6:12 X Review Packe... Packet #2 e to show ALL WORK. Uplo The expression 6-(3x-2i)2 is e 1) -9x² + 12xi + 10 2) 9x² - 12xi +2 3) -9x² +10 4) -9x² + 12xi-4i+6

Answers

Answer 1

The simplified expression of 6 - (3x - 2i)² is -9x² + 12xi + 10.

To simplify the expression 6 - (3x - 2i)², we need to expand the square and perform the necessary calculations. Let's go through the steps:

Step 1: Square the binomial (3x - 2i)²:

(3x - 2i)² = (3x - 2i)(3x - 2i)

Step 2: Expand using the FOIL method:

(3x - 2i)(3x - 2i) = 9x² - 6xi - 6xi + 4i²

Step 3: Simplify the expression by combining like terms and using the fact that i^2 = -1:

9x² - 6xi - 6xi + 4i² = 9x² - 12xi - 4

Step 4: Combine the simplified expression with the initial expression:

6 - (3x - 2i)² = 6 - (9x² - 12xi - 4)

Step 5: Distribute the negative sign to each term inside the parentheses:

6 - (9x² - 12xi - 4) = 6 - 9x² + 12xi + 4

Step 6: Combine like terms:

6 - 9x² + 12xi + 4 = -9x² + 12xi + 10

Therefore, The simplified expression of 6 - (3x - 2i)² is -9x² + 12xi + 10. Therefore, the answer is option 1) -9x² + 12xi + 10.

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Related Questions

What is Quadrilaterals and parallelograms

Answers

Answer:

Step-by-step explanation:

A quadrilateral is a polygon with four sides. There are many special types of quadrilateral. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel .

A quadrilateral is a polygon with four sides. There are many special types of quadrilateral. A parallelogram is a quadrilateral in which both pairs of opposite sides are parallel .

Figure below shows the demand curve for chicken Price per Pound $2.50 --- $1.50 - - - 400 500 Pounds of Chicken (thousands) Between points L and M, the price elasticity of demand is O 0.44, and demand is elastic 0.44, and demand is inelastic 2.25, and demand is elastic 2.25, and demand is inelastic 0.028, and demand is inelastic

Answers

The demand between points L and M is elastic because the elasticity of demand is less than 1.

What is the elasticity of demand between points L and M?

Between points L and M, the price elasticity of demand is 0.44, and demand is elastic.The price elasticity of demand is a measure of how much the quantity demanded of a commodity changes in response to a change in the price of that commodity.

The demand curve for chicken price per pound is given in the question below:

Figure below shows the demand curve for chicken Price per Pound $2.50 --- $1.50 - - - 400 500 Pounds of Chicken (thousands)Between points L and M, the price elasticity of demand is 0.44, and demand is elastic.

Demand is elastic because the elasticity of demand is less than 1.

When the elasticity of demand is less than 1, it means that a small increase or decrease in price will have a larger effect on the quantity demanded.

This implies that the consumers are price-sensitive and are willing to change their demand for the commodity based on a small change in price.

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What is the unit rate for the ratio 100 points/ 4 games?

Answers

Answer:

25

Step-by-step explanation:

100 divided by 4 = 25

the perimeter of the trapezoid is 12x+7. which represents the missing side length​

the perimeter of the trapezoid is 12x+7. which represents the missing side length

Answers

Answer:

A) 3x + 1

Step-by-step explanation:

? = (12x + 7) - (3x + 3) - (2x + 1) - (4x + 2)

? = 3x + 1\

Answer:

The answer is A

Step-by-step explanation:

When looking at the question, the perimeter in total is 12x + 7. so you have to add what you already know:

3x + 3

2x + 1

4x + 2

______

9x + 6

12x + 7 - 9x + 6 = 3x + 1

i need help hurryyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

i need help hurryyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyyy

Answers

The answer is 40 I got you fam

Answer:

The angle x, has the measurement of 40°

Step-by-step explanation:

Step 1:  Define complementary angles

Complementary Angles: Two angles are complementary when the sum of them is equal to 90°.  For example, 30° and 60° are complementary because they add up to 90°.

Step 2:  Figure out the complementary angle

Since ∠ABD and ∠DBC are complementary, that means that they should add up to 90°.  Since the angle value of ∠ABD is 50°, that means that the angle value of ∠DBC should be 90° - 50° = x.

90° - 50° = x

40° = x

Answer: The angle x, has the measurement of 40°

how many coorinates are on a coordinate plane?
A. 1
B. 6
C. 4

Answers

Answer:

4

Step-by-step explanation:

if you're talking about quadrants on a coordinate plane then it is 4:)

coordinate planes are separated into four quadrants (qI,qII,qIII,qIV) shaped like a plus sign, 2 positive quadrants and 2 negative.

Answer:

4! They are called quadrants and quad means 4 <3

Step-by-step explanation:

what is the volume of the solid generated when the region in the first quadrant bounded by the graph of y=x3, the y-axis, and the horizontal line y=1 is revolved about the y-axis?

Answers

The volume of the solid is 4/5π.

The volume of a solid generated by revolving a region around a line is given by V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region, respectively, and y is a function of x.

In this case, the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Therefore, the volume of the solid generated when the region is revolved about the y-axis is given by

V = ∫0 1 π(y)2dy

= ∫0 1 πx6dx

= π/7

= 4/5π

The volume of the solid is calculated using the formula V = ∫a b π(y)2dy, where a and b are the lower and upper limits of the region and y is a function of x. In this case, the lower limit is a=0 and the upper limit is b=1, since the region is bounded by the graph of y=x3, the y-axis, and the horizontal line y=1. Integrating from a=0 to b=1 gives the volume of the solid as V = ∫0 1 πx6dx = π/7 = 4/5π.

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Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x = 1, and f(2) = 6. Which statement is correct? f is concave up on (1,2). None of the other choices are correct. O f is concave down on (1,2). O f is not concave down on (1,2). O f is not concave up on (1,2)

Answers

Since f''(x) = 0, f is neither concave up nor concave down on the interval (1, 2).None of the other options is correct.Therefore, the correct option is: None of the other choices are correct.

Given that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x = 1, and f(2) = 6.

Now, we know that the equation of tangent is y = mx + c where, m = 2 and c = 3 (since it passes through (1, 3))

Hence, the tangent is given by y = 2x + 3

Also, it is given that f(2) = 6.

We can find the derivative of the function f(x) as follows:

f(x) is differentiable for x > 0, therefore,f '(x) exists f '(x) is the derivative of f(x)

f '(x) gives us the slope of tangent at any point x

Now, at x = 1, the slope of the tangent is 2

So,f '(1) = 2Also, we know that f(2) = 6

Therefore, f(x) passes through the points (1, 3) and (2, 6)

So, we can find the equation of the curve using the slope-intercept form of equation of a straight line:

Let y = f(x)

For x = 1, y = 3.

Therefore, 3 = f(1).

For x = 2, y = 6.

Therefore, 6 = f(2).

So, the equation of the curve is given by:

f(x) = 3 + 3(x-1) = 3x

Now, we can find the second derivative of the function f(x) as follows:

f(x) = 3x

Let us find the first derivative of the function:

f '(x) = 3

Hence, the second derivative is zero, i.e., f''(x) = 0.

Now, if f''(x) > 0, the function is said to be concave up and if f''(x) < 0, the function is said to be concave down.

Hence, since f''(x) = 0, f is neither concave up nor concave down on the interval (1, 2).

None of the other options is correct.

Therefore, the correct option is: None of the other choices are correct.

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If $1 is 3% and $2 is 7% and w1 is 0.1, beta of the portfolio is

Answers

The beta of the portfolio, considering $1 with a beta of 3% and $2 with a beta of 7% and a weight of 0.1 (w1), is 6.6%.


The beta of a portfolio measures its sensitivity to overall market movements. To calculate the beta of a portfolio, we need the individual asset weights and betas of each asset. Given that $1 has a beta of 3% and $2 has a beta of 7%, with a weight of 0.1 (w1), we can determine the beta of the portfolio.

To calculate the beta of the portfolio, we use the following formula:

β(portfolio) = (w1 * β1) + (w2 * β2) + ...

In this case, the portfolio contains two assets, so the formula becomes:

β(portfolio) = (w1 * β1) + (w2 * β2)

Substituting the given values:

β(portfolio) = (0.1 * 3%) + (0.9 * 7%)

β(portfolio) = 0.3% + 6.3%

β(portfolio) = 6.6%

Therefore, the beta of the portfolio is 6.6%.

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To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9

Answers

Answer:

your mom

1234567891011

What is the value of 3/4

Answers

Answer:

0.75

0.25 less than 1

Step-by-step explanation:

i dont get it

Answer:

0.75 is the answer

pls pls help whoever gets it right gets marked brainliest and 15 pts!!

pls pls help whoever gets it right gets marked brainliest and 15 pts!!

Answers

Answer:

Below

Step-by-step explanation:

Vertical angles are equal so    8x+3 = 9x-2

                                                     x = 5 °

Since they are equal, if they each are 45° they are complementary ( which means they add to 90°)

8x + 3   = 8 ( 5) + 3   = 43 °    <===== so they are NOT complementary !

If the square root of n = 3/2, what is the negative square root of n ?

Answers

Answer:

use math.way

Step-by-step explanation:

has the answers

plz just solve the questions 3 and 4 only thank you brainiest will be given out to the correct answer

plz just solve the questions 3 and 4 only thank you brainiest will be given out to the correct answer

Answers

Answer:

3. the proportional relationship is that for every cup of blue paint, you need 5 cups of yellow paint. so the relationship between the yellow and blue paint that keeps it proportional is 5 time the cups of blue paint, is how many cups of yellow paint you need

4. constant of proportionality is 5 because for every cup of blue paint, you need 5 cups of yellow paint:

2 * 5 = 10

1 * 5 = 10

3 * 5 = 10

Step-by-step explanation:

Jessica is filling her swimming pool with water. The pool will hold 500 gallons of water,
and Jessica can pump water in at a rate of 30 gallons per hour. Write an equation that
will show how many gallons of water are in the pool as Jessica is filling it.

Answers

Answer:   30*x=Y?

Step-by-step explanation:

can i have help plz i rally need it

can i have help plz i rally need it

Answers

The answer is D. 4:3

what is 72 percent of 30

Answers

Answer:

72% of 30 is 21.6

Step-by-step explanation:

Write 72/100 as a fraction, then multiply it by 30.

72/100 X 30 = 21.6

Calucator 72 ÷ 100 x 30 = 21.6

72 percent of the value 30 will be:  \(\frac{18}{25} * 30 = 21.6\) we get this value by using  fraction method.

What are fraction?

A fraction represents a whole object or part of a collection. A fraction consists of two parts. The number at the top of the line is called the counter. Indicates how many equal parts of the whole or collection are taken. The number below the line is called the denominator. This gives the total number of equal parts divided into a whole, or the total number of equal objects in a collection.

If you divide the whole evenly, the number of parts will be a fraction.

If you divide the pie into 8 halves and place one of them on a plate, each plate is said to contain one-eighth of his pie. It is read as "one eighth" or "one times eight".

We know that:

4% of a number = \(\frac{1}{25}\)

therefore 4*18 = 72% of the same number will be: \(\frac{18}{25}\)

So we can say that \(\frac{18}{25} * 30 = 21.6\)

So the value of 72% of thee number 30 will be: 21.6

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BRAINLIEST PLS HELPpp

BRAINLIEST PLS HELPpp

Answers

Answer:

It should be 0.

Hope it helps

Answer:

undefined

Step-by-step explanation:

Given ( -1 , 0) = ( x1 , y1) and ( -1 , 6) = ( x2 , y2)

slope (m)

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

= ( 6 - 0) / ( -1 +1)

= 6/ 0

= undefined

On december 31, 2020, berclair inc had 600 million shares of common stock and 3 million shares of 9%, $100 par value cumulative preferred stock issued and outstanding. on march 1, 2021 berclair purchased 24 million shares of its common stock as treasury stock. berclair issued a 5% common stock dividend on july 1, 2021. four million treasury shares were sold on october 1. net income for the year ended december 31, 2021, was $1,050 million. the income tax rate is 25%. also, understanding at december 31 were incentive tock options granted to key executives on september 13, 2016. the options are exercisable as of september 13, 2020 for 30 million common shares at an exercise price of $56 per share. compute berclair's basic and diluted earnings per share

Answers

No, it is not possible to determine Berclair's basic and diluted earnings per share with the given information.

Is it possible to determine Berclair's basic and diluted earnings per share with the given information?

No, it is not possible to determine Berclair's basic and diluted earnings per share with the given information alone. The calculation of earnings per share involves considering the weighted average number of shares outstanding, including any potential dilutive securities such as stock options or convertible securities.

The information provided does not specify the weighted average number of shares outstanding or any potential dilutive securities.

To accurately calculate the basic and diluted earnings per share, we would need additional information such as the weighted average number of shares outstanding during the year and any potential dilutive securities, along with their impact on the earnings per share calculation.

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What is thr answer of (a-b) (a+2b)​

Answers

Answer:

Step-by-step explanation:

Use FOIL method

F -> First

O Outside

I inside

L Last

(a - b)(a + 2b)= a*a + a *2b + (-b)*a + (-b)*2b

                     = a² + 2ab - ab - 2b²

Combine like terms

                       = a² + ab - 2b²

the area of earth's dry land is about 58 million square miles. The land area of North America is about 16% of Earth's land area. What is the approximate land area of North America. PLs ANSWER NOW

Answers

Answer:

58 million = .16a

a = 362.5 million square miles

The location of the obstacle course, Transformation Fitness Studios, often gets crowded. Therefore, the company opened a second location, Reflections of You, on the other side of town. The obstacle course at Reflections of You is the same as the one at Transformation Fitness Studios, except it is a horizontal reflection. This means all the checkpoints have been reflected in the y-axis.


Using the checkpoints at Transformation Fitness Studios, A(0,5), B(−9,5), and C(−4,5), find the coordinate locations of their respective checkpoints, A′, B′, and C′, at the Reflections of You obstacle course.



A′(0,5), B′(−9,5), C′(−4,5)


A′(0,−5), B′(−9,−5), C′(−4,−5)


A′(0,5), B′(9,5), C′(−4,5)


A′(0,5), B′(9,5), C′(4,5)

Answers

The correct answer for the coordinate locations of their respective checkpoints, A′, B′, and C′  is: A′(0,−5), B′(−9,−5), C′(−4,−5)

Since the Reflections of You obstacle course is a horizontal reflection, the x-coordinates of the checkpoints remain the same, while the y-coordinates change sign.

Given the checkpoints at Transformation Fitness Studios:

A(0, 5)

B(-9, 5)

C(-4, 5)

The respective coordinates of the checkpoints at Reflections of You are:

A'(0, -5)

B'(-9, -5)

C'(-4, -5)

Therefore, the correct answer is:

A′(0,−5), B′(−9,−5), C′(−4,−5)

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4•(2+5)^2 -5^2 how do I solve this?

Answers

Answer:

4•(2+5)^2 -5^2 = 171

Step-by-step explanation:

Do BIDMAS
(brackets, indices, division, multipy, add, sub)

so brackets
4*7^2-5^2
then do the indices
4*49-25
then the multiply
196-25
= 171
Hope this helps

Answer: Brackets => 4 x (7)^2 - 5^2
               Indices/Orders => 4 x 49 - 25

               Multiplication => 196 - 25

               Subtraction => 171

How to find the length of the segment indicated?

How to find the length of the segment indicated?

Answers

Answer:

Step-by-step explanation:

it is 2x

Find the greatest common divisor of 63 and 42

Answers

Answer:

21

Step-by-step explanation:

Frequenc


Consider the frequency distribution to the right. Complete parts (a)


through (c) below.


15


Value


607


549


603


586


588


606


5


7


13


6


7 7

Answers

a) Mean: Approximately 590.17

b) Median: 585

c) Mode: 614

To find the mean, median, and mode of the given frequency distribution, we need to calculate the corresponding statistical measures using the provided values and frequencies.

a) Mean:

The mean is calculated by summing up the products of each value and its corresponding frequency, and then dividing by the total number of observations.

In this case, we have:

(614 × 13) + (535 × 8) + (610 × 9) + (585 × 12) + (584 × 5) + (601 × 7)

= 7,982 + 4,280 + 5,490 + 7,020 + 2,920 + 4,207

= 31,899

Now, we divide this sum by the total number of observations:

31,899 / (13 + 8 + 9 + 12 + 5 + 7)

= 31,899 / 54

≈ 590.17

Therefore, the mean of the frequency distribution is approximately 590.17.

b) Median:

The median is the middle value of a data set when it is ordered in ascending or descending order.

To find the median, we need to arrange the values in ascending order along with their corresponding frequencies:

535, 584, 585, 601, 610, 614

Now, we need to find the cumulative frequency.

Starting from the lowest value, we add up the frequencies until we reach or exceed half the total number of observations:

535 (8)

535 + 584 (8 + 5 = 13)

535 + 584 + 585 (13 + 12 = 25)

535 + 584 + 585 + 601 (25 + 7 = 32)

Since the cumulative frequency of 32 exceeds half the total number of observations (54/2 = 27), the median will lie in the group containing 585.

Therefore, the median of this frequency distribution is 585.

c) Mode:

The mode is the value(s) that appear(s) most frequently in a data set. In this case, the highest frequency is 13, which corresponds to the value 614.

Thus, the mode of this frequency distribution is 614.

To summarize:

a) Mean: Approximately 590.17

b) Median: 585

c) Mode: 614

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FrequencConsider the frequency distribution to the right. Complete parts (a)through (c) below. 15Value607549603586588606571367

The path of a basketball during a free throw can be modeled with the function shown, where x is time, in tenths of a second, since releasing the ball and f(x) represents height in feet. Which statements correctly describe this function? A. The basketball reaches a maximum height of 7 feet. B. The basketball reaches a maximum height of 20 feet. C. The height of the ball at time 0 is –9 feet. D. The height of the ball at time 0 is 6 feet. E. The graph is symmetric about the line x = 5.5.

The path of a basketball during a free throw can be modeled with the function shown, where x is time,

Answers

Answer: The answer is

-A

-D

-E

Step-by-step explanation:

Got 100%.

Have a Good Day!

The correct statement about the function of basketball is as follows:

The basketball reaches a maximum height of 7 feet.The height of the ball at time 0 is 6 feet.The graph is symetric about the line  x=5.5.

What is a function?

A function is a relationship between two variables and in a function each value of x must have a value of y.

How to identify the statement?

By watching the graph carefully we can see that the highest point at which the graph lies is (5.5,7) and in this question y element describes the height.

When we put value of x equal to 0 we found the value of y equal to 6 which shows the height.

The graph is symetric about the line at x=5.5 because it is decreasing at a constant rate.

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5. 3x = 6. 40x how many time do I need to multiply thee number for them to be the ame

Answers

The equation 3x = 6.4 can be solved for x by dividing both sides of the equation by 3: 3x/3 = 6.4/3; x = 2.13

So, for 3x and 6.4x to be equal, x must be equal to 2.13. This means that you need to multiply the number 6.4 by 2.13 to equal 3. The equation 3x = 6.4 represents the relationship between two variables, x and 3x. We are trying to find the value of x that would make 3x equal to 6.4. To do this, we divide both sides of the equation by 3. Dividing both sides of an equation by the same number does not change the relationship between the variables; it only scales down the variable's value by the same factor.

So, by dividing both sides of the equation by 3, we get:

3x/3 = 6.4/3

x = 2.13

Finally, to make 6.4x equal to 3, we need to divide 6.4 by 2.13: 6.4 / 2.13 = 3. So, we need to multiply 6.4 by 2.13 to equal 3.

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What is sin 60°?
O A. /
O B. v3
2
O c.
OD. TO
O E. 13
O F. 1

Answers

Answer:

Sqaure root of 3 divided by 2

Step-by-step explanation:

The value of function  sin 60° is √3/2.

What is Trigonometry?

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

We need to find the value of sin 60°

Sin 60 degrees is nothing but sin π/3

The sine function we obtain by dividing the opposite side by hypotenuse.

sin theta = Opposite side/ hypotenuse

sin 60=√3/2

The value of sin 60 degrees is square root of three by two.

Hence, the value of function  sin 60° is √3/2.

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What is 45+72/6*4+3+17+99-45/8?

Answers

Answer:

206.375

Step-by-step explanation:

45+72/6 * 4 = 45 + 48 = 93

93 + 3 = 96

96 + 17 +113

113 + 99 = 212

212 - 45/8 = 206.375

Other Questions
a 31.5 g wafer of pure gold initially at 69.9 c is submerged into 63.3 g of water at 26.9 c in an insulated container. the specific heat capacity for gold is 0.128 j/(gc) and the specific heat capacity for water is 4.18 j/(gc). what is the final temperature of both substances at thermal equilibrium? ME NEEDS SOME HELP WITH MATH PLS Some firms eventually experience problems increasing their capacity to produce output as the demand for their product increases. For these firms, supply is less elastic at low levels of output and more elastic at high levels of output. supply is more elastic at low levels of output and less elastic at high levels of output. market power is substantial. supply is perfectly inelastic. when we are rounding to the nearest hundred thousand place Between what two hundred thousand is 729,398 label the end points In JKL, the measure of L=90, JK = 7. 3 feet, and KL = 4. 7 feet. Find the measure of J to the nearest tenth of a degree Assume that starting next year, you will receive payments of $ 777 every year for 7 years. The discount rate it 4 %. What is the present value of these payments Which structure sends signals about what you see to the brain? retina lens cornea in reality, reactants don't have to react in perfect whole-numbers of moles. in a two-reactant synthesis reaction, usually, one reactant gets entirely used up (and determines how much product is made), even if that means using fractions of a mole of reactant. for instance, when solid, metallic aluminum al and red, liquid bromine br2 are brought together, they make a white solid according to the reaction 2al 3br2 2albr3. if 5.0 moles of aluminum al was reacted with 10 moles bromine br2, all five moles of aluminum would react, with only 7.5 moles bromine. (2:3 mole ratio) this would produce only 5.0 moles of albr3, leaving 2.5 moles of excess br2 behind. 5. now assume 3 moles al and 4 moles br2 react a)which chemical is the limiting reactant? Plz help me with this question Is disk scheduling, other than fcfs scheduling, useful in a single-userenvironment? explain your answer. Quisssssss :'^(A = 102A + 4A - 3A What makes fertilizers a benefit to the farming industry A clothing store has a markup of 98% on the wholesale price of jeans. If the wholesale price of mens jeans is $24.00, what will be the retail price? 8. What is missing in a time of chaos? Congress has given the Federal Reserve a mandate to do which of the following? OA. Maintain price stability OB. Conduct policy to encourage reduce the unemployment rate to 0% O C. Conduct policy to maximize stock prices O D. All of the above OE. None of the above Which of these passages from "The Cactus" conveys an image of heroic admiration? A. Without protest, he allowed her to twine about his brow this spurious bay of Spanish scholarship. B. Trysdale's friend, the brother of the bride, stood at a sideboard complaining. c. On the table stood a singular-looking green plant in a red earthen jar. In the diagram, X is the midpoint of vz and wY. W V X N Y Why is AVWX EAZYX? (G.6) (1 point) O A. Side-Angle-Side O B. Angle-Angle-Side O C. Angle-Side-Angle Raju Tamang bought 40 kg of rice Rs 80 per kg. He sold 25 kg of rice at Rs 84 per kg and the remaining quantity at Rs 76 per kg .Find his profit or loss percent in the transaction. Astronauts experience similar feelings of dizziness and disorientation upon arrival in space and upon their arrival back on earth. what does this indicate to researchers? a. the vestibular sense is very sensitive to changes in climate. b. the vestibular sense may be capable of sensory adaptation. c. the vestibular sense is not affected by changing conditions. d. the vestibular sense may be confused by zero-gravity climates. please select the best answer from the choices provided a b c d what is the last spell harry uses against voldemort?