Four students were asked to convert the polar coordinates (4, 11pi/6) to a complex number using technology. Select the correct work.

Sum of first n natural numbers, i.e., n(n + 1)/2 is an example of sum of numbers.

Sum is defined as a way of putting all the things like numbers, quantities, etc. together. Alternate words used for sum are “all together, “put together,” and “total,” etc. For example, the sum of first five natural numbers. First five natural numbers are 1, 2, 3, 4, and 5, then sum of first five natural numbers is written as 1 + 2 + 3 + 4 + 5 = 15

Similarly, Sum of First n Natural Numbers :

We have to calculate the sum of the sequence of first n natural numbers. Consider the first n natural numbers as 1, 2, 3, 4,…., n. This represents an AP with first term a = 1 and last term l = n. As we know Sum formula for Arithmetic Progression, S = (n/2) (a + l)

= (n/2)(1 + n)

= n(n + 1)/2

Therefore, the sum of the first n natural numbers is given by n(n + 1)/2.

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The following triangles are congruent.

Yes AAA

To write 3 more than 5, we use the mathematical operation of addition and the notation 5 + 3 = 8.

To write 3 more than 5, we need to use the mathematical operation of addition. Addition is the process of combining two or more numbers to find the total or sum.

In this case, we are given the number 5 and we are asked to find the number that is 3 more than it. To do this, we can use the mathematical notation: 5 + 3 = 8.

This notation means that we are adding 3 to 5, which results in 8. The "+" symbol is the addition operator and it is used to indicate that we are performing an addition operation. The "=" symbol is used to indicate that the result of the addition is 8.

Another way to write 3 more than 5 is to use the phrase "5 plus 3". This phrase indicates that we are adding 3 to 5 to get 8.

Therefore, In short, to write 3 more than 5, we use the mathematical operation of addition and the notation 5 + 3 = 8. This means that we are adding 3 to 5, resulting in 8. It can also be written as "5 plus 3", indicating the same operation.

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Therefore , the solution of the given problem of parallelograms comes out to be Figure 2 and Figure 4 are of the same area.

A simple quadrilateral with two sets of equal spacing is known as a parallelogram in Euclidean geometry. Both set of opposite ends are straight and equal in a particular type of quadrilateral termed as a parallelogram. Parallelograms come in four varieties, three of which are exclusive. The four different shapes are rhombuses, parallelograms, squares, and rectangles. A quadrilateral is a parallelogram if it has two sets od parallel sides. In a parallelogram, all cross-sectional lengths of the opposing angles and angles are equal.

Here,

Given :

Four parallelogram are given with different area we have to find the

parallelogram area equal is :

We observe from the given image ,

We get

Figure 2 and Figure 4 are of the same area.

Therefore , the solution of the given problem of parallelogram comes out to be Figure 2 and Figure 4 are of the same area.

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Step-by-step explanation:

the ratio is 25/50 (25 kg in 50 minutes).

as a ratio is basically a fraction (just with a special meaning), we can simplify it as a "normal" fraction :

25/50 = 1/2

in other words, the hippo can eat 1 kg in 2 minutes.

now the answer to the question is easy :

how many minutes to eat 60 kg ?

remember, when we multiply one part of the fraction by a factor, we need to multiply the other post by the same factor to keep the overall value.

so, 60 kg = 60×1 kg

we multiply the numerator by 60, therefore, we need to multiply the denominator by 60 too. and we get

1/2 × 60/60 = 60/120

it takes the hippo 120 minutes to eat 60 kg.

Answer:The steps in solving the quadratic function 7x – 9 = 7x^2 – 49x by completing the square are as follows:

Add and subtract (49/2)^2 = (36) to the right-hand side of the equation to complete the square. This gives us:

7x - 9 = 7x^2 - 49x + 36

Factor out the coefficient of the x^2 term, which is 7, on the right-hand side of the equation. This gives us:

7x - 9 = 7(x^2 - 7x + 6)

Take the square root of the number inside the parenthesis and add and subtract it, to get:

7x - 9 = 7(x - 3.5)^2 - 2.25

Now we can add 9 to both sides of the equation to get:

7x = 7(x - 3.5)^2 + 0.75

Now we can divide both sides by 7 to get:

x = (x - 3.5)^2 + 0.75/7

Now we can solve the equation by taking the square root of both sides and adding and subtracting 3.5 to get:

x = 3.5 ± √(x^2 - 7x + 6)

Now we have our solutions, x = 3.5 + √(x^2 - 7x + 6) and x = 3.5 - √(x^2 - 7x + 6) which are the solutions of the quadratic equation.

Step-by-step explanation:

Answer:

56, 112, 16

Step-by-step explanation:

I just know

The difference between the largest 7-digit and the smallest 8-digit number is 1.

The aim is to find the largest 5-digit and the smallest 8-digit numbers, and then we need to determine the difference between these two values.

Let's start by finding the smallest 8-digit number.

We know that 0 is the smallest digit that can not be used in the highest place value, so we will consider the next smallest digit, 1; therefore, it can be used in the highest place value.

Thus, we can create the required 8-digit smallest number with 0 and 1.

Hence, the smallest 8-digit number is 10000000.

Now, we will discover the largest 7-digit number.

As we know, the largest digit is 9, which can be used anywhere. So, we will form the largest 7-digit number with the digit 9.

Thus, the largest 7-digit number is 9999999.

Now, find the difference between these two values.

So, we can determine the difference between the smallest 8-digit number and the largest 7-digit number by subtracting the smallest from the largest.

Thus, we get,

⇒10000000 - 9999999

⇒1

Hence, 1 is the difference between the smallest 8-digit and the largest 7-digit numbers.

--The given question is incomplete; the complete question is

"What is the difference between the largest 7-digit number and the smallest 8-digit number?"--

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On Solving we get that the zero of the polynomial "3x -9" is x = 3 .

The polynomial function is a type of function which involves only non negative integer powers or involves only positive integer exponents of a variable in an equation .

the polynomial function is given as : 3x-9 ;

to find the zeros of the polynomial we equate the given polynomial to zero(0) .

we get ; 3x - 9 = 0 ;

⇒ 3x = 9 ;

dividing both sides by 3 ,

we get ;

⇒ x = 3 .

Therefore , the zero is x = 3 .

The given question is incomplete , the complete question is

What is the zero of the polynomial "3x - 9" ?

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Answer:

Complementary Angles, Supplementary Angles, Adjacent Angles, Linear Pair, and vertical Angles.

Step-by-step explanation:

C is calculated from solving simultaneous equation generated, the value of C is equal to 10

The information from the problem helps to derive the equations which are solved simultaneously to get A and B then substituted to solve for C

A + A + B = 17and A + B + B = 13 are the given equations

2A + B = 17

A + 2B = 13

solving with calculator will result to

A = 7 and B = 3

substitution to solve for C

and C = A + B

C = 7 + 3

C = 10

hence c is equal to 10

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To prove that if KB = (p ⇒ q)∧(r∨s)∧(¬p)∧(¬ ⇒ ¬t)∧(¬q∨t)∧(¬p∧r ⇒ u)∧(w∨t), then KB |= (u ∧ w) using resolution, we can start by assuming the negation of the conclusion, (¬u ∨ ¬w)

Then use the resolution to derive the empty clause, which would mean that our assumption is false and therefore the conclusion is true.

Here is one possible sequence of resolution steps:

step 1: Assume ¬u

step 2: ¬p∧r ⇒ u (from KB)

step 3: ¬p∧r (by resolution with step 2)

step 4: ¬p (from KB)

step 5: r (by resolution with step 3)

step 6: ¬q∨t (from KB)

step 7: t (by resolution with step 5)

step 8: ¬ ⇒ ¬t (from KB)

step 9: (by resolution with step 7)

step 10: p ⇒ q (from KB)

step 11: q (by resolution with step 9)

step 12: ¬q∨t (by resolution with step 6)

step 13: t (by resolution with step 7)

step 14: w∨t (from KB)

step 15: w (by resolution with step 13)

step 16: ¬u ∨ w (by resolution with steps 1 and 15)

step 17: (by resolution with steps 10 and 16)

Since we have derived the empty clause, our assumption (¬u ∨ ¬w) is false, and we have proven that KB |= (u ∧ w) by resolution.

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The measure of ∢1 is 40 degrees.

What is the measure of angle?

The measure of an angle is a numerical value that represents the amount of rotation of one ray around a common endpoint, called the vertex, compared to another ray. The measure of an angle is usually measured in degrees (°).

The measure of an angle can be found by using the following formula:

Measure of ∢1 = 180 - (measure of ∢2 + measure of ∢3)

In this case, we are given the measures of ∢2 and ∢3:

∢2 = 102 degrees

∢3 = 38 degrees

So, we can substitute these values into the formula:

Measure of ∢1 = 180 - (102 + 38) = 180 - 140 = 40 degrees

Therefore, the measure of ∢1 is 40 degrees.

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A positive and negative angle that are coterminal to angle 2π / 7 are 16π / 7 and - 12π / 7, respectively.

Two consecutive angles are coterminal if and only if the difference between their measures equals 2π radians. Given an angle θ, then the family of coterminal angles can be derived from following equation:

θ' = θ + 2π · i, where i is an integer.

Where θ' is a coterminal angle, in radians.

First, determine a positive coterminal angle: (i = 1)

θ' = 2π / 7 + 2π

θ' = 16π / 7

Second, determine a negative co-terminal angle: (i = - 1)

θ' = 2π / 7 - 2π

θ' = - 12π / 7

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Answer: 900

Step-by-step explanation:

Add 150 + 250 + 50 = 450 .

After 450 * 2 = 900

The fraction of the fruit that Kri that is   [tex]\frac{3}{32}[/tex]. To find the fraction, you have to determine the value of the total data.

As per data given are banana = 10 and apple = 22. We will determine the fraction that Kri take by sum up the fruit and then determine the fraction where the maths as follow:

Total fruit = banana + apple

Total fruit = 10 + 22

Total fruit = 32

Then find Kri fraction as follow

Kri fraction = Kri fruit : total fruit

Kri fraction = 3 : 32 = [tex]\frac{3}{32}[/tex]

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The average cost of the given question is $115.11.

Average Cost:

The average cost is the total cost of goods divided by the number of units produced or sold. It is used to determine the cost of each unit produced or sold. Without more information about your costs and the number of products you have produced or sold, it is not possible to determine the average cost.

To calculate the average cost of the product, you will need to subtract the gross margin percentage from 100% and then divide the result into the selling price.

First, convert the gross margin percentage to a decimal: 3% = 0.03

Then, subtract the gross margin from 1: 1 - 0.03 = 0.97

Finally, divide the selling price by the result: 111.55 / 0.97 = 115.11

So your average cost is $115.11

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Always insert the x-coordinate first before the y-coordinate.

A coordinate system in geometry is a method for determining the precise location of points or other geometrical objects on a manifold, such as Euclidean space, using one or more integers, or coordinates. The spherical, cylindrical, and cartesian coordinate systems are the three most used ones. Both a cylinder-based coordinate system and a cartesian one will be examined in this chapter. Both horizontal and vertical coordinate systems are used to describe data. Vertical coordinate systems find data's relative height or depth, whereas horizontal coordinate systems locate data over the surface of the globe.

However, you can opt to trace your point in any co-ordinate as per the plot data. But the usual sequence is 1, 2, 3, 4 quadrant and x, y plane respectively.

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Answer: 41

Step-by-step explanation: please someone tell me is 49 or 48 because I think. It looks like 48.

90 - 48 = 41

The ladder will now reach 21.7 ft.

Geometry is a branch of mathematics that deals with shapes, sizes, angles, and dimensions of objects.

Given is that a 45-foot ladder is placed against the side of a house so that it reaches 27 feet in height. Cooper grabs the ladder by its base and pulls it 4 feet farther away from the house.

Refer to the image attached. We can write in ΔCEB as -

EB² = 45² - 27²

EB² = (45 + 27)(45 - 27)

EB² = 72 X 18

EB² = 1296

EB = √1296

EB = 36 ft

Now -

AB = AE + EB = 36 + 4 = 40

From ΔDAB, we can write -

BD² = 45² - 40²

BD² = (45 + 40)(45 - 40)

BD² = 95 X 5

BD² = 475

BD = 21.7 ft

Therefore, the ladder will now reach 21.7 ft.

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In maths, equivalent is different from equality. The same means the same in all respects, but equivalent means similar but not identical.

Equivalent generally refers to two numbers, terms, or expressions that have the same value. There are many ways to express equivalent quantities.

Equivalent formulas : Two formulas are said to be equivalent if they give the same result when solved. For example, suppose the number 2 is equivalent to 1 + 1.

Equivalent Fractions: Two fractions are equivalent if they represent the same value, proportion, or amount. Equivalent fractions are present with different numerators and denominators. Example: 2/5 = 4/10 = 6/15.

Equivalence ratio: An equivalence ratio is a ratio that can express a similarity between numbers or values. They are similar in proportion and have the same value. For example, 1:3 and 2:6 are equivalent ratios.

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The substitution which should be made to rewrite given equation  4x⁴ + 21x² + 20 = 0 as a quadratic equation is U = x² .

The Quadratic Equations are the type of polynomial equations which has the highest degree of 2 ,

The quadratic equations are algebraic equation of the second degree in the variable x .

given equation is ⇒ 4x⁴ + 21x² + 20 = 0 ;

we have to make this equation as a quadratic equation ,

So , we substitute , U as x² in given equation ,

we get ;

⇒ 4(x²)² + 21x² + 20 = 0 ;

⇒ 4(U)² + 21U + 20 = 0  ;

the equation becomes as  ⇒ 4U² + 21U + 20 = 0  , which is a quadratic .

Therefore , the substitution of U = x² , should be used .

The given question is incomplete , the complete question is

What substitution should be used to rewrite  4x⁴ + 21x² + 20 = 0 as a quadratic equation ?

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When Richter scale magnitude is less 3. 0 to 3. 9, the frequency of occurrence in the whole world will be over 100,000 per year.

The Richter magnitude of an earthquake is determined from the logarithm of the amplitude of waves recorded by seismographs (adjustments are included to compensate for the change in distance between different seismographs and the epicenter of the earthquake). The original formula is: [tex]Mₗ = log_{10}(A) - log_{10}(A₀ ) = log_{10}( \frac{A}{ A₀}) \\ [/tex]. The classification starts with "small" for magnitudes between 3.0 and 3.9, where earthquakes generally begin to be felt, and ends with "major" for magnitudes greater than 8.0, where significant damage is expected. The National Earthquake Information Center now locates about 20,000 earthquakes worldwide each year, or about 55 per day.

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Answer:
1. y = 1/4x-1 or y = 0.25x-1

Step-by-step explanation: Hello! You can do this by using the slope-intercept equation.  The slope-intercept formula is y = mx+b.  You have the x and y coordinates already, which is all you need to solve the equation.  m = slope, b = y-coordinate in the formula y = mx+b.  The first thing you have to do is find the slope.  To find the slope, use the formula (y2 - y1)/(x2-x1).  The y-coordinates are the second numbers in the coordinate pairs, and the x-coordinates are the first numbers in the coordinate pairs.  Put the information in the formula.  You now have: (0 - (-2))/(4 - (-4)).  Two negatives make a positive, so you can simplify this equation by writing (0 + 2)/(4 + 4).  Add both equations.  You now have 2/8.  You can simplify this even more by dividing the numerator and denominator by 2.  2/8 divided by 2/2 = 1/4.  You now know the slope is 1/4.  

The next thing you have to do is use the point-slope formula.  The point-slope formula is y - y1 = m(x - x1).  m = slope, so put the slope you know (1/4) in the equation.  y - y1 = 1/4(x - x1).  You also know that y1 = -2 and x1 = -4 from the given coordinate pairs.  Fill this information in.  
y - (-2) = 1/4(x - (-4)).  Two negatives make a positive, so you can simplify this into: y + 2 = 1/4(x + 4).  Distribute 1/4 to x and -4.  1/4 x x = 1/4x, and 1/4 x 4 = 1.  You now have y + 2 = 1/4x + 1.  Subtract 2 from both sides.  y + 2 - 2 = 1/4x + 1 - 2. You now have y = 1/4x-1.  This is in the format y = mx+b, which is what you are supposed to do.  The answer for question 1. is y = 1/4x-1.  Hope this helps you with the rest of the problems! If you still need help after this, I can teach you how to do the second question as well.

The triangles ΔUVW are ΔUKL discovered to be similar by AA Similarity theorem.

Similar triangles are defined as triangles that have the same shape, but then their sizes may differ. Thus, if two triangles are said to be similar, then it means that their corresponding angles are congruent and  also their corresponding sides are in equal proportion

There are three triangle similarity theorems, namely; Angle-Angle (AA), Side-Angle-Side (SAS) or Side-Side-Side (SSS).

Now, looking at the given image, we see that ∠UVW ≅ ∠UKL because they are both corresponding angles.

Similarly, we can say that ∠UWV ≅ ∠ULK because they are corresponding angles.

Thus, ΔUVW is similar to ΔUKL by AA similarity theorem.

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The greater than sign is '>' . If one value is greater than the other, use greater than. For example, 8 is greater than 7. Therefore, we can write greater than 7 is x >7.

Greater than symbol:

In mathematics, the greater than sign is placed between two values ​​where the first number is greater than the second number. For example, 10 > 5. Here 10 is greater than 5. For inequalities, the greater-than sign always refers to the greater value, and the sign consists of two equal length dashes joined at an acute angle on the right.

As we know math problems don't always end evenly. We may need to include inequalities such as greater than and less than signs. Statements can be expressed as mathematical expressions.

Example: 'x' is the number of students in the class. If she has more than 45 students in her class, and she has 5 students join her class again, then she has more than 50 students in her class. This statement is expressed mathematically as x + 5 > 45. fish . Crocodiles always want to eat more fish, so they can eat more fish, regardless of how many mouths they have open.

One of the best ways to remember the "greater than" and "less than" signs is to think of them as little alligators (or crocodiles). The numbers on either side represent the number of fish. Crocodiles always want to eat more fish, so they can eat more fish, regardless of how many mouths they have open.

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The shortest side of the right-angle triangle is its base therefore the shortest side is XY.

There are various different kinds of triangles that exists for example there is an isosceles triangle, right angle triangle equilateral triangle acute angle triangle, obtuse angle triangle hey and many more many. So in a right angle triangle the size of each side is different. As we know that the side opposite to the right angle is known as hypotenuse which is the longest side of the rightangle triangle and the adjacent side the hypotenuse is called base which is the shortest side of a right-angle triangle XYZ.

Also the sum of all the interior angles of a triangle should be equal to 180 degrees.

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Answer: D , Y + 4 = 2/3 (x-5)

Step-by-step explanation: Since the equation has to be parallel, both equations need to have the same slope; in this case it is 2/3. Then, you can plug in the point into the equations to ascertain if it’s a true statement or a false statement.

Answer:

$0.40

Step-by-step explanation:

4% = 0.04

10 times 0.04 = $0.40

So, sale tax is $0.40

The mirror image of (3,2) in X-axis => (-3,-2), Y-axis => (3,-2).

The term mirror image of the point is a reflected duplication that appears identical but in reverse.

Here we have given points (3,2).

And we have to find the mirror image of this point with respect to the y-axis that is the mirror image is a point whose distance is the same from the origin O (0, 0) and the same from both axes as of the point (3,2).

As we all know that (3,2) lies on the first quadrant, then the mirror image with respect to the y-axis must lie on the second quadrant.

And we all also know that In the second quadrant, here the x-coordinate of any point (x, y) is negative.

Therefore, while we looking into the given graph we have identified that the mirror image is (-2, 3).

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