwardly at the numeral "1" on the clock confront, demonstrating that it is within the 1 o'clock position.

The miniature hand, on the other hand, focuses between the numerals "2" and "3" on the clock confront, roughly midway between them.

Since there are 60 minutes in an hour and the diminutive hand moves around the clock confront at a consistent rate, it shows that 27 minutes have passed since the hour started.

Hence, the miniature hand is closer to the numeral "3" but not however at it. The moment hand may be anyplace on the clock confront, because it moves persistently.

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Answer:

[tex]a_{n}[/tex] = 6n

Step-by-step explanation:

there is a common difference between consecutive terms, that is

12 - 6 = 18 - 12 = 6

this indicates the sequence is arithmetic with nth term

[tex]a_{n}[/tex] = a₁ + d(n - 1)

where a₁ is the first term and d the common difference

here a₁ = 6 and d = 6 , then

[tex]a_{n}[/tex] = 6 + 6(n - 1) = 6 + 6n - 6 = 6n

The vertex of the equation of the parabola y = 2( x - 3 )² + 1 is (3,1).

Given the equation of the parabola in the question:

y = 2( x - 3 )² + 1

To determine the vertex of the parabola, we use the vertex form of a parabola which is expressed as:

Vertex form: y = a(x - h)² + k

Where (h, k) represents the vertex of the parabola.

The given equation is already in the vertex form:

y = 2( x - 3 )² + 1

Hence, comparing the given equation, y = 2(x - 3)² + 1, with the vertex form, we can see that:

h = 3 and k = 1

Therefore, the vertex is (3,1).

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The value of X is 7.

Given that the set of number are in pattern,
X, 5, 9, 27, 15, 21.

To find the value of X such that given numbers are in pattern.

The next three number are three times of first three numbers respectively.

Let a, b, c is the first three numbers then 3a, 3b, 3c are next three numbers.

Consider the given set of numbers,  X, 5, 9, 9 × 3, 5 × 3, 21.

By using the data and the pattern set gives,

3X = 21.

Divide by 7 on both sides,

X = 7.

Hence, the value of X is 3

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The functions of the coefficients of the quadratic equation indicates that the correct statements are;

a. The y-intercept of the function is (0, c)

c. The coefficient b determines the horizontal shift of the parabola compared to the parent function

d. If a is negative, the parabola opens upwards

The quadratic equation is; y = a·x² + b·x + c

The functions of the coefficients of the above quadratic function are;

a = The scale factor, and the coefficient that determines the direction the projectile faces.

a < 1; Indicates that the graph is wider than the parent function

a > 1; Indicates that the graph is narrower than the parent function

a < 0; Indicates that the parabola opens downward

a > 0; Indicates that the parabola opens upwards

b = The coefficient b together with coefficients a and c determines the coordinate of the vertex of the graph of the quadratic function, which is; (-b/(2·a), -D/(4·a))

Where;

D = The discriminant

Therefore, b determines the x-value, and therefore, the horizontal shift of the parabola compared to the parent function

c = The y-coordinate of the y-intercept of the quadratic function, which is (0, c)

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As per the given data, the area of the rectangular field is approximately 204 square meters.

To find the area of the rectangular field, we need to multiply its length by its width.

Given that the length is 18 2/5 m and the width is 11 2/23 m, we need to convert these mixed fractions into improper fractions for easier calculation.

Length: 18 2/5 m = (5 * 18 + 2)/5 = 92/5 m

Width: 11 2/23 m = (23 * 11 + 2)/23 = 255/23 m

Now, we can calculate the area of the rectangular field:

Area = Length * Width

     = (92/5) m * (255/23) m

     = (92 * 255)/(5 * 23) m^2

     = 23460/115 m^2

     = 204 m^2 (rounded to the nearest whole number)

Therefore, the area of the rectangular field is approximately 204 square meters.

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Your question seems incomplete, the probable complete question is:

A rectangular field is 18 2/5 m long and 11 2/23 m wide. Find its area. ​

The solution to the system of equations is  x = 5.4 and y = -1.4

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

-x=y-4 y=4x+9

So, we have

-x = y - 4

y = 4x + 9

Rewrite the equation as

x = -y + 4

y = 4x + 9

So, we have

y = 4(-y + 4) + 9

Open the bracket and evaluate

5y = 9 - 16

So, we have

y = -1.4

Recall that

x = -y + 4

So, we have

x = 1.4 + 4

Evaluate

x = 5.4

Hence, the solution is  x = 5.4 and y = -1.4

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The meaning of "The field of a relation R" is a constraint on the values that can be stored in that attribute.

We are given that;

The statement The field of a relation R

Now,

According to the web results, the field of a relation R is the set of all values that appear in the relation R. In other words, it is the union of all the attributes (columns) of R. For example, if R is a relation with attributes A, B, and C, then the field of R is the set of all values that appear in A, B, or C. The field of R can also be denoted by F.

The field of a relation is different from the domain of an attribute, which is the set of all possible values that an attribute can take. For example, if A is an attribute that can only take integer values, then the domain of A is the set of all integers. The domain of A may be larger than the field of A, which is the set of all values that actually appear in A. The domain of an attribute defines a constraint on the values that can be stored in that attribute.

Therefore, by the domain the answer will be a constraint on the values that can be stored in that attribute.

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