Solve for X round to the nearest tenth

The difference between Z₁ and Z₂ is -10 + 0i.

Z₁ - Z₂ locates on the real axis, this is solved using the concept of complex numbers.

Option b is correct.

Real numbers and imaginary numbers combine to form complex numbers, which have two components. Complex numbers serve as the foundation for more complex arithmetic, including algebra.

Complex numbers are those that are represented as a+ib, where a and b are actual numbers and i is an imaginary number termed a "iota." i  has the value (√-1).

From the graph we can know:

Z₁ (-5,2) = -5 + 2i

Z₂ (5,2) = 5 + 2i

The difference between Z₁ and Z₂ is Z₁ - Z₂

So, Z₁ - Z₂ = (-5 + 2i) - (5 + 2i)

Z₁ - Z₂ = - 10 + 0i

Thus, Z₁ - Z₂ locates on the real axis.

Correct option is: b

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Answer:

Option B

Step-by-step explanation:

I just finished the test on edge. confirmed correct

Answer: 6

Step-by-step explanation:

The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, 42

The factors of 78 are: 1, 2, 3, 6, 13, 26, 39, 78

Then the greatest common factor is 6.

Heres something you need to learn about the greatest common factor (gcf)

What is the Greatest Common Factor?

The largest number, which is the factor of two or more numbers is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors that are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

Let us consider the example given below:

Greatest Common Factor (GCF)

For example – The GCF of 18, 21 is 3. Because the factors of the number 18 and 21 are:

Factors of 18 = 2×9 =2×3×3

Factors of 21 = 3×7

Here, the number 3 is common in both the factors of numbers. Hence, the greatest common factor of 18 and 21 is 3.

Similarly, the GCF of 10, 15 and 25 is 5.

How to Find the Greatest Common Factor?

If we have to find out the GCF of two numbers, we will first list the prime factors of each number. The multiple of common factors of both the numbers results in GCF. If there are no common prime factors, the greatest common factor is 1.

Finding the GCF of a given number set can be easy. However, there are several steps need to be followed to get the correct GCF. In order to find the greatest common factor of two given numbers, you need to find all the factors of both the numbers and then identify the common factors.

Find out the GCF of 18 and 24

Prime factors of 18 – 2×3×3

Prime factors of 24 –2×2×2×3

They have factors 2 and 3 in common so, thus G.C.F of 18 and 24 is 2×3 = 6

Also, try: GCF calculator

GCF and LCM

Greatest Common Factor of two or more numbers is defined as the largest number that is a factor of all the numbers.

Least Common Multiple of two or more numbers is the smallest number (non-zero) that is a multiple of all the numbers.

Factoring Greatest Common Factor

Factor method is used to list out all the prime factors, and you can easily find out the LCM and GCF. Factors are usually the numbers that we multiply together to get another number.

Example- Factors of 12 are 1,2,3,4,6 and 12 because 2×6 =12, 4×3 = 12 or 1×12 = 12. After finding out the factors of two numbers, we need to circle all the numbers that appear in both the list.

Greatest Common Factor Examples

Example 1:

Find the greatest common factor of 18 and 24.

Solution:

First list all the factors of the given numbers.

Factors of 18 = 1, 2, 3, 6, 9 and 18

Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24

The largest common factor of 18 and 24 is 6.

Thus G.C.F. is 6.

Example 2:

Find the GCF of 8, 18, 28 and 48.

Solution:

Factors are as follows-

Factors of 8 = 1, 2, 4, 8

Factors of 18 = 1, 2, 3, 6, 9, 18

Factors of 28 = 1, 2, 4, 7, 14, 28

Factors of 48 = 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The largest common factor of 8, 18, 28, 48 is 2. Because the factors 1 and 2 are found all the factors of numbers. Among these two numbers, the number 2 is the largest numbers. Hence, the GCF of these numbers is 2.

If you know it, dont read it

b) 52/25

is the right answer

3y + 2x = 44 is the equation of the line through (10, 8) and (4, 12).

A linear equation has the slope-intercept form y = mx + b. Variables in the equation are x and y. When x is 0, the integers m and b provide the line's slope (m) and the value of y. Because (0,y) is the location where the line crosses the y-axis, the value of y when x is 0 is referred to as the y-intercept.

Given, two coordinates of a line \(\left(10,8\right) and \left(4,12\right)\)

The slope of the line formula is:

\(m = \frac{y₂ - y₁}{ x₂ - x₁}\)

Let's substitute our numbers.

\(m = -\frac{8 -12}{4-10}\)  =  -4/6

The GCF of these two numbers is 2

So, our slope  =  -2/3

The general equation of a line is y = mx +c

Therefore the equation of the line is y = -2/3x + c

Since, this line passes through ( 10, 8 )

Hence, it must satisfy these coordinates

8 = -2/3 * 10 + c

44/3 = c

Thus the equation of the line is y = -2/3x +44/3

the equation of the line is 3y + 2x = 44.

Therefore, The equation of the line that passes through (10, 8) and (4, 12) is 3y + 2x = 44.

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a. The tree diagram that summarizes the given probabilities is attached.

b.  The probability that the individual does not participate in sports, given that he graduate sis  0.2 =  20%.

We apply Bayes' theorem to calculate:

Probability (Does not participate in sports if graduates)  = (P(Does not participate in sports) * P(Graduates | Does not participate in sports)) / P(Graduates)

The given data include: probability of not participating in sports = 0.02 probability of graduating given no participation in sports = 0.82 probability of graduating  = 0.18

Probability (Does not participate in sports if graduates)  = (0.02 * 0.82) / 0.18 = 0.036 / 0.18=  0.2

| Sports | No Sports |

                          |-------|--------|

Student participates | 0.18  | 0.62  |

                          |-------|--------|

Student does not participate | 0.02  | 0.78  |

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Work Shown:

360/n = 360/3 = 120

Answer:

120 degrees

Step-by-step explanation:

A triangle has Three sides, so according to the given information, it should also have three lines of symmetry. To calculate the degrees apart each line of symmetry is in a triangle, we can use the same formula

Degrees apart = 360 degrees / number of sides

For a triangle:

Degrees apart= 360 degrees / 3 sides

Therefore, the lines of symmetry in a triangle are 120 degrees apart

The product of (1.78 × 10⁻⁷) and (5.03 × 10⁻⁵) in scientific notation is approximately 8.95 × 10⁻¹², rounded to three significant digits.

To express the product of (1.78 × 10⁻⁷) and (5.03 × 10⁻⁵) in scientific notation, we need to multiply the numerical parts and add the exponents.

First, we multiply the numerical parts: 1.78 × 5.03 = 8.9474.

Next, we add the exponents: (10⁻⁷) × (10⁻⁵) = 10⁻⁷⁺⁻⁵ = 10⁻¹².

Putting it all together, we have 8.9474 × 10⁻¹².

To round to the appropriate number of significant digits, we consider the precision of the original values. Both 1.78 and 5.03 have three significant digits. Therefore, we round the product to three significant digits, which gives us 8.95.

Thus, the product expressed in scientific notation, rounded to the appropriate number of significant digits, is approximately 8.95 × 10⁻¹².

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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 nearest Whole number, you can round 56.25% to 56%, 56% of the smoothie is guava juice

The percentage of the smoothie that is guava juice, we can use the following formula:

Percentage = (Part / Whole) * 100

In this case, the part refers to the amount of guava juice, which is 18 fluid ounces, and the whole refers to the total amount of the smoothie, which is 32 fluid ounces.

Let's substitute these values into the formula:

Percentage = (18 / 32) * 100

Simplifying the calculation:

Percentage = 0.5625 * 100

Percentage = 56.25

Therefore, 56.25% of the smoothie is guava juice.

Alternatively, if you prefer to round the percentage to the nearest whole number, you can round 56.25% to 56%.

Hence, approximately 56% of the smoothie is guava juice.

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Answer:

$531.83

Step-by-step explanation:

88*4=352

75+120+85+140=420. Take away the 200 he was allowed. Leaves 220

220*.20 =44

18.50*4=74

gas is set at 61.83

Sum each of those.

352+44+74+61.83= $531.83

Option-c is correct that is F.DIST.RT(x, Deg_freedom1, Deg_freedom2) when the right-tailed probability for a value x on the F(df1,df2) distribution.

Given that,

We have to find which option is correct  for the right-tailed probability for a value x on the F(df1,df2) distribution.

We know that,

returns the degree of diversity (right-tailed) F probability distribution for two data sets. This function can be used to compare the levels of diversity between two data sets. For instance, you may compare the test results of high school freshmen who are men and women to see if there is a difference in the variability between the sides.

Syntax

F.DIST.RT(x,deg_freedom1,deg_freedom2)

The following arguments are used with the F.DIST.RT function syntax:

The value at which the function should be evaluated.

Degrees of freedom numerator required: Deg freedom1.

Degrees of freedom in the denominator, required by Deg freedom2.

Therefore, Option-c is correct that is F.DIST.RT(x, Deg_freedom1, Deg_freedom2) when the right-tailed probability for a value x on the F(df1,df2) distribution.

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Too easy XD I don’t remember how to do that T-T

Answer:

40 I think is the correct answer.

Answer: 85

Step-by-step explanation: To solve this, look at where the line is at 1 HOUR. We can see that the line is right above 80, so 85 is a safe estimate

Answer:

a and b

Step-by-step explanation:

............. ...... ..

Answer:

The answer is B

Step-by-step explanation:

\(\frac{x}{4}=16\\\mathrm{Multiply\:both\:sides\:by\:}4\\\frac{4x}{4}=16\cdot \:4\\\mathrm{Simplify}\\x=64\)

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

Answer:

Try 17

Step-by-step explanation:

The greatest common factor of \(20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}\) is \(10x^{4} y\) .

The greatest common factor of a set of numbers is defined as the largest number that divides all the numbers in that given set and leaves 0 as remainder in each case.

In the given expression

\(20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}\)

Applying Prime Factorization and Writing all the terms in the above expression as

\(20x^{6} y=10x^{4}y *2x^{2}\)

\(40x^{4} y^{2} =10x^{4} y*4y\)

\(10x^{5} y^{5} =10x^{4}y*xy^{4}\)

As we can see that \(10x^{4} y\) is common and greatest in all the terms .

Hence \(10x^{4} y\) is the Greatest common factor.

Therefore , the greatest common factor of \(20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}\) is \(10x^{4} y\) , the correct option is (a)\(10x^{4} y\).

The given question is incomplete , the complete question is

What is the greatest common factor of \(20x^{6} y+40x^{4} y^{2} -10x^{5} y^{5}\)

(a)\(10x^{4} y\)

(b)\(5x^{2} y^{5}\)

(c)\(5x^{4} y\)

(d)\(20x^{6} y\)

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Answer:

132 chocolates

Step-by-step explanation:

We know that after Ramesh arranges his chocolates in rows, the number of rows multiplied by the number of chocolates in each row will give us the total number of chocolates, 17424.

Let the number of rows be x.

From the question, the number of chocolates in each row will also be x.

\(=> x * x = 17424\\\\x^2 = 17424\\\\=> \sqrt{x^2} = \sqrt{17424} \\\\x = 132\)

Therefore, he placed 132 chocolates in each row.

Answer:

-4t-11

Step-by-step explanation:

rearrange the numbers

2t-6t-9+2

Add negative 2

2t-6t-11

2-6

-4t-11

Answer:

\( \sf \large \: V = -1.5\)

Step-by-step explanation:

Let's solve the equation step by step,

v=u+ at

V = 2 + -7(0.5)

V = 2 + -3.5

V = -1.5

Answer: Your answers are

A. 1, 287 ways

B. 154,440 ways

Hope this helped :D

Please mark me brainliest

The minimum total cost for fencing the area with metal fencing is $1,347.68 (approx.) and the minimum total cost for fencing the area with wooden fencing is $6,738.40

Scenario 1: The rectangular area is a square.

Let the side of the square be x. Then, the area of the square is x^2 = 28,000.

Solving for x, we get:

x = sqrt(28,000) = 167.32 ft (approx.)

The total cost for fencing the area with metal fencing is: 4x($2 per ft) = 4(167.32)($2) = $1,338.56 (approx.)

The total cost for fencing the area with wooden fencing is:

4x($5 per ft) = 4(167.32)($5) = $6,693.12 (approx.)

Therefore, the minimum total cost for fencing the area with metal fencing is $1,338.56 (approx.) and the minimum total cost for fencing the area with wooden fencing is $6,693.12 (approx.). The dimensions are 167.32 ft by 167.32 ft (approx.).

Scenario 2: The rectangular area has a length that is twice its width.

Let the width of the rectangle be x. Then, the length of the rectangle is 2x. The area of the rectangle is: A = length x width = 2x^2 = 28,000

Solving for x, we get: x = sqrt(14,000) = 118.32 ft (approx.)

The length of the rectangle is: 2x = 2(118.32) = 236.64 ft (approx.)

The total cost for fencing the area with metal fencing is: 2(2x + 236.64)($2 per ft) = 2(2(118.32) + 236.64)($2) = $1,341.28 (approx.)

The total cost for fencing the area with wooden fencing is: 2(2x + 236.64)($5 per ft) = 2(2(118.32) + 236.64)($5) = $6,706.40 (approx.)

Therefore, the minimum total cost for fencing the area with metal fencing is $1,341.28 (approx.) and the minimum total cost for fencing the area with wooden fencing is $6,706.40 (approx.). The dimensions are 118.32 ft by 236.64 ft (approx.).

Scenario 3: The rectangular area has a length that is three times its width.

Let the width of the rectangle be x. Then, the length of the rectangle is 3x. The area of the rectangle is:

A = length x width = 3x^2 = 28,000

Solving for x, we get:

x = sqrt(9,333.33) = 96.55 ft (approx.)

The length of the rectangle is:

3x = 3(96.55) = 289.66 ft (approx.)

The total cost for fencing the area with metal fencing is:

2(3x + 289.66)($2 per ft) = 2(3(96.55) + 289.66)($2) = $1,347.68 (approx.)

The total cost for fencing the area with wooden fencing is:

2(3x + 289.66)($5 per ft) = 2(3(96.55) + 289.66)($5) = $6,738.40 (approx.)

Therefore, the minimum total cost for fencing the area with metal fencing is $1,347.68 (approx.) and the minimum total cost for fencing the area with wooden fencing is $6,738.40 (approx.). The dimensions are 96

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Answer:

84 sq. inches

Step-by-step explanation:

When you section off each, you can find the area of each shape and add together to make composite.

Triangle on left is 6 sq. inches

Rectangle on right (5x10) is 50 sq. inches

Rectangle on bottom (7x4) is 28 sq. inches

Solution:

Given that Kyle only took his shower 264 times when he was told 330 times, this implies that the percentage of times he took his shower is evaluated as

Since he took a shower 80% of the time, the percentage of time he pretended is thus evaluated as

Hence, he pretended to take a shower 20% of the time.

The BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

BMI stands for Body Mass Index.

It's a measure of body fat based on height and weight that applies to both adult men and women.

BMI is an easy-to-perform screening tool for body fat levels that can help identify individuals who have health risks linked with excess body fatness.

It's important to keep in mind that the BMI measurement should not be used as a diagnostic tool for health conditions and is only one component in an overall evaluation of a person's health status.

Using the formula below, we can calculate the BMI of an 118-lb adult who is 5 feet 4 inches tall: BMI = (weight in pounds / (height in inches x height in inches)) x 703

First, we need to convert the height into inches:5 feet 4 inches = 64 inches

Next, we plug the values into the formula and solve for the BMI:

BMI = (118 / (64 x 64)) x 703BMI = (118 / 4,096) x 703BMI = 0.0288 x 703BMI = 20.2464

Therefore, the BMI of an 118-lb adult who is 5 feet 4 inches tall is approximately 20.25.

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Answer:

132ft^2

Step-by-step explanation:

Answer:

opposites

Step-by-step explanation:

The highest point on a bell-shaped curve represents the peak or maximum value of the distribution. This point is known as the mode of the distribution.

In a bell-shaped curve, also known as a normal distribution or Gaussian distribution, the data is symmetrically distributed around the mean. The curve is characterized by a central peak, and the highest point on this peak corresponds to the mode.

The mode represents the most frequently occurring value or the value that has the highest frequency in the dataset. It is the point of highest density in the distribution.

The bell-shaped curve is often used to model naturally occurring phenomena and is widely applied in statistics and probability theory. The mode provides information about the most common or typical value in the dataset and is useful for understanding the central tendency of the distribution.

While the mean and median also have significance in a normal distribution, the highest point on the bell-shaped curve specifically represents the mode, indicating the value with the highest occurrence in the dataset.

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Hence proved that 3 can divides (4n + 5) for all natural numbers n.

To show that 3 divides (4n + 5) for all natural numbers n, we need to show that there exists some integer k such that:

4n + 5 = 3k

We can rearrange this equation as:

4n = 3k - 5

Since 3k - 5 is an odd number (the difference of an odd multiple of 3 and an odd number), 4n must be an even number. This means that n is an even number, since the product of an even number and an odd number is always even.

We can then write n as:

n = 2m

Substituting this into the original equation, we get:

4(2m) + 5 = 8m + 5 = 3(2m + 1)

So we can take k = 8m + 5/3 as an integer solution for all natural numbers n.

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Hence proved that 3 can divides (4n + 5) for all natural numbers n.

To show that 3 divides (4n + 5) for all natural numbers n, we need to show that there exists some integer k such that:

4n + 5 = 3k

We can rearrange this equation as:

4n = 3k - 5

Since 3k - 5 is an odd number (the difference of an odd multiple of 3 and an odd number), 4n must be an even number. This means that n is an even number, since the product of an even number and an odd number is always even.

We can then write n as:

n = 2m

Substituting this into the original equation, we get:

4(2m) + 5 = 8m + 5 = 3(2m + 1)

So we can take k = 8m + 5/3 as an integer solution for all natural numbers n.

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