13-3i=-8 what does i equal

As, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively. So,  if a commutes with d, then it must be block diagonal.

Let's suppose that d is a diagonal matrix with repeated diagonal entries grouped contiguously, i.e.,

d = \(\begin{pmatrix} D_1 & 0 & 0 & \cdots & 0 \ 0 & D_1 & 0 & \cdots & 0 \ 0 & 0 & D_2 & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & D_k \end{pmatrix}\),

where \(D_1, D_2, \dots, D_k\) are scalars and appear with frequencies \(m_1, m_2, \dots, m_k\), respectively, so that \(m_1 + m_2 + \dots + m_k = n\), the size of the matrix.

Suppose that \(a\) is a matrix that commutes with d, i.e., ad = da.

Then, for any \(i \in {1, 2, \dots, k}\), we have

\(ad_{ii} = da_{ii}\)

Here, \(d_{ii}\) denotes the \(i$th\) diagonal entry of d, i.e., \(d_{ii} = D_i\) for \(i = 1, 2, \dots, k\). Since d is diagonal, \(d_{ij} = 0\) for \(i \neq j\), and

hence

\(ad_{ij} = da_{ij} = 0\)

for all \(i \neq j\).

Therefore, a is also diagonal, with diagonal entries \(a_{ii}\), and we have

\(a = \begin{pmatrix} a_{11} & 0 & 0 & \cdots & 0 \ 0 & a_{11} & 0 & \cdots & 0 \ 0 & 0 & a_{22} & \cdots & 0 \ \vdots & \vdots & \vdots & \ddots & \vdots \ 0 & 0 & 0 & \cdots & a_{kk} \end{pmatrix}\)

Thus, a is block diagonal, with diagonal blocks of size \(m_1 \times m_1\), \(m_2 \times m_2\), \(\dots\), \(m_k \times m_k\), respectively.

Therefore, if a commutes with d, then it must be block diagonal.

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A) horizontal asymptote: y = 7 B) vertical asymptote: x = -4, 5 is the required answers for horizontal and vertical asymptotes of the curve.

The horizontal asymptote of a curve is a horizontal line that the curve approaches as x approaches infinity or negative infinity. The vertical asymptote of a curve is a vertical line that the curve approaches but never crosses as x approaches a certain value. In this case, the horizontal asymptote is found by letting x approach infinity in the fraction and observing what the value of y approaches. In the limit as x approaches infinity, the x^2 term dominates and thus y approaches 7, which is the horizontal asymptote. To find the vertical asymptote, we find the values of x where the denominator equals 0 and the numerator is not equal to 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5. Thus, the vertical asymptotes are x = -4 and x = 5. To find the vertical asymptotes, we look for the values of x where the denominator of the function equals 0 and the numerator does not equal 0. In this case, the denominator x^2 + x - 20 = 0 has roots of -4 and 5, which means that x = -4 and x = 5 are the vertical asymptotes of the function. These values of x represent the values at which the function is undefined, and as x approaches these values from either side, the value of the function approaches positive or negative infinity.

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Answer:

205.599

Step-by-step explanation:

Answer:

205.599 yards

Step-by-step explanation:

1 meter = 1.09361 yards

Multiply 188 meters by 1.09361 yards

188 meters = (1.09361 yards) x (188 meters)

                   = 205.599 yards

The statement "The whole number has one digit if and only if the whole number is less than 10" is true for converse statement. Then the correct option is C.

A inverse statement is one that is derived by opposing the supposition and result of a relative clause.

Let p: The whole number has one digit.

Let q: The whole number is less than 10.

The statement "The whole number has one digit if and only if the whole number is less than 10" is true for converse statement.

If p → q, then, q → p

Then the correct option is C.

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Answer:

x=26.6 when y=8

Step-by-step explanation:

y=Kx, k=y/x, when y is 3 and x is 10,

k=3/10= 0.3

but when y is 8, x will be given by

x=y/k

x=8/0.3

x=26.6 approximately 27

The linear functions are: y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

As a general rule, linear functions take any of the following forms:

y = mx + b

Ax + By = C

y - y1 = m(x - x1)

Any equation that take a different form is not a linear function

Using the above as a guide, the linear functions are:

y + 1 = 5(x - 9), -y + 1 = 5(x − 9), 7y + 2x = 12, -7y + 2x = 12, 4y = 24,  and -4y = 24

Other functions are nonlinear

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Answer:

The University of Montana ski team has ten entrants in a men's downhill ski event. The coach would like the first, second,

9514 1404 393

Answer:

Step-by-step explanation:

Each is a point on the graph of cost versus number of pencils.

The point on the left tells you 4 pencils cost $0.80. The point on the right tells you 5 pencils cost $1.00.

The difference between the points tells you that one additional pencil adds $0.20 to the cost.

_____

Additional comment

We don't know what "situation" is being referred to. The graph may be completely irrelevant to the situation.

Answer:

7.8287

Step-by-step explanation:

Sin(34)=x/14

14 x Sin(34)

Answer:

Step-by-step explanation:

Opposite side of the angle 34  is x & hypotenuse which is opposite to 90 is 14

\(Sin \ 34 = \dfrac{Opposite \ side}{hypotenuse}\\\\0.56 = \dfrac{x}{14}\\\\\\0.56*14=x\)

x = 7.84

Yes, always.

A sequence is a function that takens a positive integer and maps it some other number. For any integer you plug into the sequence, you only ever get one output.

Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

Answer:

He should recieve $2.42

Step-by-step explanation:

First, add the three $10 bills. This gives us 30 dollars.

Next, subtract, you will have to regroup. It should look like this when you line it up.

30.00

- 27.58

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

Now, you regroup and subtract, then you get your answer. Which is 2.42.

Hoped this helped!

Answer:

SORRYYYYYYY!!!!!!!!!!!

Answer:

#1  (0,-4)

#2  (5,0)

#3  (3,1)

Step-by-step explanation:

#1.  (-3, 2) (0, y)  slope = -2

slope = rise/run    therefore slope = -2/1  or down 2 and over 1

so from -3 to 0 you are going over 3 units (or 3 times)  Therefore to find y at x=0, you have to move three steps, or 3 times -2 = -6      so 2-6 = -4

so y intercept (b)  = -4 0r (0,-4)

#2   (-7,-4)  (x,0)  slope (m) = 1/3   -7+12=5    x=5

#3   (4,-3)   (x, 1)   slope (m) = -4   (4/-1)   Moving one unit in slope  means

-3=4=1 for Y and 4-1=3 for X    therefore the point is (3, 1)

Answer:

B

Step-by-step explanation:

Hello!

y = 88° (opposite are equal)

z = 180° - 128° = 52° (straight angle = 180°)

x = 180° - 140° = 40° (straight angle = 180°)

Answer:

x=40°

y=88°

z=52°

Step-by-step explanation:

Solution Given:

x+140°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for x.

x=180°-140°

x=40°

\(\hrulefill\)

y°=88°

Since the vertically opposite angle is equal.

therefore, y=88°

\(\hrulefill\)

z+128°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for z.

z=180°-128°

z=52°

The option that depicts a translation is option B. See the attached image and the explanation for this answer below.

Translation in Math refers to the movement of a shape vertically or horizontally along the x or y-axis without altering its original dimensions.

Going by the above definition, it is clear that Option B is the translated image (assuming that the original image is as given in the image attached.

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The length of AC is equal to the length of BC, which is equal to y times the square root of 2/3. Since we have the value of y is 6cm, the exact length of AC is 14.9cm.

What is Pythagoras Theorem?

Pythagoras' theorem is a fundamental principle in geometry that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

First, we can draw a diagonal from A to D to create two congruent triangles: ACD and ABD. Since these triangles share side AD and diagonal AC is perpendicular to BD, we know that they are right triangles.

Let's call the length of AC "x". Then, using the Pythagorean Theorem in triangle ACD, we get:

x² = AD² - CD²

Similarly, using the Pythagorean Theorem in triangle ABD, we get:

BD² = AD² + AB²

Since DE = EB, we know that triangle EBD is an isosceles triangle, so we can use the Pythagorean Theorem in triangle EBD to get:

EB² = BD² / 4

Since DE = EB, we can substitute this expression for EB in terms of BD into the above equation to get:

DE² = BD² / 4

But we know that DE = EB, so we can substitute "EB" for "DE" to get:

EB² = BD² / 4

Combining this with the previous equation, we get:

BD² / 4 = EB² = (BD² + AB²) / 4

Simplifying, we get:

3BD² / 4 = AB² / 4

Multiplying both sides by 4/3, we get:

BD² = (4/3) AB²

Now we can substitute this expression for BD² into the equation we derived for x²:

x² = AD² - CD² = AD² - (BD² - AB²) = AD² - BD² + AB²

Substituting (4/3) AB² for BD², we get:

x² = AD² - (4/3) AB² + AB² = AD² - (1/3) AB²

To solve for x, we need to know the lengths of AD and AB. We don't have this information, but we do know that ABCD is a kite, so opposite sides are congruent.

This means that AD = BC and AB = CD. Let's call this length "y". Then:

x² = y² - (1/3) y² = (2/3) y²

Solving for x, we get:

x = √((2/3) y²) = y / √(3/2)

Since we don't know the length of y, we can't find the exact value of x. However, we can simplify the expression for x by rationalizing the denominator:

x = y / √(3/2) * √(2/3) / √(2/3) = y √(2/3)

x = 6√(2/3) = 4.89      ......(AD = BC, & AD = 6 cm)

x = 4.9 cm

AC = AE + EC

EC = cos45 * DC = 1/√2 * 7

EC = 4.9

AC = 10 + 4.9 = 14.9 cm

Therefore, the length of AC is equal to the length of BC, which is equal to y times the square root of 2/3. Since we have the value of y is 6cm, the exact length of AC is 14.9cm.

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The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.

The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.

When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.

To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.

For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.

In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.

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\(\bold{\huge{\red{\underline{ Solution}}}}\)

\(\bold{\underline{ We \: have\: given :-}}\)

\(\sf{ 7x - 3y = 20. ...eq(1 ) }\)

\(\sf{ y = 5x - 4. ...eq(2) }\)

Here, we will use the substitution method for solving the above equations.

\(\bold{\underline{Subsitute \: eq(1)\:in \: eq(2)}}\)

\(\sf{ 7x - 3(5x - 4) = 20 }\)

\(\sf{ 7x - 15x + 12 = 20}\)

\(\sf{ - 8x + 12 = 20 }\)

\(\sf{ - 8x = 20 - 12 }\)

\(\sf{ - 8x = 8}\)

\(\sf{ x = 8/-8}\)

\(\sf{ x = - 1. ...eq( 3 )}\)

\(\bold{\underline{Subsitute \: eq(3)\:in \: eq(2)}}\)

\(\sf{ y = 5(-1) - 4 }\)

\(\sf{ y = - 5 - 4 }\)

\(\sf{ y = - 9 }\)

\(\sf{\blue{ Hence, \: The \:value \:of \:x \:and \:y \:is\: - 1 \: and \:-9}}\)

The first statement is false and the rest of the options are true.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

1. 25% of 512 is equal to 1/4 x 500, false due to 500.

2. 90% of 133 is equal to 0.9 x 133, true because 90% is equal to 0.90.

3. 30% of 44 is equal to 3% of 440, true because the value of both is the same.

4. The percentage of 21 is 28 is equal to the percentage of 30 is 40, true because the percentage of both cases is identical.

The first statement is false and the rest of the options are true.

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Through the graph we will determine if the line integral of each vector field is positive, negative, or zero. The answer to this question is:

-Positive

-Negative

-Zero

-Negative

-Zero

-Zero

What is the Line integral?

A line integral, also known as the route integral, curve integral, or curvilinear integral, is used to find the surface's area in three dimensions. In this integral, the function is evaluated along a curve. There are several applications of line integrals, such as in the field of electromagnetics, to find the force applied on a charged particle moving along a curve in a force field created by a vector field.

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Answer:

10y + 6 hope this helps :)

Step-by-step explanation:

We show that at n = 1 the basis step works, but the inductive step fails.

Let consider the Inequality

\(\frac{1}{2}\cdot\frac{3}{4}\dots\dots\frac{2n-1}{2n} < \frac{1}{\sqrt{3n}}\)

We must demonstrate that while the fundamental step of mathematical induction proves the aforementioned inequality, the inductive step does not.

Mathematical induction is a method of proof used in mathematics to prove that a statement is true for all natural numbers.

It involves proving that a statement holds true for a base case (typically zero or one), and then proving that, if it holds true for any given natural number, it must also hold true for the next natural number.

This process is repeated until the statement has been shown to be true for all natural numbers.

Basic Step: n = 1

1/2 < 1/√3, which is true.

Hence we proved that at n = 1  the basic steps of mathematical induction works.

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The complete question is:

Suppose that we want to prove that

\(\frac{1}{2}\cdot\frac{3}{4}\dots\dots\frac{2n-1}{2n} < \frac{1}{\sqrt{3n}}\)

for all positive integers n.

Show that if we try to prove this inequality using mathematical induction, the basis step works, but the inductive step fails.

Answer:

\(m\angle BCD = 32^{\circ}\)

Step-by-step explanation:

Given

\(m\angle DAB = 32^{\circ}\)

See attachment for basketball blackboard

Required

Find \(m\angle BCD\)

In the attachment:

\(m\angle BCD\) and \(m\angle DAB\) are opposite angles

And in a parallelogram, opposite angles have the same measure.

This implies that:

\(m\angle BCD = m\angle DAB = 32^{\circ}\)

So:

\(m\angle BCD = 32^{\circ}\)

Answer:

\(\frac{4}{5}\)

0.8

Step-by-step explanation:

Happy to help:)

Answer:409600

Step-by-step explanation:I multpiled and got 409600

The given set A = {10, 11, 12, 13}, has the cardinal number n(A) = 4, and it has 15 non-empty subsets.

In the question, we are given a set A = {10, 11, 12, 13}.

We are asked for the cardinal number of the set n(A).

Also, we are asked for the number of non-empty subsets of A.

The cardinal number of any set A is given as n(A), which represents the number of elements in set A.

For the given set A = {10, 11, 12, 13}, the number of elements are 4.

Thus, the cardinal number of the set A is, n(A) = 4.

The number of non-empty subsets of any set A, with cardinal number n, is given by the formula, 2ⁿ - 1.

The given set A = {10, 11, 12, 13}, has the cardinal number n(A) = 4.

Thus, the number of non-empty subsets of set A = 2⁴ - 1 = 16 - 1 = 15.

Thus, the given set A = {10, 11, 12, 13}, has the cardinal number n(A) = 4, and it has 15 non-empty subsets.

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