The Imaginary part is [tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]
What is complex number?A complex number can be represented in the form a + bi, where a and b are real numbers. A complex number is a part of a number system that extends the real numbers by adding an element designated by the symbol.Mathematical Complex Numbers. Complex numbers are those expressed as a+ib, where a, b are real numbers and I is a fictitious number called a "iota." I is equal to (-1). A complex number is, for instance, 2+3i, where 2 is a real number (Re) and 3i is an imaginary number (Im).Real and imaginary components are combined to form complex numbers, which have two elements. The foundation of more complex mathematics, like algebra, are complex numbers. They are applicable to a wide range of real-world situations, particularly in the fields of electronics and electromagnetism.[tex]& \frac{5+2 i}{-1+\sqrt{3} i} \times \frac{-1-\sqrt{3} i}{-1-\sqrt{3} i} \\[/tex]
[tex]& =\frac{-5-5 \sqrt{3} i-2 i+2 \sqrt{3}}{4} \\[/tex]
[tex]& =\frac{-5+2 \sqrt{3}}{4}+i\left(\frac{-5 \sqrt{3}-2}{4}\right) \\[/tex]
Imaginary part
[tex]& \frac{-5 \sqrt{3}-2}{4}[/tex]
The complete question is,
Find the imaginary part of 5+2i/-1+√3i
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The complex number -i5 has -i5 as its imaginary component.
What is the imaginary part in given terms?The given complex number is -i√5, which can be written as:-i√5 = 0 - i√5The imaginary part of the complex number is -i√5.Here's a step-by-step explanation:A complex number having the real part and the imaginary part.The real part is the coefficient of the real unit (i.e., 1), while the imaginary part is the coefficient of the imaginary unit (i.e., i).In this case, the given complex number is -i√5.We can write this as 0 - i√5, where 0 is the real part and -i√5 is the imaginary part.Therefore, the imaginary part of the complex number -i√5 is -i√5.
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The following equation has an error in one of the operations.
2(x−4y)+3y=2x+11y
Which answer would correct the error?
1. Change 2(x−4y)+3y to 2(x+4y)−3y.
2. Change (x−4y) to (x+4y).
3. Change 2x+11y to 2x−11y.
4. Change 2(x−4y)+3y to 2(x−4y)−3y.
answer is 2 because if we expand the bracket we get 2x–8y+3y which is 2x–5y but if it was 2(x+4y) it would be equal to 2x+8y+3y therefore being 2x+11y
Describe the error in finding the perimeter of the figure. And find the perimeter
Answer:
The length of 5 inches should be counted 1 time.
Step-by-step explanation:
The 5 inches between the triangle and rectangle is inside the shape. So, it doesn't count as perimeter.
What is the Interquartile range of 41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75,97
Answer:
Step-by-step explanation
Sort the data: 41, 41, 43, 43, 45, 50, 52, 53, 54, 62, 63, 63, 67, 75, 97
Find the median (Q2): 53
Split the data set into two parts: Q1 (25th percentile) and Q3 (75th percentile)
Q1: 41, 41, 43, 43, 45, 50, 52, 53
Q3: 54, 62, 63, 63, 67, 75, 97
Find the median (Q1) of Q1 and the median (Q3) of Q3:
Q1 = 45
Q3 = 63
Finally, calculate the IQR by subtracting Q1 from Q3:
IQR = Q3 - Q1 = 63 - 45 = 18
So, the interquartile range of the given data set is 18. This means that 50% of the data falls within a range of 45 + 18 = 63 and 45 - 18 = 27.
PLEASE HURRY This figure consists of a rectangle and semicircle.
What is the area of this figure?
Use 3.14 for π.
Enter your answer as a decimal in the box.
(Image: A shape made up of a rectangle and a semicircle, with the semicircle on top of the rectangle. The rectangle has a width of 6 centimeters and a height of 4 centimeters.)
cm²
A shape made up of a rectangle and a semicircle, with the semicircle on top of the rectangle. The rectangle has a width of 6 centimeters and a height of 4 centimeters.
The area for this figure is given as follows:
38.13 cm².
How to obtain the area of the figure?The composite area of the figure is obtained by the sum of the areas of each component of the figure.
The figure is composed as follows:
Rectangle of width 6 centimeters and height of 4 centimeters.Semi-circle of diameter = 6 centimeters = radius of 3 centimers.The area of the rectangle is given by the multiplication of the dimensions, hence:
Ar = 6 x 4 = 24 cm².
The area of the semicircle is given by half the multiplication of π = 3.14 by the radius square, hence:
As = 0.5 x 3.14 x 3² = 14.13 cm².
Hence the total area is given as follows:
A = Ar + As
A = 24 + 14.13
A = 38.13 cm².
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I need this for math homework anyone on tonight to help? 5/8 = x/12 x=
x = 15/2
do u need an explanation?
original pice $65.00 with a 10% discount
Answer: 58.5
Step-by-step explanation: 65.00 - 10% = 58.5
Answer: $58.50
Step-by-step explanation: Orignal Price: $65.00
10% discount = -$6.50
$65.00 - $6.50 = $58.50.
What is the difference in rainfall from the wettest and driest months ?
The difference in rainfall between the wettest and driest months is the amount of precipitation.
What do you mean by precipitation?Precipitation refers to any form of moisture that falls from the atmosphere to the ground, including rain, snow, sleet, hail, and other forms of precipitation. Precipitation is an important aspect of the Earth's water cycle, as it provides the water that replenishes rivers, lakes, and aquifers, and sustains the growth of plants and animals.
The amount of precipitation that falls in a given area can vary widely, depending on many factors such as geography, temperature, and prevailing weather patterns. For example, areas near the equator tend to receive more rainfall than areas located closer to the poles, and areas with high elevations tend to receive more snow than areas that are closer to sea level.
The distribution of rainfall and other forms of precipitation across a region can also be affected by the prevailing winds, air masses, and topographical features. For example, mountainous areas may receive more rainfall due to the prevailing winds and the way that air masses interact with the terrain.
The difference in rainfall between the wettest and driest months is the amount of precipitation that occurs in the wettest month minus the amount of precipitation that occurs in the driest month. This difference can vary greatly depending on the location and climate of a region.
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Find the area of the rectangle
The area of the given rectangle will be A = 9x² - 64 yards².
What is a rectangle?
Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. Various definitions include an equiangular quadrilateral, A closed, four-sided rectangle is a two-dimensional shape. A rectangle's opposite sides are equal and parallel to one another, and all of its angles are exactly 90 degrees.
The area of the rectangle is A = a*b
Given is l =(3x+8) yards
b = (3x-8)yards
So the area of the rectangle is A = l*b
A = (3x+8)(3x-8)
A = 3x² - 8²
A = 9x² - 64
hence the area of the given rectangle will be A = 9x² - 64 yards².
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True or False
In a regular convex polygon all sides and angles are congruent and you can only draw diagonals inside the polygon.
I need help ASAP!!!!!
Answer:
Nope
Step-by-step explanation:
No, because if you add the angles of B and C (since they're asking for line BC), they must equal the angles of A and D (Since the other line was AD)
The sum of B and C is 90+45 which = 135
The sum of A and D is 90+135 which = 225
135 =/= 225
factor completely 6ax-15x
Factorization of 6ax - 15x is 3x.(2a - 5)
What is expression?Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.
Given expression,
6ax - 15x
It can be written as
3×2 . a . x - 3×5 . x
Factoring out common factor
3x.(2a - 5)
Hence, 3x.(2a - 5) is the factorization of 6ax - 15x.
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i need help with this question
The exponential function from the table is f(x) = 2 [tex](0.5)^x[/tex].
The graph is given below.
Option D is the correct answer.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
The exponential function is given as,
f(x) = m[tex]a^x[/tex]
Now,
From the table,
2 = m[tex]a^0[/tex]
m = 2
1 = m[tex]a^1[/tex]
m = 1/a ____(1)
0.5 = m[tex]a^2[/tex]
m = 0.5/[tex]a^2[/tex] _____(2)
Now,
From (1) and (2).
1/a = 0.5/[tex]a^2[/tex]
a = 0.5
Now,
f(x) = 2 [tex](0.5)^x[/tex]
Thus,
The exponential function is f(x) = 2 [tex](0.5)^x[/tex].
The graph is given below.
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Which of the following pairs of numbers results in a product that is irrational? Choose a, b, c or d.
The result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.
What are irrational numbers?A real number that cannot be stated as a ratio of integers is said to be irrational; an example of this is the number √2. Any irrational number, such as p/q, where p and q are integers, q≠0, cannot be expressed as a ratio. Once more, an irrational number's decimal expansion is neither ending nor recurrent.
1. The product of the numbers are:
a. √2 (√8) = √16 = 4
b. √49 (∛ 8) = 14
c. √3 (2/ √3) = 2
d. √2(4)
Option d is the correct answer.
Similarly, taking the product:
2. Option a is correct.
3. Option d is correct.
4. Option b is correct.
Hence, the result of the product for the following pairs of number is irrational for 1. Option d √2(4). 2. Option a. 3. Option d. 4. Option b.
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What are the intercept(s) of f(x) = x2?
Answer:
x intercept: (0,0)
Step-by-step explanation:
y intercept: (0,0)
A pyramid is composed of six isosceles triangles and a hexagonal base. Each isosceles triangle has a height of 6 in. and a base of 10 in. The area of the hexagonal base is 259.8 in².
What is the surface area of the pyramid?
Enter your answer in the box.
in²
The surface area of the pyramid, given the height and base of the triangles, and the area of the hexagonal base, is 439. 8 square inches
How to find the surface area ?Let's determine the area of the six isosceles triangles using the formula;
= 6 x 1 /2 x base x height
= 6 x 1 / 2 x 10 x 6
= 180 square inches
The surface area of the pyramid is therefore;
= Area of triangles + Area of hexagonal base
= 180square inches + 259.8 square inches.
Add the values, we get;
= 439. 8 square inches
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Answer: 439.8
Step-by-step explanation:
2. What is the difference in rainfall from the wettest and driest months?
The difference in rainfall between the wettest and driest months is 3.97 inches.
What is a bar graph?A bar graph is a graphical depiction of information, amounts, or numbers using bars or strips. They are utilized to contrast and compare various data types, frequencies, or other measurements of several categories of data.
On the graph, there are two axes. The numerical data is displayed against the category data on one axis, which is used to depict the numerical values.
Given the graph which shows the rainfall of the wettest and driest months,
here red blocks are for the driest months and blue blocks show the wettest months,
From the graph, we can see that the wettest month has a rainfall height of 2.3 inches
The driest month has a rainfall of -1.67 inches
So the difference between the two will be;
2.3 - (-1.67)
= 2.3 + 1.67 = 3.97 inches
Hence the difference is 3.97 inches.
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The complete question is,
The bar graph shows the differences in a city’s rainfall from the historical average. What is the difference in rainfall between the wettest and the driest months? Write your answer as a decimal.
The difference in rainfall between the wettest and the driest months is inches.
If the car climbs 60 m vertically how far must the car have travelled horizontally?
The the gradient of the slope is 2/15
The horizontal distance which the car must have travelled is equal to 450 meters.
How to calculate the horizontal distance?Mathematically, the gradient (slope) of a geometric figure or line can be calculated by using this formula:
Pitch (slope) = V/H
Where:
V represents the rising vertical distance of an object.H represents the horizontal distance an object runs through.Based on the given image, we have the following distances and gradient (slope):
Rising vertical distance = 60
Horizontal distance (Run) = x
Gradient (slope) = 2/15
Substituting the given parameters into the formula, we have;
2/15 = 60/x
2x = 900
x = 450
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Find the surface area of the sphere. Use 3.14 for pi.
A. 1519.8 yd2
B. 276.3 yd2
C. 6079.0 yd2
D. 552.6 yd2
Answer:
A
Step-by-step explanation:
please memorize this formula for area of sphere
A=4π r²
so d = 22, which means r=11
so A = 4* π*11² = 4*121*π =484π = 1519.76
Double question, double points!
The potential energy increases as the charges or the poles get further apart.
Static charges does not build up by polarization.
What is a field force?A field force is a force that acts on a particle without physical contact. It arises from the presence of a field, such as an electric field, magnetic field, or gravitational field.
The field exerts a force on a particle based on its charge, mass, or other property, and the strength of the force is determined by the field intensity and the properties of the particle. For example, an electric field exerts a force on a charged particle, while a gravitational field exerts a force on a mass.
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please help me. {adding this so i am allowed to post this question.
Answer:
The base is 8 and the height is 3. Multiply.
8 * 3 = 24
You will then multiply your product by 1/2.
24 * 1/2 = 12
The area is 12 inches squared.
Step-by-step explanation:
Hope it helps! =D
Answer:
[tex] {12cm}^{2} [/tex]
Step-by-step explanation:
Given
[tex]a = \frac{1}{2} bh[/tex]
b= 8in
h= 3in
8x3 = 24
24 ÷ 2 (Same as multiplying by half)
Explain what AB means and what AB/ means. How are these two meanings related?''
AB vector is a vector whereas AB bar is a line segment.
What is a vector ?
The vectors are described as an object containing both significance and course. Vector describes the motion of an item from one point to any other. Vector math may be geometrically picturised via the directed line segment.
The duration of the phase of the directed line is known as the value of a vector and the angle at which the vector is inclined shows the path of the vector. The start line of a vector is referred to as “Tail” and the finishing factor (having an arrow) is referred to as “Head.”
The difference is in their names itself.
AB vector is a vector whereas AB bar is a line segment.
A vector has a direction and a magnitude while a line segment ( scalar ) has only magnitude.
Therefore, AB vector is a vector whereas AB bar is a line segment.
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Which angle measures 40 i-Ready
Answer:
<YTZ
Step-by-step explanation:
Vertical angles are congruent.
<VTW measures 40°.
<YTZ is vertical to angle VTW.
m<YTZ = m<VTW
m<YTZ = 40°
Answer: <YTZ
Cincinnati’s budget is $1,130,000,000 and it’s population is 302,605. How many dollars per person are provided by the budget?
Answer:
3734.24100725
Step-by-step explanation:
This is related for all problems like this, not just this one:
When you see the key words below, this is what it means, and you can craft an equation from it:
Per = division
Of = multiplication
Using this above, we can replace the words with an equation:
The question is asking the amount of money per person.
Remember above, per means division:
Money/person
We know the amount of money and the number of people, so let's plug it in:
1,130,000,000/302,605
After division:
3734.24100725, final answer.
Hope this helps :D
Can yall help me pls i really need it
Kevin's solution is incorrect. He found the area of the triangle as [tex]bh[/tex], not [tex]\frac{1}{2}bh[/tex].
The correct area of the triangle is [tex]\frac{1}{2}(8)(5)=20 \text{ in}^2[/tex].
How much is invested at 5% and 7%, with annual interest is $490, with a total of $8000
The amount invensted at 5% and 7% are 3500 and 4500 respectively.
What is a system of equations?A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.
Given that, an amount $8000, is invested at 5% and 7%, with annual interest is $490,
For this we will establish the a system of equations,
x + y = 8000......(i)
0.05x + 0.07y = 490
Multiplying by 100,
5x + 7y = 49000.....(ii)
Multiplying eq(i) by 5,
5x + 5y = 40000
Subtract eq(i) from eq(ii)
2y = 9000
y = 4500
Put y = 4500 in eq(i)
x = 8000 - 4500
x = 3500
Hence, the amount invensted at 5% and 7% are 3500 and 4500 respectively.
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A roller coaster car rapidly picks up speed as it rolls down a slope. As it starts
down the slope, its speed is 4 m/s. 3 seconds later, at the bottom of the slope,
its speed is 22 m/s. What is the cars acceleration?
calculate the length of AC to 1 decvimL POINT
Answer:The length of AC to one decimal place in the trapezium is 18.1 cm
Step-by-step explanation: Using Pythagoras theorem, we can find the length AC
Pythagoras theorem
c² = a² + b²
Therefore, draw a line from the point B to the line AD and call it line BX.
BX ║ CD
Therefore,
16² - 7² = BX²
256 - 49 = BX²
BX² = 207
BX = √207
BX = 14.3874945699
BX = 14.4 cm
Therefore,
11² + 14.4² = AC²
121 + 207.36 = AC²
AC = √328.36
AC = 18.120706388
AC = 18.1 cm
Which graph shows a proportional relationship that passes through the point (2, 1)?
The required graph of the equation is given by y=x/2
What are linear equations?Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from the basics such as the addition and subtraction of algebraic expressions.
Given here: A graph proportional to the line that passes through the point.
Now one of the graph has the equation y= x/2
we can treat this line as some proportional equation with 1/2 as the constant.
And it also passes through the point (2,1)
Hence, The required graph of the equation is given by y=x/2
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The options containing the graph are attached
What is the value of x in the triangle?
Answer: D. [tex]5\sqrt{3}[/tex]
Step-by-step explanation:
[tex]\tan 30^{\circ}=\frac{x}{15}\\\\x=15 \tan 30^{\circ}\\\\x=5\sqrt{3}[/tex]
Solve the inequality: −5x−4≤6
x > -2
Step-by-step explanation:Inequalities compare the values of 2 expressions.
Solving for x
To solve the inequality, we need to isolate x. First, add 4 to both sides.
-5x ≤ 10Then, divide by 5.
-x ≤ 2Finally, divide both sides by -1. When multiplying or dividing an inequality by a negative, switch the direction of the sign.
x > -2Interpreting the Answer
Verbally, the answer is that x is greater than or equal to -2. This means that any x-value greater than -2 (including -2 itself) will make the original inequality, −5x−4 ≤ 6, true. For example, let's plug in 0.
-5(0) - 4 ≤6-4 ≤ 6This statement is true, which proves our answer is correct.