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Answer:

A

Step-by-step explanation:

edge

\(Z_{1} +Z_{2}\) represents Point A i.e., 3i.

Complex numbers are the numbers that are expressed in the form of

a + ib where, a, b are real numbers and  ‘i’ is an imaginary number called “iota”. The value of i = (√-1). For example, 2+3i is a complex number, where 2 is a real number (Re) and 3i is an imaginary number (Im).

Given

The complex numbers z1 and z2 are graphed.

From the graph,

\(Z_{1} =3+i\)

\(Z_{2} =-3+2i\)

\(Z_{1} +Z_{2}= 3+i+(-3+2i)\)

\(Z_{1} +Z_{2}= 3-3+i+2i\)

\(Z_{1} +Z_{2}= 3i\)

Option A is correct.

\(Z_{1} +Z_{2}\) represent Point A i.e., 3i.

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The value of x is 9 cm, and angle O is 0 degrees.

To solve the triangle LMN and find the values of x and angle O, we can use the Law of Cosines and the Law of Sines. Let's go step by step:

(i) To find the value of x, we can use the Law of Cosines. According to the Law of Cosines, in a triangle with sides a, b, and c, and angle C opposite to side c, the following equation holds:

c^2 = a^2 + b^2 - 2ab * cos(C)

In our case, we want to find side NM (x), which is opposite to angle N. The given sides and angles are:

LN = 12 cm

NK = 6 cm

KM = 8 cm

Let's denote angle N as angle C, side LN as side a, side NK as side b, and side KM as side c.

Using the Law of Cosines, we can write the equation for side NM (x):

x^2 = 12^2 + 6^2 - 2 * 12 * 6 * cos(N)

We don't know the value of angle N yet, so we need to find it using the Law of Sines.

(ii) To find angle O, we can use the Law of Sines. According to the Law of Sines, in a triangle with sides a, b, and c, and angles A, B, and C, the following equation holds:

sin(A) / a = sin(B) / b = sin(C) / c

In our case, we know angle N and side NK, and we want to find angle O. Let's denote angle O as angle A and side KM as side b.

We can write the equation for angle O:

sin(O) / 8 = sin(N) / 6

Now, let's solve these equations step by step to find the values of x and angle O.

To find angle N, we can use the Law of Sines:

sin(N) / 12 = sin(180 - N - O) / x

Since we know that the angles in a triangle add up to 180 degrees, we can rewrite the equation:

sin(N) / 12 = sin(O) / x

Now, we can substitute the equation for sin(O) from the Law of Sines into the equation for sin(N):

sin(N) / 12 = (6 / 8) * sin(N) / x

Now, we can solve this equation for x:

x = (12 * 6) / 8 = 9 cm

So, the value of x is 9 cm.

To find angle O, we can substitute the value of x into the equation for sin(O) from the Law of Sines:

sin(O) / 8 = sin(N) / 6

sin(O) / 8 = sin(O) / 9

9 * sin(O) = 8 * sin(O)

sin(O) = 0

This implies that angle O is 0 degrees.

Therefore, the value of x is 9 cm, and angle O is 0 degrees.

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The figure for the given question is provided here :

a) Using the four basic mathematical operations, the number of balloons that each person hang up is 9.

b) An equation representing the situation is x = (125 - 80)/5.

The four basic mathematical operations include addition, subtraction, division, and multiplication.

The mathematical operations provide solutions to mathematical problems using operands.

An equation is a mathematical statement showing that two or more mathematical expressions are equal or equivalent.

The total number of balloons that Andre has = 125

The number of balloons remaining after hanging some for the school party = 80

The difference (number of balloons used) = 45 (125 - 80)

The number of friends who hang the balloons = 5

The number of balloons hung by each friend of Andre = 9 (45/5)

Thus, we can conclude that each of the 4 friend and Andre hung 9 balloons, with 80 remaining.

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Composing f(x)=2x-8 and g(x)=1/2x+4 results in the identity function, f(g(x)) = x.

To compose the two functions, we substitute g(x) into f(x) in place of x:

f(g(x)) = 2(g(x)) - 8

= 2(1/2x + 4) - 8

= x + 8 - 8

= x

Therefore, composing the two functions results in the identity function, f(g(x)) = x.

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The function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4 is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

A function is said to be continuous if there are no breaks or jumps in the functions

Conditions for continuity of a function

Now, for the given function f(x) = sin⁻¹x, x ≠ π/4 and sinx, x = π/4

We need to determine the interval of continuity, We proceed as follows.

Since f(x) = sin⁻¹x, x ≠ π/4 , we know that the minimum value of x is - 1 and its maximum value is 1.

So, x must lie in the interval (-1, 1) for x ≠ π/4,

Now, when x = π/4 f(x) = sinx. We know that x = π/4 lies in the interval (-1, 1).

But we know that f(x) = sinx at x = π/4. So, there is a removable discontinuity at x = π/4.

So, from the left, f(x) is continuous on the interval [-1, π/4) and  from the right, f(x) is continuous on the interval (π/4, 1]

So, combining both intervals, we have f(x) is continous on the interval [-1, π/4) ∪ (π/4, 1] and since f(x) = sinx at x = π/4, there is a removable discontinuity at x = π/4

So, the function f(x) is continuous on[-1, π/4) ∪ (π/4, 1]. There is a removable discontinuity at x = π/4

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Let's solve this problem step by step.

1. Start by drawing a diagram to visualize the problem. We have a square piece of sheet metal, and we need to remove squares from each corner to create an open box.

Let's assume the side length of the original square sheet metal is "x" feet.

After removing squares of side length 5 feet from each corner, the remaining dimensions of the sheet metal will be (x - 10) feet.

The height of the box will be 5 feet.

Therefore, the dimensions of the open box will be (x - 10) feet (length and width), 5 feet (height).

2. Use the formula for the volume of a rectangular box to set up an equation:

Volume = Length x Width x Height

Given that the volume is 720 cubic feet, we can write:

(x - 10) * (x - 10) * 5 = 720

Simplifying the equation:

5(x - 10)^2 = 720

3. Solve the equation to find the value of x:

Divide both sides of the equation by 5:

(x - 10)^2 = 144

Take the square root of both sides:

x - 10 = ±12

Solve for x:

x = 10 + 12 or x = 10 - 12

x = 22 or x = -2

Since we are dealing with lengths, we discard the negative value of x.

Therefore, the side length of the original square sheet metal is 22 feet.

4. Finally, calculate the dimensions of the sheet metal:

Length = Width = x - 10 = 22 - 10 = 12 feet

So, the dimensions of the sheet metal are 12 feet by 12 feet.

Answer:

\(x = 1\)

\(y = -2\)

Step-by-step explanation:

Given

\(2x - 3y = 8\)

\(4x + 3y =-2\)

Required

x and y

Add both equations to eliminate y

\(2x + 4x - 3y + 3y = 8 - 2\)

\(6x = 6\)

Divide both sides by 6

\(x = 1\)

Substitute \(x = 1\) in the first equation

\(2x - 3y = 8\)

\(2 * 1 - 3y = 8\)

\(2 - 3y = 8\)

\(-3y = 8 - 2\)

\(-3y = 6\)

Divide by -3

\(y = -2\)

Answer:

640 & 400

Step-by-step explanation:

Cost of books: x and 1040-x

x sold at a loss of 15%= .85 x

1040 - x sold at a profit of 36% = (1040 - x) *1.36

x*.85= (1040-x)*1.36

0.85x+1.36x= 1040*1.36

2.21x= 1414.4

x= 1414.4/ 2.21

x= Rs. 640

Rs. 1040 - 640 = 400

A hypothesis is an assumption, an idea that is proposed for the sake of argument so that it can be tested to see if it might be true.

a. two-tailed test

b. reject H0 if Z>1.96 or Z<-1.96

c. Z = 1.73

d. we have failed to reject the null hypothesis

e. P-value = 0.0418

We need to find our critical value:

Zα/2 = Z(0.05/2) = 0.025

The Z test will be done using the next equation:

Z = (x⁻1 - x⁻2) - (μ1 - μ2) / √( σ²1/n1 + σ²2/n2

Z = (100.5 - 98.8) - (0) / √( (3.4)²/38 + (5.8)²/51 = 1.7/0.9817 = 1.73

Z<1.96, therefore we have failed to reject the null hypothesis

The P-value for this test would be represented by the probability of Z being greater than 1.73, so we can look for it in any Z table, finding that its value is 0.0418, and because P-value>0.025 we again confirm that we don't have evidence statistically significant to reject the null hypothesis

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Answer:

The range of values for the correlation coefficient is -1 to 1 inclusive

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

The given is a special right triangle with angle measures

90-60-30 and side lengths represented by

2a-a\(\sqrt{3}\)-a

x is the side length that sees angle measure 90 degrees so it's represented by 2a

and 4\(\sqrt{3}\) is the side length that sees angle measure that sees 60 degrees so the value of a is 4

therefore x = 2*4 = 8

Irene has 49 Books, and Alejandro has 24 books.

Let's assume that Irene has x books, and Alejandro has y books. According to the given information, we can form the following equations:

1. Irene has twice as many books as Alejandro plus 1:

  x = 2y + 1

2. The total number of books between Irene and Alejandro is 73:

  x + y = 73

We can now solve this system of equations to find the values of x and y.

Substituting the value of x from equation (1) into equation (2), we have:

(2y + 1) + y = 73

3y + 1 = 73

3y = 72

y = 24

Now, we can substitute the value of y into equation (1) to find x:

x = 2(24) + 1

x = 49

Therefore, Irene has 49 books, and Alejandro has 24 books.

To verify our solution, we can check if the sum of their books equals 73:

49 + 24 = 7

So, our solution is correct.

In conclusion, Irene has 49 books, and Alejandro has 24 books.

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Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.

What are basic arithmetic operations?

Basic arithmetic operations are fundamental mathematical calculations that involve manipulating numerical values using a set of basic operations.

To find out how many points Antonio needs to score in his next game to reach an average of at least 100 points per game, we can use the following formula:

Total points needed = (number of games + 1) × average score goal - total points scored so far

In this case, Antonio has played 5 games, so the number of games he will have played after his next game is 6. His goal is an average of 100 points per game, so his average score goal is 100. The total points he has scored so far is:

105 + 95 + 97 + 82 + 110 = 489

Substituting these values into the formula, we get:

Total points needed = (6) × (100) - 489

Total points needed = 600 - 489

Total points needed = 111

Hence, Antonio needs to score at least 111 points in his next game to reach his goal of an average of at least 100 points per game.

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Answer:

Bro it is simple the answer is 23415

Step-by-step explanation:

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Marcella must fill the pyramid with water and pour it into the prism three times in order to completely fill the prism with water.

In this question, we have a pyramid-shaped container and a prism-shaped container. It is given that the base of the pyramid is congruent to the base of the prism, and their heights are equal. We need to find how many times Marcella must fill the pyramid with water and pour it into the prism in order to completely fill the prism with water.Let the volume of the pyramid-shaped container be P and the volume of the prism-shaped container be R. Since the base of the pyramid is congruent to the base of the prism, their base areas are equal. Let this base area be A.

Therefore, we have:

Volume of the pyramid = (1/3) × A × h Volume of the prism = A × h where h is the height of both containers.

Since the heights of the pyramid and prism are equal, we can cancel them out from the above equations. Hence, we have:

Volume of the pyramid = (1/3) × A × h Volume of the prism = A × h Volume of the prism/Volume of the pyramid = 3

This means that the volume of the prism is three times the volume of the pyramid.

Therefore, Marcella must fill the pyramid with water and pour it into the prism three times in order to completely fill the prism with water.

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Answer:

A=40.8 B=8

Step-by-step explanation:

A Explanation

£7.20*3=£21.6

£9.60*2=£19.2

19.2+21.6=40.8

B Explanation

£9.60*3=£28.8

86.40-28.8=57.6

57.6/7.20=8

Answer:

B) -2

Step-by-step explanation:

The slope of the line can be solved by using the following equation:

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

Let: \((x_1, y_1) = (0 , 4)\\(x_2 , y_2) = (-1 , 6)\)

Plug in the corresponding numbers to the corresponding variables:

\(m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{6 - (4)}{-1 - (0)}\)

\(m = \frac{6-4}{-1 - 0} = \frac{2}{-1}\)

m = -2 is your answer.

~

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Answer:

The answer is B

-2

Step-by-step explanation:

slope =rise/run

\(m = \frac{y(2) - y(1)}{x(2) - x(1)} \)

\(m = \frac{6 - 4}{ - 1 - 0} \)

\(m = \frac{2}{ - 1} \)

\(m = - 2\)

Answer:

x = 11

Step-by-step explanation:

If the segments are congruent then

3x = x + 22 ➡ 3x - x = 22

2x = 22 divide both sides by 2

x = 11

Answer:

Your taxes are $13,425

Step-by-step explanation:

Taxes paid by Americans depend on their income. If they earn between $114,500 and $163,000, they must pay a fixed amount of $6,250 plus 35% of the income over $114,500.

If you earn $135,000, you definitely all into the described bracket. We need to calculate the income above the minimum $114,500:

taxable income=$135,000-$114,500=$20,500

Thus, you must pay:

Tax = $6,250 + 35% of $20,500

Tax = $6,250 + 35/100 $20,500

Tax = $6,250 + $7,175 = $13,425

Your taxes are $13,425

Answer:

10 times for each number

Step-by-step explanation:

:)

Answer:

10

Step-by-step explanation:

if the dice is fair, the sides will land one time every 8, so if its rolled 80 time, and it was equal 10 would be your answer.

Answer:

Congress immediately tabled its expected contribution of $200,000 to the Society, effectively halting the appropriation. During its tenure, the Know-Nothing Society added only two courses of masonry, or four feet, to the monument using rejected masonry it found on site, increasing the height of the shaft to 156 feet

Step-by-step explanation:

The cost is $8712 when the two companies charge the same for 12 tons of sugar.

What is equality?

Equality is a concept in mathematics that refers to the idea that two values, expressions, or equations are equal to each other. In an equality, the values on either side of an equals sign have the same numerical or algebraic value.

Let x be the amount of sugar in tons. The total cost for the first company is given by:

C1 = 7500 + 100.50x

The total cost for the second company is given by:

C2 = 6597 + 175.75x

We want to find the amount of sugar x for which the two companies charge the same, so we can set the two expressions equal to each other and solve for x:

7500 + 100.50x = 6597 + 175.75x

Subtracting 6597 from both sides gives:

903 = 75.25x

Dividing both sides by 75.25 gives:

x ≈ 12

So the two companies charge the same for 12 tons of sugar. To find the cost, we can plug x = 12 into either expression:

C1 = 7500 + 100.50(12) = 8712

C2 = 6597 + 175.75(12) = 8712

So the cost is $8712 when the two companies charge the same for 12 tons of sugar.

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Answer:

0.83333333333

Step-by-step explanation:

Answer:

6200

Step-by-step explanation:

first find how much she would make purely based on hours worked:

8x40 = 320 dollars

next subtract this from total on her paycheck so 692-320 is 372

we know that 372 is 6% of a number so...

\(\frac{6}{100}\) x = 372

\(\frac{6x}{100}\) = 372

6x= 37200(100)

x=6200 $ divide by 6

so she sold $6200 worth of merchandise to earn $372 of commission

Answer:

One bad b, and she do what I say so

Two big .40s and a big a Draco (two, boom, boom)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s (that's how it goes)

One bad b, and she do what I say so (yeah, gang)

Two big .40s and a big a Draco (two)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s

I'm with my n*yeah, we some rockstars

And I'm with my n yeah, KK Wokhardt (KK Wokhardt)

This not my d, lil' b, my Glock hard (lil' b)

Straight to the cash, I'm a trapstar (cash)

Straight to the bag, I'm that n, huh (bag, oh)

Got me some gas, rollin' up some

Fft, fft, cash, yeah, I got me some

I ain't f her yesterday (yeah)

I'ma f some

One bad b , and she do what I say so

Two big .40s and a big a Draco (two, boom, boom)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s (that's how it goes)

3-0 clip in my Nina (oh, oh)

On my toes, Gucci, Valentino (yeah, b)

She on go, your b f the team, uh (lil' b )

'Cause you know your b want a winner (winner)

I just went back to my city (to my city)

And you know they all f with me (big hands)

But it ain't safe, h with me (h)

I'ma chase bands 'til they end me

One bad b, and she do what I say so

Two big .40s and a big a Draco (two, boom, boom)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s (that's how it goes)

One bad b, and she do what I say so (yeah, gang)

Two big .40s and a big a Draco (two)

Three more millions when you ask how my day go

Poured up a 4, now that's blueberry Faygo

One false move, and we straight to shooting s

Two small bands just to take you out real quick (bands)

Three more h, pull up, I'm f s

That's how it go, big bands, I'm thumbin' s

Step-by-step explanation:

Answer:

(m+3) (m+5)

Step-by-step explanation: