Factorise fully 10c - 25

The product of the five complex numbers is 52 + 18i.  (i - 1) / 4 is the first term in the original product, (1/ (1 + i)) * (1 - i / (1 - i)). Therefore, we can see that the simplified result and the first term in the pair are reciprocals of each other, and they are both related algebraically to the original product through the use of reciprocal and conjugate pairs

.

a.

To perform the multiplication (2 + i)(3 - i)(1 + 2i)(1 - i)(3 + i), we can use the associative and distributive properties of multiplication, as well as the fact that i^2 = -1.

First, we can simplify (2 + i)(3 - i) by using the distributive property:

(2 + i)(3 - i) = 6 - 2i + 3i - i^2 = 7 + i

Next, we can simplify (1 + 2i)(1 - i) by using the difference of squares formula:

(1 + 2i)(1 - i) = 1 - i + 2i - 2i^2 = 3 + i

Finally, we can multiply (7 + i)(3 + i)(3 + i) using the distributive property:

(7 + i)(3 + i)(3 + i) = (733 + 73i + i33 + i3i) + (73i + 7ii + i3i + iii)

= (63 + 28i + 4i^2) + (21i + 7i^2 + 3i^2 + i^3)

= (63 + 28i - 4) + (21i - 7 - 3i - i)

= 52 + 18i

Therefore, the product of the five complex numbers is 52 + 18i.

b.

To simplify the expression [(1/ (1 + i)) * (1 - i / (1 - i))], we can start by finding a common denominator for the two fractions:

[(1/ (1 + i)) * (1 - i / (1 - i))] = [(1 - i) / (1 + i)(1 - i)] * [(1 - i) / (1 - i)]

= (1 - 2i + i^2) / (1 - i^2)

= (1 - 2i - 1) / (1 + 1)

= -i/2

The simplified result -i/2 is related to the first term in the product (1/ (1 + i)) in that they are reciprocals of each other. That is, the first term in the product is the reciprocal of (1 + i), and -i/2 is the reciprocal of the product (1 + i). Algebraically, this can be shown as follows:

(1/ (1 + i)) * (-i/2) = (-i/2) / (1 + i) = (-i/2) * (1 - i) / (1 - i^2)

= (-i/2) * (1 - i) / 2 = (i - 1) / 4

Note that (i - 1) / 4 is the first term in the original product, (1/ (1 + i)) * (1 - i / (1 - i)). Therefore, we can see that the simplified result and the first term in the pair are reciprocals of each other, and they are both related algebraically to the original product through the use of reciprocal and conjugate pairs.

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Answer: the answer is -32

Step-by-step explanation: multiply -2 by itself 5 separate times.

Answer:

-32

Step-by-step explanation:

-2×-2×-2×-2×-2=4×4×-2

=-32

Answer:

4x−5y=−10 hopefully this helps

Answer:

2x+3y = 12

Step-by-step explanation:

multiply 3 and 4

multiply -2 by -x

multiply y and 3

Summary:

2x+2y = 12

If my answer is incorrect, pls correct me!

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According to the statement the ratio of the length of segment P'Q' to the length of segment Q'R' is the answer is option A, 1 : 1.

To find the ratio of the length of segment P'Q' to the length of segment Q'R', we need to first find the coordinates of the new vertices of the dilated triangle.
Since the center of dilation is at the origin, we can use the formula for dilation:
P' = (4*-5, 4*4) = (-20, 16)
Q' = (4*3, 4*4) = (12, 16)
R' = (4*3, 4*-4) = (12, -16)
Now we can find the lengths of the segments P'Q' and Q'R':
P'Q' = sqrt[(12-(-20))^2 + (16-16)^2] = sqrt(32^2) = 32
Q'R' = sqrt[(12-12)^2 + (-16-16)^2] = sqrt(32^2) = 32
Therefore, the ratio of the length of segment P'Q' to the length of segment Q'R' is:
P'Q' : Q'R' = 32 : 32 = 1 : 1
So the answer is option A, 1 : 1.

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A philosophy professor assigns letter grades on a test according to the following scheme is A score that falls within the top 12% of all scores on the test would receive an A grade. A.

The grading scheme for the philosophy professor is:

A: Top 12% of scores

B: Scores below the top 12% and above the bottom 58%

C: Scores below the top 42% and above the bottom 25%

D: Scores below the top 75% and above the bottom 8%

F: Bottom 8% of scores

To clarify, the percentages given in the scheme are used to determine the cutoffs for each letter grade.

A score that falls within the top 12% of all scores on the test would receive an A grade.

It is important to note that the percentages given in the grading scheme are not fixed values, but rather are dependent on the distribution of scores on the test.

For instance, if the scores on the test were very tightly clustered together, it is possible that the cutoff for an A grade might be higher than the top 12%.

This grading scheme rewards students who perform well on the test while still allowing for some degree of variation in scores.

Students perform poorly relative to their peers may receive a lower letter grade but are still given the opportunity to learn and improve in future assignments.

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Answer:

Total no ways can be taken

Step-by-step explanation:

Answer:

Binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation with a radix of 2.

The given value, 55%, is a statistic. A statistic is a numerical summary of a sample.

To determine whether it is a statistic or a parameter, we need to understand the definitions of these terms:

- Statistic: A statistic is a numerical value that describes a sample, which is a subset of a population. It is used to estimate or infer information about the corresponding population.

- Parameter: A parameter is a numerical value that describes a population as a whole. It is typically unknown and is usually estimated using statistics.

In this case, since the study includes all 3237 seniors at the college, the value "55%" represents the proportion of the entire population of seniors who own a computer. Therefore, it is a statistic.

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Answer:

99

Step-by-step explanation:

We can set up and solve this equation:

X + X - 50 = X + 49

X = 99

The solution of x for the equation \(\sqrt{3x - 4} = 2\sqrt{x-5}\) is x = 16.

Given,

The equation; \(\sqrt{3x-4} =2\sqrt{x-5}\)

We have to solve this equation to get the value of x.

That is,

\(\sqrt{3x-4} =2\sqrt{x-5}\)

Square both sides to remove square root.

\(\sqrt{3x-4} ^{2} = (2\sqrt{x-5} )^{2}\)

We get,

3x - 4 = 4 (x - 5)

That is,

3x - 4 = 4x - 20

Here,

20 - 4 = 4x - 3x

Then,

x = 16

That is,

The solution of x for the equation \(\sqrt{3x - 4} = 2\sqrt{x-5}\) is x = 16.

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Answer: ok

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

Answer:

3/8 for the second question

Step-by-step explanation:

number of shaded portion on total number

Answer:

2070 / 6930 = 0.2987.....x 100 = 29.87%

The correct option would be "None of these" since the projection is an ellipse and not any of the given options (2, 4, 16, or "This option").

To determine the projection of the region D onto the xy-plane, we need to find the intersection curve of the two paraboloids.

First, let's set the two equations equal to each other:

3x² + (12/24)y² = 16 - x²

Next, we simplify the equation:

4x² + (12/24)y² = 16

Multiplying both sides by 24 to eliminate the fraction:

96x² + 12y² = 384

Dividing both sides by 12 to simplify further:

8x² + y² = 32

Now, we can see that this equation represents an elliptical shape in the xy-plane. The equation of an ellipse centered at the origin is:

(x²/a²) + (y²/b²) = 1

Comparing this with our equation, we can deduce that a² = 4 and b² = 32. Taking the square root of both sides, we have a = 2 and b = √32 = 4√2.

So, the semi-major axis is 2 and the semi-minor axis is 4√2. The projection of region D onto the xy-plane is an ellipse with a major axis of length 4 and a minor axis of length 8√2.

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The correct option is a. The equation for the line tangent to the curve 2xy - y² = 1 at x = 1 is given by y = x - 1.

Differentiating 2xy - y² = 1 with respect to x using the product rule gives:

2y + 2x(dy/dx) - 2y(dy/dx) = 0

dy/dx(2x - 2y) = - 2y + 2

Simplifying gives:

dy/dx = (y - 1) / (x + y)

At x = 1, the curve passes through the point (1, 1). Substituting these values into the equation gives:

dy/dx = (y - 1) / (x + y)

dy/dx = (y - 1) / (1 + y)

dy/dx = (1 - 1) / (1 + 1)

dy/dx = 0

Therefore, the slope of the line tangent to the curve at x = 1 is zero.

Since the line is tangent to the curve at (1, 1), its equation is given by:

y - 1 = 0(x - 1)

y = x - 1

Hence, the correct answer is option (a) y = x - 1.

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Answer:

426

Step-by-step explanation:

find area of bottom: 26 x 15 = 390

find area of triangle: 8 x 9 = 72/2 = 36

390 + 36 = 426

Answer:

It would be 426 ft.

Step-by-step explanation:

First, you find the size of the rectangle and that is 390 ft. Then the area of the triangle which is 9 multiplied by 8 then divided by 2. Last, add the area of the triangle and the rectangle to get you an answer of 426 ft.

hey its me again and it c vecause 9f c

The arithmetic sequence is solved and the nth term is Aₙ = 5 + ( n - 1 )12

Given data ,

Let the terms of the AP be represented as

a₂ = 17, a₄ = 41, and a₇ = 77

So , a + d = 17

Now , a₂ + 2d = 41

On simplifying , we get

2d = 24

Divide by 2 on both sides , we get

d = 12

So , the first term is a = a₂ - 12

a = 5

So , the nth term of AP is Aₙ = 5 + ( n - 1 )12

Hence , the arithmetic progression is solved

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The cylinder has a surface area of 248 square feet. (approximately)

A solid object's surface area is a measurement of the overall area that the object's surface takes up. A three-dimensional shape's surface area is the sum of all of its faces.

Radius of the cylinder = \(\pi\)

Height of the cylinder =\(3\pi\)

Value of \(\pi\) = 3.14

Surface area of the cylinder.

We know that,

Cylinder surface area = 2r(h + r)

Substituting the required values,

Hence,

The cylinder's surface area is 248 square feet.

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Answer:

y=10x

Step-by-step explanation:

Find the slope of the original line and use the point-slope formula

y−y1=m(x−x1)  to find the line parallel to y=10x−45

.

Answer:

The slope to the question provided is -2.

Hey there!

The slope of the given line is -2

We can solve this by doing rise over run. Pick a point and see how much it goes up (positive number) or down (negative number) - numerator - and put it over the number it goes left (negative number) or right (positive number) - denominator. For example, in this situation, we can start at the point (2, -1), and we can see that we go up 2 and left 1, until we get to the next point (1, 1). Therefore, our fraction would be \(\frac{2}{-1}\), or -2.

Hope it helps and have a great day!

Using the fundamental counting principle, it is found that there are 24 different combinations she can wear.

The sweaters and the pants are independent, and this is why the fundamental counting principle is used.

Fundamental counting principle:

States that if there are p ways to do a thing, and q ways to do another thing, and these two things are independent, there are p*q ways to do both things.

Thus:

T = 6 * 4 = 24

There are 24 different combinations.

A combination in mathematics is a selection of items from a fixed that have amazing members, making the order of selection irrelevant (not like permutations). For instance, given a set of three fruits—say let's an apple, an orange, and a pear—one can choose between three combinations: an apple and a pear, an apple.

A hard and fast S's ok aggregate is, more precisely, a subset of S's ok amazing components. As a result, two combinations are equal if and best if each contains the same players. (The ties between the people in each group are not considered.)

(n/k) ={ n(n - 1) . . . (n – k + 1)}/{k(k - 1) . . . 1}

n!/{k!(n - k)!}

k > n.

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Step-by-step explanation:

speed = distance/time

time = t = distance/speed

t = 180/b + (400-180)/c = 180/b + 220/c = 20(9/b + 11/c)

Answer:

Flour = 5 1/4 Cups

Sugar = 3 Cups

Milk = 1 Cup

Step-by-step explanation:

4 Dozens = Respectively 1 3/4, 1, and 1/3 Cups -->

4(3) = 12 Dozens --> Otherwise A Gross

--> Multiply the formula by 3

7/4 x 3 = 21/4

1 x 3 = 3

1/3 x 3 = 1

Convert to a mixed number

Thus You have your answers

Hope this helps!

Mr. Vickers earned $4,097 in commission last month, as 7.5% of his total sales of $54,620. Convert the 7.5% commission rate into a decimal. hence, 7.5% is equal to 0.075.

Mr. Vickers earns a 7.5% commission on his total sales. Last month, he had sales of $54,620. To calculate how much commission he earned last month, we need to first convert the 7.5% commission rate into a decimal. 7.5% is equal to 0.075. We then multiply the total sales of $54,620 by the decimal value of 0.075 to calculate the commission.

To calculate the commission, we use the following formula: total sales x commission rate = commission.

54,620 x 0.075 = 4,097

Therefore, Mr. Vickers earned $4,097 in commission last month, as 7.5% of his total sales of $54,620

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A)  number of ways in which president is not next to the VP =3628800-725760 =2903040

B) Number of ways =9*9!=3265920

C) number of ways VP is in one end  =2*9!=725760

Permutations and combinations are  ways of representing groups of objects by selecting them  and sub-setting them into sets. It defines different ways of arranging a particular data group. When we choose data or objects from a particular group, it is called a permutation and the order in which they are presented is called a combination. Both concepts are very important in mathematics.

a)

number of ways to line up 10 members =10! =3628800

number of ways so that VP and president are next to each other =N(consider president and VP as 1 member which can interchange in 2 ways , and now we need to arrange 9 members) =2*9!=725760

therefore number of ways in whcih president is not next to the VP =3628800-725760 =2903040

b)

Number of ways =N(9 choices for left most posiition except VP and arrange rest of 9 persons)

=9*9!=3265920

c)

number of ways VP is in one end =N(choose 1 place out of 2 end for VP and then arrange rest of 9 )

=2*9!=725760

therefore number of ways VP is not at one end =3628800-725760 =2903040

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