10 points + BRAINEST

Yes, the modulus of a complex number is the same as the absolute value.

The modulus of a complex number, z = x + yi, is represented as |z| = √(x² + y²) and it is a scalar value that gives the distance of the complex number from the origin in the complex plane.

The absolute value of a complex number is the same as its distance from the origin in the complex plane. The absolute value of a complex number is also represented as |z| = √(x² + y²) which is the same as the modulus.

The modulus and the absolute value are often used interchangeably when referring to the magnitude of a complex number.

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Answer:

your answer is 5/12

Step-by-step explanation:

becuase im right

[tex]\dfrac{10}{2+3} +\dfrac{6+3}{3}[/tex]

[tex]\dfrac{10}{5} +\dfrac{9}{3}[/tex]

[tex]\dfrac{10}{5} \rightarrow2\\\dfrac{9}{3} \rightarrow3[/tex]

[tex]2+3[/tex]

[tex]=\fbox{5}[/tex]

The list that gives the sample space for pulling 2 marbles from the bag with replacement is given as follows:

List 4.

A sample space is a set that contains all possible outcomes in the context of an experiment.

The fact that the experiment is with replacement means that for each of the two marbles, there are two possible outcomes.

Then, applying the Fundamental Counting Theorem, the total number of outcomes is given as follows:

4 x 4 = 16.

This means that the correct list is either the list 3 or the list 4.

As there is replacement, it is possible to take two purple marbles, even though there is only one purple marble, as the same can be taken with replacement, and thus the correct list is given by list 4.

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Answer: List 4

Step-by-step explanation: This answer is here to confirm the other answer. It got me 100% on my test.

Also I know the right answer because I got it right

So good luck on y'all's math tests :)

Here is some proof that the answer is List 4

The way to analyze data using frequency tables will be:

A frequency table is a way to organize and summarize data by counting the number of times each value appears in the data set. To examine and analyze data using a frequency table, you can follow these steps:

You can also use the frequency table to create graphical representation of data like histograms, bar charts, and pie charts to make the data more visually appealing and easier to understand.

Based on the analysis, you can make conclusions about the data and make decisions. Overall, frequency tables can be very useful in understanding the distribution of data and identifying patterns and trends.

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Complete question

How do one examine and analyze data using frequency tables?

A) The price that the store charges its customers for the skis is; $91.20

B) The percent of the original price that is the final price is; 160%

C) The percent INCREASE from the original price to the final price is; 60%

The Percentage increase is defined as the difference between the final value and the initial value, expressed in the form of a percentage.

We are given;

Wholesale price = $57

Markup rate = 60%

From the above information given, the amount of markup will be:

Amount of mark up = 60% × $57

= 0.6 × $57

= $34.20

Therefore, the new price will be:

= $57 + $34.20

= $91.20

In conclusion, the percentage of the original price will be 160% and the percentage increase is 60%.

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Complete question is;

A store that sells skis buys them from a manufacturer at a wholesale price of $57. The store's markup rate is 60%

A. What price does the store charge its customers for the skis?

B. What percent of the original price is the final price?

C. What is the percent INCREASE from the original price to the final price?

Answer: $6.90

Step-by-step explanation:

20%  --->  .20

34.50 x .20 = 6.9

Answer: 132 with a remainder of 5

Step-by-step explanation: 137/6 gives us 22 an multiplying 22x6 gives us 132 leaving us with a remainder of 5.

Answer:

He can sell 22 groups of crickets and have 5 left over

Step-by-step explanation:

There are an infinite number of planes in a 3 dimensional coordinate system.

The 3 dimensional coordinate system is made up of three axes (x, y, and z) that are all perpendicular to each other. These axes create a 3D space that can be used to plot points and objects. In this 3D space, an infinite number of planes can be created. Planes are defined by a mathematical equation that gives the values of the x, y, and z components. These equations can be manipulated to create planes that are parallel, perpendicular, or angled in relation to the coordinate system axes. Additionally, planes can be shifted up, down, left, right, forward, and backward, creating an infinite number of potential planes in a 3D coordinate system.

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The production method that breaks a complex job into a series of smaller tasks is called option 1: assembly line.

What is assembly line?

A production method known as an assembly line divides the creation of a good into steps that are finished in a predetermined order.

The most often utilised technique in the mass manufacture of goods is assembly lines. Because they train unskilled workers to complete particular activities, they lower labour costs.

So, in assembly line a large complex job is first divided into small jobs.

Then the trained workers do the smaller jobs and in a fixed order.

Therefore, this process is known as assembly line.

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Reason:

Subtract 5 from both sides

[tex]\sqrt{\text{x}}+5 = 0\\\\\sqrt{\text{x}}=-5\\\\[/tex]

But recall that the range of the parent square root function is the set of nonnegative values. There's no way to have [tex]\text{y} = \sqrt{\text{x}}[/tex] produce a negative number.

Therefore, the equation [tex]\sqrt{\text{x}}=-5[/tex] has no solutions.

----------------------------

Here's what happens if we squared both sides

[tex]\sqrt{\text{x}}=-5\\\\(\sqrt{\text{x}})^2=(-5)^2\\\\\text{x}=25\\\\[/tex]

That's the potential answer, but we need to verify.

[tex]\sqrt{\text{x}}+5 = 0\\\\\sqrt{25}+5 = 0\\\\5+5 = 0\\\\10 = 0\\\\[/tex]

We get a contradiction, which rules out x = 25 being a possible solution.

----------------------------

If you are a visual learner, then check out the graph below.

The curve [tex]\text{y} = \sqrt{\text{x}}+5[/tex] never touches the x axis; this means there's no way for it to have a root and it verifies why [tex]\sqrt{\text{x}}+5 = 0[/tex] has no solutions.

I used GeoGebra to make the graph, but Desmos is another useful option.

On solving the provided question, we can say that in the triangle If AL = 2, LS = 6,LM =  4, and ST=x+ 2,  as its given, M is the mid point and LM || ST , ST = 4

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.]

in the triangle

If AL = 2, LS = 6,LM =  4, and ST=x+ 2,

as its given, M is the mid point and LM || ST

so LM = ST

4 = (x + 2)

2 = x

ST = 4

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Answer: No they cannot

Step-by-step explanation:

6+4.5 = 10.5 which is greater than 7.5 meaning it cannot create a right angled triangle

The polynomial equation kx^2 - 2x^4 = 0 has no real solutions, for any non-zero value of k.

The equation kx^2 - 2x^4 = 0 has the form of a polynomial equation, where k and x are variables. To find the nonzero value of k that will cause the equation to have 2 real solutions, we need to analyze the roots of the equation.

The roots of the equation are the values of x that make the equation equal to zero. To find the roots, we can set each factor of the polynomial equal to zero and solve for x:

kx^2 = 0 and 2x^4 = 0

The first equation gives us x = 0, which is not a valid solution, because it is not a real number.

The second equation gives us x^4 = 0, then x = 0. But x = 0 is not a valid solution for this equation, as it is not a real number.

Therefore, the polynomial equation kx^2 - 2x^4 = 0 has no real solutions, for any non-zero value of k.

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Answer: 8th graders should be encouraged to read more. This is because they have the least read pages on average. If you calculate the average number of pages read, the 6th-grade students have a total of 25 pages, the 7th-grade students have a total of 34 and the 8th-grade students have a total of 23. It is because of their lowest total number of pages read that the 8th graders would have the most and should be encouraged to read more.

The answers are:

1. 2(x2 + 6x + 9) = 3 + 18

2. 2(x2 + 6x) = 3

Quadratic equation is a second-order polynomial equation in a single variable x ax2+bx+c=0. with a ≠ 0 . Because it is a second-order polynomial equation the fundamental theorem of algebra guarantees that it has at least one solution

Let's take a look at the first choice:

2(x² + 6x + 9) = 3 + 18

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x + 2·9 = 3 + 18

2x² + 12x + 18 = 3 + 18

2x² + 12x - 3 = 18 - 18

2x² + 12x - 3 = 0

Let's take a look at the second choice:

2(x² + 6x) = 3

Now, we will multiply 2 with every member of the other multiplier on the left side:

2·x² + 2·6x = 3

2x² + 12x = 3

2x² + 12x - 3 = 0

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The restaurant owns the 225 forks if 4% of the fork owned by the restaurant.

Percentage are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

A dishwasher at a restaurant washes 9 fork.

These fork represent 4% of the fork owned by the restaurant.

Now, Solving the question:

We can get our answer by displaying as an equality

= 9 to 4/100

= x to 100/100

You can multiply 4 by 25 to get 100 so to get the amount of forks, multiply 9 by 25

=9 × 25 = 225

Hence, The restaurant owns the 225 fork.

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The required representation of given number line is x ∈ (-10,  ∞).

The idea of inequality, which is the state of not being equal, especially in terms of status, rights, and opportunities, is at the core of social justice theories. However, because it frequently means different things to different people, it is prone to confusion in public discourse.

According to question:

We have number line,

By using baby curve method.

The representation of the line is ,

Let the line is x axis

Then

x ≥-10

x ∈ (-10,  ∞)

Thus, the required inequality is  (-10,  ∞).

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Answer:

-25

Step-by-step explanation:

-5 times 5 is -25

The roots of a quadratic equation are the values of x for which the equation holds true. aα^2+bα+c=0 if and only if α is a root of the quadratic equation.

A quadratic equation has the conventional form ax^2+bx+c=0, where a, b, and c are real values and a0.

The coefficient of x^2 is "a." The quadratic coefficient is what it is termed. The coefficient of x is "b." The linear coefficient is its name. The constant term is "c."

The roots of a quadratic equation are the values of x for which the equation holds true. aα^2+bα+c=0 if and only if α is a root of the quadratic equation.

A quadratic equation may have two real roots that are different from one another, two equal roots, or no real roots at all.

The locations where the graph of the quadratic polynomial intersects the x-axis are known as the roots of a quadratic equation graphically.

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Based on the estimates above, they sold 3 left-handed and 17 right-handed gloves.

17 right-handed gloves and 3 left-handed gloves were sold.

We must create a set of equations to address this issue.

The total number of gloves sold was 12, and the total income was 940.

Gloves for the right hand (x) = 45.

gloves for the left hand (y) = 50.

Equations x+y=20...

45x + 50y = 561 is the first equation (ii)

Equation derived from equation I x + y = 12 – y (iii)

Equation (ii) becomes 45x + 50y = 940

by substituting equation (iii):

x = 12 - u 45

(12 - y) + 50y = 940;

540 - 45y + 50y = 940;

540 + 7y = 561;

7y = 21 y = 3

Equation I becomes x + y = 20 for y = 3, x + 3 = 20x, and 20- x = 17.

Based on the estimates above, they sold 3 left-handed and 17 right-handed gloves.

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The graph of the system of equations y = -2x + 3 and 2x + 4y = 8 is a pair of straight lines passing through the points (2/3, 5/3).

y = -2x + 3 …. (1)

2x + 4y = 8 …. (2)

Substitute eqn (1) in (2)

2x + 4 (-2x + 3) - 8 = 0

Using the multiplicative distributive property, we get

2x - 8x + 12 = 8

By rearranging the above eqn, we get

2x - 8x = 8 - 12

-6x = - 4

Dividing both sides by -2, we get

3x = 2

x = 2/3

Put the value of x in eqn (1)

y = -2 (2/3) + 3

y = -4/3 + 3

y = (-4 + 9)/3

y = 5/3

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The degree measures of angles d, e, and f are 64 degrees, 99 degrees, and 17 degrees, respectively.

What is the measures of the angles in a triangle?

If we add all three angles in any triangle we get 180 degrees. So, the measure of angle A + angle B + angle C = 180 degrees. This is true for any triangle in the world of geometry.

A) The sum of the angles in a triangle is 180 degrees. Using this fact, we can write:

m∠d + m∠e + m∠f = (4x-4) + (6x-3) + x = 11x - 7

Since this is the sum of the angles in the triangle, it must equal 180 degrees. Therefore, we can write:

11x - 7 = 180

Solving for x:

11x = 187

x = 17

Therefore, x = 17.

B) Now that we know x, we can find the measure of each angle by substituting it into the expressions given for each angle:

m∠d = 4x - 4 = 4(17) - 4 = 64 degrees

m∠e = 6x - 3 = 6(17) - 3 = 99 degrees

m∠f = x = 17 degrees

Therefore, the degree measures of angles d, e, and f are 64 degrees, 99 degrees, and 17 degrees, respectively.

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The following expression shows the main expression after the negative exponents have been eliminated: A. m⁷n³n/m.

In Mathematics, an exponent can be defined as a mathematical operation that is used in conjunction with an algebraic expression to raise a quantity to the power of another and it is generally written as bⁿ.

By applying the property of exponents based on the law of indices for the division of powers, we have the following:

b⁻ⁿ = 1/bⁿ

In this context, the exponent n⁻¹ in the given algebraic expression would be rewritten based on the law of indices for the division of powers as follows;

n⁻¹ = 1/n

Substituting the given parameters into the given algebraic expression, we have the following;

(m⁷n³)/mn⁻¹ = (m⁷n³)/m × n

(m⁷n³)/m × n = (m⁷n³n)/m

(m⁷n³)/mn⁻¹ = m⁷n³n/m

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Answer:

Step-by-step explanation:

its A

A triangle can be formed with the side length of 3.5 cm, 4.5 cm and 7.5 cm.

The one side of the triangle should always measure lower than the sum of remaining two sides of triangle. Based on this concept, let's check the sum and compare it with remaining side to find the possibility of triangle construction.

Side a + side b > side c

3.5 + 4.5 > 7.5

Adding the digits

8 > 7.5

Side b + side c > side a

4.5 + 7.5 > 3.5

Adding the digits

12 > 3.5

side c + side a > side b

3.5 + 7.5 > 4.5

Adding the digits

11 > 4.5

The sums are always greater than remaining side based on the mentioned lengths. Thus, the triangle can be formed.

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If swimming 1/4 of a mile uses about the same number of calories as running 1 mile.

a.  The distance her sister have to swim to use the same number of calories Gilda used during the marathon is 6 1/2 mile.

b. The number of miles that he would have to run to use the same number of calories used during his swim is 20 miles.

a. Number of miles:

1/4 swim / 1 run = x swim / 26 run

Cross multiply

= 6 1/2 mile

b.  Number of miles:

1/4 swim / 1 run = 5 swim/x

Cross multiply

x = 20 miles

Therefore the number of mile is 6 1/2 miles and 20 miles.

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The complete question is:

Swimming 1/4 of a mile uses about the same number of calories as running 1 mile.

a. Gilda ran a 26 mile marathon. About how far would her sister have to swim

to use the same number of calories Gilda used during the marathon?

b. Juan swims 5 miles a day. About how many miles would he have to run to

use the same number of calories used during his swim?

The  range of this absolute value function is 5 ≤ y < ∞, the correct option is C

Domain is the set of values for which the given function is defined.

Range is the set of all values which the given function can output.

We start by determining the vertex of the absolute value function

Given;

A graph of the function

Now,

From the graph we can observe that the starting of function in y axis is from 5 and ending is at infinite

Therefore the range will be 5 ≤ y < ∞.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Let's solve ~

Ratio of side of bigger rectangle to that to corresponding side of smaller rectangle (as they are similar) is :

[tex]\qquad \sf  \dashrightarrow \: \dfrac{20}{8} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 2.5[/tex]

So, the bigger rectangle is a scaled up version of the smaller version with a scale factor of 2.5

So, our required answer will be :