Writing Exercises
353. Why does (a + b)² result in a trinomial, but (a − b)(a + b) result in a binomial?

The quotient of the complex numbers is 3[cos(240)+ isin(240)] option (D) is correct.

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have two complex number is given.

The quotient of the complex numbers:

[tex]= \rm \dfrac{12\left[cos\left(320\right)+isin\left(320\right)\right]}{4\left[cos\left(80\right)+isin\left(80\right)\right]}[/tex]

= 3[cos(320-80)+ isin(320-80)]

= 3[cos(240)+ isin(240)]

Thus, the quotient of the complex numbers is 3[cos(240)+ isin(240)] option (D) is correct.

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

The average speed in approximately 184.62 miles per hour.

We have been given that in the race Math 600, drivers must complete 200 laps of 3 miles each. Dave drove the first 150 laps at 180 mph and the last 50 laps at 200 mph.

First of all, we will find the number of miles in 150 laps and 50 laps as:

150 X 3 miles = 450 miles

50 X 3 miles = 150 miles.

Now, we will find time taken to complete each distance as:

Time = 450/180 =2.5 hr

Time = 150/200 = 0.75 hr

Average speed = 184.62

The average speed in approximately 184.62 miles per hour.

Learn more about Speed:

https://brainly.com/question/4313883

#SPJ4

Answer:

C) 12 m

Step-by-step explanation:

Answer: 3[tex]i[/tex]

Step-by-step explanation: The reason for this is because [tex]i[/tex] =

[tex]\sqrt{-1}[/tex], and when [tex]\sqrt{-1}[/tex] is multiplied to [tex]\sqrt{9}[/tex], it becomes [tex]\sqrt{-9}[/tex]. Since [tex]\sqrt{9}[/tex] can be simplified to 3, we can just multiply [tex]i[/tex] to 3. This becomes 3[tex]i[/tex].

Hope this helped!

Answer:

3i

Step-by-step explanation:

Answer: x = 32

Step-by-step explanation:

If m∠ORS = m∠SRQ = 3x - 6 and since the two angles are a linear pair they total 180°. This means half or only one section = 90°

solve for x

3x - 6 = 90

add 6 to both sides

3x = 96

divide each side by 3

x = 32

The distance from the center of dilation, P, to.the image vertice S' is; 6 units.

It follows from the task content that the center of dilation of the triangle QRS is point P and the length of segment PS in the pre-image is; 8 units.

Hence, since the dilation factor as given in the task content is; three-fourths, it therefore follows that the distance of point P to S' in the image is; (3/4) × 8 = 6units.

Read more on dilation;

https://brainly.com/question/10253650

#SPJ1

There are 15 rows of seats in the theater

The given parameters are:

The number of rows is calculated as:

Rows = Total number of people/People per row

This gives

Rows = 357/24

Evaluate the quotient

Rows = 14.875

Round up the number

Rows = 15

Hence, there are 15 rows of seats in the theater

Read more about sequence at:

https://brainly.com/question/6561461

#SPJ1

The maximum height of the tray is 1.8 meters and the tray is in the air for 2 seconds

The distorted information (i.e. the function) in the question is:

h(t) = -0.2t^2 + 0.4t + 1.6

Differentiate the function

h'(t) = -0.4t + 0.4

Set to 0

-0.4t + 0.4 = 0

Subtract 0.4 from both sides

-0.4t = -0.4

Divide by -0.4

t = 1

Substitute t = 1 in h(t) = -0.2t^2 + 0.4t + 1.6

h(1) = -0.2(1)^2 + 0.4(1) + 1.6

Evaluate

h(1) = 1.8

Hence, the maximum height of the tray is 1.8 meters

In (a), we have:

t = 1

This represents the time to reach the maximum height.

The time spent in the air is:

T = 2t

This gives

T = 2 * 1

T = 2

Hence, the tray is in the air for 2 seconds

Read more about quadratic functions at:

https://brainly.com/question/11535666

#SPJ1

Answer:

y = - 6/7 x - 10/7

Step-by-step explanation:

Slope = (y2-y1) / (x2-x1)

= 6/-7 = -6/7

y = -6/7 x - a

passes by (-4,2)

2 = 24/7 - a, a = -10/7

y = -6/7 x - 10/7

The sample size that gives 99% confidence level and estimate will be within 3 ounces is 0.7386[tex](standard deviation)^{2}[/tex].

Given  confidence level 99% and margin of error is 3 ounces of true mean.

Margin of error is the difference between the actual values and the calculated value of mean.

Sample size is the number of items taken from the population as a sample for research.

We have to find the sample size.

First we have to find the z value for the corresponding p value of 0.99.

z value=2.58

Margin of error=z*σ/[tex]\sqrt{n}[/tex]

3=2.58σ/[tex]\sqrt{n}[/tex]

[tex]\sqrt{n}[/tex]=2.58/3 σ

Squaring both sides

n=[tex]2.58^{2}[/tex]σσ

Hence the sample size needed is 2.58 ([tex](standard deviation)^{2}[/tex].

Learn more about margin of error at https://brainly.com/question/24289590

#SPJ4

Answer:

2

Step-by-step explanation:

So the midpoint of AB can be calculated by finding the length of AB, dividing it by 2 and then adding it to A. So the length of AB is equal to B-A or in general the difference between two values is |a-b| where the order doesn't matter, but assuming B is the right side (meaning it should be greater than A) the length should be B-A. in this case A = -5 and B = 3 so the length is 3 - (-5) = 8. The length is 8 so the midpoint is half of that which is 4, now adding 4 to the left side (A) you get -5 + 4 = -1. So the midpoint of AB lies at -1. Now the midpoint of AC can be found using the same process. 7 - (-5) = 12 => 12/2 = 6 => -5 + 6 = 1 so the midpoint of AC is at 1. Now to find how many units from the midpoint AB to AC you just subtract the midpoint of AB from AC. this gives you 1 - (-1) which is 2.

The petrol cost for Anne's journey of 120km is $16.236

Her car has a fuel consumption of 8.2 litres per 100 km .

Therefore,

100 km = 8.2 litres

120 km = ?

cross multiply

volume(litres) = 8.2 × 120 / 100 = 984 / 100 = 9.84 litres

Therefore,

1 litres = 1.65 dollars

9.84 litres = ?

cross multiply

cost of fuel used = 1.65 × 9.84 / 1

cost of fuel used = $16.236

learn more on cost here: https://brainly.com/question/21968536

#SPJ1

When the above complex expression has been simplified the solution to the above expression is = 2003/8016.

The formula is given as:

1 - [tex]\frac{1}{n}[/tex] = [tex]\frac{n-1}{n}[/tex]

From the stated express, we have:

(1 - (1/2)) * (1 - (1/3)) * (1 - (1/4)) *( 1 - (1/2004))

→ ((2-1)/2)  ((3-1)/3) ((4-1)/4) ((2004 -1)/2004)

→ (1/2) * (2/3) * (3/4) * (2003/2004)

→ [tex]\frac{ 1* 2003}{4*2004}[/tex]

= 2003/8016

Learn more about complex progression at:
https://brainly.com/question/11089283
#SPJ1

Answer:

When the above complex expression has been simplified the solution to the above expression is = 2003/8016.

What is the formula for solving the above?

The formula is given as:

1 -  =

From the stated express, we have:

(1 - (1/2)) * (1 - (1/3)) * (1 - (1/4)) *( 1 - (1/2004))

→ ((2-1)/2)  ((3-1)/3) ((4-1)/4) ((2004 -1)/2004)

→ (1/2) * (2/3) * (3/4) * (2003/2004)

→

= 2003/8016

Step-by-step explanation:

The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.

In the equation given:

Note that:

x²-3x+2 = square root √x-2 + 2

Therefore:

x⁴-6x³+9x²= square root x-2

x² = 3.375

Convert 3.35 into fractions and will get 27/8. So, The Approximate the solution to the equation using three iterations of successive approximation is option b: 27/8.

Learn more about Successive approximation from

https://brainly.com/question/27278132

#SPJ1

Answer:

[tex]\frac{1}{8}[/tex]

Step-by-step explanation:

2 ( [tex]\frac{1}{4}[/tex] )²

= 2 × [tex]\frac{1}{16}[/tex] ← cancel 2 and 16 by 2

= 1 × [tex]\frac{1}{8}[/tex]

= [tex]\frac{1}{8}[/tex]

The fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.

We assume the drop in the level of water to be d cm.

Since the container is cylindrical in shape, its volume is given as:

V = πr²h, where V is the volume, r is the radius, and h is the height.

In the question, we are given that the diameter of the can is 30 cm.

Hence its radius = 30/2 = 15 cm.

The capacity of the container is given to be 30 liters or 30*1000 = 30000 cm³.

The volume of the oil used = 1 liter or 1*1000 = 1000 cm³.

Thus, substituting V = 1000, r = 15, and h = d, in the formula of the volume, V = πr²h, we get:

1000 = π(15)²(d),

or, d = 1000/(225π) = 1.4147.

Thus, the fall in the water level is 1.4147 cm.

Therefore, the fall in the level of oil is 1.4147 cm when the total volume of oil consumed is 1 liter.

Learn more about the volumes of cylinders at

https://brainly.com/question/9554871

#SPJ4

Answer: 34

Step-by-step explanation:

[tex]V=\frac{4}{3}(\pi)(2^{3}) \approx \boxed{34}[/tex]

Answer:

160000

Step-by-step explanation:

if im wrong sorry

Answer:

the answer is 10

Step-by-step explanation:

. Hello !

Because firstly divide 400 by 2

Jeff received 280$ from his mother

Such questions are the simplest as it needs you to just write the conditions accordingly which then simplifies and provides you the answer.

This question can be solved using two tricks which are shown below:-

Trick  1 :

1 – 1/4 = 3/4 (used for the 1st 7 days)

1/4 – 410 (used for 8th and 9th days)

(3/4)/7 ——- (1/4 – 10)/2

(3/4) x (2/7) = 3/14 ——- (1/4 – 10)

1/4 – 3/14 = (7 – 6)/28 = 1/28 ——- 10

28/28 ——- 10 x 28 =$ 280

Trick 2 :

7 days ——- 3/4

1 day ——- 3/28

2 days ——- 6/28

6/28 ——- (1/4 – 10) = 7/28 – 410

1/28 ——- 10

28/28 ——- 10 x 28 = $280

Thus Jeff received 280$ from his mother.

Learn more about simple math here :

https://brainly.com/question/23678

#SPJ4

Step-by-step explanation:

1.) ˆ B = 7∘ ,  ˆ A = 28 ∘ ,  a = 27

-----------------------------------------------------------------------------------------

2.) c ≈ 28.0

-----------------------------------------------------------------------------------------

3.) The triangle has the following measures.

A  =  36 ˚

a  =  14  units

B  =  105 ˚  

b  =  23 units

C  =  39 ˚  

c  = 15  units

------------------------------------------------------------------------------------------

4.) a  ≅  15.0 units

B  =  145 ˚

b  ≅  22.9 units

The complete equation of the polynomial is 2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2

The equation is given as:

_x(x^2 - _x) + _x^3 = _x(_x^2 + _x) - x^2

Complete the blanks using alphabets

ax(x^2 - bx) + cx^3 = dx(ex^2 + fx) - x^2

Open the brackets

ax^3 - abx^2 + cx^3 = dex^3 + dfx^2- x^2

Factorize the expression

(a + c)x^3 - abx^2 = dex^3 + (df - 1)x^2

By comparison, we have:

a + c = de

-ab = df - 1

Rewrite the second equation as:

ab + df = 1

So, we have:

a + c = de

ab + df = 1

Set a = 2 and c = 10.

So, we have:

a + c = de ⇒ de = 2 + 10 ⇒ de = 12

ab + df = 1 ⇒2b + df = 1

Express 12 as 3 * 4 in de = 12

de = 3 * 4

By comparison, we have:

d = 3 and e = 4

So, we have:

2b + df = 1

This gives

2b + 3f = 1

Set b = 11.

So, we have:

2 * 11 + 3f = 1

This gives

22 + 3f = 1

Subtract 22 from both sides

3f = -21

Divide by 3

f = -7

Hence, the complete equation is:

2x(x^2 - 11x) + 10x^3 = 3x(4x^2 - 7x) - x^2

Read more about polynomials at:

https://brainly.com/question/4142886

#SPJ1

Answer:

The function f has an inverse because it is one-to-one.

Step-by-step explanation:

The condition for a function to have an inverse is that every x coordinate maps to a single y - coordinate. As illustrated by the diagram attached in the second picture, every x value maps to one y value therefore satisfying the condition making the function have an inverse.

The graph which represents the relationship between the year and the computers value is; Choice A.

According to the task content, it follows that the computer loses 1/3 of its value every year. Hence, it follows that the value of the computer each year is 2/3 of its previous value.

Hence, the relationship can best be modelled by an exponential function, a decay function to be more specific and can best be represented by Choice A.

Read more on graphs;

https://brainly.com/question/4025726

#SPJ1

We have proven that BC = DE using the Segment addition postulate

The segment addition postulate states that given two points A and C, a third point B lies on the line segment AC if and only if the distances between the points satisfy the equation AB + BC = AC

The reasons for the proof are given below:

Statement                                Reason

BD = BC + CD                          Segment addition postulate

CE = CD + DE                           Segment addition postulate

BD = CE                                    Given

BC + CD = CD + DE                  Substitution property

BC = DE                                   Subtraction property

Hence, we have proven that BC = DE using the Segment addition postulate

Learn more on Segment addition postulate here: https://brainly.com/question/2134445

#SPJ1

Answer:

m = 2

Step-by-step explanation:

[tex]m = \frac{rise}{run} =\frac{y_{2}-y_1}{x_2-x_1}[/tex]

[tex]=\frac{6 - 8}{2 - 3} \\= \frac{-2}{-1}\\ = 2[/tex]

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{The formula for finding the slope:}[/tex]

[tex]\mathbf{\dfrac{y_2 - y_1}{x_2 - x_1} = slope}[/tex]

[tex]\huge\textbf{Some people understand formula like:}[/tex]

[tex]\mathbf{\dfrac{rise}{run} = slope}[/tex]

[tex]\huge\textbf{Breaking down the question:}[/tex]

[tex]\mathbf{y_2 \rightarrow \boxed{\textbf{6}}}[/tex]

[tex]\mathbf{y_1 \rightarrow \boxed{\textbf{8}}}[/tex]

[tex]\mathbf{x_2 \rightarrow \boxed{\textbf{2}}}[/tex]

[tex]\mathbf{x_1 \rightarrow \boxed{\textbf{3}}}[/tex]

[tex]\huge\textbf{What your equation should look like:}[/tex]

[tex]\mathbf{\dfrac{6 - 8}{2 - 3} = slope}[/tex]

[tex]\huge\textbf{Simplify the equation we came up with:}[/tex]

[tex]\mathbf{\dfrac{6 - 8}{2 - 3} = slope}[/tex]

[tex]\mathbf{\rightarrow \dfrac{-2}{-1} = slope}[/tex]

[tex]\mathbf{\rightarrow -2 \div -1 = slope}[/tex]

[tex]\mathbf{\rightarrow 2 = slope}[/tex]

[tex]\huge\textbf{Thus, the answer should most likely be:}[/tex]

[tex]\huge\boxed{\mathsf{Slope \rightarrow \boxed{\textsf{2}}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Using proportions, the horse 8 feet from the center would have to make 96 revolutions.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

A horse 24 feet from the center of a merry-go-round makes 32 revolutions. If it is 8 feet and wants the same distance, how many revolutions will it need? The rule of three is:

24 feet - 32 revolutions

8 feet - x revolutions

The measures are inverse proportional, hence:

8x = 24 x 32

x = 24 x 32/8

x = 96 revolutions.

More can be learned about proportions at https://brainly.com/question/24372153

#SPJ1

Answer:

Let the no. be x

51 + x = -1

x = -1-51

x = 1 + 51

Answer:

-52

Step-by-step explanation:

51 + (-52) = -1

Hello,

2³ = 2 × 2 × 2 → answer A

The difference for both the rhombus and square are as follows;

Therefore, the difference for both the shapes(square and rhombus)are as follows:

learn more rhombus and square here: https://brainly.com/question/2690905

#SPJ1

Answer: C. He can show that the measures of arcs AB, AC, and BC are all equal to 120°.

Step-by-step explanation:

Each angle of an equilateral triangle measures 60°, so by the inscribed angle theorem, each arc created by a pair of adjacent vertices will measure 120°.