The length of the vector that represents z₁ = 6-8i is 10 because √6² + (-8)² = √√100 = 10.
a.
Find at least seven other complex numbers that can be represented as vectors that have length 10.

Answer:

27.64

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

u replace x with -3

=4(2)-³

=4(0.125)

=0.5

=1/2

The equation of the line that passes through the point (-6, 2) and has slope of -1/2 is y = (-1/2)x - 1

The slope of the line = -1/2

The slope of the line is the change in y coordinates with respect to the change in x coordinates of the line

The slope intercept form

y = mx + b

Where m is the slope of the line

b is the y intercept form

The coordinates of the point = (-6, 2)

Substitute the values in the equation

2 = (-1/2)(-6) + b

2 = 3 +b

b = 2 -3

b = -1

The equation will be

y = (-1/2)x - 1

Hence, the equation of the line that passes through the point (-6, 2) and has slope of -1/2 is y = (-1/2)x - 1

The complete question is :

What is the equation of a line that passes through (-6, 2) and has a slope of -1/2 ?

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Answer: 243x^5 + 2025x^4y + 6750x^3y^2 + 11250x^2y^3 + 9375xy^4 + 3125y^5

Step-by-step explanation:

1. To find each term, use BINOMIAL EXPANSION THEOREM (best to look up theorem on your own).

2. Expand the summation (after finding each term).

3. Simplify the exponents for each term.

> 1 • (3x)^5 • (5y)^0 + 5 • (3x)^4 • (5y)^1 + . . . + 1 • (3x)^0 • (5y)^5

4. Simplify.

If the angle elevation to the plane A = 30 degrees and B = 40 degrees , then the Airplane is 359.11 feet high .

In the question ,

it is given that

the distance between the two observer = 1050 feet

the measure of angle A is = 30°

the measure of angle B is = 40°

By angle sum property angle C is = 180 - (30 + 40)

= 180 - (70)

= 110

By Sine Law .

Sin(110)/1050 = Sin(30)/a = Sin(40)/b

Using , Sin(110)/1050 = Sin(30)/a ,

we get ,

Sin(110)/1050 = 0.5/a

a = 558.69

Using Sin(110)/1050 = Sin(40)/b

b = 718.24

By using Sine Law

Sin(40)/h = Sin(90)/558.69

h = 359.11

Therefore , If A = 30 degrees and B = 40 degrees , then the Airplane is 359.11 feet high .

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Answer:

third option

Step-by-step explanation:

| - 2x | = 4

the absolute value function always gives a positive value, however, the expression inside can be positive or negative , that is

- 2x = 4 ( divide both sides by - 2 )

x = - 2

or

- (- 2x) = 4

2x = 4 ( divide both sides by 2 )

x = 2

solutions are x = - 2 , x = 2

these are illustrated on the number line by solid circles at - 2 and 2

this is indicated on the third number line

Number line represents the solutions to |–2x| = 4 is third number line (x1 = -2, x2= 2).

Solving steps :

1. Calculate

Calculate the absolute value.

|-2x| = 4

Use |ab| = |a| * |b| to transform the expression.

|-2x|

|-2| * |x|

The absolute value of any number is always positive.

2 * |x|

We did it!

|-2x| = 4

2 * |x| = 4

2. Divide both sides

Divide both sides of the equation by 2.

2 * |x| = 4

2 * |x| ÷ 2 = 4 ÷ 2

Any expression divided by itself equals 1.

|x| = 4 ÷ 2

Calculate the quotient.

|x| = 2

3. Separate into possible cases

Use the absolute value definition to rewrite the absolute value equation as two separate equations.

|x| = 2

x = 2

x = -2

4. The equation has 2 solutions.

x1 = -2, x2= 2

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In the given rectangular prism vector line IM and LM intersect each other. Option B is correct.

It is defined as a six-faced shape, a type of hexahedron in geometry. It is a three-dimensional shape. It is also called a cuboid.

Six faces, twelve sides, and eight vertices make up a rectangular prism (corners). Three of the 12 edges meet to create right angles at each vertex.

Since from all 12 edges vector line IM and LM meet to form right angles at each vertex.

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Thus, in the given rectangular prism vector line IM and LM intersect each other. Option B is correct.

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The trigonometric ratio (trig ratio) for the angle in this right-angled triangle should be expressed as fractions in simplest terms as follows:

Sin(M) = 21/121

Cos(L) = 10/11

Tan(K) = 21/100

In Mathematics, a trigonometric ratio (trig ratio) can be calculated by using this mnemonic SOHCAHTOA:

Sinθ = Opposite/Hypotenuse

Sin(M) = KM/ML

Sin(M) = √21/11

Taking the square of both the numerator and denominator, we have:

Sin(M) = (√21)²/11²

Sin(M) = 21/121

For the cosine of an angle in a right-angled triangle, we have:

Cosθ = Adjacent/Hypotenuse

Cos(L) = KL/ML

Cos(L) = 10/11

For the tangent of an angle in a right-angled triangle, we have:

Tanθ = Opposite/Adjacent

Tan(K) = KM/KL

Tan(K) = √21/10

Taking the square of both the numerator and denominator, we have:

Tan(K) = (√21)²/10²

Tan(K) = 21/100

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Answer:

seven multiplied by x to the second power multiplied by the difference of two multiplied by x subtract 3 multiplied by the product of three multiplied by z multiplied by 3 add four.

Step-by-step explanation:

This is a useless question, word form isn't in any sort of ACTUAL GLOBAL TEST. So don't stress over this.

Part (d)

If xy > 0, then the two items x and y must have the same sign.

Examples where x,y are both positive

Examples where x,y are both negative

This places us in either the first quadrant or third quadrant (Q1 and Q3)

======================================================

Part (e)

If y < 0, then we have points like (2,-5) and (1,-7). The x coordinate doesn't matter as long as the y coordinate is negative.

Visually speaking we are below the x axis. This places the point in Q3, Q4, or on the negative y axis. The point cannot be on the x axis. You can think of this point as being underground or underwater.

======================================================

Part (f)

If x = 0, then the point is on the vertical y axis. Recall that y intercepts always occur when x = 0. Two examples would be (0,4) and (0,12).

Answer:

(d)  The set of all points in quadrants I and III (x and y have the same sign).

(e)  The set of all points below the x-axis.

(f)  The set of all points on the y-axis.

Step-by-step explanation:

The Cartesian plane is divided into four quadrants.  

Quadrant I is the upper right quadrant and the rest follow in a counterclockwise direction.

Part (d)

For xy > 0, x and y should either both be positive or both be negative, i.e. have the same sign.

Therefore, the description that satisfies the given condition is:

Part (e)

For y < 0, y is always negative.

Quadrants III and IV are below the x-axis.

Therefore, the description that satisfies the given condition is:

Part (f)

The only place where x = 0 is the y-axis.

Therefore, the description that satisfies the given condition is:

For the given conditions, the length of box=6.92 feet, width of box=3.46 feet and height of box=2.31 feet.

Each object in three dimensions takes up some space. The volume of this area is what is being measured. The space occupied within an object's boundaries in three dimensions is referred to as its volume. It is also referred to as the object's capacity.

Here,

area of material=72 feet²

V=lbh

l=2b

72=lb+2lh+2bh

substitute l as 2b,

72=2b²+4bh+2bh

36=b²+3bh

3bh=36-b²

h=(36-b²)/3b

v=lbh

v=2b*b*(36-b²)/3b

v=2b*(36-b²)/3

=(72b-2b³)/3

differentiate the v,

v'=1/3(72-6b²)

v'=0

72-6b²=0

6b²=72

b²=12

b=√12

b=3.46 feet

l=2b=6.92 feet

h=(36-b²)/3b

=(36-12)/3*3.46

h=2.31 feet

The box measures 6.92 feet long, 3.46 feet wide, and 2.31 feet tall under the specified circumstances.

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Answer:

[tex]W=2\sqrt{3}=3.46\; \sf ft\;(2\;d.p.)[/tex]

[tex]L=4\sqrt{3}=6.93\; \sf ft\;(2\;d.p.)[/tex]

[tex]H = \dfrac{4\sqrt{3}}{3}=2.31\; \sf ft\;(2\;d.p.)[/tex]

Step-by-step explanation:

If the length is twice the width:

Surface area of the box

[tex]\implies SA = WL + 2WH + 2LH[/tex]

[tex]\implies SA = W(2W) + 2WH + 2(2W)H[/tex]

[tex]\implies SA = 2W^2 + 2WH + 4WH[/tex]

[tex]\implies SA = 2W^2 + 6WH[/tex]

If the surface area is 72 ft²:

[tex]\implies 2W^2 + 6WH = 72[/tex]

[tex]\implies 6WH = 72 - 2W^2[/tex]

[tex]\implies H = \dfrac{72 - 2W^2}{6W}[/tex]

[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]

Volume of the box

[tex]\implies V = LWH[/tex]

[tex]\implies V = (2W)WH[/tex]

[tex]\implies V = 2W^2H[/tex]

Substitute the found expression for H into the formula for volume:

[tex]\implies V = 2W^2\left(\dfrac{36 - W^2}{3W}\right)[/tex]

[tex]\implies V = \dfrac{2W^2(36 - W^2)}{3W}[/tex]

[tex]\implies V = \dfrac{2W(36 - W^2)}{3}[/tex]

[tex]\implies V = \dfrac{72W - 2W^3}{3}[/tex]

[tex]\implies V =24W-\dfrac{2}{3}W^3}[/tex]

To find the value of W when the volume is at its maximum, first differentiate the equation for volume with respect to W:

[tex]\implies \dfrac{\text{d}V}{\text{d}W}=24-2W^2[/tex]

Now set the derivative to zero and solve for W:

[tex]\implies 24-2W^2=0[/tex]

[tex]\implies 2W^2=24[/tex]

[tex]\implies W^2=12[/tex]

[tex]\implies W=\sqrt{12}[/tex]

[tex]\implies W=2\sqrt{3}[/tex]

As length is twice the width:

[tex]\implies L=2 \cdot 2\sqrt{3}[/tex]

[tex]\implies L=4\sqrt{3}[/tex]

To find H, substitute the found value of W into the expression for H:

[tex]\implies H = \dfrac{36 - W^2}{3W}[/tex]

[tex]\implies H = \dfrac{36 - (2\sqrt{3})^2}{3(2\sqrt{3})}[/tex]

[tex]\implies H = \dfrac{36 - 12}{6\sqrt{3}}[/tex]

[tex]\implies H = \dfrac{24}{6\sqrt{3}}[/tex]

[tex]\implies H = \dfrac{4}{\sqrt{3}}[/tex]

[tex]\implies H = \dfrac{4\sqrt{3}}{3}[/tex]  

Answer: tell me the soulation like how do you solve it then I can help

Step-by-step explanation:

The error is that the student used the formula for a reflection in the x-axis, and the correct endpoints are: C'(1, 1) and D'(3, -2)

Rotation simply means turning.

In a cartesian plane, if a point P, whose position vector is (x,y), is rotated through 270° about the origin, the position of the image P' is (y, -x)

But the reflection in the x-axis is defined as (x,y) => (x, -y) i.e. if a position vector of a point is (x,y), the position vector of its image in the x-axis is  (x, -y)

Given: C(-1, 1) and D'(2, 3)

Therefore, the student used the formula for a reflection in the x-axis. The 2nd option is the answer.

The correct endpoints are: C'(1, 1) and D'(3, -2)

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Answer:

m = -5/3

Step-by-step explanation:

Slope is defined as the change in y / change in x or [tex]\frac{y2-y1}{x2-x1}[/tex]

The order of the points don't matter so we can do:

[tex]\frac{-1-(-6)}{5-8}=\frac{-5}{3}[/tex]

-5/3 is as simple as the fraction can be.

The possible dimensions of the rectangular garden with an area of 72 square yards are (4,18), (8,9), (6,12), (2,36)

The measurement that expresses the size of a region on a plane or curved surface is called area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas the area of a plane region or plane area refers to the area of a form or planar lamina.

Area is the entire amount of space occupied by a flat (2-D) surface or an object's shape. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a shape on paper is the area that it occupies. Consider your square as being composed of smaller unit squares.

Given,

The area of a rectangular garden is 72 square yards.

And also given that the dimensions of the garden are not prime numbers.

LCM of 72 is,

=2×2×2×3×3

Therefore, the possible dimensions of the garden are:

(4,18)

(8,9)

(6,12)

(2,36)

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The number of cards Camila sold is 50cards

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100. It is represented by the symbol “%”. For example if 10% of 200 students in a school are boys, the the number of boys in the school is 10/100× 200= 20students

Similarly Camila sold 10% of the card sold on mother's day. The number of cards sold on mother's day is 500.

Therefore Camila sold 10/100×500= 50cards

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Answer:

Step-by-step explanation:

1. The equation in​ a slope-intercept form describing the relationship is y = -4000x + 27000.

2. The daily sales of Fun Noodles at the price of $5.50 is  5000.

The Pool Fun Company has learned that, by pricing a newly released Fun Noodle at $5, sales will reach 7000 Fun Noodles per day during the summer. Raising the price to $6 will cause the sales to fall to 3000 Fun Noodles per day.

The relationship between sales​ price, x, and the number of Fun Noodles​ sold, ​ y, is linear. The ordered pair are (5, 7000) and (6, 3000).

The equation in slope intercept form describing the relationship is as follows:

1. y = mx + b

where

Therefore,

m = 3000 - 7000 / 6 - 5

m = - 4000

Let's find the y-intercept using (6, 3000)

3000 = -4000(6) + b

3000 + 24000 = b

27000 = b

Hence, the equation is y = -4000x + 27000

2. The daily sales of Fun Noodles at the price of $5.50 can be computed as follows;

y = -4000(5.5) + 27000

y = -22000 + 27000

y = 5000

Therefore, the daily sales is 5000.

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Answer:

Below

Step-by-step explanation:

If she buys a loaf of bread she has   only 6 dollars for tomatoes

   $ 6 / 1.20 $/POUND = 5 POUNDS OF TOMATOES

(8-2) / 1.20 = # TOMATOES

Answer:

The numerator is the top number of a fraction.

your welcome! <3

Answer:

Numerator is on the the top of the fraction

Step-by-step explanation:

x

_     x is the numerator

y

If triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E' , then measure of the side DE is 14.

In the question ,

it is given that ,

The triangle CDE is dilated by scale factor of 1/4

and the new triangle formed after dilation is C'D'E' .

it is given that the measure of the side D'E' = 3.5 .

let the measure of the the side DE = x

So , according to the question ,

x *(1/4) = 3.5

On cross multiplication,

we get ,

x = 4* 3.5

x = 14

Therefore , If triangle CDE is dilated by a scale factor of 1/4 to form triangle C'D'E' , then measure of the side DE is 14.

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1) The percentage of students who will get a score below 275 is; 0.15%

2) Yes, any score below 275 is significantly different from the mean.

The empirical rule states that for a normal distribution, 68% of the distribution are within one standard deviation from the mean, 95% are within two standard deviation from the mean and 99.7% are within three standard deviations from the mean.

The formula for z-score is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

1) We are given;

Population mean; μ = 500

Sample mean; x' = 275

standard deviation; σ = 75

Thus;

z = (275 - 500)/75

z = -3

This is 3 standard deviations from the mean. Thus;

The percentage of students who will get a score below 275 is;

(100 - 99.7)/2 = 0.15%

2) Yes, any score below 275 is more than 3 standard deviations away from the mean and can be considered significantly different from the mean.

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The total annual premium for this insurance will be $14,219.

Define premium.

An amount that the insured pays on a regular basis to the insurer to cover his risk is known as a premium. In terms of finance, a premium is the sum of the costs associated with an option or the distinction between the higher price paid for a fixed-income instrument and the relevant face amount. For many different insurance policies, including health, homeowner's, and rental insurance, premiums are typically paid. Automobile insurance is a typical example of an insurance premium.

Solution explained:

A/Q, as we calculate,

Annual Premium for one worker is = [tex]33000 X \frac{10.51}{100}[/tex] = $3468.3

Annual Premium for four workers is = 4 X 3468.3 = $13873.2

Annual Premium for the secretary is = 26000 X [tex]\frac{1.33}{100}[/tex] = 345.8

Therefore, the total annual premium for this insurance will be

= 13873.2 + 345.8 = 14219

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The probability that exactly 4 insects will survive is 0.8975

Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, 0 indicates impossibility of the event and 1 indicates certainty.

probability= sample space/total possible outcome

the total possible outcome for the insecticide to kill insect is 60%

If 4 will survive out of 13, it means 7 will be killed by the insecticide, the percentage is now 7/13×100 = 53.85%

Therefore the probability for 4 insect to survive is 53.85/60= 0.8975

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Answer: Force = 300 NewtonsMass = 25 kgAcceleration = Force / Mass = 300 Newtons / 25 kg = 12 metres / second^2.

Second law of Newton

Data:

Newton's second law formula

          F = m * a

We clear for acceleration

  [tex]\boldsymbol{\sf{\dfrac{F}{m}=\dfrac{\not{m}*a}{\not{m}} \iff \ \dfrac{F}{m}=a \longmapsto \ a=\dfrac{F}{a} }}[/tex]

                                                        [tex]\boldsymbol{\sf{a=\dfrac{300 \ N}{25 \ kg} }}[/tex]

We know very well that to find the acceleration, we decompose N= Kg*m/s^2.

                                                        [tex]\boldsymbol{\sf{a=\dfrac{300 \not{kg}*\frac{m}{s^2} }{25 \not{kg}} }}[/tex]

                                                        [tex]\boldsymbol{\sf{a=12 \ \dfrac{m}{s^{2}} }}[/tex]

The order of least to greatest of given decimal numbers is 3.75, 3.9, 4.2, 4.25, 4.5.

The given decimal number are 4.5, 3.9, 4.25, 3.75, 4.2

Numerical order is a way of arranging a sequence of numbers. This could be in ascending or descending order.

Ascending order: Ascending order means to arrange numbers in increasing order, that is, from smallest to largest.

The order of decimal numbers

Now, least to greatest of decimal numbers is

3.75<3.9<4.2<4.25<4.5

Therefore, the order of least to greatest of given decimal numbers is 3.75, 3.9, 4.2, 4.25, 4.5.

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Answer:

2:7 or [tex]\frac{2}{7}[/tex]

Step-by-step explanation:

The cone total is 4 and the total orders is 14

[tex]\frac{4}{14}[/tex] = [tex]\frac{2}{7}[/tex]

Answer:

45.90

Step-by-step explanation:

$60.00 15% off = $51.00

$51.00 10% off = 45.90

By examining the slope at different points, we can see that the slope is constant.

The term slope has to do with a measure of how steep the line of best fit is for a relationship that exists between two variables. In this case, we are considering the relationship between the amount paid and the time taken.

A straight line graph is expected to have a constant slope. To show that the slope is constant, let us look at two points on the graph; (0, 0) (9, 675) and (0, 0) (7, 525)

In the first case;

m = [tex]y_{2} - y_{1} /x_{2} - x_{1}[/tex]

m = 675 - 0/9 - 0

m = 75

In the second case;

m = [tex]y_{2} - y_{1} /x_{2} - x_{1}[/tex]

m = 525 - 0/7 - 0

m = 75

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Answer:

2.4

Step-by-step explanation:

The bottom is a right triangle.  You know the 2 legs, you need the hypotenuse.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]1^{2}[/tex] + [tex]1^{2}[/tex] = [tex]c^{2}[/tex]

1 + 1 = [tex]c^{2}[/tex]

2 = [tex]c^{2}[/tex]

[tex]\sqrt{2}[/tex] = [tex]\sqrt{c^{2} }[/tex]

[tex]\sqrt2[/tex] = c

Now we know the 2 legs for the larger triangle on top.

[tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

[tex]\sqrt{2} ^{2}[/tex] + [tex]2^{2}[/tex] = [tex]c^{2}[/tex]

2 + 4 = [tex]c^{2}[/tex]

6 = [tex]c^{2}[/tex]

[tex]\sqrt{6}[/tex] = [tex]\sqrt{c^{2} }[/tex]

[tex]\sqrt{6}[/tex] = c

[tex]\sqrt{6}[/tex] rounded to the tenths place is 2.4