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The reflection across the x-axis will have the coordinates (x, -y).

         The x-axis and y-axis are found in graphs, and both have positive and negative ends. The horizontal axis is called the x-axis, and the vertical axis is called the y-axis.

         The x-axis has positive integers on its right and negative integers on its left. The y-axis has positive integers above the zero coordinate and negative integers below the zero coordinate.

         If we take a point on the upper side of the x-axis, its coordinates will be (x, y). While drawing its reflection on the x-axis, we need to draw the point on the vertically opposite plain. Thus, the coordinates of the reflection will be (x, -y).

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Answer:

-6

Step-by-step explanation:

follow

BODMAS

bracket=(11-8)=3

3!= 3x2x1=6

multiplication= -2x6= -12

subtraction=6-12=-6

Answer:

it would be C 9x because a product is the answer from a multiplication equation (:

Answer:

ok.

Step-by-step explanation:

Answer:

$8

Step-by-step explanation:

first you have to find one

0.5 ounce = $2.40 ÷ 3 = $0.80

1 ounce = 0.8 × 2 = $1.60

5 ounces $1.60 × 5 = $8

Answer:

Equation of line in slope-intercept form is: y = -8x-39

Step-by-step explanation:

Given points are:

(-4, -7) and (-6, 9)

The slope-intercept form is given by the equation

\(y = mx+b\)

Here m is the slope of the line and b is the y-intercept.

m is found using the formula

\(m = \frac{y_2-y_1}{x_2-x_1}\)

Here

(x1,y1) = (-4-7)

(x2,y2) = (-6,9)

Putting the values in the formula

\(m = \frac{9+7}{-6+4} = \frac{16}{-2} = -8\)

Putting slope in general equation

\(y = -8x+b\)

Putting (-6,9) in the equation

\(9 = -8(-6)+b\\9 = 48+b\\b = 9-48\\b = -39\)

Putting the value of b we get

\(y = -8x-39\)

Hence,

Equation of line in slope-intercept form is: y = -8x-39

Using the long division method, it is proved that (x + 2) is a factor of (x³ + 8), because the result of the remainder is 0.

To show that (x + 2) is a factor of (x³ + 8) using long division, we can divide (x³ + 8) by (x + 2) and see if the remainder is 0. If the remainder is 0, then (x + 2) is a factor of (x³ + 8). Here's how the long division would look:

        x² - 2x + 4

x+2 | x³ + 0x² + 0x + 8

      - (x³ + 2x²)

    --------------------

         -2x² + 0x + 8

       - (-2x² - 4x)

         ---------------

              4x + 8

            - (4x + 8)

              --------

                 0

Since the remainder is 0, we can conclude that (x + 2) is a factor of (x³ + 8).

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The volume of the figure is approximately 1591.63 cm³.

We have,

To find the volume of the figure with a semicircle on top of a cone, we can break it down into two parts: the volume of the cone and the volume of the semicircle.

The volume of the Cone:

The formula for the volume of a cone is V = (1/3)πr²h, where r is the radius of the base and h is the height of the cone.

Given that the diameter of the cone is 14 cm, the radius (r) is half of the diameter, which is 7 cm.

The height (h) of the cone is 17 cm.

Plugging the values into the formula, we have:

V_cone = (1/3)π(7 cm)²(17 cm)

V_cone = (1/3)π(49 cm²)(17 cm)

V_cone = (1/3)π(833 cm³)

V_cone ≈ 872.67 cm³ (rounded to two decimal places)

The volume of the Semicircle:

The formula for the volume of a sphere is V = (2/3)πr³, where r is the radius of the sphere. In this case, since we have a semicircle, the radius is half of the diameter of the base.

Given that the diameter of the cone is 14 cm, the radius (r) of the semicircle is half of that, which is 7 cm.

Plugging the value into the formula, we have:

V_semicircle = (2/3)π(7 cm)³

V_semicircle = (2/3)π(343 cm³)

V_semicircle ≈ 718.96 cm³ (rounded to two decimal places)

Total Volume:

To find the total volume, we add the volume of the cone and the volume of the semicircle:

V_total = V_cone + V_semicircle

V_total ≈ 872.67 cm³ + 718.96 cm³

V_total ≈ 1591.63 cm³ (rounded to two decimal places)

Therefore,

The volume of the figure is approximately 1591.63 cm³.

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Answer:

Step-by-step explanation:

-1

Answer:

1 1/2 feet or 1.5 feet

Step-by-step explanation:

Dave cuts a 12-foot-long streamer into 8 pieces of equal length. How long is each piece

From the question:

8 pieces = 12 feet

1 piece = x feet

Cross Multiply

8 pieces × x feet = 1 piece × 12 feet

x feet = 1 piece × 12 feet/8 pieces

x feet = 3/2 feet

x feet = 1 1/2 feet or 1.5 feet

Therefore, the length of each feet =

1 1/2 feet or 1.5 feet

Answer:

Step-by-step explanation:

Total games:

a) The square root of complex number, 2i is equals to the ±( 1 + i).

b) The square root of complex number, (1 - √3i) is equals to the ±1/√2(√3 - 1). The rectangular coordinates plane of both present in above figure.

Square root of a number is defined as a value which on multiplication by itself, results the original number. If p is the square root of q then it is denoted as p=√q. We have to determine the square root of complex numbers and express them in rectangular coordinates. For a nonzero complex number z, its square roots are √z =√r exp( i(2πk + θ)/2), k = 0,1

(a) The magnitude of 2i is r =√(2² + 0) = 2, and the principal argument is θ = π/2. So, (2i)½ = r½ exp(i (2πk + π/2)/2) , k = 0, 1

For first root, substuting, k = 0

=> (2i)½ = 2½ exp(i (2π×0 + π/2)/2)

=> (2i)½ = √2 exp(i (π/2)/2)

=> (2i)½ = √2 exp(i π/4) = √2(cos(π/4) + i sin(π/4)

=> (2i)½ = √2( 1/√2 + i(1 /√2)) = 1 + i

For second root substuting, k = 1

=> (2i)½ = 2½ exp(i (2π×1 + π/2)/2)

=> (2i)½ = √2 exp(i (5π/2)/2)

=> (2i)½ = √2 exp(i (5π/4) = √2( cos(5π/4) + i sin(5π/4)

=> (2i)½ = √2(- 1/√2 + i(-1 /√2)) = - (1 + i)

Hence, square root of 2i is ±( 1 + i).

b) 1 -√3i

The magnitude and principal argument of 1 −√3i are respectively, r = √(1² + (√3)²) = 2 and θ = tan⁻¹ ( -√3/1) = - π/3. Similar to part(a), square root of (1 - √3i) is written as (1 - √3i)½ = r½ exp(i (2πk - π/3)/2), k= 0, 1

For first root , k = 0

(1 - √3i)½ = √2 exp(i (2π×0 - π/3)/2)

=> (1 - √3i)½ = √2 exp(i (- π/6) )

=> (1 - √3i)½ = √2( cos(-π/6) - i sin(π/6))

=> (1 - √3i)½ = √2( cos(π/6) - i sin(π/6))

=> (1 - √3i)½ = √2( √3/2 - i (1/2)) = 1/√2(√3 - 1)

For second root, k = 1

(1 - √3i)½ = √2 exp(i (2π×1 - π/3)/2)

=> (1 - √3i)½ = √2 exp(i (5π/3)/2)

=> (1 - √3i)½ = √2 exp(i (5π/6))

=> (1 - √3i)½ = √2 (cos(5π/6) + i sin(5π/6))

=> (1 - √3i)½ = √2 (- √3/2 + i(1/2) ) = - 1/√2(√3 - i)

so, (√1- √3i ) is ± 1/√2(√3 - 1). Hence, we got all required square roots.

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Complete question:

1. Find the square roots of (a) 2i; (b) 1 - √3i and express them in rectangular coordinates.

Main Answer:The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

Supporting Question and Answer:

How can we express a vector as a linear combination of  vectors using a system of equations?

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

   2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Final Answer:Therefore,the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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The linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

To express a vector as a linear combination of  vectors using a system of equations, we need to find the coefficients that multiply each given vector to obtain the desired vector. This can be done by setting up a system of equations, where each equation corresponds to the components of the vectors involved.

Body of the Solution:

(a) To show that the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3, we need to demonstrate two conditions: orthogonality and linear independence.

Orthogonality: We need to show that each pair of vectors is orthogonal, meaning their dot product is zero.

u1 · u2 = (2)(-3) + (0)(0) + (3)(2) = -6 + 0 + 6 = 0

u1 · u3 = (2)(0) + (0)(7) + (3)(0) = 0 + 0 + 0 = 0

u2 · u3 = (-3)(0) + (0)(7) + (2)(0) = 0 + 0 + 0 = 0

Since the dot product of every pair of vectors is zero, they are orthogonal.

  2.Linear Independence: We need to show that the vectors u1, u2, and u3 are linearly independent, meaning that no vector can be written as a linear combination of the other vectors.

We can determine linear independence by forming a matrix with the vectors as its columns and performing row operations to check if the matrix can be reduced to the identity matrix.

[A | I] = [u1 | u2 | u3 | I] =

[2 -3 0 | 1 0 0]

[0 0 7 | 0 1 0]

[3 2 0 | 0 0 1]

Performing row operations:

R3 - (3/2)R1 -> R3

R1 <-> R2

[1 0 0 | -3/2 1 0]

[0 1 0 | 0 1 0]

[0 0 7 | 0 0 1]

Since we can obtain the identity matrix on the left side, the vectors u1, u2, and u3 are linearly independent.

Therefore, the vectors u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) form an orthogonal basis for R^3.

(b) To write v = (1, 2, 3) as a linear combination of u1, u2, and u3, we need to find the coefficients x, y, and z such that:

v = xu1 + yu2 + z*u3

Substituting the given vectors and coefficients:

(1, 2, 3) = x(2, 0, 3) + y(-3, 0, 2) + z(0, 7, 0)

Simplifying the equation component-wise:

1 = 2x - 3y

2 = 7y

3 = 3x + 2y

From the second equation, we can solve for y:

y = 2/7

Substituting y into the first equation:

1 = 2x - 3(2/7)

1 = 2x - 6/7

7 = 14x - 6

14x = 13

x = 13/14

Substituting the found values of x and y into the third equation

3 = 3(13/14) + 2(2/7)

3 = 39/14 + 4/7

3 = 39/14 + 8/14

3 = 47/14

Therefore, we have determined the values of x, y, and z as follows:

x = 13/14

y = 2/7

z = 47/14

Thus, we can write the vector v = (1, 2, 3) as a linear combination of u1 = (2, 0, 3), u2 = (-3, 0, 2), and u3 = (0, 7, 0) as:

v = (13/14)u1 + (2/7)u2 + (47/14)u3

Therefore, v can be expressed as a linear combination of the given vectors.

Therefore, the linear combination of v = (13/14)u1 + (2/7)u2 + (47/14)u3  

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The product of a rational and an irrational number can be either rational or irrational, depending on the specific numbers involved.

To illustrate this, let's consider an example:

Let's say we have the rational number 2/3 and the irrational number √2.

Their product would be (2/3) * √2.

In this case, the product is irrational.

The square root of 2 is an irrational number, and when multiplied by a rational number, the result remains irrational.

However, it's also possible to have a product of a rational and an irrational number that is rational. For example, if we consider the rational number 1/2 and the irrational number √4, their product would be (1/2) * 2, which equals 1. In this case, the product is a rational number.

Therefore, we cannot make a definitive statement that the product of a rational and an irrational number is always rational or always irrational. It depends on the specific numbers involved in the multiplication.

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Answer:

20

Step-by-step explanation:

\(10x - 30\)

\(10 \times 5 - 30\)

\(50 - 30\)

\( = 20\)

Therefore, The probability of events a and b occurring together is 1/4.

The probability of both events occurring is given by the product of their individual probabilities, i.e., p(a and b) = p(a) * p(b). Therefore, p(a and b) = (3/4) * (1/3) = 1/4.
The probability of both events occurring simultaneously can be calculated using the product rule, which states that the probability of two events occurring together is the product of their individual probabilities. Applying this rule, we get that the probability of events a and b occurring together is (3/4) * (1/3) = 1/4. Thus, there is a 1/4 chance that both events will happen simultaneously.

Therefore, The probability of events a and b occurring together is 1/4.

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The value of the given expression of subtraction 0.75–0.5, in simplest fractional form is 1/4.

Use the concept of subtraction defined as:

Subtraction in mathematics means that is taking something away from a group or number of objects. When you subtract, what is left in the group becomes less.

The given expression is:

0.75–0.5

After removing the decimal it can be written as,

75/100 - 5/10

Now simplifying it, we get

(75-50)/100 = 25/100

Now convert 25/100 in their simplest form:

Since 25x4 = 100

Therefore,

25/100 = 1/4

Hence,

The simplest fractional value of 0.75–0.5 is 1/4.

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Yes, every odd integer can be written as the difference of two squares.

To prove this, let k be a positive integer. Then the difference of the squares of k+1 and k is (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1, which is an odd integer. Thus, every odd integer can be written as the difference of two squares.

To prove this, we first chose a positive integer, k. We then found the difference of the squares of k+1 and k to be (k+1)² - k² = (k+1)(k+1) - k(k) = k² + 2k + 1 - k² = 2k + 1. Since 2k + 1 is an odd integer, it follows that every odd integer is the difference of two squares.

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The concept that a message gives different meanings to different objects is called option (b) polymorphism.

Polymorphism is a fundamental concept in object-oriented programming (OOP) that allows different objects to respond to the same message or method invocation in different ways. In other words, it allows objects of different classes to be treated as if they were of the same class, as long as they implement the same method or message.

This can make code more flexible, reusable, and easier to maintain. Polymorphism is achieved through inheritance, interfaces, or overloading methods. For example, a "draw" method could be implemented differently for different shapes, such as circles, rectangles, or triangles.

Therefore, the correct option is (b) polymorphism

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Answer:

\(\triangle OPR \cong \triangle QRP\) as per AAS congruence.

Step-by-step explanation:

We are given two triangles \(\triangle OPR \ and\ \triangle QRP\).

Side OP is parallel to Side QR.

OP || QR

\(\angle O = \angle Q\)

To prove:

The two triangles are congruent i.e. \(\triangle OPR \cong \triangle QRP\)

Solution:

Let us have a look at the triangles:

\(\triangle OPR \ and\ \triangle QRP\)

1. Given that \(\angle O = \angle Q\).

2. Side OP || RQ so, \(\angle OPR = \angle QRP\) because they are the alternate angles of parallel sides. (Alternate angels are equal when a line cuts two parallel sides).

3. Side PR is common to both the sides i.e. PR = RP

Hence, by AAS congruence i.e. two angles and a side which is not between the two angles are same.

\(\therefore \triangle OPR \cong \triangle QRP\) as per AAS congruence.

(9×6/2) × 12 = 324

Explination:

The easiest way to understand what you're doing is to find the area of the base first, then extend it upwards to find the volume using height. Hence the equation: b×h=v

So how do we find the base of a triange? Remember that every single triangle can be calculated as a square, then cut in half. So 9 × 6 / 2 = 27 cm2

The next step is to calculate the volume using the height of the figure. 27 × 12 = 324 cm3

**remember to use the correct units, since area and volume are different.

Answer:

3 x + 2 < 6

3 x < - 2

x < - 2 /3

] - ∞ : - 2/3 [

Step-by-step explanation:

Answer:

A.

x > -4 and x < 0

Step-by-step explanation:

3|x + 2| < 6

3x + 6 < 6

     -6     -6

3x < 0

÷3  ÷3

x < 0

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

3|x + 2| < -6

3x + 6 < -6

     -6     -6

3x < -12

÷3     ÷3

x > -4

I hope this helps!

SOLUTION

Consider the graph shown:

From the graph the equation is:

Therefore the approximate equation is:

Substitute x=4 into the equation:

Answer:

hello what are you telling here............

Step-by-step explanation:

Answer:

True.

Step-by-step explanation:

True.

Let's say A = 5, and B = 10.

We need to swap the contents of A and B, so A will end up with 10 and B will end up with 5.

A = 5

B = 10

Introduce variable C.

C = A (now C contains 5)

A = B (now A contains 10)

B = C (now B contains 5)

In the last two steps above, you see that the values of A and B were swapped.

According to the description, element a21 will represent B. 100.

According to the question, the rows represent the type of music while the columns represent the weeks. Now the element that we have is a21. The 2 in the element stands for the rows which is the type of music and this is R and B.

The column is the weeks and since we have the column as 1, we will look at week 1 and the second bar in that week which is R and B. So, the correct description is option B.

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Step-by-step explanation:

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The tangent segments WX and YX are the same length. This can be proven by forming triangles WVX and YVX, and using the hypotenuse length rule to show the triangles are congruent.

So,

YX = WX

x-8 = 18

x = 18+8

x = 26

Answer: 3 centimeters equals 12 meters

Hope this helps!

Answer:

Three centimeters represent 12 meters.

Step-by-step explanation:

Answer:

22и + 56

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Parenthesis (add)

-8(-4и - 7) - 10и

Step 2: Distribute (multiply)

32и + 56 - 10и

Step 3: Combine like terms (и)

22и + 56