cos(-0)=3, sin 0 <0
What is the value of sin ?


2√3/ 3
√6/3
-2 √3/3
-√6/3

Answers

Answer 1

On solving the provided question we can say that - here in trigonometry [tex]sinx(2cosx - 1) = 0\\[/tex] =>  sinx = 0 and 2 cosx -1 =0

what is trigonometry?

The area of mathematics known as trigonometry examines the correlation between triangle side lengths and angles. The area first appeared in the Hellenistic era, around the third century BC. from the use of geometry in astronomical study. The area of mathematics known as exact methods deals with specific trigonometric functions and how they might be used in calculations. There are six popular trigonometric functions in trigonometry. Sine, cosine, tangent, cotangent, secant, and cosecant are their respective names and acronyms (csc). Studying the characteristics of triangles, particularly right triangles, is called trigonometry. The study of geometry, however, is the characteristics of all geometric figures.

[tex]sin 2x - sinx = 0\\-sinx + 2cosx sinx=0\\sinx(2cosx - 1) = 0\\[/tex]

sinx = 0 and 2 cosx -1 =0

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Related Questions

Find the area of a table top that is 3 1/3 feet by 2 feet

Answers

6.666666666666666 (6.6 repeating, I just don’t know how to use the sign online)

I multiplied 3 1/3 by 2

Sasha is a journalist for an online school magazine. She wants to know what topic readers are not interested in for the next publication

Sasha puts a survey on the magazine's website and considers the first 25 responses. Are conclusions drawn from this sample likey to be true for all readers of the magazine?

Answers

Answer:

Step-by-step explanation:

No, some people don't like certain things. It like saying that you pick five random people who are at a science fair and ask them if they like science, the answer would be yes, but if you went to Walmart and asked five random people if they liked science your answers would most likely end up being no. It's the same way looking at the magazines.

What is the value calculator?

Answers

A value calculator is a tool used to help assess the worth of an asset or investment.

The value calculator is designed to help individuals and businesses determine whether an asset or investment is a good value. The calculator takes into account various types of data, such as the current market value, expected future value, and any associated risk factors.

This data is then used to calculate the present value, which is the amount of money an asset or investment is worth today. The calculator also takes into account inflation and other factors that could affect the current value of the asset or investment.

The value calculator can be used to help individuals and businesses make informed decisions about their financial investments.

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3 A sphere is increasing in volume at the rate of 20 in3/s. At what rate is the radius of the sphere increasing when the radius is 4 in.? A.0.982 inls B.0.424 inls C.0.995 inls D.0.025 inls

Answers

The rate of increase of the radius is 0.025 in/sec.

What is a sphere?

A three-dimensional object with a sphere-like shape. A sphere has no vertices or edges, unlike other three-dimensional shapes. The distances between each point on its surface and its center are equal.

In other words, the distance between any two points on the surface and the sphere's center is equal. The formula for the Volume of the sphere is given by

Volume of sphere = (4/3)πr³

Where, r = radius of the sphere

Here we have

A sphere is increasing in volume at the rate of 20 in³/s.  

Here we need to find at what rate the radius of the sphere increases when the radius is 4 in.

Let v = Volume of the sphere at time t

=> Change in Volume = dv/dt  = 20

r = Radius of the sphere at time t

As we know, the Volume of the sphere, v = (4/3)πr³

Differentiate the Volume of the sphere with respect to t

=> dv/dt = (4/3)3πr³⁻¹)(dr/dt)

=> dv/dt = 4πr² (dr/dt)

=>  20 = 4πr² (dr/dt)  

=>  5 = πr² (dr/dt)  

Given that radius, r = 4

=> 5 = π4² (dr/dt)  

=> 5 = (22/7) 64 (dr/dt)  

=> 5 = 3.14(64) (dr/dt)  

=> dr/dt = (5/3.14 × 64)  

=> dr/dt = 0.024880573

=> dr/dt = 0.025

Therefore,

The rate of increase of the radius is 0.025 in/sec.

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What is the quotient (3x2 4x − 15) ÷ (x 3)? 3x 5 3x − 5 3x 1 3x − 1, r = 1

Answers

By solving the expression (3x2 +4x − 15) ÷ (x +3) the quotient is 3x-5 and r=0

What do you meant by quotient?

When solving a division problem, the quotient is obtained by dividing the dividend by the divisor.

Mathematically, we denote the outcome of this division by separating the quotient and remainder with a capital R. (see below). The entire number that results from simplifying a fraction is known as the quotient.

We can do it by long division method  the required quotient is 3x-5 and r=0

not 3x-1 , r=1

multiply the divisor with 3x we will get 3x²+9x to cancel out the first term of dividend.

Now after solving we will get -5x -15

Now, multiply the divisor by -5 we will get -5x-15 which will cancel the entire dividend.

So that the quotient is 3x-5 and r=0

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3x+2y=2 in slope intercept form!!!

Answers

Answer:

[tex] \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}[/tex]

Step-by-step explanation:

Slope-intercept is in form of y = mx + b where m is slope and b is y-intercept. We simply solve for y in term of x and then we will obtain the slope-intercept form.

Given the linear equation:

[tex] \displaystyle{3x + 2y = 2}[/tex]

First, subtract both sides by 3x:

[tex] \displaystyle{3x + 2y - 3x= - 3x + 2} \\ \\ \displaystyle{2y = - 3x + 2}[/tex]

Then divide both sides by 2:

[tex] \displaystyle{ \dfrac{2y}{2} = \dfrac{ - 3x + 2}{2}} \\ \\ \displaystyle{ y = \dfrac{ - 3x + 2}{2}}[/tex]

Separate fractions (Simplify):

[tex] \displaystyle{ y= \dfrac{ - 3x}{2} + \dfrac{2}{2}} \\ \\ \displaystyle{ y= - \dfrac{ 3}{2} x+ 1}[/tex]

And we have finally converted the equation to slope-intercept form.

What are 2 examples of composite number?

Answers

Composite numbers are whole numbers that contain more than two elements.. Examples of composite numbers include 36 and 42. These numbers are divisible by more than just 1 and themselves. 36 is divisible by 1, 2, 3, 4, 6, 9, 12, and 18. 42 is divisible by 1, 2, 3, 6, 7, 14, and 21.

Example 1: To find the factors of 36

Step 1: Start by dividing 36 by 2, which gives us 18.

Step 2: Divide 18 by 2, which gives us 9.

Step 3: Divide 9 by 3, which gives us 3.

Step 4: Divide 3 by 3 which gives us 1.

Step 5: The factors of 36 are 1, 2, 3, 4, 6, 9, 12, and 18.

Example 2: To find the factors of 42

Step 1: Start by dividing 42 by 2, which gives us 21.

Step 2: Divide 21 by 3, which gives us 7.

Step 3: Divide 7 by 7 which gives us 1.

Step 4: The factors of 42 are 1, 2, 3, 6, 7, 14, and 21.

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The price of an article is fixed at a certain percent above the cp and sold it at 5% discount . If the cp is rs16000 and sp is rs20900 with 10% vat ,how much percentage is mp more then cp ?

Answers

Markup price is 30% more then Cost price.

What is VAT?

The selling price includes a VAT (which is a form of tax) and a discount.

A Vat is a form of tax which increases the price of a good and a discount reduces the price.

The marked price is mp = cp(1 + 5%) = 1.50cp

The selling price is sp = mp(1 -10%) = 0.90mp

The gain is profit =sp -cp

= (0.90(1.50cp)) -cp

= cp(0.90·1.50 -1)

= 0.04cp

Mark up = (selling price - cost price) / cost price

(20900 - 16,000) / 16,000 = 0.306 = 30.6 %

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True or false:

If f(x) is a cubic function
and f(1) = 0, f(3) = 0 and
ƒ(4) = 0,
then f(5)=8

Answers

Answer:

FALSE

Step-by-step explanation:

It is not necessarily true that ƒ(5)=8 just because ƒ(1)=0, ƒ(3)=0, and ƒ(4)=0. In fact, it is possible for ƒ(x) to be a cubic function and for ƒ(5) to equal any number, depending on the specific form of the function and the values of its coefficients.

Find the total surface area of a cone of base diameter 7cm and height 8cm

Answers

The total surface area of a cone which has a base diameter of 7 cm and height of 8 cm is  126.5 cm ²

How to find the total surface area of a cone ?

The total surface area of a cone can be found by the formula :

= (π x radius ²) + (π x radius x height )

Radius is half of diameter so :

= 7 / 2

= 3. 5 cm

The total surface area of the cone is;
= ( π x 3. 5 ²) + ( π x 3. 5 x  8)

= 38 . 5 + 88

= 126.5 cm ²

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A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. What is the approximate area of the heptagon rounded to the nearest whole number

Answers

Rounded to the nearest whole number, the approximate area of the heptagon is 555 sq cm.

A heptagon is a seven-sided polygon. To find the area of a regular heptagon, we can use the formula:

Area = (7/4) * (perimeter) * (apothem)

where "perimeter" is the length of the heptagon's circumference and "apothem" is the distance from the centre to the midpoint of one of its sides. The radius of the heptagon is the apothem, which is 27.87 cm.

The perimeter of the heptagon can be calculated by multiplying the length of one side by the number of sides:

Perimeter = 24.18 cm * 7 = 168.26 cm

Now we can substitute these values into the area formula:

Area = (7/4) * 168.26 * 27.87

Area = approximately 554.55 sq cm.

Rounded to the nearest whole number, the approximate area of the heptagon is 555 sq cm.

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−321⋅35⋅7⋅15 what is this properties

Answers

The dots in the expression - 321⋅35⋅7⋅15 represents multiplication.

What are some alternative names for arithmetic operations?

Addition is also known as the sum, subtraction is also known as the difference, multiplication is also known as the product, and division is also known as the factor.

From higher classes, we write a dot sign in between two terms to represent that the terms are being multiplied.

Given, - 321⋅35⋅7⋅15 this represents multiplication between the numbers

- 321, 35, 7, and 15.

The result of this product is,

- 321×35×7×15

= - 1,179,675.

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Write −0.39¯¯¯¯¯ as a fraction in simplest form.

Answers

Answer:

-0.3999... = -⅖

-0.393939... = -13/33

Step-by-step explanation:

Only ones I could think of.

Answer:

-39/100

Step-by-step explanation:

1. Which word doe not have a imilar meaning to - condemn
critique
diparage
criticize
cenure

Answers

Among the given four options, the word that doesnot have similar meaning to condemn is "critique".

What is the meaning of word condemn?

The word "condemn" means to express strong disapproval or criticism of something or someone, often in a formal or official manner. It can also mean to pronounce a judgment of guilt, especially in a court of law. It implies a severe judgment or punishment. Condemn also implies the declaration of something being morally wrong or unacceptable. It is a strong word that carries a sense of condemnation or blame.

Make two sentences using the word condemn.

The sentences are given below:

The judge condemned the defendant for his crimes, sentencing him to life in prison.The community condemned the company for their unethical business practices and called for a boycott.

The word that does not have a similar meaning to "condemn" is "critique".

"Condemn" means to express strong disapproval of something or someone, often in a formal or official manner.

"Criticize" means to express disapproval or to find fault with something or someone

"Censure" means to express strong disapproval or criticism of something or someone, typically in a formal or official manner.

"Disparage" means to speak or write about in a negative way; to belittle or criticize.

"Critique" means to evaluate (a work of art, literary work, etc.) in terms of its strengths and weaknesses; to give an analysis or evaluation of something."Critique" is different because it is an analysis or evaluation of something, whereas the other words are about expressing disapproval or criticism.

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Is 3x3 a polynomial?

Answers

The degree of x-x3 is 3, or 3. It is a cubic polynomial. The formula for the 33 matrix's distinctive polynomial is f() = det (A - I3).

A polynomial is what?

A polynomial is a mathematical statement made up of variables (also known as indeterminates) and coefficients. It can be expressed using just the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. A polynomial is an equation that contains variables, constants, and exponents and is based on the operations of addition, subtraction, multiplication, and division of numbers (No division operation by a variable).

[tex]x - x^3[/tex] has a degree of 3, or 3.

The polynomial is a cubic one.[tex]f() = det (A - I3)[/tex]is the formula for the characteristic polynomial of the 33 matrix.

The characteristic polynomial of the provided 33 matrix is [tex]f() = -3 + 3 + 2.[/tex]

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a man left 1/2 of his money to his first son 3/8 to his second son, the rest 80,000 to his third son.how much did he he leave to his second son​

Answers

As per the given conditions in the question, the amount of money that the second son was left with by the man is 2,40,000.

How do you add two fractions with different denominators?

To add two fractions with different denominators, you must first find a common denominator. A common denominator is a number that is divisible by both denominators of the fractions. Once you have a common denominator, you can add the numerators of the fractions together and place the sum over the common denominator. Then simplify the fraction if possible.

What is the reciprocal of a fraction?

The reciprocal of a fraction is another fraction whose numerator and denominator are flipped. For example, the reciprocal of the fraction 2/3 is 3/2. The product of a fraction and its reciprocal is always equal to 1. To find the reciprocal of a fraction, simply swap the numerator and denominator.

Considering the conditions given in the question,let us suppose that the third son was left with x part of the money,

so we can use the equation,

part of money left for fist son + part of money left for second son + part of money left for third son = total part of money

or, 1/2 + 3/8 + x = 1

therefore, x = 1/8

Also we know that the third son was left 80,000 ,

so 1/8 of total money = 80,000

therefore, total money = 80000 * 8 =6,40,000

Now the amount left for the second son is , 3/8 of total money

which is equal to , 3/8 of 6,40,000 = 2,40,000

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A cup of tea costs $3.25 at a local cafe. Alan and his wife, Patty, have a coupon for $1 off their order. Alan says the expression 3.25t - 1 represents the cost for t cups of tea. Patty says the expression 3t + (-1) represents the cost. Are their expressions equivalent? Explain.

Answers

Answer:

Step-by-step explanation:

The expressions are not equivalent.  A cup of tea costs $3.25.  $3.25t reprensents the total cost for the number of cups of tea (t) in one order.  Subtracting the $1 coupon or adding the coupon as a negative results in the same discount.  But Patty is using the wrong cost for a cup of tea, $3 instead of $3.25.  Resulting in expressions that are NOT equivalent.

Please help
Find the value of x
Find the measure of the two marked angles

PLEASE ALSO FIND X

Answers

The value of x is 8 and  the measure of the two marked angles is  60°.

Which angles are corresponding and adjacent?

When an angle's vertex and side are shared by another angle, the two angles are said to be neighboring angles. The vertex of an angle is the point where the rays come to a halt and create the sides of the angle. When two adjacent angles share a vertex and a side, they can be either complimentary or supplementary angles.

we know that ,

10x-20=7x+4   (it is corresponding opposite angle)

3x=24

x=8

the value of x is 8.

the measure of the two marked angles is 10*8-20= 80°-20°= 60°.

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Marissa is skateboarding on a straight stretch of sidewalk. In 3.0 minutes, she travels 486 meters. What is the magnitude of her velocity during this stretch?

Answers

Marissa velocity while skateboarding is 162 meters per minute

What is an equation?

An equation is used to show the relationship between numbers and variables.

Velocity is the ratio of displacement to time taken. It is a vector quantity (has magnitude and direction) and it is given by:

Velocity = displacement / time

Marissa travels 486 meters in 3 minutes, hence:

Velocity = displacement / time

Velocity = 486 m / 3 min = 162 meters per minute

The velocity is 162 meters per minute

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Answer: The correct answer is 2.7m/s

Step-by-step explanation:

I took the test

The table shows the relationship between the participants walking and running for the week's cross-country practices. Walk (laps) 3 B 15 Run (laps) 5 10 D Total (laps) A C 40 At this rate, how many laps will the participants walk if the total distance is 16 miles? How many miles will they run? They will walk 6 laps and run 10 laps for a total of 16 miles. They will walk 9 laps and run 7 laps for a total of 16 miles. They will walk 10 laps and run 6 laps for a total of 16 miles. They will walk 5 laps and run 11 laps for a total of 16 miles.

Answers

At the given rate, we can say that they will walk 6 laps and run 10 laps for a total of 16 miles.

What is a direct proportional relationship?

In a direct proportional relationship, we can say that the output variable is found by the multiplication of the input variable and the constant of proportionality k, as follows:

y = kx.

For the first question, we have that out of a total distance of 8 miles,  and we can see that;

Walk is 3/8 of the distance.

Run is 5/8 of the distance.

Thus, the proportional relationships for the distances are given as follows:

Walked = 3/8 x Total Distance.

Ran = 5/8 x Total Distance.

We are told that the total distance is 16 miles and so;

Walked: 3/8 * 16 = 6 laps

Ran: 5/8 * 16 = 10 laps

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solve for x. each figure is a parallelogram ​

Answers

9) x = 6

10) x = 1

11) x = 0

12) x = 6

This can be solved from the property of parallelogram.

What is parallelogram?

A unique variety of quadrilateral called a parallelogram has both pairs of its opposite sides parallel and equal.

Parallelograms come in 4 different varieties, including 3 unique varieties. The four varieties are rhombuses, parallelograms, squares, and rectangles.

Properties are:

The opposing sides are equally spaced and parallel.Angles on either side are equal.The angles that are consecutive or contiguous are supplementary.All of the angles will be at right angles if any one of them is a right angle.The two diagonals cut across one another.

9) As we know, from the property of parallelogram,

SR = TQ and ST = RQ

Now, 4 + 2x = 3x - 2

or, x = 6

10) As we know, from the property of parallelogram,

EF = DC and ED = FC

17x + 1 = 18x

or, x = 1

11)  As we know, from the property of parallelogram,

YZ = XW and YX = ZW

2x + 9 = 9

2x = 0

x = 0

12)  As we know, from the property of parallelogram,

TU = SV and TS = UV

6 + 2x = 4x - 6

or, 2x = 12

or, x = 6

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Pill bluethooth Speaker consists two semisphere and cyclinder. The diameter of the cylinder and semisphere is 2 inches. the height of the cylinder is a foot. The According to the Statement please fill in the blanks. please answer the following in inch format and round it to

Answers

The volume of Pill Bluetooth Speaker is 39.78 cubic inches.

What is the volume?

Volume is the measure of the capacity that an object holds.

Formula to find the volume of the object is Volume = Area of a base × Height.

Given that, Pill Bluetooth Speaker consists two semi sphere and cylinder.

The diameter of the cylinder and semi sphere is 2 inches. the height of the cylinder is a foot.

Radius =2/2 1 inch

We know that, the volume of semi sphere is 2/3 πr³

= 2/3 ×3.14×1³

= 2.1 cubic inches

We know that, 1 foot =12 inches

The volume of cylinder is πr²h

= 3.14×1²×12

= 37.68 cubic inches

Total volume =37.68+2.1

= 39.78 cubic inches

Therefore, the volume of Pill Bluetooth Speaker is 39.78 cubic inches.

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"Your question is incomplete, probably the complete question/missing part is:"

Pill bluethooth Speaker consists two semisphere and cyclinder. The diameter of the cylinder and semisphere is 2 inches. the height of the cylinder is a foot. The According to the Statement please fill in the blanks. please answer the following in inch format and round it to nearest tenth.

a) Volume of the Bluetooth Speaker ______

I just need help with number 9 in this picture if anyone could pls help!

Answers

Is it the angle above ?

From the top of a lighthouse, the angles of depression to the top and bottom of a flagpole are 23° and 42°, respectively. If the flagpole is 75 feet from the lighthouse, how tall is the pole? [Round your answer to the nearest tenth of a foot. Type in the number only.]

Answers

Back with the braids.

An item costs $430 before tax , and the sales tax is $34. 40. Find the sales tax rate. Write your answer as a percentage

Answers

The sales tax rate on the item = 8%

We know that the sales tax is nothing but the purchase price times the percentage of tax.

An item costs $430 before tax.

This means, the purchase price is 430 dollars.

The sales tax is $34. 40

To find: the sales tax rate as a percentage

First we find a ratio of the sales tax to the cost of the items before tax.

Sales tax / Pre-tax value of item = (34.40) / 430

Now we write a proportion where the pre-tax value is proportional to 100% and solve for the percentage of sales tax.

i.e., (34.40) / 430 = sales tax percent / 100

So, the sales tax percent  = 8%

Therefore, the sales tax is of 8%

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Hannah either walks or cycles to school. The probability that she walks to school is 0.75 If she walks, the probability that she is late is 0.6 If she cycles, the probability that she is late is 0.2 Work out the probability that on any one day Hannah will not be late for school. ​

Answers

If Hanna is walking there is a 0.4 chance of not being late. 0.75 x 0.4 = 0.3 probability of not being late.

If Hanna cycles there is a chance of 0.8 of not being late. 0.6 x 0.8 = 0.48.

0.48 + 0.3 = 0.78.

In other words, there is a 78% probability of her not being late.

Can u please help? .

Answers

Answer:

x= 43

Step-by-step explanation:

The angles are corresponding angles which mean that they are equal to each other.

3x + 5 = 134  Subtract 5 from both sides

3x + 5 - 5 = 134 - 5

3x = 129  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] = [tex]\frac{129}{3}[/tex]

x = 43

I NEED HELPPPPPPPPPPPPP

Answers

Answer:

y= 12

Step-by-step explanation:

3(-12)-24

-36-24

-12

Evaluate 5c+cd5c+cd5, c, plus, c, d when c=\dfrac15c=
5
1

c, equals, start fraction, 1, divided by, 5, end fraction and d=15d=15

Answers

Answer:

the value is 4

Step-by-step explanation:

what is the value of x?

Answers

Answer:119

Step-by-step explanation:

because it's on oppisite sides on the outside

Answer:

C) 119°

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

The two given two angles are alternate exterior angles and therefore  congruent according to alternate exterior angles theorem:

x = 119°

Definition:

Alternate exterior angles are the pair of angles that are formed on the outer side of the parallel lines but on the opposite side of the transversal.

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Why arent the three rRNA genes of corn one anothers closest relatives?A. Because corn is a hybrid of yeast, cyanobacteria, and E. coliB. Endosymbiosis in the ancestor of corn gave it the ability to photosynthesize and respireC. Endosymbiosis in the ancestors of eukaryotes, and again in photosynthetic eukaryotes led to the evolution of mitochondria and chloroplasts, which retain parts of their original genomes 200. 00 grams of an organic compound is known to contain 83. 884 grams of carbon, 10. 486 grams of hydrogen, 18. 640 grams of oxygen and the rest is nitrogen. What is the empirical formula of the compound? HELP ASAP PLS 50!!!! Identify or mark the missing side or angle that would make triangle ABC a congruent to triangle PDF by SAS Which is not a factor pair of 300 Use the function f(x) = 4x2 + 8x 5 to answer the questions.Part A: Completely factor f(x). Part B: What are the x-intercepts of the graph of f(x)? Show your work. Part C: Describe the end behavior of the graph of f(x). Explain. Part D: What are the steps you would use to graph f(x)? Justify that you can use the answers obtained in Part B and Part C to draw the graph. what is the area of the shaded part, in square meters, below? Tamicca bought a Computer for $1200 and made 12 monthly payments of $115. What was the finance charge that she paid? Round your answer to the nearest cent. A city government would like to make their streets more bike-friendly with features such as protected bike lanes. However, government officials are concerned about the effect on traffic flow. They hire a software consultant agency to develop a simulation of the traffic after the proposed changes.What are the most likely benefits of creating a computer simulation of the proposal?(Select two answers)Pilihan jawabanOnce it is developed, the simulation can run at a faster speed than a real-life experiment.The simulation can try the addition of even more bike lanes without incurring significant extra cost for each lane added.As long as the software developers are not biased, the simulation will not include any bias for or against cyclists.Since they are developing the simulation on a computer, it should be able to represent the proposed changes with 100% accuracy. Choose all of the elements that are minerals by themselves and are also found in mineral compounds.leadhydrogencalciumoxygengoldtinironcarbon factoris x2 + 14x +49 How did the social structure in Latin American make it difficult for groups to work together? . Which of the following statements about your online identity is not true?Your online identity only refers to your social media platforms. Your online identity can include an alias or screen name, an online profile, an avatar and your status updates.Your online identity is who you are when you are in cyberspace.A well-maintained online identity can give people a really good impression of you and open doors to a positive future.3. What did the Magna Carta mostly protect? What was the primary objective of this treaty? At what heart rate should you start compressions on a newborn? In the figure shown, AB and CD are parallel. AB and CD are intersected by EH at points F and G, respectively. The measure of LEFA is (x - 5), and the measure of ZDGF is (73x - 365) . What is the measure, in degrees, of ZDGH? what is the volume of 35.2g of copper when copper is 8.80 g/cm3 and the density is at 20C? A major theme of The Crucible is that human beings stand up for what they believe in and steadfastly support each other even through difficulttimes. Give two examples of how this theme is developed in the play. Which expression is equivalent to -3(x+4)(x-6)-(x^2+8x-10)? What is one characteristic of the advanced culture of Harappan civilization?