Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Simplify the complex numbers using de Moivre's Theorem and match them with their solutions 2(3+1) 2. cos(20°) + sin(20°)] 2[ coo(4)+isin(7)]* (-1+i) -41 (1+1) -16 4+4731 Reset Next

The line parallel to the given line 2x+3y=6 is 2x+3y=13.

The general equation of a line is y=mx+c where m is the slope of the line and c is the y-intercept.

The slope of the given line 2x+3y=6 is

3y=(-2x)+6

y=(-2/3)x+2

y=mx+c where m is the slope of the line

so the slope of the given line is (-2/3)

as the slope of two parallel lines is equal so the slope of the line parallel to the given line is also (-2/3)

(y-y1)=m(x-x1) where x1 is the x-coordinate and y1 is the y-coordinate.

Here x1=2 and y1=3

(y-3)=m(x-2)

y-3=(-2/3)x+4/3

3y-9=(-2x)+4

3y+2x=13

2x+3y=13

The line 2x+3y=13 is parallel to the given line 2x+3y=6.

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The zeroes of this polynomial equation is [tex]$4 x^2-4 x-3$[/tex] are [tex]\frac{3}{2}$[/tex] and [tex]$-\frac{1}{2}$[/tex].

First form the equation

As per the given data the given polynomial equation is [tex]$4 x^2-4 x-3$[/tex].

Here we have to determine the zeroes of a polynomial equation is [tex]$4 x^2-4 x-3$[/tex].

We know that the zeroes of a polynomial are evaluated by equating them with zero.

Therefore p(x)=0

[tex]& \Rightarrow 4 x^2-4 x-3=0[/tex]

Then solve to find the zeroes

[tex]& 4 x^2-4 x-3=0 \\[/tex]

[tex]& \Rightarrow 4 x^2-6 x+2 x-3=0 \\[/tex]

2x(2x - 3) + 1(2x - 3) = 0

(2x - 3) (2x + 1) = 0

[tex]& \Rightarrow x=\frac{3}{2},-\frac{1}{2}[/tex]

Then do verification

We know that for a given polynomial [tex]$a x^2+b x+c$[/tex]

Sum of the zeroes [tex]$=-\frac{b}{a}$[/tex] and product of the roots [tex]$=\frac{c}{a}$[/tex]

Sum of the zeroes [tex]$=\frac{3}{2}-\frac{1}{2}=1$[/tex]

Again, [tex]$-\frac{b}{a}=\frac{4}{4}=1$[/tex]

Product of the zeroes [tex]$=\frac{3}{2} \times-\frac{1}{2}=-\frac{3}{4}$[/tex]

Again, [tex]$\frac{c}{a}=-\frac{3}{4}$[/tex]

Thus, the relationship between the zeroes and the coefficients of the polynomial is verified.

Hence, the zeroes of this polynomial are [tex]\frac{3}{2}$[/tex] and [tex]$-\frac{1}{2}$[/tex].

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Therefore , the solution of he given problem of linear equation comes out to be x = 5.

A linear equation is one that has the form y=mx+b in algebra. B is the slope, and m is the y-intercept. It's usual to refer to the previous clause as a "linear equation with two variables" because y and x are variables. The two-variable linear equations known as bivariate linear equations. There are several instances of linear equations: 2x - 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, and 3x - y + z = 3. It is referred to as being linear when an equation has the form y=mx+b, where m stands for the slope and b for the y-intercept.

Here,

Given : 2x-4=6

To prove x =5

Thus,

We have to find the value of x

=> 2x =10

=> x =10/2

=> x =5

Therefore , the solution of he given problem of linear equation comes out to be x = 5.

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A transformation that alters the size of a figure is called a dilation (similarity transformation). It needs a scale factor of k and a central point. Depending on the value of k, the dilatation is either an enlargement or a decrease. The dilation is an enlargement if |k|>1.

If two figures have the same shape but different sizes, they are said to be comparable. A stiff motion combined with a rescaling constitutes a similarity transformation. In other words, a similarity transformation can change shape without changing location or size.

A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.

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Answer: N= x24 over 3

Step-by-step explanation:

Answer:

n0p = 120°

Step-by-step explanation:

m0n + n0p = 180°

60° + n0p = 180°

n0p = 120°

Therefore, the players are 6.84 meters apart from each other.

An item that is propelled by the application of an external force and then travels freely while being affected by gravity and air resistance is referred to as a projectile. Projectiles are generally used in sports and combat, despite the fact that every item traveling through space is a projectile.

The straight line that traverses a point with a slope equal to the derivative of the curve at that location is said to be the tangent line to a plane curve at that point in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

If we let x be the distance between the players, then we can use the tangent function to relate the angle of elevation to the distance between the player and the basket:

tan(40°) = 3.5/x

tan(50°) = 3.5/(x+1)

We can solve for x in both equations, and set them equal to each other, we get x= 6.84m

Therefore, the players are 6.84 meters apart from each other.

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5/32 of the time, the product of the two numbers on the face-up sides will be greater than 36.

The likelihood of an event happening is gauged by probability. Many things are impossible to completely predict in advance. Using it, we can only make predictions about how probable an event is to happen, or its chance of happening.

There are 64 possible options to look at (8 x 8).

If one die is a 1, then no combinations will be possible, even if the other die is an 8.

If one dice is a 2, then no combinations will be possible, even if the other die is an 8.

If one dice is a 3, then no combinations will be possible, even if the other die is an 8.

If one die is a 4, then no combinations will be possible, even if the other die is an 8.

If one die is a 5, the second die must be an 8 for the result to be more than 36. So, (5, 8) is effective.

If one die is a 6, the second die must be a 7 or an 8 to produce a result greater than 36. Therefore, both (6, 7) and (6, 8) are valid.

If one die is a 7, the other die can be a 6, 7, or 8 to get a result that is more than 36. As a result, (7, 6), (7, 7) and (7, 8) all function.

If one die is an 8, the other die can be a 5, 6, 7, or 8 to get a result that is more than 36. Therefore, (8, 5), (8,6), (8,7), and (8,8) are valid.

Out of a total of 64 possible combinations, there are a total of 1 + 2 + 3 + 4 = 10 that are successful.

As a result, the response is 5/32 because 10/64 = 5/32.

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The distance of each chord from the centre of the circle are √119  and √128 respectively .

Given,

Radius of a circle = 12 cm

AB = 10 cm

CD = 8 cm

Now, we get

BG = 10/2 = 5 cm

HD = 8/2 = 4 cm

(A perpendicular coming from the centre, which is not a diameter, bisects the chord.)

Now,

BE = ED = EF = 12 cm (All radii of a circle are equal.)

Now, by Pythagoras Theorem, we get

H² = P² + B²

For GE —

(BE)² = (GE)² + (BG)²

or, (12)² = GE² + (5)²

or, 144 = GE² + 25

or, GE² = 144 — 25

or, GE² = 119

or GE = ±√119

or GE = √119 (Since, length cannot be negative.)

For HE —

(DE)² = (HE)² + (HD)²

or, (12)² = HE² + (4)²

or, 144 = HE² + 16

or, HE² = 144 — 16

or, HE² = 128

or, HE = ± √128

or, HE = √128 or 8√2(Since, length cannot be negative.)

Hence , the distance of each chord from the centre of the circle are √119  and √128 respectively .

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No, one mole is not equal to one gram. For an object, the mole and gram numerical values differ.

1 gram, what is it?

One mole consists of an Avogadro number of atoms. If you are aware of the mole quantity, you can convert a mole into grams.

The mole (symbol: mol) is the unit of material quantity used by the International System of Units. The amount of a substance determines how many elementary entities of that substance are present in an object or sample. The mole must contain precisely 6.02214076×10²³ elementary entities.

A mole's relationship to a gram is

The product of the number of Moles of an object to its atomic weight equals one gram.

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Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.

The algebraic equation y=mx+b stands in for a linear equation. The slope is m, and B is the y-intercept. The last phrase referred to a "simple formula with two elements" where both y and x are variables. Bivariate linear equations are calculations involving two variables. Here are a few examples: The outcomes are 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3. If the answer to a mathematical equation is in the form y=mx+b, where m denotes the slope and b the y-intercept, the equation is said to be linear.

Here,

Given :

According to parallelogram laws

adjacent side sum is 180 degree

=> 4y + 3x-18 = 180

=> 4y+3x = 162

and

2x+12+3z = 180

=> 2x + 3z = 168

and

=> 3x+3z = 162

=> x + z =54

=> z = 54-x

So,

2x + 3(54-x) = 168

=> 162 - 3x+2x =168

=> -x = 6

or x =-6

and

z = 60

and

y = 162 - 3x /4

=> y= 162 +18 /4

=> y =180/4

=> y = 45

Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.

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If we pull 3 socks then there is a 100% possibility that 2 socks will be of same colour.

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportional ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.

The likelihood that a specific occurrence will occur. (2): the proportion of the total number of available outcomes to the number of outcomes in an exhaustive set of equally probable options that result in a certain occurrence.

There are 9 red socks and 11 blue socks

So if we find a red/blue sock in the first turn,

The second can be both blue or red so we can't be sure it will be matching or not.

At third turn any one colour of sock will match with any of the two already pulled before if they are different.

So, if we pull 3 socks then there is a 100% possibility that 2 socks will be of same colour.

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Answer:

13.

Step-by-step explanation:

Let X be the number.

Given information from the question, we can formulate an equation:

Six times a number less 20 = 4 times the same number increased by 6

6X - 20 = 4X + 6

From the equation, we can solve for X.

6X - 4X = 6 + 20

2X = 26

X = 26 ÷ 2

X = 13

Therefore the number is 13.

The value of the unknown number is = 13.

Let the unknown number be expressed by the variable = x.

According to the question, the mathematical linear equation in one variable that is 'x' can be expressed as:

=> 6x - 20 = 4x + 6

=> 6x - 4x = 6 + 20

=> 2x = 26

=> x = 26/2

=> x = 13

Therefore, the value of 'x' which is the unknown number is 13.

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Answer:

Step-by-step explanation:

The simple explanation is that the hypotenuse and sides of a right triangle are always shorter than one another. Therefore, any side's to any hypotenuse's ratio will never be greater than 1. The figure is no longer a triangle when the angle is 0 or 90 degrees because one of the sides vanishes and the other side lines up with the hypotenuse. For this reason, sin and cosine have values of 0 or 1 in these extreme situations.

Answer:

16p^12 q^4

Step-by-step explanation:

Open up the parenthesis and simplify.

2^4 is 16

p^3 times ^4 is p^12

q times ^4 is q^4

So your answer is 16p^12 q^4

Answer:

16p^12 q^4

Step-by-step explanation:

This is because the power 4 will multiple with all the variables inside

hence, p^3 will become p^12

and q^1 will become q^4

the power 4 will also change 2 into 2^4 which is 16

Answer:

Step-by-step explanation:

To find values of y we substitute values of x in the given expression so when x = 0

y = (0)^2 - 6(0) + 3

  = 3.

x = 1, y = 1^2 - 6(1) + 3 = -2

x = 3, y = 3^2 - 6(2) + 3 = 0.

Use these values to draw the graph

(a)  Read this from the graph

Coordinates of the minimum should be 3, -6)

(b) Equation of the line of symmetry is the vertical line through the minimum point ( x = 3).

(c)  Read these from the graph.

(the points where the graph cut the x-axis).

(d) and e - read the values from your graph.

(0.818  , 1.546)  is the point that is part of solution.

point (0,2) and (2,0) are not the part of solutions.

3y - 2x ≤ 3

y + 3x  ≤ 4

these are the system of inequalities.

What are Inequalities?

Inequality is a relationship between two expressions or values that is not equal to each other. Therefore, inequality emerges from a lack of balance.

Given in this question,

There are two lines L1 and L2.

From the graph we can find the two points that lies on the line L1 be

(0,1) and (3,3).

similarly From the graph we can find the two points that lies on the line L2 be

(0,4) and (2,-2).

From the two points (x1 , y1) and (x2,y2) we can write the equation of the Line from the following formula :

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex].   This is the equation of line for given two points.

Equation of line L1 :

[tex]y-1=\frac{3-1}{3-0} (x-0)[/tex]

3y - 3 = 2x ----------(ii)

Equation of line L1 : 3y - 2x = 3.

Equation of line L2 :

[tex]y-4=\frac{-2-4}{2-0} (x-0)[/tex]

y   = -3x + 4 ----------(ii)

Equation of line L2 : y + 3x = 4.

The point that is the part of the solution :

putting the value of y from equation (ii) in equation (i).

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

-9x-2x = -12+3

-11x = -9

  x = 0.818

y = -3(0.818) +4 = +1.546

so Point of intersection is (0.818  , 1.546)

This is the point that is part of solution.

The point that is not below both the lines are not part of solution.

the point that are not part of solution are:

3y - 2x ≥ 3  ->  (0,2)

y + 3x  ≥ 4   ->  (2,0)

point (0,2) and (2,0) are not the part of solutions.

Inequalities are for shaded portion :

3y - 2x ≤ 3

y + 3x  ≤ 4

these are the system of inequalities.

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Answer:

yea yea

Step-by-step explanation:

The equation that represents the length of the square dining room in feet is (1/4)x - 5/6.

The area of a square is a product of it's any two sides or a product of diagonals divided by two. If a side has a length 'a' then the diagonal is a√2.

The perimeter of a square is the sum of the lengths of all the sides.

We know the perimeter of a square is 4×side.

We also know that 1 foot is equal 12 inches.

Given, A square dining room table has a perimeter of (12x - 40)".

Now if we factor out a 4 we'll have the side inside the bracket which is,

4(3x - 10)'', This is in inches to convert it to feet we have to divide what is inside the bracket by 12 which is,

= (3/12)x - 10/12 feet.

= (1/4)x - 5/6 feet.

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The length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.

We know that the length of the arc of a circle = Radius of the circle × angle subtended by the arc (in radians)

Here radius of the circle is 27 m

The angle subtended is 120°

Hence we will first convert the angle into radians

Angle in radians = Angle in degree X π/180

= 120 X π/180

= 2π/3

Therefore, the length of the arc = 27 X 2π/3

= 18π m

Therefore, the length of the arc that subtended an angle of 120° with a radius of 27 m is 18π m.

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Answer:

Step-by-step explanation:

You need to add both of the angles you already know (1 and 2). If you add angle 1 and angle 2 you get 74. This means m < J K M would be 74°.

Answer:

74 degrees

Step-by-step explanation:

You have to add angles 1 and 2

35 +39=74

Therefore, 74 is the answer

The duckweed increases by a percentage each day which is calculated by the equation

(1230.25t/16)/a - 1.

This equation can be further simplified to 1230.25t/16a - 1 and then multiplied by 100 to get a percentage.

So the percentage increase of duckweed each day is calculated by multiplying 1230.25t/16a - 1 by 100.

1230.25t/16a×100

This will give us the percentage of increase each day, rounded to the nearest whole number.

For example, if the initial number of fronds is 1000 and the number of days is 2, the percentage increase of duckweed will be (1230.25(2)/16(1000)) - 1 = 24.6%, rounded to the nearest whole number which is 25%.

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The equation of the linear function is A(t) = -975t + 15000

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table of values, we have:

A(t)         t

11,100   4

7200   8

3300   12

From the above table of values, we can see that

As t increase by 4, the value of A(t) decreases by 3900

This means that the table of values is a linear relation, and the slope is

slope = -3900/4

slope = -975

A linear equation is represented as

y = mx + c

Where

slope = m

So, we have

A(t) = -975t + c

Using the points on the table, we have

11000 = -975 * 4 + c

Evaluate

c = 15000

So, we have

A(t) = -975t + 15000

Hence, the equation is A(t) = -975t + 15000

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Therefore , As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).

Several dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).

Here,

Maria You've erred, you know that. You don't understand the points at all. The attachment can be used to your advantage.

The property of rational numbers, according to which there are an endless number of terminating decimals between any two terminating decimals, must be used in order to plot any terminating decimal on the coordinate plane.

On the X axis, indicate -0.5 between 0 and -1.

Mark integer 2 on the Y axis in a similar manner.

Draw a line perpendicular to the Y axis, passing through (-0.5,0), and a line perpendicular to the X axis, passing through (0,2).

These two lines must cross at the specified position (-0.5,2).

As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).

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The slope shows a change in the amount of fuel left in each mile. Since the slope is -0.04, the amount of fuel left drops by 0.04 gallons each mile

The slope of a line governs its steepness. Using mathematics, the gradient is expressed as "gradient overflow" (the change in y divided by the change in x). The slope is the ratio of the vertical (rise) to the horizontal (run) change in distance between any two sites. Every time the equation for a straight line is written as y = mx + b, the slope-intercept representation of the equation is utilized. At the location of the y-intercept, the line has a slope of m, b, and c. (0, b). As an example, the y-intercept of the equation y = 3x - 7 has a value of 3. (0, 7).

given

It is evident that with each additional row, the distance is increased by one mile and the fuel level is altered.

From one row to the next in the table, the amount of fuel left changes by -0.04 gallons.

The distance in the table that changes from one row to the next is 1 mile.

The slope is the pace at which the amount of fuel left changes in relation to the change in distance.

The line that passes through the places listed in the table has a slope of -0.04 degrees.

The slope shows a change in the amount of fuel left in each mile. Since the slope is -0.04, the amount of fuel left drops by 0.04 gallons each mile.

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The answer is:

- 1 < x < 1

I hope this is correct

Answer: y<-5x+9

Step-by-step explanation:

Slope is -5, y-intercept is 9 and the shaded area is on the left side (meaning y is less than the line). The line is dotted which means that the answer will less than but not equal to.