y = (1/3)x - 2 is an equation of a line where the slope of the line is 1/3 and the y-intercept of the line is -2.
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
y = (1/3)x - 2
This is in the form of y = m + c
So,
This is an equation of a line.
The slope of the line = 1/3
The y-intercept of the line is -2.
Thus,
y = (1/3)x - 2 is an equation of a line.
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What is a 45 degree triangle called?.
A 45-degree triangle is called a right-angle triangle.
A 45-degree angle is exactly half of a 90-degree angle formed between two rays.
It is equal to half of a straight angle or a 90-degree angle. An angle bisector of a 90-degree angle creates two equal 45-degree angles. The 45-degree angle can be found in many everyday objects, such as scissors, doors, and windows. It is also known as the angle created by a square's diagonal and its sides.
It is an acute angle and two angles measuring 45 degrees form a right angle or a 90-degree angle. We know that an angle is formed when two rays meet at a vertex.
Thus, A 45-degree triangle is called a right-angle triangle.
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Which relation is a function?
Responses
{(1, 2), (2, 3), (3, 4), (4, 5)}
{(1, 2), (3, 4), (5, 6), (1, 8)}
{(1, 2), (2, 1), (1, 3), (3, 1)}
{(0, 2), (0, 4), (0, 6), (0, 8)}
The relation that is a function is
{(1, 2), (2, 3), (3, 4), (4, 5)}
Option A 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,
A function can have different inputs but the same output.
i.e many to one.
But a function can not same input and different output.
i.e one to many.
Now,
{(1, 2), (2, 3), (3, 4), (4, 5)}
This is a function because each input has a different output.
This is a one-to-one function.
{(1, 2), (3, 4), (5, 6), (1, 8)}
This is not a function because 1 has different outputs 2 and 8.
{(1, 2), (2, 1), (1, 3), (3, 1)}
This is not a function because 1 has different outputs 2 and 3.
{(0, 2), (0, 4), (0, 6), (0, 8)
This is not a function because 0 has different outputs 2, 4, 6, and 8.
Thus,
{(1, 2), (2, 3), (3, 4), (4, 5)} is a function.
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Can someone help me with this please?
Pleas show steps.
Solving the system of equations:
x + y = 45
y = 2x
We can see that he made a total of 30 hot dogs and 15 hamburgers.
How to write and solve the system of equations?We can define the variables:
x = number of hamburgersy = number of hot dogs.We know that he cooked a total of 45 dishes, then we can write the equation
x + y = 45
And he cooked twice as many hot dogs as hamburgers, then we can write:
y = 2x
Then we can write a system of equations at:
x + y = 45
y = 2x
We can replace the second equation into the first one, then we have:
x + (2x) = 45
3x = 45
x = 45/3
x = 15
And the solution of y is:
y = 2x
y = 2*15 = 30
The solution of the system is:
x = 15
y = 30
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There are 14 dogs at the dog park on a busy Saturday. 2 of them are springer spaniels.
What is the probability that a randomly selected dog is a springer spaniel?
Write your answer as a fraction or whole number.
Answer:1/7
Step-by-step explanation: You take the amount that are springer spaniels and you put them with the whole of the dogs in the park 14 so you would have 2/14. You can reduce this fraction to 1/7 by dividing both the top and bottom of the fraction by 2.
tangent lines help (15 pts)
The required perimeter of the polygon is 92 cm.
What is a polygon?Polygon is defined as a geometric shape that is composed of 3 or more sides these sides are equal in length, and an equal measure of angle at the vertex,
Examples of polygons, equilateral triangles, squares, pentagons etc
here,
∠B ≅ ∠C
tangent drawn from D = tangent drawn from B
tangent drawn from D = 11.5 cm
The perimeter of the polygon is given = as the sum of a tangent from all points
= 11.5 + 11.5 + 11.5 + 11.5 + 10.5 + 10.5 + 12.5 + 12.5
= 92 cm
Thus, the required perimeter of the polygon is 92 cm.
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you want to sell 1/lb jars of mixed peanuts and cashews for five dollars . you paid three dollars per pound for peanuts and six dollars per pound of cashews . you plan to combine four parts peanuts and one part cashews to make your mix . you have spent $70 on materials to get started . how many jars must you sell to break even ?
Answer:
To calculate the number of jars you need to sell to break even, we can use the following formula:
(Cost of materials + Cost of ingredients per jar) / Price per jar = Number of jars needed to break even
We know that the cost of materials is $70, the cost of ingredients per jar is $18 ( $12 for peanuts + $6 for cashews) and the price per jar is $5.
Plugging in these values into the formula we get:
($70 + $18) / $5 = (88/5) = 17.6 jars
So, you need to sell at least 17.6 jars to break even.
--------------------
Cost of materials / (Price per jar - Cost of ingredients per jar) = Number of jars needed to break even
We know that the cost of materials is $70, the cost of ingredients per jar is $18 ( $12 for peanuts + $6 for cashews) and the price per jar is $5.
Plugging in these values into the formula we get:
$70 / ($5 - $18) = 70 / -13 = -5.38 jars
It is not possible to sell -5.38 jars, which means you are making a loss. This indicates that your cost of materials and ingredients is higher than the price you are selling the jars for. To break even, you will have to lower your costs or increase the price of the jars.
Mihka i on a long road trip, and he average 65 mph for 3 hour while he' driving on the highway. While he' driving on ide road for 1 hour, he only average 45 mph. What i the total ditance that he cover on her road
trip?
Mishka travels 230 kilometres in total on her road trip.
Mishka travels at a 65 km/hr average speed on the highway.
Mishka's time spent driving at this speed on the highway is 3 hours.
Mishka travels at an average rate of 35 km/h on the side road.
Driving at this speed on a side road took Mishka one hour.
Mishka travelled a total distance.
Having said that,
Speed equals Distance/Time
Or, Distance = Speed X Time.
Mishka travelled a total of Mishka miles on the roadway =
= Highway Speed X Highway Travel Time
= 65 X 3
= 195 km
Mishka travelled the following distance via side roads:
= Speed on side street X Travel time
= Speed on side road X Time taken on side road
= 35 X 1
= 35 km
Total distance travelled by Mishka = Distance travelled on highway + Distance travelled on side road
= 195 + 35
= 230 km
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y is directly porportional to x
when y=30 and x=6
a)work out an equation connecting y and x
b)work out the value of y when x =12
a. The equation connecting y and x is: y = 5x.
b. The value of y = 60.
What is the Equation of a Direct Proportional Relationship?Given that y is directly proportional to x, the equation that is connecting y and x can be expressed as y = kx, where k is the constant of proportionality.
a. We are given that when y = 30, x = 6, therefore, find the value of k by substituting the values of x and y into y = kx:
30 = k(6)
30/6 = k
5 = k
k = 5
Substitute the value of k into y = kx to write the equation:
y = 5x
b Substitute x = 12 into y = 5x:
y = 5(12)
y = 60
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How much is a 90 angle?.
A 90-degree angle, also known as a right angle, is an angle that measures exactly 90 degrees.
A 90-degree angle is an angle that measures exactly 90 degrees. It is also known as a right angle, since it is an angle that forms a right angle.
In geometry, angles are measured in degrees, and a full rotation is equal to 360 degrees. The angle formed by two intersecting lines is measured by the amount of rotation needed to bring one line to overlap the other. A 90-degree angle is formed by rotating one line by exactly 90 degrees, so that the two lines form a right angle.
A right angle is an angle that measures 90 degrees and it is represented by a small square at the angle's vertex. This square is a symbol of the angle's measure. In addition, the right angle is the only angle that can be used in geometry to create perpendicular lines which are lines that meet at 90 degrees.
In real-world applications, right angles are found in many things such as the corners of a room, the corners of a square or rectangle, and the corners of tools like a square, a ruler, and a protractor.
Therefore, In short, a 90-degree angle, also known as a right angle, is an angle that measures exactly 90 degrees. It's represented by a small square at the angle's vertex, and it's the only angle that can be used in geometry to create perpendicular lines.
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Suppose you through a ball horizontally. How is the way the ball moves similar to the motion of the planets around the sun?
The forces acting on a horizontally moving ball in the air are gravity or the force of its own weight, and the force that displaces the ball in the horizontal direction.
What is force?Force is an external agent that acts on a body to cause it to move or stop. There are various types of forces, such as magnetic forces, nuclear forces, frictional forces, and so on.
The product of a moving body's mass and acceleration yields force, which is derived from Newton's second law of motion. As a result, as the mass of the object increases, the force required to change its state increases.
The forces acting on a moving ball horizontally are the normal force that displaces it in that direction and the downward force of gravitation equal to its weight. Air resistance acting on the ball can also be considered.
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I seriously need help on this question, can someone help?
Answer:
a. A + C < B + C
Step-by-step explanation:
when we know that A < B, then adding the same amount to both sides did not change the relationship between both sides.
this is like having a balance with 2 cups. one side is heavier than the other, so the heavier cup is down.
if we add the same weight to both cups, the situation will not change.
that is why a. is the right answer.
b. would only be right, if C is negative.
for positive C the same argument as for A applies. a smaller amount (or weight) stays smaller also after multiplying both sides by the same number.
but because this option would only be right for a subset of the possible values, this is not true in general.
c.
this is not true at all.
if we multiply the expression by -1, then the inequality sign has to flip. < becomes >, > becomes <.
which did not happen here.
Segment VU is parallel to segment LM. Find the missing length.
L
M24 U
44
27
24
39
?
11
8
N
The missing length LN for the similar triangles is found to be 33 units.
Define the term similarity of triangles?A pairing of triangles are said to be comparable if pairs of equivalent angles in those triangles are congruent.We can conclude that the next pair must indeed be equal if the first two angle pairs are. When all three pairs of angles are equal, the sides of the 3 triangles must therefore be proportionate.For the stated triangles.
Using the similarity of triangles, the ratios of the sides of the triangles are equal.
Let the missing length LN be 'x'.
Thus,
8/ 24 = 11 / x
x = 24*11 / 8
x = 33
Thus, the missing length LN for the similar triangles is found to be 33 units.
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The correct question is-
Segment VU is parallel to segment LM. Find the missing length LN.
The answer is 44. By setting up a proportion, it would look like 8/24 = 11/33. The question is asking for the length of LN. So you would add 11 + 33, which will give you the answer of 44.
I need help I’ll give BRAINLIESt
Player A is more consistent with a range of 7.
What is IQR or interquartile range?The interquartile range serves as a gauge for where a data set's "middle fifty" lies. An interquartile range (IQR) measures where the majority of the values lay, whereas a range measures where a set's start and finish are.
Arranging the data in ascending order for player A,
1, 1, 2, 2, 3, 3, 4, 4, 8.
The range of this data set is the last term minus the first term which is,
= 8 - 1.
= 7.
Arranging the data in ascending order for player B,
1, 1, 2, 4, 4, 5, 5, 5, 10.
The range of player B is 10 - 1 = 9.
We know less range signifies more consistency therefore, Player A is more consistent.
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An architect is designing a water fountain for a park. She uses the given function to model the water jets flowing from the fountain's nozzles,
where h(x) gives the height of the water jet, in feet, x feet from its starting point.
The two adjacent columns that show an interval with an average rate of change of -0.3 are column 7ᵗʰ and 8ᵗʰ.
We have a function used by an architect is designing a water fountain for a park. The function is defined as h(x) = - x²/20 + x + 15
where h(x) --> height of the water jet, in feet,
x --> distance from its starting point in feet.Also , the average rate of change = - 0.3
Average rate of change is used to measure the change in value of function per unit, on average over an interval. It is derived from the slope line which is formed bu joining the end points of graph. Formula is represented as
A(x) = {F(b) - F(a)}/(b - a)
where b and a are end points of interval.
In this case, this formula is used as
A(x) = {H(x₂) - H(x₁)}/(x₂ - x₁ )
=> -0.3 = {H(x₂) - H(x₁)}/(x₂ - x₁ )
As we see in above figure the difference between the any two values of x is equals to 2 i.e., the final value - initial value = 2 in an interval.
So, x₂ - x₁ = 2
=> -0.3 = {H(x₂) - H(x₁)}/2
=> -0.3× 2 = H(x₂) - H(x₁)
=> -0.6 = H(x₂) - H(x₁)
=> H(x₂) = H(x₁) - 0.6
so, the columns which follows this relationship are the following
distance , x 12 14
Height of jet , h(x) 19.8 19.2
Hence, the required relationship is H(x₂) = H(x₁) - 0.6.
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Complete question:
An architect is designing a water fountain for a park. She uses the given function to model the water jets flowing from the fountain's nozzles,
where h(x) gives the height of the water jet, in feet, x feet from its starting point. select two adjacent columns that show an interval with an average rate of change of -0.3
how many solutions does 3(2x+1)=2(3x+2) have
The given expression 3(2x+1) = 2(3x+2) does not have a solution.
What is Linear equation ?
A linear equation is an equation that can be written in the form ax + b = 0, where x is a variable and a and b are constants. This type of equation is used to describe relationships between two variables, and it can be used to find the solution to a variety of problems.
Given expression ,
3(2x+1) = 2(3x+2)
3*2x+3 = 2*3x + 4
shifting 6x to the LHS , we get
6x+3 = 6x+ 4
6x-6x = 4-3
As 6x-6x is 0 , so there is no solution
0 = -1
Here we do not have a solution as there is no x exponent.
Hence, The given expression 3(2x+1) = 2(3x+2) does not have a solution.
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6) Se tienen 60 lápices, 90 esferos y 120 borradores y se quieren distribuir paquetes en los que haya
estos tres tipos de artículos. ¿cuál es el máximo número de paquetes que se puede armar usando
todos los artículos? ¿Cuántos lápices, esferos y borradores deben ir en cada paquete?
5 pencils, 2 pens, and 3 erasers should go in each package.
The goal is to determine the maximum number of packages that can be built using 60 pencils, 90 pens, and 120 erasers, each package containing 5 pencils, 2 pens, and 3 erasers. To achieve this, we need to calculate the number of packages each item can be used in and take the minimum result.
Starting with pencils, we can make 60/5 = 12 packages. For pens, we can make 90/2 = 45 packages. Finally, for erasers, we can make 120/3 = 40 packages. The minimum result is 40 packages, meaning that the maximum number of packages we can build is 40.
Therefore, each package should contain 5 pencils, 2 pens, and 3 erasers. Any extra items will not be used in the packages. By taking the minimum result, we ensure that all items are used in an equal manner and no items are left unused. In conclusion, the maximum number of packages that can be built using 60 pencils, 90 pens, and 120 erasers is 40, each containing 5 pencils, 2 pens, and 3 erasers.
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Write the equation of the hyperbola with centre at (4, 2), vertex at (4, 5), one asymptote with equation 4y - 3x = -4.
x2a2y2b2=1 x 2 a 2 y 2 b 2 = 1 is the conventional form of a hyperbola equation with the origin as the center and the vertices (a,0) (a, 0) and co-vertices (0b), (0b).
How do you find the equation of a hyperbola given center and vertex?A right circular cone and a plane are intersected at an angle that intersects both of the cone's halves to create a hyperbola in analytic geometry. There are two distinct unbounded curves that result from this intersection, and they are mirror reflections of one another.The set of all points (x, y) in a plane that are part of a hyperbola has a positive constant as the difference between their distances from the foci.Every hyperbola, like the ellipse, has two axes of symmetry. A line segment called the transverse axis, which has vertices for endpoints and runs through the hyperbola's centre. On the transverse axis-containing line, the foci are located. The co-vertices serve as the endpoints of the conjugate axis, which has a perpendicular relationship to the transverse axis. When the transverse and conjugate axes connect, they form the centre of a hyperbola. Two asymptotes also cross the centre of every hyperbola. The asymptotes of a hyperbola's branches are as it moves out from its center.When graphing the hyperbola and its asymptotes, the central rectangle of the hyperbola, whose sides run across all of its vertices and covertices and are centred at its origin, is a valuable tool. Simply draw and extend the diagonals of the central rectangle to represent the hyperbola's asymptotes.The axes in this section will either be on or be parallel to the x- and y-axes, and we will focus on hyperbolas that are positioned vertically or horizontally in the coordinate plane. The two situations that we'll look at are those that have the origin as their centre of gravity and those that have it somewhere else.The Complete Question is hyperbola equation.
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A worker spent 2 hours and 40 minutes making 20 products. If he works at the same productivity, how long will it take the worker to make 30 units?
Answer:
Step-by-step explanation:
The Time Taken to make 20 products = 2hours and 40 minutes = 160 minutes
Time taken to make 10 units = 80 minutes
Time taken to make 30 units = time taken to make 20 units + time taken to make 10 units
= 160 minutes + 80 minutes
= 240 minutes or 4 hours.
The worker needs 4 hours to make 30 units.
The ratio can be calculated as follows:
The first is to convert hours to minutes
2 hours 40 minutes = (2×60)+40 = 120+40 = 160 minutes
The next step is to compare worth comparison
[tex]\frac{a1}{b1}[/tex] = [tex]\frac{a2}{b2}[/tex]
[tex]a_{1} = 160 minutes\\a_{2} = X\\b_{1} = 20 products\\b_{2} = 30 products[/tex]
So,
[tex]\frac{160}{20} = \frac{X}{30}[/tex]
X = [tex]\frac{(160.30)}{20}[/tex]
X = [tex]\frac{4800}{20}[/tex]
X = 240 minutes
The next is to convert minutes into hours
240 minutes ÷ 60 minutes
= 4 hours
The worker needs 4 hours to make 30 units.
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2x^5 different from (2x)^5
The difference between the two expressions:
2x^5 and (2x)^5
Is the coefficient that multiplies the variable.
How are the two expressions different?We want to see how the expressions:
2x^5 and (2x)^5
Are different.
Remember that the exponents can be distributed, then we can write the rule:
(a*b)^n = (a^n)*(b^n)
Then we can rewrite the second expression as:
(2x)^5 = (2^5)*x^5 = (2*2*2*2*2)*x^5 = 32x^5
So the difference between the two expressions is the coefficient that is multiplying the variable x.
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In a baket of muffin 15% of the muffin are blueberry. How many are not blueberry?
The percentage that is not blueberry in a bake of muffin is 85%
What is a percentage?Percentage is defined as the number that represents a ratio of a total that is divided by 100 equal parts. It is represented by the symbol %.
To solve this problem we must perform the following algebraic operations with the given information:
Information about the problem:
%Total = 100%Blueberry = 15%Not blueberry = ?Calculating the percentage that is not blueberry in a bake of muffin:
% Not blueberry = %Total - %blueberry
% Not blueberry = 100 - 15
% Not blueberry = 85
85% of the bake is not blueberry
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9. A water tank already contain 55 gallon of water when Baxter begin to fill it. Water flow into the tank at a rate of 8 gallon per minute. Write a linear equation to
model thi ituation. Find the volume of water in the tank 25 minute after Baxter
begin filling the tank
So, 25 minutes after Baxter began filling the tank, the volume of water in the tank is 255 gallons.
A linear equation can be used to model the situation where water is flowing into a tank at a constant rate. The equation would be in the form:
V = 55 + 8t
Where V is the volume of water in the tank (in gallons), t is the time (in minutes) that has passed since Baxter began filling the tank, and 55 and 8 are the y-intercept and slope respectively
To find the volume of water in the tank 25 minutes after Baxter began filling it, you would substitute 25 for t in the equation above:
V = 55 + 8(25) = 55 + 200 = 255 gallons
So, 25 minutes after Baxter began filling the tank, the volume of water in the tank is 255 gallons.
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What are the zeroes of f/x x2 − X − 2?.
The zeros of function f(x) = x² -x - 2 are: x = 2 and x = -1
Consider given polynomial function f(x)=x² -x - 2
As we know the zeros of a function are nothing but the values of the variable of the function that makes the function value equal to 0.
To find the zeros of function f(x), we need to equate f(x) to zero then solve it for x.
⇒ f(x) = 0
⇒ x² -x - 2 = 0
using the Quadratic Formula where
a = 1, b = -1, and c = -2
[tex]\Rightarrow x=\frac{-b\pm \sqrt{b^2 -4ac} }{2a}\\\\\\ \Rightarrow x = \frac{1\pm \sqrt{9} }{2}\\\\\\\Rightarrow x = \frac{1\pm 3 }{2}[/tex]
Thus x = 2 and x = -1 are zeros.
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The complete question is:
What are the zeros of f(x)=x² -x - 2 ?
hi can you help it will help me
The exact value of the letter D is three and three-tenths.
What is a number line?A number line is a one-dimensional horizontal line where we can represent any real number. The origin of the number line is represented by zero left to it are all negative real numbers and right to it are all positive real numbers.
By observing the number line there are 10 subsections between two integers.
The letter D is in between two integers 3 and 4 so it can be from 3.1 to 3.9.
In between those ten subsections, the letter D is in the third subsection.
Therefore it is Three and three-tenths.
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What percentage profit did she make on costs
Answer:21
Step-by-step explanation:
What are the 4 types of division?.
There are four types of division are:
DividendDivisorQuotient RemainderNow, According to the question:
Division is one of the four basic math operations with addition, subtraction, and multiplication. Division is an important operation because it is common in everyday life and helps people understand multiplication better. Division is splitting a group into equal parts. Division is used to split up a class into equal groups for a game or activity or even split a pizza into equal portions between a group of friends.
The dividend is the number that is being divided in the division process.The number by which the dividend is being divided by is called the divisor. The quotient is a result obtained in the division process.Sometimes, we cannot divide things exactly.Learn more about Division at:
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How do you write greater than or equal to 6?.
The correct way to write greater than or equal to 6 is A ≥6 where it tells that A having greater than or equal to value than 6.
In mathematics,
→The greater than symbol (>) is used to indicate that one value is larger than another. For example, if we say "A > B," this means that the value of A is greater than the value of B.
→The less than symbol (<) is the opposite, it indicates that one value is smaller than another. For example, if we say "A < B," this means that the value of A is less than the value of B.
→The greater than or equal to symbol (≥) indicate that one value is larger than or equal to another. For example, if we say "A ≥ B," this means that the value of A is greater than or equal to the value of B.
→The less than or equal to symbol (≤) indicate that one value is smaller than or equal to another. For example, if we say "A ≤ B," this means that the value of A is less than or equal to the value of B.
These symbols are commonly used in mathematical expressions, equations, and inequalities.
To write "greater than or equal to 6" in mathematical notation, you would use the greater than or equal to symbol (≥) followed by the letter 6. For example:
A ≥6
This means that A having greater than or equal to 6.
Therefore, the correct way to write greater than or equal to 6 is A ≥6 where it tells that A having greater than or equal to value than 6.
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What is modulus of 4i?.
The modulus of the complex number 4i is 4.
Now, According to the question:
Consider the given number 4i .
The number is a complex number which is of the form z = x + iy .
We can write the above question as z = 4i where x = 0 and y = 4 . The modulus of the complex number is given by:
[tex]|z| =\sqrt{Re(z)^2+Im(z)^2}[/tex]
where real part is x and imaginary part is y. Hence the modulus of a complex number is :
[tex]|z| =\sqrt{0^2+4^2}[/tex]
[tex]|z| = \sqrt{16} \\[/tex]
|z| = 4
Hence the modulus of the complex number 4i is 4.
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How do I convert improper fractions into mixed numbers?
Answer:
Step-by-step explanation: Divide the numerator by the denominator.
Write down the whole number part of the quotient.
Take the remainder and write it over the original denominator.
The following triangles are similar. Which of the properties could be used to solve x:
if the triangles are similar , then ,
The small trapezoid is a scaled-down version of the large trapezoid, but is also a mirror image.
So the side x corresponds to the length 45 in the larger trapezoid.
[tex]45 = 2x + 4 \\ 2x = 45 - 4 \\ x = \frac{41}{2} \\ x = 20.5[/tex]
x is an obtuse angle and sin x = 0.43.
Find the value of x.
Answer: 154.53
Step-by-step explanation:
sin x° = 0.43
t = arcsin (0.43) = 25.47
x= 18 - t= 18 - 25.47 = 154.53
