Please help quick show work and explain

Please Help Quick Show Work And Explain

Answers

Answer 1
The maximum height of the ball is of: 5 feet.The ball is at the maximum height at a time of: 0.25 seconds.The ball hits the ground at a time of: 0.809 seconds.

How to obtain the measures?

The height of the ball after x seconds is given by the quadratic function presented as follows:

y = -16t² + 8t + 4.

This is a concave down parabola, hence the vertex of the function is the maximum point.

The coefficients of the quadratic function are given as follows:

a = -16, b = 8, c = 4.

Then the x-coordinate of the vertex is given as follows:

x = -b/2a = -8/-32 = 0.25.

The maximum height of the ball is given as follows:

y = -16(0.25)² + 8(0.25) + 4 = -1 + 2 + 4 = 5 feet.

The ball hits the ground when:

y = 0.

Hence:

-16t² + 8t + 4 = 0.

Solving the quadratic equation, the positive solution is given as follows:

t = 0.809 seconds.

The graph of the quadratic function is given by the image shown at the end of the answer.

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Please Help Quick Show Work And Explain

Related Questions

If k is a negative integer, which of these is DEFINITELY NEGATIVE? A. k* (k-1) * (k - 2) B. k* (k+1) C. k* (-50) D. (50-k)​

Answers

Answer:

only A ans bellow

Step-by-step explanation:

let k= -4

A. k * (k - 1) * ( k - 2)

= -4 * (-4 -1) * ( -4 -2)

= -4* (-5) * (-6)

= 20*-6

= -120

B. k * ( k+1)

= -4 * ( -4+1)

= -4 * (-3)

= + 12

C. k * (-50)

= -4 * (-50)

= + 200

D . (50 - k)

= 50 - (-4)

= 50 + 4

= + 54

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if k is negative then k(k-1)(k - 2) will be definitely negative.

What is Number system?

A number system is defined as a system of writing to express numbers.

Given that k is a  negative integer.

We need to find which of the given options are defnitely negative.

Let us consider k as -3.

k(k-1)(k - 2)

-3(-3-1)(-3-2)

-3(-4)(-5)=-60

Which is negative.

k(k+1)=-3(-3+1)=6 +ve

k (-50)=-3(-50)=150 +ve

(50-k)​=50-(-3)=53 +ve.

Hence, if k is negative then k(k-1)(k - 2) will be definitely negative.

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a line with a slope of 2 passes through the points (10,8) and (w,6). what is the value of w?

Answers

Answer:

w = 9

Step-by-step explanation:

Use a slope formula to solve. Subtract the y's put that on top and subtract x's and put that on the bottom. This calc should equal 2 that was given.

(8-6)/(10-w) = 2

2/(10-w) = 2

Cross-multiply.

2 = 2(10-w)

Distributive property

2 = 20 - 2w

Add 2w

2 + 2w = 20

Subtract 2

2w = 18

divide by 2

w = 18/2 = 9

Or you can logic it out...8-6 is 2 on top. Need a 1 on the bottom (bc 2/1 is 2) 10-9 is 1 for on the bottom. w = 1

pool workers conducted a chi-square goodness-of-fit test at the 5% significance level. the chi-square value is 1.3892 and the p-value is 0.7081. what can the pool workers conclude?

Answers

The pool workers can conclude that there is not a statistically significant difference between the expected and observed results.

The chi-square value is 1.3892 and the p-value is 0.7081 The p-value of 0.7081 is greater than the 5% significance level, meaning that the null hypothesis can not be rejected.

This means that the difference between the expected and observed results is not statistically significant, and the observed results are likely due to random chance. This means that there is not a significant difference in the observed results from the expected results, and the null hypothesis is accepted.

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8.
Are the two ratlos below proportional? *
5
15
6' 18
Mark only one oval.
a. No, because the unit rates are not equal.
b. Yes, because the unit rates are the same.
c. No, because the rates are the same.
d. Yes, because the unit rates are not equal.
2 points

Answers

Made possible via methods. In light of this, 5, 6, 15, and 18 are in proportion. The same unit rates prove that.

Rates and proportions are they equivalent?

A ratio, on the other hand, is the comparison of the sizes of two values, whereas a proportion is a part, share, or quantity in relation to an overall total. Each of the three measures has unique characteristics, and a rate is just one number divided by another.

The same units apply to proportions, or not?

Due to the consistency of the units and their equivalent, each ratio compares the same units—inches and feet—and is therefore similar. Compare two ratios using the same units when using proportions.

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a company wants to encrypt a document containing important passwords. to do this, the sum of two positive numbers will need to be minimized. if the product of both numbers is 47, what is the minimum sum?

Answers

The requried, "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.

To find the minimum sum of two positive numbers whose product is 47, we can use the concept of the arithmetic mean-geometric mean inequality (AM-GM inequality).

The AM-GM inequality states that for any two positive numbers, the arithmetic mean (average) is always greater than or equal to the geometric mean. Mathematically, it can be expressed as:

AM ≥ GM

For two positive numbers "a" and "b," the arithmetic mean is (a + b) / 2, and the geometric mean is √(ab).

Given that the product of the two numbers is 47 (ab = 47), we want to find the minimum value of their sum (a + b).

Using the AM-GM inequality:

(a + b) / 2 ≥ √(ab)

Substitute ab = 47:

(a + b) / 2 ≥ √47

Now, let's solve for the minimum sum (a + b):

a + b ≥ 2(√47)

a + b ≥ 2 * √(47)
a + b ≥  13.711.        

Since "a" and "b" are positive numbers, the minimum sum (a + b) is 13.711.

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What is the solution to this system of linear equations?
2x + y = 1
3x - y = -6

Answers

Answer:

x = -1

y = 3

Step-by-step explanation:

2x + y = 1

3x - y = -6

Let's find x first by adding both equations

5x = -5

x = -1

Now put -1 in the spot of the variable x

2(-1) + y = 1

-2 + y = 1

y = 3

[tex]\sqrt{x} \sqrt{x} 100\\[/tex]

Answers

Answer:

100 isn't under the root, so the roots over the x cancel and you have 100x as the answer

Step-by-step explanation:

100 isn't under the root, so the roots over the x cancel and you have 100x as the answer

How do I solve for x in #34 and #35?

Answers

Answer:

  34. x = 3 1/3

  35. x = 5.2

Step-by-step explanation:

Given figures involving triangles with angle bisectors and parallel segments, you want to solve for x.

In each case, you need to make use of two proportional relationships. An angle bisector divides the triangle proportionally. An segment parallel to one side of the triangle divides it proportionally.

34.

Using the angle bisector relation, you have ...

  QP/PT = QS/ST

  x/3 = 5/ST   ⇒   x = 15/ST

Using the parallel segment relation, you have ...

  PT/QR = ST/SR

  3/2 = ST/3   ⇒   ST = 9/2

Using the value of ST in the equation for x gives ...

  x = 15/(9/2) = 30/9 = 10/3

  x = 3 1/3

35.

Using the angle bisector relation, you have ...

  EF/ED = CF/CD

  7.2/9 = CF/6   ⇒   CF = 6(7.2/9) = 4.8

Using the parallel segment relation, you have ...

  CB/BA = CF/FE

  x/7.8 = 4.8/7.2

  x = 7.8(4.8/7.2)

  x = 5.2

__

Additional comment

In each case, we assigned a numerical value to the intermediate variable (ST, CF). We didn't actually need to do that.

Establish the identity.
1+ tan^2 (-0) = sec^2 0
Which of the following four statements establishes the identity?

pls help asap i can’t pass this class without passing this test :(

Answers

The correct statement that establishes the identity is the third one: "The reciprocal of the cosine of an angle is equal to the secant of the angle."

Here's how you can prove this using the other three statements:

"The tangent of an angle is equal to the sine of the angle divided by the cosine of the angle."

"The reciprocal of the sine of an angle is equal to the cosecant of the angle."

"The reciprocal of the cosine of an angle is equal to the secant of the angle."

"The reciprocal of the tangent of an angle is equal to the cotangent of the angle."

To prove the identity, we can start by substituting the first statement into the equation on the left side of the identity:

$1 + \tan^2 (-0) = 1 + \left( \frac{\sin (-0)}{\cos (-0)} \right)^2 = 1 + \frac{\sin^2 (-0)}{\cos^2 (-0)}$

Next, we can use the fourth statement to write the right side of the identity in terms of the cotangent:

$1 + \frac{\sin^2 (-0)}{\cos^2 (-0)} = 1 + \frac{1}{\cot^2 (-0)} = \frac{1}{\cot^2 (-0)}$

Now we can use the second statement to write the right side of the identity in terms of the cosecant:

$\frac{1}{\cot^2 (-0)} = \frac{1}{\frac{1}{\sin^2 (-0)}} = \csc^2 (-0)$

Finally, we can use the third statement to write the right side of the identity in terms of the secant:

$\csc^2 (-0) = \frac{1}{\sec^2 (-0)} = \sec^2 (-0)$

Therefore, the third statement establishes the identity.

a cylindrical water tank with its circular base parallel to the ground is being filled at the rate of 4 cubic feet per minute. the radius of the tank is 2 feet. how fast is the level of the water in the tank rising when the tank is half full? give your answer in feet per minute.

Answers

In the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.

What is a cylinder?

One of the most fundamental curvilinear geometric shapes, a cylinder has historically been a three-dimensional solid.

It is regarded as a prism with a circle as its base in basic geometry.

In several contemporary fields of geometry and topology, a cylinder can alternatively be characterized as an infinitely curved surface.

So, we know that:

The rate at which water is being filled is 4 ft³.

The radius of the cylinder is 2 ft.

Now, the time in which the level of water in the tank rises when the tank is half full:

Area of cylinder: πr²

πr² =  12.566 ft³

Next, multiply 4 by 12.566 to get how quickly the water is rising:

12.566 ft³/4 ft³/min = 3.14 m

According to this, a foot of water rises every roughly 3.14 minutes, or 1/3.14 - 0.318 ft/min, or 3.82 in/min.

Therefore, in the given cylinder we know that it takes the water around 3.14 minutes to rise 1 ft.


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You know distance and speed and want to find the time

You know time and distance and want to find the speed

You know speed and time and want to find the distance

Answers

Answer:

time=speed÷distance

speed=distance×time

distance=speed ÷time

Step-by-step explanation:

from the answers we get a relationship between speed,distance and time.there by when with two you can find the other

What is the 5th term in this sequence? 1, -8, -17

Answers

The value of the fifth term in the given sequence as represented in the task content is; -35.

What is the value of the fifth term in the sequence as given?

It follows from the task content that the value of the fifth term in the given sequence is to be determined.

On this note, it follows from the observation that the given sequence is arithmetic and the nth term, T (n) = a + ( n - 1 ) d.

where, a = first term = 1

and d = common difference = -8 - 1 = -17 - (-8) = -9.

Therefore, the fifth term is given as;

T (5) = 1 + ( 5 - 1 ) -9

= 1 + (4 × -9)

= 1 - 36

= -35.

On this note, the fifth term of the sequence as required is; -35.

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A system of equations consists of a line s of the equation y = x – 5 and a line t that passes through the points (0, 2) and (8, –4). Answer the questions about line t to write the equation.

What is the slope of line t?

–0.75
What is the y-intercept of line t?

2
What is the equation in slope-intercept form of line t?

y = –0.75x + 2

Answers

The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

What is a linear equation?

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The line t that passes through the points (0, 2) and (8, -4) is given as,

(y - 2) = [(- 6 - 2) / (8 - 0)](x - 0)

y - 2 = - 0.75x + 0

y = -0.75x + 2

The line 't' is y = -0.75x + 2 which has a slope of negative 0.75 and the y-intercept is 2.

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Please help! Its algebra!

Answers

Step-by-step explanation:

don't panic. just read carefully and write equations for every relation described in the text.

perimeter = 34 cm = side 1 + side 2 + side 3

side 1 = 2×side 3

side 3 = (side 1) / 2

side 2 = (side 1) + 4

now we use the last 2 equations in the first :

34 = side 1 + ((side 1) + 4) + (side 1)/2

68 = 2×(side 1) + 2×((side 1) + 4) + side 1

68 = 2×(side 1) + 2×(side 1) + 8 + side 1

68 = 5×(side 1) + 8

60 = 5×(side 1)

side 1 = 60/5 = 12 cm

side 2 = (side 1) + 4 = 12 + 4 = 16 cm

side 3 = (side 1)/2 = 12/2 = 6 cm

you see ? it is all just straight forward. no mystery.

the only trick is to find forms of the various equations to have only one variable in the main equation. like we did here with side 1 and side 3.

In a company, 80% of the workers are men. If 780 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.

There are [enter your response here] workers in all.

Answers

Answer:

3900

Step-by-step explanation:

20%=1/5

780 is 20%

780x5 equals total since 20% 80% is 3120

There are 30 giraffe and 6 penguin at the zoo. Which tatement correctly compare the two quantitie?

Answers

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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identify the value of f(x) and x from the given coordinates

Answers

Answer:

1

Step-by-step explanation:

For function f(x), the average rate of change from x = a to x = b is:

average rate of change = (f(b) - f(a))/(b - a)

Here we have:

f(a) = f(-3) = -2.88

f(b) = f(2.5) = 2.62

average rate of change = (2.62 - (-2.88))/(2.5 - (-3)) = 1

please solve theta
csc^2 theta=cot theta+3

Answers

The value of θ will -45° or 26.56°

What are trigonometric identities?

Trigonometric Identities are the equalities that involve trigonometry functions and holds true for all the values of variables given in the equation.

Given that, cosec²θ = cotθ + 3

Solving for θ,

∵ cosec²θ = cot²θ+1

∴ cot²θ+1 = cotθ + 3

cot²θ-cotθ-2 = 0

Factorizing and solving, we get

(cotθ+1)(cotθ-2) = 0

cotθ+1 = 0

cotθ = -1

θ = -45°

or, cotθ-2 = 0

cotθ = 2

θ = 26.56°

Hence, The value of θ will -45° or 26.56°

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A bag holds 23 cups of sugar. A recipe for chocolate chips cookies uses 1 cups of sugar. How many batches of chocolate chip cookies can be made with one bag of sugar?

Please have a step by step explanation so I can mark you as Brainliist. ​

Answers

Answer: 1 batch

Step-by-step explanation:

1 batch = 24 - 36 cookies

So here we have 23 cups of sugar, and we know that each chocolate chip cookie uses 1 cup, so we can only make 23 cookies

Which is only 1 batch of cookies can be made.

Answer:

23 batches of cookies

Step-by-step explanation:

I think this problem is kind of straightforward:

1 bag = 23 cups

1 batch = 1 cup

We need to find how many batches = 1 bag

To find that out, we have to divide bags by batches, but we don't know the number of batches yet. (Also, they're not the same units)

Instead, we can use the respective cups of sugar to divide (because they do have the same units)

So we divide the number of cups of sugar in a bag (23) by the number of cups in a batch (1):

23 ÷ 1 = 23 batches

I hope this explanation was simple enough

find the number a such that the limit exists. lim x→−2 4x2 + ax + a + 12 x2 + x − 2

Answers

The limit exists and equals -4 when a = 28.

How to illustrate the limit?

From the information, we want to find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2.

It should be noted that this will be illustrated as:

(4x² + ax + a + 12) / (x² + x − 2)

We will substitute x = -2 into the value of x in the Illustration. This will be:

(16 - 2a + a + 12) / (4 - 2 - 2)

16 - 2a + a + 12 = 0

-a = -28

a = 28

Using lhopital rule, we'll find the derivative. This will be:

8x + a / 2x + 2

Substitute x = -2

(-16 + 28) / (-4 + 1)

= 12 / -3

= -4

Therefore the limit exists and equals -4 when a = 28.

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Complete question

find the number a such that the limit exists. lim x→−2 4x² + ax + a + 12 divided by x² + x − 2

Which graph represents function f?
f(x) = 2|x − 1|– 3

Answers

Answer:

graph D

Step-by-step explanation:

if x = 0

y = 2 |-1| - 3

y = 2 (1) - 3

y = 2 - 3

y = -1


A (0, -1)


if x = 1

y = 2 |1-1|  - 3

y = 2 (0) - 3

y = -3


B (1,-3)

What is 1x1 because I do not know what is it

Answers

Answer:

The answer is 1

Step-by-step explanation:

Answer:

1

Step-by-step explanation:

(93 points) Eloise bought 2 boxes of crackers to share with her friends. Her friends ate 12 of the first box and 34 of the second box.

A. 1/2 box

B. 2/3 box

C. 3/4 box

D. 1 1/3

Answers

Answer:

The answer is C, 3/4 of a box

For a recipe, harris uses 2 cups of sugar for each cup of flour. how many cups of flour does harris need when he uses 1 cup of sugar?

Answers

Answer:

1/2 a cup of flour

Step-by-step explanation:

Sugar to flour ratio:
2 to 1
That means for every 2 sugar Harris needs 1 cup flour
There are twice as many cups of sugar of cups of flour
Since 1/2 times 2 is 1 that means the ratio is ture

2 to 1 = 0.5 to 1

Hope this helps :) im kinda bad at explaining


Write an equation that represents the line.
Use exact numbers.

Answers

answer : y = 4/5x - 22/5

y = mx + b

get m or slope (aka "rate" or "speed")

(fun fact : see how the graph is a straight line? a lot of calculus is trying to get the rate or speed or slope of a curved graph)

(-3,-6) (2,-2)

(y2 - y1)/(x2-x1)

-2 + 6/2 + 3

m = 4/5

(if you make the 2 points a triangle bottom is 5 and the right side is 4)

line formula

y - y1 = m (x - x1)

y + 6 = 4/5 ( x + 2 )

y = 4/5x + 8/5 - 6

y = 4/5x + 8/5 - 30/5

y = 4/5x - 22/5

side note : since the graph doesnt go thru (0,0) the graph is NOT PROPORTIONAL

select the correct answer from each drop down menu

choices: the rate of function eight is (greater than), (less than), (equal to) the rate of change a function b

(neither function is ), (only function b is) , (only function a is) , (both functions are) increasing.

The y intercept of function a is (less than) , (greater than), (equal to) the y-intercept of function B

whatever is in the parentheses are the choices. please help

Answers

The rate of change of function A is greater than the rate of change of function B.

The y-intercept of function A is less than the y-intercept of function B.

How to calculate the rate of change of the function?

The rate of change is also called the slope of a linear equation and is defined as the rate of change of y-values divided by the corresponding change in x-values.

For function A, we are told that the line passes through the points (2, 3) and (-1, -3). The rate of change is gotten from the formula;

Rate of change = (y₂ - y₁)/(x₂ - x₁)

Rate of change = (-3 - 3)/(-1 - 2)

Rate of change = -6/-3

Rate of change = 2

For function B, we are given that the equation of the line is;

y = ¹/₂x + 2

Now, formula for equation of a line in slope intercept form is;

y = mx + c

where ;

m is slope and c is y-intercept

Thus, slope is 1/2 and y-intercept is 2

For function A, we can find the y-intercept as;

3 = 2(2) + c

c = 3 - 4

c = -1

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Select the correct answer from each drop-down menu. which formulas return true, if the value in cell b4 is 12 and the value in c4 is 29? and return true, if the value in cell b4 is 12 and the value in c4 is 29.

Answers

the correct answer from each drop-down menu. which formulas return true,.if the value in cell b4 is 12 and the value in c4 is 29.: A. =B4=12 AND C4=29

The correct answer is A. =B4=12 AND C4=29, as this is the only formula that returns true if the value in cell b4 is 12 and the value in c4 is 29.

Both B. =(B4=12) AND (C4=29) and D. =(B4+C4)=41 are correct, but they do not fit the given criteria.

C. =B4+C4=41 does not return true for the given values, as 12 + 29 does not equal 41.

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please help me with this

Answers

Answer: The first one is equivlent because you move the variable to the left collect like terms and then divide both terms.

Step-by-step explanation:

Joseph is signing up for a gym membership with a one-time fee to join and then a monthly fee to remain a member. Let CC represent the total cost of the gym membership over t months. A graph of CC is shown below. Write an equation for CC then state the slope of the graph and determine its interpretation in the context of the problem.

Answers

Answer:

The equation for the total cost of the gym membership over t months is CC = Jo + M * t, where Jo represents the one-time fee to join, M represents the monthly fee to remain a member, and t represents the number of months for which the membership is valid.

The slope of the graph is M, the monthly fee to remain a member. The interpretation of the slope in the context of the problem is that it represents the cost per month of remaining a member of the gym.

What is x+3y ≥ 3
Help?

Answers

Answer: x

3

3

y

Step-by-step explanation:

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Which of the following domains are the most closely related, in that they share a unique common ancestor? a) archaea and bacteria b) archaea and eukaryac) bacteria and eukarya d) None of the above; all three domains evolved from different ancestors. e) None of the above; all three domains are equally related to one another. a variance is the difference between standard and actual prices and quantities. is this statement true or false? Write a function called morseCode that encodes an English phrase into Morse code. The function should also convert a Morse code phrase into English. Use one blank between each Morse-coded letter and three blanks between each Morse-coded word. Pass the function the input string that needs to be encoded or decoded, and a flag that is set to to encode into Morse-code and is set to 1 to decode into English. Use pointers for all strings. match these people and battles to their proper descriptions. 1 . general halleck was the battle in which johnston and lee attacked mcclellan 2 . battle of seven pines commanded army of the potomac 3 . jackson and lee kept union army in washington d.c. 4 . robert e. lee commanded army of virginia 5 . 'stonewall' jackson commanded union forces in the east 6 . mcclellan defeated pope in the second battle of bull run 7 . antietam was the bloodiest single-day battle Arrange the organic compounds from most soluble in water to least soluble in water: Most soluble in water Least = soluble in water... His love of letterforms is evidenced by an exceptional ability to integrate words and images into a total composition. He achieved concise statements by combining telegraphic copy (text), powerful geometric forms, and symbolic imagery created by simplifying natural forms into almost pictographic silhouettes. Among his well-known works are the Dubonnet advertising campaign, the 1931 poster for the ocean liner L Atlantique, and typefaces for the Deberny and Peignot type foundry, including Bifur, a quintessential art deco display typeface. Which of the following can be associated with intrinsic motivation? Multiple Choice allowance praise enjoyment reward 7 the area of the rhombus corporations in the u.s., as compared to other countries, tend to: question 14 options: have a median leverage ratio that's equal to the average international median leverage ratio. underutilize debt. have relatively high leverage ratios due to the tax benefits gained. have extremely high debt-equity ratios. rely less on equity financing than they should. 12. Look at this shape:Which imageshows a reflection and why? joe and bill throw identical bals vertically upward. joe throws his ball with an initla speed twice as high as the bull. if there is no air resistance the max height of joes ball will be suppose you and a coworker are given a difficult task that requires you to give 110%, but your coworker does not pick up the slack. how do you approach the situation? Which situation is the bestexample of irony?A. You forgot the keys, so you are locked out.B. An old beat up car wins a race against a sportscar.C. You find your sunglasses in the last place youlook for them. The British divided the province of Bengal into *A British and Hindu sectionA Hindu and Muslim sectionA Muslim and British SectionThree equally divided partsAnalyze: Why did the British divide the Hindus and Muslims? What was probably the purpose of their strategy? Full paragraph, full credit. the first words macbeth utters in the play echo a line already spoken (i.iii.38). what significant effect does shakespeare create through this device? steven is looking at banks for checking and savings accounts. some offer home loans and others do not. steven may need a home loan sometime in the next few years. but he wonders if he should really ask what kinds of loans the bank makes, because he is getting a checking account, not a home loan. which statement below gives the best reason for steven to consider loan availability in choosing a checking account? 7GRADE QUESTION!!! WHERE IS THE ALLITERATION??? THIS IS A POEM BTWWhat else could the boy have done? Wasntflight both an escape and a great uplifting?And so he flew. But how could he appreciatehis freedom without knowing the exact pointwhere freedom stopped? So he flew upwardand the sun dissolved the wax and he fell.But at last in his anticipated plummetinghe grasped the confines of what had beenhis liberty. You say he flew too far?He flew just far enough. He flew preciselyto the point of wisdom. Would ithave been better to flutter ignorantlyfrom petal to petal within some gardenforever? As a result, flight for him was notupward escape, but descent, with his wingsdisintegrating around him. Should it matterthat neither shepherd nor farmer with his plowwatched him fall? He now had his answer,laws to uphold him in his downward plunge.Cushion enough for what he wanted. compose 560 tenths + 48 thousandths