question which angles are a pair of alternate exterior angles? angle 3 and angle 6 angle 3 and angle 6 angle 4 and angle 6 angle 4 and angle 6 angle 2 and angle 8 angle 2 and angle 8 angle 1 and angle 5 angle 1 and angle 5

Answers

Answer 1

The pair of angles from the given options that are a pair of alternate exterior angles is:

C. ∠2 and ∠8

What are Alternate Exterior Angles?

Alternate exterior angles are pairs of exterior angles that lie alternate to each other along a transversal that cuts across two parallel lines.

Thus, in the image given, we have the following alternate exterior angles:

∠2 and ∠8

∠1 and ∠7

Therefore, the pair of angles from the given options that are a pair of alternate exterior angles is:

C. ∠2 and ∠8

the complete question is

Which angle are a pair of alternate exterior angles

A. Angle 4 and angle 6

B. Angle 3 and angle 6

C. Angle 2 and angle 8

D. Angle 1 and angle 5

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Question Which Angles Are A Pair Of Alternate Exterior Angles? Angle 3 And Angle 6 Angle 3 And Angle

Related Questions

What is the frozen food example of the free market and exit concept?

Answers

Answer:  Food is Food

Step-by-step explanation:

Determine the quadrant in which each angle lies -7

Answers

It lies in the quadrant IV.

Since we know that a full circle is broken into four parts known as quadrants into regions of π/2.Since quadrant  1 ranges from 0 to π/2,  quadrant 2 ranges from π/2 to π, then quadrant 3 ranges from π to 3π/2, and at last quadrant 4 ranges from 3π/2 to 2π.

And we know 2π is equal to approx  6.28 radians,  so each quadrant will have  2π/ 4 = π2  ≈1.57 radians

So for angle  -7 it will be =  −7/(π/2) ≈−4.45.

So  moving around the circle,  it appears halfway through the quadrant IV.

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on her desk.
Susan has a box for paperclips
The box is 6 centimeters long, 3 centimeters
wide, and 2 centimeters high. What is the
volume of the box?

Answers

Answer:

36 cm³

Step-by-step explanation:

6x3x2 = (36 cm³)
Length x Width x Height

PLEASE ANSWER QUICK

Evaluate the expression when n = 3:

−|−4n|

Answers

Answer:

12

Step-by-step explanation:

-4 X 3 =-12

=-(-12)

=12

What is the slope of the line that passes through the points (-7, -2) and
(-2, -22)? Write your answer in simplest form.

Answers

Answer:

m = -4

Step-by-step explanation:

We are given the points (-7, -2) and (-2, -22), and we want to write the slope of the line.

The slope (m) can be calculated from two points using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points.

We already have everything we need to calculate the slope, however, let's label their values to help avoid any confusion and mistakes for later.

[tex]x_1=-7\\y_1=-2\\x_2=-2\\y_2=-22[/tex]

Now, substitute these values into the formula. Remember that the formula has subtraction, and we're dealing with negative numbers here.

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-22--2}{-2--7}[/tex]

Simplify.

m=[tex]\frac{-22+2}{-2+7}[/tex]

Add.

m=[tex]\frac{-20}{5}[/tex]

Divide.

m = -4

The slope of the line is -4.

Topic: slope

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What is the equation of the given line?


y = 5

x = 3

x = 1

y = 3

Answers

Answer:

y=x+2

Step-by-step explanation:

use the formula y=mx+c

first u find m which is the gradient 3-1/5-3 = 2/2=1

sub in any point to find the c

5=1(3)+c

c=2

y=1x+2

Ava read a total of 40 books over 5 months. If Ava has read 72 books so far, how many months has she been with her book club? Assume the relationship is directly proportional.

Answers

Answer:  9 months

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

Explanation:

She read 40 books over 5 months. This means her unit rate is 8 books per month (since 40/5 = 8)

x = number of months

(unit rate)*(number of months) = total books read

8x = 72

x = 72/8

x = 9

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

Another way to solve

(40 books)/(5 months) = (72 books)/(x months)

40/5 = 72/x

40x = 5*72 ... cross multiplying

40x = 360

x = 360/40

x = 9

Apply the distributive property to factor out the greatest common factor. 40 f + 30

Answers

Answer:

10(4f + 3)

Step-by-step explanation:

Both terms here are multiples of 10 hence we can factor out ten which is the greatest common factor resulting in 10(4f + 3)

how do u solve subtraction of number bases

Answers

Answer: Say you want to perform the following subtraction in base 5. Borrow a 5 from 3 fives. 3 fives in now 2 fives. Then, add that 5 to the 1 to make it 6.

Step-by-step explanation: there

127,056 rounded to the nearest to ten thousand

Answers

Answer: 10000

Step-by-step explanation: That is as close to ten thousand as you can get

what are the probabilities that the three subsystems, as well as the entire system, are operational?

Answers

Three subsystems are reliability-wise in series and make up a system. Subsystem 1 has a reliability of 99.5%, subsystem 2 has a reliability of 98.7% and subsystem 3 has a reliability of 97.3% for a mission of 100 hours.

We suppose that the system consists of one operating series subsystem, an identical stand-by subsystem, and a switch. Each subsystem consists of N components.

When the operating subsystem fails, the spare is put in motion by the switch immediately. The failed subsystem is restoring or changing the failed component. Because of the memoryless property of the exponential distribution of components lifetime, the renewal of a failed element means the renewal of the whole subsystem. We assume that there is a single repair facility. A renewal time is a random variable having distribution depending on a failed component. We suppose that the lengths of restoring periods of components are represented by identical copies of nonnegative random variables.

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Describe and correct the error in solving the equation below.

Answers

Answer:

86

Step-by-step explanation:

Help me please, find area these shapes, easy, I will give brainliest and points

Answers

Answer:

red - 1/2 × b × h

=1/2 × 3 × 4

= 6

green - 1/2 × b × h

= 1/2 × 4 × 4

= 8

Kylie is training for an upcoming marathon and has committed to running
more than 21 miles today. If she runs from her house, she can run along two
loops: a short path that is 3 miles in length, and a long path that is 6 miles in
length. Select the inequality in standard form that describes this situation. (x
= the number of loops on the short path, y = the number of loops on the long
path).

Answers

Answer: 3x+6y > 21

Step-by-step explanation:

total distance kylie runs is the combined amount of loops from both paths. 3x represents however many loops she runs times the length of the short path. 6y represents however many loops she runs times the long path. Both of them have to add up and be greater than 21.

-14<4x+6<18

Please break it down for me

Answers

Basically, this is a domain. Well, a condition.

It's saying that any value that you subsitute in x , which is then multiplied by 4 and added 6, must ALWAYS be greater than -14, but lesser than 18.

English only please

Create an equivalent expression for 1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six.

1.4 cubed over 1.2 squared
1.2 squared over 1.4 cubed
1.4 to the eighteenth power over 1.2 to the twenty-fourth power
1.2 to the twenty-fourth power over 1.4 to the eighteenth power

Answers

Answer:

2.8 squared

2.6 cubed

2.6 twenty-fourth power

2.6 eighteenth power

its korrect now

The required simplified solution of the given expression is 1.2 to the twenty-fourth power over 1.4 to the eighteenth power. Option D is correct.

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
1.4 cubed over 1.2 raised to the fourth power all raised to the power of negative six is given as,
x = [1.4³/1.2⁴]⁻⁶
x = 1.4⁻¹⁸ / 1.2⁻²⁴
x = 1.2²⁴ / 1.4¹⁸

Thus, the required simplified solution of the given expression is 1.2 to the twenty-fourth power over 1.4 to the eighteenth power. Option D is correct.

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a bag contains 1 gold marbles, 10 silver marbles, and 20 black marbles. someone offers to play this game: you randomly select one marble from the bag. if it is gold, you win $3. if it is silver, you win $2. if it is black, you lose $1.

Answers

The expected value is 3/31.

The number of gold marbles in the bag is 1.The number of silver marbles in the bag is 10.The number of black marbles in the bag is 20.The total number of marbles in the bag is 1 + 10 + 20.The total number of marbles in the bag is 31.The amount of money to be won if we select a gold marble is $3.The amount of money to be won if we select a silver marble is $2.The amount of money to be lost if we select a gold marble is $1.The probability of selecting a gold marble is 1/31.The probability of selecting a silver marble is 10/31.The probability of selecting a black marble is 20/31.The expectation value is the sum of the product of probabilities and the corresponding value of the marbles.Expectation = 3(1/31) + 2(10/31) - 1(20/31)Expectation = (3 + 20 - 20)/31Expectation =3/31

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Can someone please help mee (20 points
brainliest!!!)

Answers

Answer:

16,300,000 viewers

Step-by-step explanation:

We have two ordered pairs and we can write an equation in the slope intercept form of the line from the information that we have.

y = mx + b  y is the number of viewers and x in the number of minutes of ads.

m is the slope.  That is the change in y over the change in x.  We will use the two points given to find this.

(14, 10,000,000) (25, 17,000,000)  

slope:

[tex]\frac{y{1}- y{2} }{x_{1}-x_{2} }[/tex] = [tex]\frac{17,000,000 - 10,000,000}{25-15}[/tex] =[tex]\frac{7,000,000}{10}[/tex] = 700,000

Now we need the b or the y-intercept.  We will use the slope and one of the points to find this.  We could use either point. I am going to use the point (15, 10,000,000)

y = mx + b

I will use 10,000,000 for y

I will use 15 for x

I will use 700,000 for the slope.

I will plug these numbers in and solve for b

10,000,000 = 700,000(15) + b

10,000,000 = 10,500,000 + b  Subtract 10,500,000 from both sides

-500,000 = b

Now we can write the equation

y = mx + b

y = 700,000x -500,000 Plug is the 24  for x to solve for the number of views.

y = 700,000(24) -500,000

y = 16,800,000 - 500,000

y = 16,300,000

maths lit scope term 3 grade 10

Answers

Answer:

add a pic

Step-by-step explanation:

x=7 y=4 HELP I WILL GIVE BRAINLIEST.

362x+836y+918334

Answers

Answer: 924212

Step-by-step explanation:

362x+836y+918334

362(7)+836(4)+918334

(362 x 7) + (836 x 4)+918334

question 12(multiple choice worth 1 points) (03.05 lc) what is the volume of a sphere with a radius of 6 inches? 112π cubic inches 288π cubic inches 290π cubic inches 300π cubic inches

Answers

 volume of a sphere with a radius of 6 inches is 288π cubic inches.

What is volume of a sphere?

A sphere is a collection of points in space that are separated from the center by an amount r. The volume of a solid in three dimensions is the area it occupies. The cubic is the unit of volume ( in3,ft3,cm3,m3 , etc ). Ensure that all measurements are made in the same unit before estimating the volume. A sphere's volume, V, is equal to four thirds of pi times the square of the radius.

V=43πr3

Half of the connected sphere's volume makes up a hemisphere. A sphere's volume is 2/3 that of a cylinder with the same radius and height that is equal to its diameter.

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convert 1264 base 8 to base 10

Answers

1264₈ = 1•8³ + 2•8² + 6•8¹ + 4•8⁰

1264₈ = (2³)³ + 2•(2³)² + 3•2•2³ + 2²

1264₈ = 2⁹ + 2⁷ + 3•2⁴ + 2²

1264₈ = 512 + 128 + 3•16 + 4

1264₈ = 692

After converting the base, 1264 base 8 is equal to 692 base 10.

To convert a number from base 8 (octal) to base 10 (decimal), we need to evaluate the value of each digit in the base 8 number and then calculate the equivalent decimal value.

Given the number 1264 in base 8, we can break it down into its digits:

1 * 8³ + 2 * 8² + 6 * 8 + 4 * 1

Simplifying this expression:

1 * 512 + 2 * 64 + 6 * 8 + 4 * 1

Evaluating the multiplication:

512 + 128 + 48 + 4

Adding the products together:

692

In summary, to convert a number from base 8 to base 10, we evaluate the value of each digit by multiplying it with the corresponding power of 8, and then sum up the results. This gives us the equivalent decimal value of the number.

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pls solve this question step by step ​

Answers

Answer:

a) 50, b) -40, c) 3

Step-by-step explanation:

Arithmetic mean is the average of the numbers.

a) (40 + 60)/2 = 100/2 = 50

b) (- 60 - 20)/2 = - 80/2 = - 40

c) (7/3 + 11/3)/2 = (18/3)/2 = 6/2 = 3

Formula we use is,

→ Mean = (x + y)/2

a) 40 and 60 = ?

→ (40 + 60)/2

→ 100/2 = 50

Thus, the mean is 50.

b) -60 and -20 = ?

→ (-60 - 20)/2

→ -80/2 = -40

Thus, the mean is -40.

c) (7/3) and (11/3) = ?

→ ((7/3) + (11/3))/2

→ (18/3)/2

→ 6/2 = 3

Thus, the mean is 3.

I need help with how to do the vertical line test on a graph, I forgot.

Answers

Answer: To graph a vertical line that goes through a given point, first plot that point. Then draw a straight line up and down that goes through the point, and you're done!

Step-by-step explanation: pls give brainliest

10. The average age of 4 boys is 14 years, when one boy leaves the group, the average age of the remaining boys becomes 15 years. How old is the 4th boy?​

Answers

Answer: the 4th boy is 11

Step-by-step explanation:

Let's denote the age of the boys as: x₁, x₂, x₃, x₄.

Then,

[tex]\displaystyle\\\frac{x_1+x_2+x_3}{3}=15[/tex]

Multiply both parts of the equation by denoting by 3:

x₁+x₂+x₃=15(3)

x₁+x₂+x₃=45

Hence,

[tex]\displaystyle\\\frac{x_1+x_2+x_3+x_4}{4} =14\\\\\frac{(x_1+x_2+x_3)+x_4}{4} =14\\\\\frac{45+x_4}{4}=14[/tex]

Multiply both parts of the equation by denoting by 4:

45+x₄=14(4)

45+x₄=56

45+x₄-45=56-45

x₄=11

Hans needs to rent a moving truck. Suppose Company A charges a rate of $40 per day and Company B charges a $60 fee plus $20 per day. for what number of days is the cost the same. Please also explain how you got the answer

Answers

Answer: x=3

Step-by-step explanation:

1. Hans needs to rent a moving truck. Suppose Company A charges $40.00 per day and Company B charges a $60.00 fee plus $20.00 per day, for what number of days is the cost the same?

Let x = # of days, since Company A charges $40/day then cost after x days = 40x

Let x = # of days, since Company B charges $20/day plus $60 fee, then cost after x days = 20x + 60

a. For what # of days is the cost the same?

   When the cost is the same => 40x = 20x + 60

                                                    40x - 20x = 60

                                                             20x = 60

                                                                 x = 60/20

                                                                 x = 3

 The cost is the same after 3 days.

 

 Checking:

$40(3)  = $20(3) + $60

$120    = $60 + $60

$120    = $120

Lily's limos charges $150 to rent a limo plus $40 an hour. ron's luxury rides charges $200 to rent a limo plus $30 an hour. at how many hours do the companies charge the same price? write and solve a single equation to prove and show at how many hours the companies charge the same price.

Answers

Upto 5 hours companies will charge at the same price.

what are comparing functions ?

Functions can be represented in a variety of ways. A function, for instance, can be depicted using an input-output table, a graph, and an equation.It's occasionally necessary to compare two functions that are represented in different ways because of an issue. You might be asked, for instance, which function is greater for a given number or which function increases more quickly after being presented with a table and a graph.

Given that :For a limo rental, Lily's limos charges $150 plus $40 per hour. For a limo rental, Ron's Luxury Rides charges $200 plus $30 per hour.

Based on the given condition ,

equation is 150 + 40x = 200 + 30x

40x - 30x = 200 - 150

10x = 200 -150

10x = 50

x =[tex]\frac{50}{10}[/tex]

x = 5

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Evaluate each expression. When the answer is not a whole number, write your answer as a simplified fraction.

1. -4 x (-6)
2. -24 x (-7/6)
3. 4 ÷ (-6)
4. 4/3 ÷ (-24)

Answers

The result of each arithmetic operation is

1) -4×(-6)=24

2) -24 × [tex]-(\frac{7}{6})[/tex] = 28

3) 4 ÷ (-6) = [tex]-\frac{2}{3}[/tex]

4) [tex]\frac{4}{3}[/tex]÷(-24)=[tex]-\frac{1}{18}[/tex]

Part 1

-4×(-6)=24

Part 2

-24 × [tex]-(\frac{7}{6})[/tex] =[tex]\frac{(24)(7)}{6}[/tex]

=[tex]\frac{168}{6}[/tex]

=28

Part 3

4 ÷ (-6) =[tex]-\frac{4}{6}[/tex]

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

Part 4

[tex]\frac{4}{3}[/tex]÷(-24)= [tex](\frac{4}{3})(-\frac{1}{24} )[/tex]

=[tex]-\frac{4}{24}[/tex]

=[tex]-\frac{1}{18}[/tex]

Hence, the result of the following arithmetic operation is

1) -4×(-6)=24

2) -24 × [tex]-(\frac{7}{6})[/tex] = 28

3) 4 ÷ (-6) = [tex]-\frac{2}{3}[/tex]

4) [tex]\frac{4}{3}[/tex]÷(-24)=[tex]-\frac{1}{18}[/tex]

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The price of Stock A at 9 A.M. was ​$12.74. Since​ then, the price has been increasing at the rate of ​$0.08 each hour. At noon the price of Stock B was ​$13.24. It begins to decrease at the rate of ​$0.09 each hour. If the two rates​ continue, in how many hours will the prices of the two stocks be the​ same?

Answers

Answer:

3 hours

Step-by-step explanation:

but it can be a cent off, so it might be wrong.

Please help - thanks
Insert parentheses in the appropriate places:

8+ 3-2 ×9 =17
28 ÷ 4+3 × 4+3 =28
5× 3+2 ×6 ÷3 =50
6× 9-4 +3-3 ×4=30
5 ×3+2× 6÷3 =19
5× 3+2×6 ÷3 =25

Answers

1. The correct arithmetic operation with parentheses is 8 + (3 - 2) × 9 = 17

2. The correct arithmetic operation with parentheses is 28 ÷ (4 + 3) × (4 + 3) = 28

3. The correct arithmetic operation with parentheses is  5 × (3 + 2) × 6 ÷ 3

4. The correct arithmetic operation with parentheses is 6 × (9 - 4) + (3 - 3) × 4

5. The correct arithmetic operation with parentheses is (5 × 3) + (2 × 6) ÷ 3 = 19

6. the correct arithmetic operation with parentheses is 5 × [3 + 2 × (6 ÷ 3)] = 35

What are arithmetic operations?

Arithmetic operations are mathematical operations that involve multiplication, division , addition and subtraction.

Arithmetic operations follow the rule of BODMAS where

B represents brackets, O represents orders of powers or roots, D represents division, M represents multiplication,A represents addition and S represents subtraction

How to insert parentheses in the appropriate places:

1. How to insert parentheses in the appropriate places in 8 + 3 - 2 × 9 = 17

Since the expression evaluates to 17, we put a parentheses between 3 and - 2. So,

8 + (3 - 2) × 9 = 8 + 1 × 9

= 8 + 9

= 17

So, the correct arithmetic operation with parentheses is 8 + (3 - 2) × 9 = 17

2. How to insert parentheses in the appropriate places in 28 ÷ 4 + 3 × 4 + 3 = 28

Since the expression evaluates to 28, we a parentheses between 4 and + 3. So,

28 ÷ 4 + 3 × 4 + 3 = 28 ÷ (4 + 3) × (4 + 3)

= 28 ÷ 7 × (4 + 3)

= 4  × 7

= 28

So, the correct arithmetic operation with parentheses is 28 ÷ (4 + 3) × (4 + 3) = 28

3. How to insert parentheses in the appropriate places in 5 × 3 + 2 × 6 ÷ 3 = 50

Since the expression evaluates to 50, we put a parentheses between 3 and + 2. So,

5 × 3 + 2 × 6 ÷ 3 = 5 × (3 + 2) × 6 ÷ 3

= 5 × 5 × 2

= 50

So, the correct arithmetic operation with parentheses is  5 × (3 + 2) × 6 ÷ 3

4. How to insert parentheses in the appropriate places in 6 × 9 - 4 + 3 - 3 × 4 = 30

Since the expression evaluates to 30, we put a parentheses between 9 - 4 and 3 - 3. So,

6 × 9 - 4 + 3 - 3 × 4 = 6 × (9 - 4) + (3 - 3) × 4

= 6 × 5 + 0 × 4

= 30 + 0

= 30

So, the correct arithmetic operation with parentheses is 6 × (9 - 4) + (3 - 3) × 4

5. How to insert parentheses in the appropriate places in 5 × 3 + 2 × 6 ÷ 3 = 19

Since the expression evaluates to 19, we put a parentheses between 2 and 6, and also 5 and 3. So,

5 × 3 + 2 × 6 ÷ 3 = (5 × 3) + (2 × 6) ÷ 3

= 15 + 12 ÷ 3

= 15 + 4

= 19

So, the correct arithmetic operation with parentheses is (5 × 3) + (2 × 6) ÷ 3 = 19

6. How to insert parentheses in the appropriate places in 5 × 3 + 2 × 6 ÷ 3 = 35

Since the expression evaluates to 35, we put a parentheses between 6 and 3 and also both 3's. So,

5 × 3 + 2 × 6 ÷ 3 = 5 × [3 + 2 × (6 ÷ 3)]

= 5 × [3 + 2 × 2]

= 5 × [3 + 4]

=  5 × 7

= 35

So, the correct arithmetic operation with parentheses is 5 × [3 + 2 × (6 ÷ 3)]  = 35

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Which evidence from "A Cub Pilot" supports the central idea that if you believeand trust in yourself, no one should be able to shake your confidence."My imagination began to construct dangers out of nothing, and they multipliedfaster than I could keep the run of them.""I was quaking from head to food, and I could have hung my hat on my eyes,they stuck out so far.""...when you get into a dangerous place, don't turn coward. That isn't going tohelp matters any.""All of my confidence in that crossing vanished."AE The product of two consecutive even number is 12 more than the square of the smaller number. Find the smaller number due to scarce resources, every individual, whether rich or poor, faces a(n) (one word) cost when choosing to produce or consume more of one good over another. A recipe calls for 4.5 teaspoons of Suger for 3 dozen cookies explain the process to find how much is needed for each dozen Maths help 10 points awarded and brainiest for correct answer which action woudl the nurse take to minimize psychological stress in an anxsious client who has beena dmitted to the psychiatric unit Pe un stadion se gsete un grup de sportiv cuprins ntre 50 i 100 care se pot grupa n coloane de cte 12 18:24 tarif fiecare dat rmn ase sportiv care nu pot forma o coloan complet care este numrul minim de sportiv? Va rog sa ma ajutati repede!!!! what are the proper rationales for all healthcare professionals to ask patients about conditions that may be associated with military service? (select all that apply.) the tiles (right angled triangles) are arranged around a parallelogram-shaped tile. Calculate the area of the parallelogram. b= 36 h= 13.2 a hexagon inscribed in a circle has three consecutive sides each of length 3 and three consecutive sides each of length 5. the chord of the circle that divides the hexagon into two trapezoids, one with three sides each of length 3 and the other with three sides each of length 5, has length equal to $m/n$, where $m$ and $n$ are relatively prime positive integers. find $m n$. place the following in order (top down) of how they would appear in the heading of deli llama's annual income statement for the fiscal year ended march 31, 2020. Someone Help please according to sfac no. 2, "qualitative characteristics of accounting information", is "the quality of information that enables users to perceive its significance." (enter only one word per blank.) What is an equivalent form of 12(p + 5) 11(3q + 4)? 21pq + 1 60p 77q 12p 33q + 16 12p 33q + 9 Summarize the similarities and differences between the lliad and the odyssey Label each statement as either matching the Articles of Confederation "A" or theConstitution "C"1. No executive branch2. All states must approve amendments(changes)3. Each state gets one representative inCongress4. Congress has the ability to collect taxesfrom the states5. 3 branches of government: Executive,Legislative, Judicial6. No federal court system7. 2 houses in Congress: one based onstate population, one with equalrepresentation (2 reps/state) I need an answer please with age, small crystals or clumps of gel may form in the vitreous humor of the eye that cast shadows on the retina. what are these tiny objects called? The use of _____ can enhance meaning by providing a type of punctuation, emphasizing a point, or drawing attention to a key thought. according to the , an organization exists not only to satisfy customer wants and needs but also to preserve or enhance individuals and the communitys long-term best interests.