What is the slope of a line parallel to the y-axis?​

On evaluating the expression (1 - 1i) + (3 + 2i), the value for a and b are 4 and 1 respectively.

What is an expression?

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

To evaluate the expression (1 - 1i) + (3 + 2i), we simply add the real parts and the imaginary parts separately -

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

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

= 4 + i

The value for a is obtained as 4

The value for b is obtained as 1.

Therefore, the result is 4 + i, which is in the form a + bi.

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The perimeter of the shape formed is,

⇒ P = 24√13 units

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Three congruent rectangles are joined as shown.

And, The length of each rectangle is 3 times its width.

Here, The area of each rectangle is 39 square units.

Let the length of the rectangle = 3x

And, The width of the rectangle = x

Hence, We get;

Area of rectangle = Length x Width

⇒ 39 = 3x × x

⇒ 39 = 3x²

⇒ x² = 13

⇒ x = √13

Hence, The length of the rectangle = 3√13

And, The width of the rectangle = √13

Thus, The perimeter of the figure is,

⇒ P = 3 × [ 2 (3√13 + √13) ]

⇒ P = 6 × 4√13

⇒ P = 24√13 units

Therefore, The perimeter of the shape formed is,

⇒ P = 24√13 units

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The missing values in the ratio tables are  

For table 1, 150, 250, and 500

For table 2, 200, 400, and 600

A ratio is a mathematical comparison of two quantities or values. It is expressed as the quotient or fraction of one value to another value.

Ratios are often written in the form of a:b or a/b, where a and b are the two quantities being compared.

To complete the following table determine the ratio of the table using the values in the table and calculate the remaining values

Here we have

The ratio table -1

Pages   50                        

Hours    1      3      5      10

Here, the ratio of page/ hours = 50/1 = 50

Let the x, y, and z be the values

According to ratio

=> x/3 = y/5 = z/10 = 50

=> x/3 = 50 => x = 150

=> y/5 = 50 => y = 250

=> z/10 = 50 => z = 500

The ratio table - 2

Feet    100

Hours   1       2     4     6  

The ratio of feet/ second = 100/1 = 100

Let a, b, and c be the values

=> a/2 = b/4 = c/6 = 100

=> a/2 = 100 => a = 200

=> b/4 = 100 => b = 400

=> c/6 = 100 => c = 600

Therefore,

The missing values in the ratio tables are  

For table 1, 150, 250, and 500

For table 2, 200, 400, and 600

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q^2 is the resulting expression for the exponent

Given the expression below

[tex]\frac{q}{q^{-1}\cdot q\cdot q^{-1}}[/tex]

Using the product and division law of indices, we will have:

a^m * a^n. = a^m+n

a^m/a^n = a^m-n

Applying this law, the denominator of the expression will be:

[tex]\frac{q}{q^{-1}\cdot q\cdot q^{-1}} = \frac{q}{q^{-2+1}}\\\frac{q}{q^{-1}\cdot q\cdot q^{-1}}=\frac{q}{q^{-1}}\\\frac{q}{q^{-1}\cdot q\cdot q^{-1}}=q^{1+1}=q^2[/tex]

Hence the resulting expression of the exponents is q^2

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Answer:

0.3:0.7 3:7

Step-by-step explanation:

Answer:

A)  (-7, 6)

Step-by-step explanation:

The graph of the inverse function is a reflection in the line y = x.

The mapping rule for a reflection in the line y = x is:

Therefore, if point (6, -7) is on the graph of the function f(x), the point that is on the graph of the inverse function f⁻¹(x) is:

The graphical representation that would be best for the doctor's data is a box plot. The correct option is the last option Box plot

From the question, we are to determine the graphical representation that would be best for the doctor's data

In this case, the doctor is interested in the heights of 14-year-olds in the state of Texas, and has gathered data from a random sample of 1,000 pediatricians in the state. A box plot would allow the doctor to see the range of heights observed in the sample, as well as any potential outliers or unusual observations. It would also allow for easy comparison of the heights of different groups or regions within the state, if desired.

A box plot is a graphical representation of a data set that displays the minimum, maximum, median, and quartiles of the data.

Hence, a box plot would be the best graphical representation for the doctor's data. It can help visualize the spread and distribution of the data and identify any outliers.

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Answer: You have a probability of 1/2.

Step-by-step explanation: Since there are 12 marbles in total, and there are 6 green marbles, you have a 1 in 2 chance to draw a green marble.

The explicit formula of the geometric sequence is given as follows:

[tex]a_n = 100(4)^{n-1}[/tex]

The recursive formula of the geometric sequence is given as follows:

A geometric sequence is a sequence of numbers where each term is obtained by multiplying the previous term by a fixed number called the common ratio (q). In other words, a geometric sequence is a sequence where each term is a fixed multiple of the previous term.

The explicit formula of the sequence is given as follows:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

For the recursive formula, we just take the first term and each consecutive term is the previous term multiplied by the common ratio.

There are 100 views in day one, hence the first term is given as follows:

[tex]a_1 = 100[/tex]

The number of viewers is multiplied by 4 each day, hence the common ratio is given as follows:

q = 4.

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Answer:(4 + 3) x 2

Step-by-step explanation:

Vesi snowboards 4 hours before lunch and 3 hours after lunch each day, so the total time she spends snowboarding each day is:

4 + 3 = 7 hours

The question is asking how many hours Vesi snowboarded in 2 days, so we need to multiply the daily total by 2:

7 x 2 = 14

Therefore, the expression that represents this real-world situation is:

B. (4 + 3) x 2 = 14.

Option A adds 2 hours which is not correct as Vesi snowboards 7 hours each day, not 2 hours. Option C multiplies and divides, which is not necessary in this case. Option D multiplies and subtracts, which is also not correct.

The amount of snow that fell each week was 2 units (assuming the units are consistent with the original scenario.

Snowfall measurement is the process of determining the amount of snow that falls at a particular location during a specific period of time. Accurate snowfall measurement is important for a variety of reasons, including transportation safety, weather forecasting, and water resource management.

If the same amount of snow fell the following winter, but the same amount of snow fell each week, and there were the same number of weeks, then we need to divide the total amount of snow by the number of weeks to find the amount of snow that fell each week.

Looking at the diagram, we can estimate the total amount of snow that fell by counting the number of asterisks (*) in the diagram. There are 8 asterisks, which represent the total amount of snow that fell over the winter.

Since there are 4 weeks (the same number of weeks as the original scenario), we can divide the total amount of snow by 4 to find the amount of snow that fell each week:

Total amount of snow = 8 asterisks

Amount of snow that fell each week = Total amount of snow / Number of weeks

= 8 / 4

= 2

Therefore, the amount of snow that fell each week was 2 units (assuming the units are consistent with the original scenario).

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Set 2:

T. Slope = (9-5)/(10-7) = 4/3 __16.  Slope = (2-(-2))/(9-(-5)) = 4/14

B. Slope = (-4-2)/(-5-(-8)) = -6/3 __ 8.  Slope = (-8-(-6))/(2-(-10)) = -2/12

H.  Slope = (-1-(-2))/(-4-2) = -3/-6 __ 3.  Slope = (-7-1)/(-8-(-2)) = -8/6

S.  Slope = (7-9)/(-11-(-4)) = -2/-7 __ 5. Slope = (3-(-2))/(-3-(-4)) = 5/1

O. Slope = (-6-(-1))/(4-5) = -5/-1 __ 14.  Slope = (6-(-4))/(-7-(-2)) = 10/-5

Set 3:

K. Slope = (-3-(-3))/(2-1) = 0/1 __ 9.  Slope = (-4-(-1))/(6-8) = -3/-2

R. Slope = (5-0)/(-3-3) = 5/-6 __ 1.  Slope = (-5-(-6))/(-8-(-11)) = 1/3

E. Slope = (-2-4)/(8-12) = -6/-4 __ 15. Slope = (3-4)/(-5-(-5)) = -1/0

U.  Slope = (-9-(-3))/(7-7) = -6/0 __ 12. Slope = (9-(-3))/(-5-(-2)) = 12/3

O.  Slope = (5-1)/(2-3) = 4/-1 ____ 6.  Slope = (8-8)/(7-(-3)) = 0/10

H.  Slope = (-8-(-6))/(-7-(-1)) = -2/-6 _ 10. (-5, 3) and (7, -7) Slope = (-7-3)/(7-(-5)) = -10/12

A set is a collection of distinct objects, usually numbers, that are grouped together in a manner that follows specific rules. Sets can be used to determine if an element belongs to the set or not, and can also be used to perform operations such as unions and intersections. Sets are an important tool in mathematics, and they can help simplify complex problems.

The Mathematician had to calculate the slope between two points for each of the sets given. To calculate the slope, the Mathematician had to subtract the y-values of the two points and divide by the difference between the x-values of the two points. The Mathematician then had to match the answers to the corresponding letter or number and write the letter in the matching numbered box at the bottom of the page. By doing this, the Mathematician was able to solve the riddle and arrive at work on time.

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Answer:

y=-1/4x-2/3

Step-by-step explanation:

The location of the region's centroid is (0, 2/5).

What does the region border by the curves' centroid look like?

We must first determine the limits of integration and the formulas for the x-coordinate and y-coordinate of the centroid in order to determine the centroid of the area enclosed by the curves y=2-x2 and y=x.

We shall integrate across the range [-1,1] since the curves intersect at (1,1) and (-1,1).

We must assess the following integral in order to determine the centroid's x-coordinate:

x' = (1/A) ∫[a,b] xf(x) dx

Where: A is the region's area (which we can find by integrating the difference between the two curves).

A = ∫[a,b] (f(x) - g(x)) dx

In this case, f(x) = 2 - x² and g(x) = x, so

A = ∫ [-1,1] (2 - x² - x) dx

= [2x - (1/3)x³ - (1/2) x²] | from -1 to 1

= (4/3)

Now we can evaluate the x-coordinate of the centroid:

x' = (1/A) ∫ [-1,1] x*(2-x²-x) dx

= (1/ (4/3)) ∫ [-1,1] (2x - x³ - x²) dx

= (3/4) [(x²/2) - (1/4) x⁴ - (1/3) x³] | from -1 to 1

= 0

Hence, the x-coordinate of the centroid is 0.

To find the y-coordinate of the centroid, we need to evaluate the following integral:

y' = (1/A) ∫[a,b] (1/2) [f(x)² - g(x)²] dx

y' = (1/ (4/3)) ∫ [-1,1] (1/2) [(2-x²) ² - x²] dx

= (3/4) [(8/15) x⁵ - (2/3) x³ + (1/2) x] | from -1 to 1

= (2/5)

Hence, the y-coordinate of the centroid is 2/5.

Therefore, the centroid is (0,2/5).

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Answer:

94.3/C

Step-by-step explanation:

Hope this helps!

Answer: because we need it for life

Step-by-step explanation: we do math because when we go to pay something we need money and they say this much money or when you cook it said 3/4 and you don’t know what is 3/4 is also on tests.

the width of the garden is approximately 6.77 feet, and the length is approximately 11.77 feet (since it is 5 feet more than the width).

what is rectangle?

A rectangle is a four-sided polygon with opposite sides that are parallel and equal in length.

Let's denote the width of the garden by x. Then, according to the problem statement, the length of the garden is x + 5.

The total width of the garden and the walkway is x + 2(3) = x + 6, and the total length is x + 5 + 2(3) = x + 11.

The area of the garden itself is x(x + 5), and the area of the garden and the walkway is (x + 6)(x + 11).

The area of the walkway is the difference between the two: (x + 6)(x + 11) - x(x + 5) = 210.

Expanding and simplifying this expression, we get:

x^2 + 17x - 135 = 0

We can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

In this case, a = 1, b = 17, and c = -135, so we have:

x = (-17 ± sqrt(17^2 - 4(1)(-135))) / 2(1)

x = (-17 ± sqrt(769)) / 2

We can discard the negative solution, so we have:

x = (-17 + sqrt(769)) / 2

x ≈ 6.77

Therefore, the width of the garden is approximately 6.77 feet, and the length is approximately 11.77 feet (since it is 5 feet more than the width).

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Answer: 20 inches

Step-by-step explanation: Let's quickly create some equations to represent what's going on. We can say i are inches and m are miles. Then, 5i=3m because 5 inches represents 3 miles.

5i=3m

5/3i=1m One mile represents 5/3 of an inch/

12(5/3i)=12m We multiply by 12 since we want to know what 12 miles are

60/3i=12m=20i      12 miles is equal to 20 inches

Hope this helps! For practice, if 10 inches represented half a mile on a map, how many feet are represented by 36 miles?

10 is the appropriate response to the expression.

Carlos gave the erroneous response of 29.

Carlos made the error of doing addition and subtraction operations prior to multiplication and division operations, as is evident.

Every mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Everything with a variable value is anything whose value changes over time. Typically, alphabetical letters like a, b, c, m, n, p, x, y, and z are used to denote expression variables. A combination of several variables and integers can be used to create a variety of expressions.

From the question:

We must assess the expression utilizing the PEMDAS order of operations and contrast the results:

20 - (2x6) + 8 ÷ 4

= 20 - 12 + 2

= 10

Carlos gave the erroneous response of 29. It seems that Carlos determined the expression to be: 20 - (2x6) + 8 ÷ 4 = 29

Carlos made the error of doing addition and subtraction operations prior to multiplication and division operations, as is evident. Multiplication and division must be done before addition and subtraction, per the PEMDAS order of operations.

Carlos ought to have determined the expression to be:

20 - (2x6) + 8 ÷ 4 = 20 - 12 + 2 = 10

Hence, 10 rather than 29 is the appropriate response to the expression.

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The equivalent expressions are A3, B2, C3, D4 and E5.

Expression in math is a combination of numbers, symbols, and operations that represent a value or a relationship between values. Expressions are used to represent relationships between numbers, variables, and other mathematical objects. Expressions are the basic building blocks of algebra and calculus, and allow us to solve problems and describe relationships between different quantities. Expressions help us to understand math better, as they allow us to express complex ideas in concise, clear, and concise form.

Once the wires are connected by matching the equivalent expressions, the code word is 8+7+(-3).

This is happening because in order to unlock the communication system, you need to match the equivalent expressions in order to find the code word. By evaluating each expression, you can determine which of the expressions are equivalent and then connect the wires accordingly. By connecting the wires, you can then find the code word which will unlock the communication.

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Answer:

62 miles per hour

Step-by-step explanation:

62 x 6 gets you 372 easy

NO || PR using the converse of the Triangle Proportionality Theorem are not parallel.

The Triangle Proportionality Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.

Conversely, if a line divides two sides of a triangle proportionally, then it is parallel to the third side.

In this problem, we are given a right triangle NQM, where line PR intersects the sides NM and QM at points P and R, respectively. We are also given that NM = 16, PM = 12, RM = 6, and QR = 8. We want to verify that NO || PR.

To do this, we will use the converse of the Triangle Proportionality Theorem. We know that PR divides NM proportionally, so we need to show that it also divides QM proportionally.

Using the ratios of corresponding side lengths of similar triangles, we can write:

PM / RM = PN / RN

Substituting the given values, we get:

12 / 6 = PN / (16 - 6)

2 = PN / 10

PN = 20

Similarly, we can write:

QR / RM = QN / RN

Substituting the given values, we get:

8 / 6 = QN / (16 - 6)

4 / 3 = QN / 10

QN = 40 / 3

Now we can check if PR divides QM proportionally:

PM / QN = 12 / (40 / 3) = 9 / 5

PN / RM = 20 / 6 = 10 / 3

Since these ratios are not equal, we can conclude that PR does not divide QM proportionally.

Therefore, by the converse of the Triangle Proportionality Theorem, we can conclude that NO is not parallel to PR.

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A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. Thus, option D is correct.

The degree of operating leverage (DOL) formula is:

DOL = Contribution Margin / Net Operating Income

We can calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Now we can calculate the DOL:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Therefore, the company's degree of operating leverage is 4.00.

The answer is (D) 4.00.

Step-by-step explanation:

Identify the relevant values from the problem statement:

Net operating income = $30,000

Fixed expenses = $90,000

Sales = $200,000

CM ratio = 60%

Calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Use the contribution margin and net operating income to calculate the degree of operating leverage:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Interpret the result:

A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. This indicates that the company has a high degree of operating leverage, which means that it is more sensitive to changes in sales volume. In other words, small changes in sales can have a big impact on the company's profitability.

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A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. Thus, option D is correct.

The degree of operating leverage (DOL) formula is:

DOL = Contribution Margin / Net Operating Income

We can calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Now we can calculate the DOL:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Therefore, the company's degree of operating leverage is 4.00.

The answer is (D) 4.00.

Identify the relevant values from the problem statement:

Net operating income = $30,000

Fixed expenses = $90,000

Sales = $200,000

CM ratio = 60%

Calculate the contribution margin using the CM ratio:

Contribution Margin = Sales x CM ratio

Contribution Margin = $200,000 x 0.60

Contribution Margin = $120,000

Use the contribution margin and net operating income to calculate the degree of operating leverage:

DOL = Contribution Margin / Net Operating Income

DOL = $120,000 / $30,000

DOL = 4.00

Interpret the result:

A degree of operating leverage of 4.00 means that a 1% change in sales will result in a 4% change in net operating income. This indicates that the company has a high degree of operating leverage, which means that it is more sensitive to changes in sales volume. In other words, small changes in sales can have a big impact on the company's profitability.

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Answer:

Results

Interest Rate -61.911%

Total of 36 Monthly Payment of $8,100.00

Total Interest Paid $-16,900.00

Step-by-step explanation:

Answer:R= 3%/year

Step-by-step explanation:

r = 225 / (2500 x 3) = 0.03

r= 0.03

converting r decimal to a percentage

R = 0.03 * 100 = 3%/year

The interest rate required to accumulate simple interest of $225.00 from a principle of $2,500.00 over 3 years is 3% per year.

Answer:

The perimeter of the shape is 41

Step-by-step explanation:

You have to add 12 plus 9 plus 7 plus 8 plus 2 plus 3, which equals forty one. I got the two and three from the little corner which isn’t labeled. I got it by subtracting 8 from 12, and 7 from 9.

The function describes this graph is y = x² + 9x + 18.

In mathematics, a graph is defined as a graphical representation or diagram that organises facts or values. The graph's points frequently reflect the relationship between two or more things.

Given:

We can see from the Graph touches the x axis at -6 and -3.

So, the factors of function are (x +6) and (x+ 3).

Then, the function represented by the graph is

y = (x+ 6) (x + 3)

y = x² + 6x + 3x + 18

y = x² + 9x + 18

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The amount of space each student will occupy is 0.25 square meters of space in the classroom.

To find the amount of space each student will occupy,

We need to first subtract the area taken up by the teacher's table and shelves from the total area of the classroom.

Then we can divide the remaining area by the number of students.

Let's say the total area of the classroom is A.

Then we have:

A - 350 ( the area available for students)

If each student occupies an area of x, then we have:

40x = A - 350

Substituting the first equation into the second equation, we get:

40x = (A - 350)

We can solve for x by dividing both sides by 40:

x = (A - 350) / 40

We know that there are 40 students, so we can substitute that into the equation:

x = (A - 350) / 40 = (360 - 350) / 40 = 0.25

Therefore, each student will occupy 0.25 square meters of space in the classroom.

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