Points z1 and z2 are shown on the graph.

Part A: Identify the points in standard form and find the distance between them.

Part B: Give the complex conjugate of z2 and explain how to find it geometrically.

Part C: Find z2 − z1 geometrically and explain your steps.

Answer: No

To check if (-5,6) is a solution to the equation y=-7, we need to substitute -5 for x and 6 for y in the equation.

If the equation is true, then the ordered pair is a solution to the equation.

If we put (-5,6) into y=-7, we get 6=-7, which is not true.

So, (-5,6) is not a solution to the equation y=-7.

The opening balance is 100.00 A. Its placement on the credit side implies funds deposited before the statement period. The specific impact on Gloria's finances and the value of B are not provided.

Based on the provided information, let's address each question:

3.2.1 The opening balance is 100.00 A (currency is not specified). This amount represents the initial balance in the bank account before any transactions occur.

3.2.2 When the opening balance is on the credit side of the bank statement, it indicates that there were funds deposited or credited to the account before the statement period. In this case, the opening balance of 100.00 A suggests that there were funds deposited or credited into the account before the statement period began.

3.2.3 If Gloria decides to withdraw money at Capital Bank ATM, her account balance will decrease by the amount of the withdrawal. The specific amount of the withdrawal is not mentioned in the provided information, so we cannot determine the exact impact on her finances. However, it's important to note that ATM withdrawals may also incur transaction fees, which could further reduce her account balance.

3.2.4 Based on the information given, the value of B is not explicitly provided. It seems to be missing or not specified in the provided data. Without knowing the value of B, it is not possible to calculate it.

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The probability of selecting a large or green marble is 0.7333.

The probability of selecting a large marble is 19/30 (19 large marbles out of 30 total marbles). The probability of selecting a green marble is 3/30 (3 green marbles out of 30 total marbles).

To find the probability of selecting a large or green marble, you need to find the probability of selecting a marble that is either large or green. This is known as the union of two events. The union of two events is found by adding the individual probabilities of each event together.

The probability of selecting a large or green marble is 19/30 + 3/30 = 22/30 = 0.7333.

Therefore, the probability of selecting a large or green marble is 0.7333.

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An equation can be written to determine the number of students that went on this trip is: C. [tex]\frac{1259}{s} + 12=\frac{1259}{s+9}[/tex]

In order to write an equation to determine the number of students that went on this trip, we would have to assign a variable and an expression to the number of students who went on the trip and the original number of students who had planned to go on the trip as follows;

Since a total of $1259 was collected from all of the students with 9 students dropping out and their portion of the money collected given back to them while the students that are all still going must contribute an additional $12, an equation to determine the number of students that went on this trip is given by;

[tex]\frac{1259}{s} + 12=\frac{1259}{s+9}[/tex]

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Complete Question:

A high school class is planning a field trip to an art museum in their city. The class collected a total of $1259 from all of the students, which will go towards renting a bus, museum admission, and lunch.

However, a week before the trip 9 students had to drop out and their portion of the collected money had to be given back to them. Due to this, the students that are all still going must contribute an additional $12 each to cover all of the cost.

Now let s be the number of students who went on the trip and s + 9 be the original number of students who had planned to go on the trip

What equation can be written to determine the number of students that went on this trip?

The area of the base of the cylinder is A = 16π units²

Given data ,

Let the area of the base of the cylinder be A

Now , the radius of the cylinder is r = 4 units

And , the height of the cylinder is h = 6 units

where A = πr²

The base of the cylinder is a circular disk of radius r units

On simplifying , we get

A = π ( 4 )²

A = 16π units²

So , the value of A is 16π units²

Hence , the area of the base is A = 16π units²

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Answer:

The original price of the television was $3620.00.

Answer:

$3620.00

Step-by-step explanation:

5% = 181

1% = 36.2

100% = 3620

Answer:

2y² + 3

Step-by-step explanation:

width of one side is 4y² - y + 6.

two equal sides of rectangle = 2(4y² - y +6) = 8y² - 2y + 12.

perimeter = 2 lengths + 2 widths

12y² - 2y + 18 = 2 lengths + 8y² - 2y + 12

2 lengths = (12y² - 2y + 18) - (8y² - 2y + 12)

= 4y² +6

length = 1/2 (4y² +6)

= 2y² + 3

The coordinates of the point of intersection of the tangent and the secant are;

T(a, b) = (9/5, -14/5)

C = (0, -1)

A tangent is a line or segment that touches a circle only once.

The equation of the line AN is; y - 2 = ((-2 - 2)/(2 - 3)) × (x - 3)

y = 4·x - 12 + 2 = 4·x - 10

y = 4·x - 10

The coordinates of the center of the circle is; ((-5 + 3)/2, (4 + 2)/2) = (-1, 3)

The radius of the circle is; √((3 - (-1))² + (2 - 3)²) = √(17)

The equation of the circle is; (x + 1)² + (y - 3)² = 17

The point C indicates;

(0 + 1)² + (y - 3)² = 17

(y - 3)² = 17 - 1 = 16

y - 3 = √(16) = ±4

y = 4 + 3 = 7, and y = -4 + 3 = -1

The coordinates of the point C is; (0, -1)

The slope of AC = (2 - (-1))/(3 - 0) = 1

AC is perpendicular to BC

The slope of BC = -1

The equation of BC is therefore; y - 4 = -(x - (-5)) = -x - 5

y = -x - 1

The equation of the segment AN is; y - 2 = ((2 - (-2))/(3 - 2))×(x - 3)

y - 2 = 4·(x - 3)

y = 4·x - 12 + 2 = 4·x - 10

-x - 1 = 4·x - 10

x-coordinate of T = 9/5

The y-coordinate of T = -9/5 - 1  = -14/5

Therefore, at the point T, we get; (9/5, -14/5)

a = 9/5, b = -14/5, C = (0, -1)

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The proposition x − y = y − x is true.

We are given that;

The equation x − y = y − x

Now,

X − y = -(y - X)

-(y - X) + 2X - 2X = y - X + X - y = y - x.

Similarly, y - x = -(x - y)

-(x - y) + 2y - 2y = x - y + y - x = X - y.

Both sides of the equation are equal.

Therefore, by the given function answer will be true.

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Answer:

Step-by-step explanation:

y  =  -5x^2

if x  =  0 , then

y  =  -5(0)

y  =  0

Answer:

B and C

Step-by-step explanation:

We can determine which three sides will form a right triangle using the Pythagorean theorem, which is

a^2 + b^2 = c^2, where

A:  

5^2 + (√8)^2 = 33^2

25 + 8 = 1089

33 ≠ 1089

Because 33 is not equal to 1089, these three lengths do not form a right triangle.

B:  

8^2 + 15^2 = 17^2

64 + 225 = 289

289 = 289

Thus, these three side lengths form a right triangle.

C:

(√2)^2 + (√2)^2 = 2^2

2 + 2 = 4

4 = 4

Thus, these three side lengths also form a right triangle.

a) The terminal point is 0.896 radius length.

b) The value returned is -0.896.

We have,

The circle's radius is 3 units long and the terminal point is located at (−2.69,−1.33)

a. Since the circle's radius is 3 units long, we divide the x-coordinate by 3:

x-coordinate of terminal point: -2.69

Number of radius lengths to the right: -2.69 / 3 ≈ -0.896

However, since the angle is measured from the 3-o'clock direction, we consider it to be in the clockwise direction.

Thus, the number of radius lengths to the right is

Number of radius lengths to the right: -(-0.896) = 0.896

Therefore, the terminal point is 0.896 radius length.

b. Using Trigonometry

cos(h) = x-coordinate of terminal point / radius length

cos(h) = -2.69 / 3 ≈ -0.896

c. As, θ = h. From the given information, we have:

θ ≈ -0.896 radians

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Answer:

Step-by-step explanation:

Ukraine wants to join the european union.Due to this Russia realize that if ukraine join the european union then if war started between Ukraine and any other country like Russia it means Ukraine and european union both attack on this country.

The image you provided is a mathematical expression written in a non-standard format. To simplify it and obtain the result of 3, we can break it down step by step.

The expression can be written as follows:

(8c8) * (8x83)

Let's simplify each part separately:

(8c8):

The term "8c8" represents the combination or binomial coefficient. In general, the combination "nCr" is calculated as n! / (r! * (n-r)!), where "!" denotes factorial. When r = n (as is the case here with 8c8), the combination simplifies to 1. Therefore, 8c8 equals 1.

(8x83):

The term "8x83" represents multiplication between the numbers 8 and 83, which equals 664.

Now, let's put it all together:

(8c8) * (8x83) = 1 * 664 = 664

According to the given expression, the simplified result is 664, not 3. Please double-check the expression or provide further clarification if needed.

The result when (-2/3m + 4) is added to (5/6m - 1/2) is 4 - 1/3m.

Hence, the correct answer is option A: -1/6m + 7/2.

To find the result when (-2/3m + 4) is added to (5/6m - 1/2), we need to combine like terms.

First, let's simplify the expression -2/3m + 4:

This can be rewritten as (4 - 2/3m).

Next, let's simplify the expression 5/6m - 1/2:

This can be rewritten as (5/6m - 3/6m).

Now, let's add the two expressions together:

(4 - 2/3m) + (5/6m - 3/6m)

Combining the constants and the terms with "m," we get:

4 + 5/6m - 2/3m - 3/6m

To simplify further, we need to find a common denominator for the fractions:

4 + 5/6m - (2/3m + 3/6m)

The common denominator for the fractions is 6:

4 + 5/6m - (4/6m + 3/6m)

Now, let's combine the like terms:

4 + 5/6m - 7/6m

Finally, we can simplify the expression:

4 - 2/6m

Simplifying further, we have:

4 - 1/3m.

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Answer:

Step-by-step explanation:

We know that,

sum of three side of triangle is 180°

So,

x + 72° + 90° = 180°

x + 162° = 180°

x = 180° - 162°

x = 18°

[tex]\underline{\rule{190pt}{4pt}}[/tex]

The value of x in the triangle is 18 degrees.

The given triangle is a right angled triangle.

We have to find the value of x.

As the triangle is a right angle one angle is 90 degrees.

And the other angle is 72 degrees.

The missing angle is x which we have to find.

By angle sum property we know that the sum of three angles is 180 degrees in a triangle.

72+90+x=180

Combine the like terms:

162+x=180

Subtract 162 from both sides:

x=180-162

When one hundred sixty two is subtracted from one hundred eighty, we get 18.

x=18 degrees

Hence, 18 degrees is the value of x in the triangle.

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Gradient is another word for slope.

Slope = rise/run = (y2-y1)/(x2-x1)

So pick 2 points.

Let's do line A first.

(1,1) and (2,4)

slope = (1-4)/(1-2)

= -3/-1 = 3

The slope (aka gradient) of line A = 3.

Line B.

(0,5) and (1,1)

slope = (5-1)/(0-1)

= 4/-1

= -4

The slope (aka gradient) of line B = -4.

Answer :

From the figure XY and WZ are opposite sides and XW and YZ are the opposite sides.

XY = WZ

3a - 4 = a + 2

3a - a = 2 + 4

2a = 6

a = 6/2

a = 3

Now put the value of a in XY

XY = 3a - 4

XY = 3(3) - 4

XY = 9 - 4

Similarly,

XW = YZ

2b = b + 1

2b - b = 1

1b = 1

b = 1

Now put the value of b in YZ

YZ = 2b

YZ = 2 × 1

Answer :

Step-by-step explanation :

As We Know that Opposite sides of the Parallelogram are equal.

SO,

(i) YZ = XW (opposite sides)

→ 2b = b + 1

→ 2b - b = 1

→ b = 1

Since, YZ = 2b

→ YZ = 2 × 1

→ YZ = 2.

Also,

(ii) XY = WZ (opposite sides)

→ 3a - 4 = a + 2

→ 3a - a = 2 + 4

→ 2a = 6

→ a = 6/2

→ a = 3 .

Since, XY = 3a - 4

putting the value of a = 3.

=> 3(3) - 4

→ 9 - 4

→ 5

XY = 5.

Therefore, Option D is the required answer.

1. The number of members who play soccer only is 59.

2. The number of members who play tennis or soccer, but not rugby, is 37.

3. The number of members who play exactly two sports is 20.

4. The number of members who play at least one sport is 195.

5. If 60 members play soccer, then 7 members play tennis.

1. To find the number of members who play soccer only, we need to subtract the members who play soccer and other sports from the total number of soccer players.

Soccer only = Total soccer players - (Soccer and Rugby) - (Soccer and Tennis) + (All three sports)

Soccer only = 68 - 6 - 7 + 4

Soccer only = 59

Therefore, 59 members play soccer only.

2. To find the number of members who play tennis or soccer but not rugby, we need to subtract the members who play all three sports from the total number of tennis and soccer players.

Tennis or Soccer (not rugby) = (Tennis + Soccer) - (All three sports)

Tennis or Soccer (not rugby) = 43 + 68 - 4

Tennis or Soccer (not rugby) = 107

Therefore, 107 members play tennis or soccer but not rugby.

3. To find the number of members who play exactly two sports, we need to add the members who play tennis and soccer (TS), tennis and rugby (TR), and soccer and rugby (RS).

Exactly two sports = TS + TR + RS

Exactly two sports = 7 + 11 + 6

Exactly two sports = 24

Therefore, 24 members play exactly two sports.

4. To find the number of members who play at least one sport, we can add the number of members who play each sport individually (Tennis, Rugby, Soccer) and then subtract the number of members who play none of the sports.

At least one sport = Tennis + Rugby + Soccer - None

At least one sport = 43 + 84 + 68 - 0

At least one sport = 195

Therefore, 195 members play at least one sport.

5. If 60 members play soccer, we can calculate the number of members who play tennis by subtracting the members who play both sports (TS) and the members who play soccer only from the total number of soccer players.

Tennis = Total soccer players - (Soccer only) - (TS)

Tennis = 60 - 59 - 7

Tennis = -6

It is not possible to have a negative number of members playing tennis. Please double-check the provided information or calculations.

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Answer:

y = kxz. y = 10.8

Step-by-step explanation:

y = kxz, where k is a constant.

12 = k(4)(5) = 20k

k = 12/20 = 0.6.

y = kxz

= (0.6) (6) (3)

= 10.8

Answer:

B and C

Step-by-step explanation:

Answer:  B and C

Step-by-step explanation:

Pythagorean Theorem:

c²=a²+b²              >where a and be are the shorter legs and c is the

                                longer/hypotenuse

Let's plug each into the pythagorean theorem

A)   Not a right triangle

33² = 5² + (√8)²

1089 = 25 +8

1089 = 33             >Not equal,  The statement is not true, so this is not a

                                 right triangle.

B)  Yes, it is a right triangle

17²=8²+15²

289=64+225

289=289       They are equal, true statement, so yes it is a right triangle

C) No, it is not a right triangle

2² = (√2)²+(√2)²

4 = 2+2

4=4              They are equal, true statement, so yes it is a right triangle

Hello !

125 * $0.29 * 6 = $217.50

The solution to the inequality indicates that the attendance in 2009 must be 826,000 or more.

Let's assume the attendance in 2009 is represented by the variable A. According to the given information, the attendance in 2008 was at least 16,700 less than the attendance in 2009.

Mathematically, we can express this as:

A - 16,700 ≥ 809,300

To find the attendance in 2009, we need to solve this inequality.

First, we add 16,700 to both sides of the inequality:

A - 16,700 + 16,700 ≥ 809,300 + 16,700

Simplifying, we have:

A ≥ 826,000

Therefore, the attendance in 2009 is greater than or equal to 826,000.

In this case, the inequality A ≥ 826,000 indicates that the attendance in 2009 must be equal to or greater than 826,000 for the statement to hold true.

If the attendance in 2009 is less than 826,000, it would not satisfy the given condition that the attendance in 2008 was at least 16,700 less than the attendance in 2009.

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The Simplified form of the expression (x+2)(x-2) - (x+3)² is -13 - 6x.

The expression (x+2)(x-2) - (x+3)², we'll follow the distributive property and simplify each term.

First, let's expand (x+2)(x-2):

(x+2)(x-2) = x(x) + x(-2) + 2(x) + 2(-2)

          = x² - 2x + 2x - 4

          = x² - 4

Next, let's expand (x+3)²:

(x+3)² = (x+3)(x+3)

      = x(x) + x(3) + 3(x) + 3(3)

      = x² + 3x + 3x + 9

      = x² + 6x + 9

Now, we can substitute these expansions into the original expression:

(x+2)(x-2) - (x+3)² = (x² - 4) - (x² + 6x + 9)

To simplify further, let's distribute the negative sign to every term inside the parentheses:

(x² - 4) - (x² + 6x + 9) = x² - 4 - x² - 6x - 9

Now, we can combine like terms:

(x² - x²) + (-4 - 9) - 6x = -13 - 6x

Therefore, the simplified form of the expression (x+2)(x-2) - (x+3)² is -13 - 6x.

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The function f(x) = (x+2)²(x-1)(x-5)² has-2 is a zero with multiplicity 2

5 is a zero with multiplicity 1 and the graph is tangent to x-axis at x = 1

For the function f(x) = (x+2)²(x-1)(x-5)²

-2 is a zero with multiplicity 2

This is represented by the factor (x+2)², indicating that -2 is a zero that appears twice in the function.

5 is a zero with multiplicity 1
This is represented by the factor (x-5), indicating that 5 is a zero that appears once in the function.

The graph is tangent to the x-axis at x = 1:

This is represented by the factor (x-1), indicating that the graph touches the x-axis at x = 1.

Therefore, the function f(x) = (x+2)²(x-1)(x-5)² has all the specified attributes.

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