Write a two-column proof for the following information. Upload your proof below.

Given: M is the midpoint of CD; CM = 5x – 2; MD = 3x + 2
Prove: x = 2

Answers

Answer 1

The required two column proof is explained below.

What is a midpoint?

A midpoint is a point which divides a line segment into two equal parts. Thus it can be referred to as the middle point of the line segment.

The two column proof for the information is given as:

M is the midpoint of CD    (Given)

CD = CM + MD   (addition property of a line segment)

CM = MD  (definition of a midpoint)

So that;

5x – 2 = 3x + 2    (Definition of midpoint)#

Then,

5x - 3x = 2 + 2 (collecting like terms)

2x = 4

x = 2

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Related Questions

How to solve pre algebra?​

Answers

Answer:

Pre-algebra is a fundamental branch of mathematics that deals with basic arithmetic operations, such as addition, subtraction, multiplication, and division, and introduces concepts like variables, equations, and inequalities. Here are some general steps to solve pre-algebra problems:

1. Identify the problem: Read the problem carefully and identify what it is asking you to do. Identify the key information and any variables that are given.

2. Translate the problem: Translate the problem into an equation or inequality, using variables to represent unknown quantities.

3. Solve the equation or inequality: Use algebraic manipulation to solve for the variable. Follow the order of operations and simplify the expression as much as possible.

4. Check your answer: Verify that your solution is correct by plugging it back into the original equation or inequality and making sure that it satisfies the conditions of the problem.

It's important to practice pre-algebra problems regularly to develop your problem-solving skills. You can find practice problems and tutorials online or in textbooks, and you can work with a tutor or teacher to get additional help. Remember to stay patient, focused, and positive, and don't be afraid to ask for help if you need it.

Pre-algebra is a branch of mathematics that deals with basic arithmetic operations, such as addition, subtraction, multiplication, and division. It also includes topics such as fractions, decimals, percentages, and basic algebraic expressions. Here are some tips for solving pre-algebra problems:

1. Understand the problem: Read the problem carefully and make sure you understand what is being asked. Identify the variables and what you are trying to solve for.

2. Translate the problem into an equation: Write down an equation that represents the problem. Use variables to represent unknown quantities.

3. Solve the equation: Use the rules of arithmetic to solve the equation. Simplify both sides of the equation by combining like terms and isolating the variable.

4. Check your answer: Plug your answer back into the original problem to make sure it makes sense.

5. Practice, practice, practice: The more you practice solving pre-algebra problems, the more comfortable you will become with the concepts and techniques involved.

Remember, pre-algebra is the foundation for all higher-level math courses, so it's important to master these concepts before moving on to more advanced topics.

I need help on 11-12 please i need this done asap! Can someone help me out

Answers

can you please show the work that needs to be solved

139(x-28)

Please help would save a girls lifeee fr fr



Answers

Answer:

69

Step-by-step explanation:

(139) + (x-28) = 180 (adjacent angles on straight line add up to 180)

x - 28 = 41

x = 69

group of students conduct an investigation to learn more about pea plants. Their data are summarized below. Plant Water per day (mL) Height after 2 weeks (cm) 1 20 11 2 50 18 3 100 24 4 20 16 Which is the independent variable in the investigation?

Answers

If Group of students conducted an investigation to learn about "pea-plants", then the "independent-variable" is  "Water-per-day (mL)".

The "Independent-Variable" is defined as a variable which is controlled by the researcher.

In the investigation of the "pea-plants", the amount of water per day (mL) given to the plants is the independent variable because it is the variable that is intentionally varied by the students.

The students are manipulating the amount of water given to each plant to observe the effect it has on the height of the plant after two weeks.

By controlling the amount of water given to each plant, the students can determine whether there is a relationship between water intake and plant growth.

Therefore, water given to plants per-day will be the "independent-variable".

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The given question is incomplete, the complete question is

Group of students conduct an investigation to learn more about pea plants. Their data are summarized below.

Plant      Water per day (mL)        Height after 2 weeks (cm)

  1                     20                                          11

 2                     50                                          18

 3                    100                                         24

 4                     20                                          16

Which is the independent variable in the investigation?

a number from 1 to 8 is chosen at random. What is the probability that the number chosen is not even

Answers

Answer:

The probability that the number chosen is not even = 4/8

Which of the following questions about a particular animal could NOT be answered using only the data collected for the tracking collars?

Answers

The question about a particular animal that could NOT be answered using only the data collected from the tracking collars would be do the movement patterns of the animal vary according to the weather? That is option C.

What are tracking collars?

A tracking collars is a neck device that usually has a GPS device attached to it which is used by biologists to track the movement of animals that are under study.

The functions of the tracking collars include the following:

It allows them to note how many miles the animal can travel in a given time.

It allows them to note the pattern of movement of the animals.

It allows them to note the location preferred by the animal to travel.

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Complete question:

Biologists often attach tracking collars to wild animals. For each animal, the following geolocation data is collected at frequent intervals.

The time

The date

The location of the animal

Which of the following questions about a particular animal could NOT be answered using only the data collected from the tracking collars?

A. Approximately how many miles did the animal travel in one week?

B. Does the animal travel in groups with other tracked animals?

C. Do the movement patterns of the animal vary according to the weather?

D. In what geographic locations does the animal typically travel?

C. Do the movement patterns of the animal vary according to the weather?

Amber baked 120 cookies to give to five friends she wants to put the same number of cookies in each bag which of the following can she use to find out how many cookies to put in each bag

Answers

Answer:

she can divide the amount of cookies to friends

Step-by-step explanation:

120/5= 24

Find the surface area of the prism a.120cm. B180cm. C34cm. D 333cm

Answers

The surface area of the prism for the given dimensions is equal to option B. 180 square centimeters.

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

In a Triangle ,

Base = 12cm

height = 5cm

Area of the triangle = ( 1/2 ) × base × height

                                 = (1/2)× 12 × 5

                                 = 30 cm²

Length of rectangle 1 = 12cm

Width of rectangle 1 = 4cm

Area of rectangle 1 = 12 × 4

                                = 48 cm²

Length of rectangle2= 13cm

Width of rectangle 2 = 4cm

Area of rectangle 2= 13 × 4

                                = 52 cm²

Length of rectangle 3 = 5cm

Width of rectangle 3 = 4cm

Area of rectangle 3 = 5 × 4

                                = 20 cm²

Surface area of the prism

= Area of two right triangles + Area of rectangle 1 + Area of rectangle 2 + Area of the rectangle3

Substitute the values of the area we have,

⇒ Surface area of the prism  = 2(30 ) + 48 + 52 + 20

⇒ Surface area of the prism  =  180 square centimeters

Therefore, the surface area of the prism is equal to option B. 180 square centimeters.

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Solve for AB in simplified, rationalized form:

20/√2 20√2/2 40/√2 10√2

Answers

Answer:

AB = (20/√2)(√2/√2) = 10√2

tia's favorite stargergy for multiplying polynomials is to make a box that fits the two factors

Answers

Using Tia's box method, the multiplication of the polynomials (x + 2)(x² -3x + 5) in the standard form is  x³ - x² - x + 10

Here, we need to multiply the polynomials (x + 2)(x² -3x + 5)

Tia's stargergy for multiplying polynomials is to make a box that fits the two factors.

Using Tia's box method,

          x²          -3x            +5

x         x³           -3x²          +5x

+2     +2x²         -6x           +10

Consider (x + 2)(x² -3x + 5)

= (x . x²) - (x . 3x) + (x . 5) + (2x²) -(2 × 3x) + (2 × 5)

= x³ - 3x² + 5x + 2x² - 6x + 10

= x³ - 3x² + 2x² + 5x - 6x + 10

= x³ - x² - x + 10

This is the required polynomial.

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Find the complete question below.

Write the slope of tangent and normal to the curve y=f(X) at (x1,y1).​

Answers

The slope of the tangent line is:

a = (df(x1)/dx)

The slope of the normal one is:

a' = -1/(df(x1)/dx)

How to find the slope of the tangent line?

For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.

So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:

df(x1)/dx

And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:

a*(df(x1)/dx) = -1

a = -1/(df(x1)/dx)

Where df/dx reffers to the derivative of f(x).

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if a1= 9 and =-3a n-1 then find the value of a5

Answers

If a₁ = 9 and sequence aₙ = -3aₙ₋₁ , then the value of a₅ is approximately equal to 729.

To find the value of a₅, we need to use the recursive formula provided, which relates each term in the sequence to the previous one. The formula given is a bit unusual, as it defines each term in terms of the negative three times the previous term. However, we can use this information to work out the value of a₅.

Starting with a₁ = 9, we can use the recursive formula to find the next few terms of the sequence:

a₂ = -3a₁ = -3(9) = -27

a₃ = -3a₂ = -3(-27) = 81

a₄ = -3a₃ = -3(81) = -243

a₅ = -3a₄ = -3(-243) = 729

Therefore, the value of a₅ is 729. We can check that this is correct by verifying that it satisfies the given recursive formula:

a₄ = -3a₃ = -3(81) = -243

a₅ = -3a₄ = -3(-243) = 729

This confirms that our solution is correct.

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The point [ -√2/2, √2/2] is the point at which the terminal ray of angle 0 intersects the unit circle. What are the values for the cosine and cotangent functions for the angle 0

O cos0 = -√2/2, cot0=-1
O cos0=√2/2, cot0= 1
O cos0= √2/2, cot0= -1/2
O cos0= - √2/2, cot0= 1/2

PLEASE HURRY

Answers

The values for the cosine and cotangent functions for the angle x is

O cos0 = -√2/2, cot0 =-1

How to find the cosine and cotangent angle

Let the angle be x

given that the point [ -√2/2, √2/2] is on the terminal ray of angle x

the x-coordinate of the point is -√2/2 and this is the cos hence

cos x = -√2/2.

To find the cotangent

the y coordinate is the sin therefore sin x = √2/2

tan x = sin x / cosx = (√2/2) / (-√2/2) = -1

and cotangent is the reciprocal of the tangent

cot x = 1 / tan x = -1/1 = -1.

cos x = -√2/2 and cot x = -1.

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9. A has some amount of money with him. He gave one half of one third from that amount One half of the amount received by B is 20. What is the amount that A originally had?​

Answers

Using the expression 5x/12 = 20, the amount that A originally had was $48.

We have,

Let x be the amount of money that A originally had.

Then, A gave away 1/2 x 1/3 = 1/6 of the amount, which is equal to x/6.

The amount received by B is 1/2 of the remaining amount,

which is (x - x/6)/2 = 5x/12.

We know that 5x/12 = 20,

Solving for x.

5x/12 = 20

5x = 240

x = 48

Therefore,

The amount that A originally had was $48.

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two 6 sided dice are rolled. What is the probability of rolling a number that is not an odd number?

Answers

Answer:1/4, 25%

Step-by-step explanation:

even number: 2,4,6

odd umber 1,3,5

even number probability when 1 dice is rolled: 3/6 = 1/2

2 dice is rolled: 1/2*1.2 = 1/4 = 25%

In a class of 50 students, they had a chance to read novel,comics and textbook 21 read novel,24 read comics and 18 read textbook 3 read only novel 9 read only comics and 2 read only textbook 5 read all the 3. illustrate your information on a venn diagram. use your diagram to find the number of students who read a. comics and novel only b. textbook and novel only c. none of the 3​

Answers

Answer:

Here is a Venn diagram that illustrates the information:

```

           ___________

          |           |

          |    N      |

          |_____  ____|

          |\    ||    /|

          | \   ||   / |

          |  \  ||  /  |

          |   \ || /   |

          |  C \||/ T  |

          |_____\v/____|

              A

```

In the diagram, N represents the set of students who read the novel, C represents the set of students who read the comics, and T represents the set of students who read the textbook. The region labeled A represents the set of students who read all three.

Using the Venn diagram, we can find the number of students who read:

a. comics and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for comics and novel, but not for textbook. This region has 9 students.

b. textbook and novel only: This corresponds to the region of the diagram that is exclusively shaded with the circles for textbook and novel, but not for comics. This region has 1 student.

c. none of the 3: This corresponds to the region of the diagram that is outside of all three circles. This region has 13 students.

Therefore, the number of students who read a. comics and novel only is 9, b. textbook and novel only is 1, and c. none of the 3 is 13. Answer: a. 9, b. 1, c. 13.

Expand and evaluate the series.

∑6n=13n
{
,
,
,
,
,
}

S6=

Answers

Answer:

The series ∑6n=1 3n is a sum of the first 6 terms of the sequence 3n, which starts with n = 1 and increases by 3 for each successive term. Therefore, the first 6 terms of the sequence are:

3(1), 3(2), 3(3), 3(4), 3(5), 3(6)

which simplify to:

3, 6, 9, 12, 15, 18

The sum of these terms is:

∑6n=1 3n = 3 + 6 + 9 + 12 + 15 + 18 = 63

Therefore, S6, the sum of the first 6 terms of the series, is 63.

An artist is stained glass window that is 3 and 1/2 ft x 2 and 3/4 ft. The artist designed to use squares of colored glass that measures 1/4 ft by 1/4 foot. How many colored squids did the artists use?

Answers

Answer:

The artist used 1680 colored squares of glass.

If 34 x 27 = 918, which of the following is true?

918 ÷ (-34) = 27
-918 ÷ 34 = -27
-918 ÷ 27 = 34
918 ÷ 27 = -34

Answers

The second choice is the correct answer. A negative number divided by a positive will remain a negative. -918/34 = -27 —> -27 = -27 (true!!).

Let’s see how we can rearrange the terms in the equation by performing opposite operation when moving them to different sides of the equal sign. For ex., subtraction and addition, multiplication and division, squared and square root, etc.

One way:
34 x 27 = 918
34 = 918/27 (not listed as a choice)

Another way:
34 x 27 = 918
27 = 918/34 (also not listed as a choice)

Another way:
34 x 27 = 918
(34 x 27) - 918 = 0
-918 = -(34 x 27)
-918/-34 = 27 (not listed as a choice)

A different way:
-918/34 = -27 (yes this is listed as a choice)

The first answer is NOT TRUE. -27 ≠ 27.
**The second answer IS TRUE!! -27 = -27.
The third answer is NOT TRUE. -34 ≠ 34.
The fourth answer is NOT TRUE. 34 ≠ -34.

In each figure, all b. Determine whether the third figure is a translation image of the first figure. Write yes or no. Explain
your answer.
미미미
a. Yes; it is one reflection after another with respect to the two parallel lines.
b. No; it is a reflection followed by a translation.
c. No; it is a reflection followed by a rotation.
d.
No; it is one reflection after another with respect to the two parallel lines.

Answers

Answer:

a

Step-by-step explanation:

Help me ASAPP Please :

Answers

The simplification of the fractions given above through multiplication would be;

1.) 9 11/12

2.) 11 19/40

How to simplify a given fraction through multiplication?

For question 1.)

2 5/6 × 3 2/4

Change the mixed fraction to single fraction;

= 17/6 × 14/4

= 17/6 × 7/2

= 119/12

= 9 11/12

For question 2.)

5 2/5 × 2 1/8

= 27/5 × 17/8

= 459/40

= 11 19/40

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Jodi’s car used 12 gallons of gas to travel 456 miles. How many miles did her car travel per gallon of gas? Show work

Answers

Answer:

To find the number of miles Jodi's car traveled per gallon of gas, we need to divide the distance traveled by the amount of gas used:

miles per gallon = distance traveled / amount of gas used

distance traveled = 456 miles

amount of gas used = 12 gallons

miles per gallon = 456 miles / 12 gallons

miles per gallon = 38 miles/gallon

Therefore, Jodi's car traveled 38 miles per gallon of gas.

Answer:

38 miles

Step-by-step explanation:

Set up your division: 456 / 12

456 divided by 12 is 38

So, Jodi's car travels at 38 miles per gallon of gas.

The perimeter of a rectangle is

35

cm

35 cm35, start text, space, c, m, end text. The rectangle's area (in

sq. cm

sq. cmstart text, s, q, point, space, c, m, end text) as a function of its length (in

cm

cmstart text, c, m, end text) is graphed.

What is the approximate average rate at which the area decreases, as the rectangle's length goes from

13

cm

13 cm13, start text, space, c, m, end text to

16

cm

16 cm16, start text, space, c, m, end text?

Answers

The average rate of decrease of the area as the length goes from 13 cm to 16 cm is given as follows:

D) 11 and 1/3 cm² per cm.

How to obtain the average rate of change?

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function.

From the graph, the parameters are given as follows:

Length of 13 cm -> Area of 60 cm².Length of 16 cm -> Area of 24 cm².

Hence the rate is approximated as follows:

r = (24 - 60)/(16 - 13)

r = -12 cm² per cm.

Which is closest to option D.

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Answer: D

I answered this on Khan Academy and my lawyer above me has the papers for the work.

See u in court...

For what value of A is the function, (x), continuous at x=0?

Answers

(i)  [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = 3

(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = -1

(iii) h(0) = 1/7

The value of λ must be 7, for h(x) to be continuous at x = 0.

The given function is,

h(x) = 1/7, when x = 0

      = 1 - 2 cos 2x, when x < π/2

      = 1 + 2 cos 2x, when x > π/2

      = x cos x/sin λx, when x < 0

Now,

(i) [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^-}{2}}[/tex] (1 - 2 cos 2x) = 1 - 2 cos π = 1 + 2 = 3

(ii) [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] h(x) = [tex]\lim_{x \to \frac{\pi^+}{2}}[/tex] (1 + 2 cos 2x) = 1 + 2 cos π = 1 - 2 = -1

(iii) h(0) = 1/7

Since the function is continuous at x = 0, so

[tex]\lim_{x \to 0}[/tex] h(x) = h(0)

[tex]\lim_{x \to 0}[/tex] x cos x/sin λx = 1/7

[tex]\lim_{x \to 0}[/tex] cos x.[tex]\lim_{x \to 0}[/tex] 1/λ(sinλx/λx) = 1/7

1/λ = 1/7

λ = 7

Hence the value of λ must be 7.

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Find the measure of each angle indicated.
Z
?
A
B
56°
98
O 82°
O 103°
O 121°
42°
C

Answers

Answer:

The correct answer is 98°.

Answer: 82

Step-by-step explanation: all the angles of the triangle have to add up to 180 you all up the other angles and you get 98. 98= angle A your trying to find the outside angle we know that a line equals 180 degrees therefore we subtract that angle from 180 and get 82 which is your answer

What is a formula for the nth term of the given sequence?
12,6,3...

Answers

Answer:

The given sequence is decreasing by a factor of 2 each time, so each term is half of the previous term.

We can write the nth term of the sequence as:

a_n = a_1 * (1/2)^(n-1)

where a_1 is the first term of the sequence (12 in this case) and n is the position of the term we want to find.

For example, to find the 4th term of the sequence, we would have:

a_4 = 12 * (1/2)^(4-1)

= 12 * (1/2)^3

= 12 * 1/8

= 1.5

Therefore, the formula for the nth term of the sequence 12, 6, 3, ... is:

a_n = 12 * (1/2)^(n-1)

Select all numbers that are irrational.

Answers

Answer:

The irrational numbers are:

368.5468432...

14.19274128...

√.156

Box 1&3 are the answer

brainiest !!!!!!!! this needs to be done asappp

Answers

The coordinates best represent the vertex of the graph is given by (1, -2).

Hence the correct option is (D).

Graph is a pictorial representation of a curve or a function or a relation.

From the given graph we can see that the curve is an upward parabola which has vertex at a point other than origin.

We can see that where the vertex is formed the value along X axis is 1 and the value along Y axis is -2 (towards down).

So the vertex of the given graph is at (1, -2).  

Hence the correct option will be (D).

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One meter of shielded microphone cable weighs 75/1,000 kilogram. What is the length of cable in coil that weigh 5 1/2 kilogram

Answers

The length of cable in the coil that weighs 5 1/2 kilograms is 1/2 meter.

Let x be the length of cable in meters that weighs 5 1/2 kilograms.

Then, we can write:

1 meter / (75/1000) kilograms = x meters / 5.5 kilograms

Simplifying the left side, we get:

1 meter / (75/1000) kilograms = 1000 / 75 meters/kilogram

= 40/3 meters/kilogram

Substituting this into our proportion, we get:

40/3 meters/kilogram * x meters = 5.5 kilograms

Multiplying both sides by 3/40, we get:

x meters = (5.5 kilograms) * (3/40) * (40/3 meters/kilogram)

               = 1/2 meter

The length is 1/2 meter

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Tommy's Diner offers its clients a choice of regular and diet soda. Last night, the diner served 18 regular sodas and 82 diet sodas. What percentage of the sodas served were regular?

Answers

The percentage of the sodas that was served which were regular would be = 18%

How to calculate the percentage of sodas served?

The quantity of regular sodas served = 18

The quantity of diet soda served = 82

The total number of soda served = 18+82 = 100

Therefore the percentage of soda that were regular would be;

= 18/100 × 100/1

= 18%

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internal service funds should not account for depreciation of capital assets used in their operations, since this would, in effect, charge the government twice for the same assets. True or False? based upon the following data: calculate the discounted payback period with a discount rate of 10%. project ainitial cost-$50,000 year 1$20,000 year 2$25,000 year 3$20,000 the following table gives total revenue and cost for a monopolist: quantity price total revenue total cost 0 0 100 1 185 150 130 2 180 290 170 3 175 415 222 4 170 520 287 5 165 600 367 6 160 655 467 7 155 685 587 8 150 685 737 if the market were competitive how much lower would the price of the good be? Which american writer popularized the phrase ""white-collar worker""?. The organizers of the expedition created ""penguin etiquette"" most likely to:. Suppose you are going to test the hypothesis that two populations have the same mean. What is the test statistic for this test when the sample averages are 6 and 7. 5 and sample 1 has a standard deviation of 16 and sample 2 has a standard deviation of 15 and both samples have 32 observations?. The data below give the number of books checked out of the school library by 15 studentsduring one month. Make a frequency table of the data.0, 3, 2, 3, 2, 1, 1, 0, 1, 2, 5, 1, 2, 3, 1. (Sorry if the photo is hard to see) I need the answer ASAP! Please helpA. The rate of emigration equals the death rateB. The birth and death rates are equivalent.C. There will be more food available then the population can consume.D. The population sizes of the organism and it's predator are equaled. A diprotic acid is titrated with a strong base. The ph at the first half-equivalence point is 3. 27. The ph at the second half-equivalence point is 8. 53. What is the value of ka2?. When you eat a slice of red pepper, what part of the plant are you eating?. Savers like Dan are likely to save more when the real interest rate ______. What's this answer?2 5/6 -3 2/4 = nike increased which account when it originally issued shares of its stock for cash?a.retained earningsb.treasury stockcmon stockd.revenues a distributed database system will support different database management systems (dbms) that may even support different models running under different computer systems. question 42 options: a) fully heterogeneous b) homogeneous c) fully homogeneous d) heterogeneous sharing some personality helps build common ground and trust and makes it more likely that people will find the social media campaign engagingT/F 4x^5e^2x^6 from 0 to 1 TRUE OR FALSE. I'd love to live in one of the galaxies near our cosmological horizon, because then I could see the black void into which the universe is expanding. calculate the expected molarity of the naoh solution. the molar mass of naoh is 39.997 g/mol. Breadcrumb trail in the project window shows: Which example shows how branches of government interact with each other? A. The Supreme Court rules on a case. B. The House of Representatives votes on a bill. C. The president recommends legislation to Congress. D. The president signs a treaty with a country in Europe.