5-5√3/2-√11 rationalize​

Answers

Answer 1

Step-by-step explanation:

[tex] \frac{5 - 5 \sqrt{3} }{2 - \sqrt{11} } [/tex]

To rationalize the surd multiply both the numerator and the denominator by

2 + √11

That's

[tex] \frac{5 - 5 \sqrt{3} }{2 - \sqrt{11} } \times \frac{2 + \sqrt{11} }{2 + \sqrt{11} } [/tex]

Multiply the numerators and the denominator separately

That's

[tex] \frac{(5 - 5 \sqrt{3} )(2 + \sqrt{11} )}{(2 - \sqrt{11})(2 + \sqrt{11} ) } [/tex]

Simplify

[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5\sqrt{33} }{?} [/tex]

[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33} }{4 - 2 \sqrt{11} + 2 \sqrt{11} - 11} [/tex]

[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33}}{4 - 11} [/tex]

[tex] \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33}}{ - 7} [/tex]

We have the final answer as

[tex] - \frac{10 + 5 \sqrt{11} - 10 \sqrt{3} - 5 \sqrt{33}}{7} [/tex]

Hope this helps you


Related Questions

The point (6, 6) is on the graph y = f(x) . Find the corresponding coordinates of this point on the graph y = 4f[1/3x +9] -7

a. (-9,17)
b. (17,-9)
c. (11,11)
d. (9,17)

Answers

Answer:

Correct answer is:

a. (-9,17)

Step-by-step explanation:

We are given that a point (6, 6) lies on the graph of [tex]y =f(x)[/tex].

Putting the values from the given point:

[tex]6 =f(6)[/tex]

That means we are given that [tex]f(6) =6[/tex] ..... (1)

And we have to find the corresponding coordinates of this point on the graph of [tex]y = 4f[\frac{1}3x +9] -7[/tex]

From equation (1), we know the value of [tex]f(6)[/tex].

so, let us convert [tex]f[\frac{1}3x +9][/tex] to a form such that it becomes equal to [tex]f(6)[/tex]

[tex]\Rightarrow \dfrac{1}{3}x +9 =6\\\Rightarrow \dfrac{1}{3}x=-3\\\Rightarrow x = -9[/tex]

So, let us put [tex]x = -9[/tex] in the given function:

[tex]4f[\frac{1}3\times (-9) +9] -7\\\Rightarrow 4f[-3 +9] -7\\\Rightarrow 4f(6) -7[/tex]

Now, using equation (1), putting [tex]f(6)=6[/tex]

[tex]\Rightarrow 4\times 6 -7\\\Rightarrow 24-7 \\\Rightarrow y = 17[/tex]

Therefore, the point the corresponding point is:

a. (-9,17)

A theme park ride carriage with a mass off 1000kg when empty needs to be accelerated at 0.5m/s2 along a horizontal track. What force is required to accelertae the empty ride carriage

Answers

Answer:

Required force (F) = 500 N

Step-by-step explanation:

Given:

Mass of carriage (m) = 1,000 kg

Acceleration (a) = 0.5 m/s²

Find:

Required force (F)

Computation:

Required force (F) = Mass × Acceleration

Required force (F) = 1,000 kg × 0.5 m/s²

Required force (F) = 500 kg-m/s²

Required force (F) = 500 N

Answer:

Answer:

Required force (F) = 500 N

Step-by-step explanation:

Given:

Mass of carriage (m) = 1,000 kg

Acceleration (a) = 0.5 m/s²

Find:

Required force (F)

Computation:

Required force (F) = Mass × Acceleration

Required force (F) = 1,000 kg × 0.5 m/s²

Required force (F) = 500 kg-m/s²

Required force (F) = 500 N

THANKS

1

3.0

(2 votes)

Step-by-step explanation:

Given:

Mass of carriage (m) = 1,000 kg

Acceleration (a) = 0.5 m/s²Find:Required force (F)Computation:Required force (F) = Mass × AccelerationRequired force (F) = 1,000 kg × 0.5 m/s²

Required force (F) = 500 kg-m/s²

Required force (F) = 500 N

Help I dont understand this

Identify any transformations that are used in each image below.
Some images may have multiple answers so make sure to include them all.

-Reflections - how many lines of symmetry and what specific type: vertical (y-axis), horizontal (x-axis), diagonal (y=x or y=-x)
-Rotations - of which order or how many degrees/angle of rotation

Answers

a. Reflectional symmetry only. The mirror line is vertical along the center of the sunglasses. The left half mirrors over this line to get the right half, and vice versa. There isn't any rotational symmetry because we can't rotate the glasses (some angle between 0 and 360 exclusive of both endpoints) to have the image be the same as the preimage.

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

b. Rotational symmetry only. The puzzle can be rotated 90 degrees and the before and after image will be the exact same. There isn't any reflectional symmetry here.

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

c. Reflectional symmetry and rotational symmetry. Effectively a combination of parts a) and b). We have a horizontal line of symmetry to go with a vertical one. The angle of rotation is 180 degrees.

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

d. Reflectional symmetry and rotational symmetry.  Similar to part c). This time the angle of rotation is 360/3 = 120 degrees. There are 3 lines of symmetry and they all pass through a vertex of the triangle, and the symmetry lines are perpendicular to the opposite side.

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

e. Reflectional symmetry and rotational symmetry. We can rotate 180 degrees and not change the image. There are two lines of symmetry which pass through the center, one line is horizontal and the other vertical.

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

f. Rotational symmetry only. We don't have reflectional symmetry due to the smaller petals not matching up when reflections happen. But we can rotate the figure 120 degrees the same way we can with figure d.

-when finding data as well as plotting data, you can find relationships within the data
displayed in charts or graphs, noticing the relationships can help build a solution a lot
easier.

this is what they wrote. ​
just type anything if u want the points.

Answers

Answer:

I came up with the answer check my questions to see it

Step-by-step explanation:

if b is the midpoint of ac and if c is the midpoint of bd, then what percent of cd is ac

Answers

Answer:

ac is 200% of cd

Step-by-step explanation:

To answer this question, we shall be making a visual representation.

Let’s take it one at a time.

Given;

b is the midpoint of ac

a b c

What this means is that a-b represents 50%, while bc represents another 50%

okay, we move on:

c is the midpoint of bd

b c d

What this means is that bc is 50%, while cd is another 50%.

So let’s combine the representations;

a 50% b 50% c 50% d

Now what does the question says again?

What percent of cd is ac?

From a to c, we can see two 50% which means 100%

while cd is just the regular 50%

So we can see that ac is actually twice cd

What we are saying here is , if cd is x, then ac is 2x

So we can restructure our question to mean, what percent of x is 2x?

That is simply 2x/x * 100 and that is 200%

Answer: ac is 200% of cd

Step-by-step explanation:

Rona mixes 2 pounds of meat with some chopped vegetables to make a mixture. She divides the mixture into 4 equal portions. Each portion weighs 3 pounds. Which equation and solution shows the total amount of chopped vegetables she used in the mixture?
One-fourth (2 + v) = 3; v = 10 pounds of chopped vegetables
One-fourth (2 + v) = 3; v = 4 pounds of chopped vegetables
4 (2 + v) = 3; v = 1 pound of chopped vegetables
4 (2 + v) = 3; v = 5 pounds of chopped vegetables

Answers

Answer:

First choice: (1/4)(2 + v) = 3; v = 10 pounds of chopped vegetables

Step-by-step explanation:

"2 pounds of meat with some chopped vegetables"

2 + v

"She divides the mixture into 4 equal portions."

(1/4)(2 + v)

"Each portion weighs 3 pounds."

(1/4)(2 + v) = 3

2 + v = 12

v = 10

Answer: (1/4)(2 + v) = 3; v = 10 pounds of chopped vegetables

Answer:

(2+v)=3   v=10

Step-by-step explanation:

Find all the solutions to \[\frac{x+4}{x+5} = \frac{x-5}{2x}.\][tex]Find all the solutions to\[\frac{x+4}{x+5} = \frac{x-5}{2x}.\][/tex]

Answers

Answer:

x = -4 + 3 i or x = -4 - 3 i

Step-by-step explanation:

Solve for x:

(x + 4)/(x + 5) = (x - 5)/(2 x)

Hint: | Multiply both sides by a polynomial to clear fractions.

Cross multiply:

2 x (x + 4) = (x - 5) (x + 5)

Hint: | Write the quadratic polynomial on the left hand side in standard form.

Expand out terms of the left hand side:

2 x^2 + 8 x = (x - 5) (x + 5)

Hint: | Write the quadratic polynomial on the right hand side in standard form.

Expand out terms of the right hand side:

2 x^2 + 8 x = x^2 - 25

Hint: | Move everything to the left hand side.

Subtract x^2 - 25 from both sides:

x^2 + 8 x + 25 = 0

Hint: | Using the quadratic formula, solve for x.

x = (-8 ± sqrt(8^2 - 4×25))/2 = (-8 ± sqrt(64 - 100))/2 = (-8 ± sqrt(-36))/2:

x = (-8 + sqrt(-36))/2 or x = (-8 - sqrt(-36))/2

Hint: | Express sqrt(-36) in terms of i.

sqrt(-36) = sqrt(-1) sqrt(36) = i sqrt(36):

x = (-8 + i sqrt(36))/2 or x = (-8 - i sqrt(36))/2

Hint: | Simplify radicals.

sqrt(36) = sqrt(4×9) = sqrt(2^2×3^2) = 2×3 = 6:

x = (-8 + i×6)/2 or x = (-8 - i×6)/2

Hint: | Factor the greatest common divisor (gcd) of -8, 6 i and 2 from -8 + 6 i.

Factor 2 from -8 + 6 i giving -8 + 6 i:

x = 1/2-8 + 6 i or x = (-8 - 6 i)/2

Hint: | Cancel common terms in the numerator and denominator.

(-8 + 6 i)/2 = -4 + 3 i:

x = -4 + 3 i or x = (-8 - 6 i)/2

Hint: | Factor the greatest common divisor (gcd) of -8, -6 i and 2 from -8 - 6 i.

Factor 2 from -8 - 6 i giving -8 - 6 i:

x = -4 + 3 i or x = 1/2-8 - 6 i

Hint: | Cancel common terms in the numerator and denominator.

(-8 - 6 i)/2 = -4 - 3 i:

Answer: x = -4 + 3 i or x = -4 - 3 i

Legolas shoots 3 arrows at once from his bow. He has 177 arrows. How many times can Legolas shoot his bow before he needs more arrows?

Answers

Answer:

59

Step-by-step explanation:

3x=177

3x represents the # of arrow he can shoot at once every time

177 represents the total # of arrow he has

Answer:

59

Step-by-step explanation:

177/3=59

PLZ ANSWER THIS QUESTION..Plzz

Answers

Answer:

x =  2 units

Step-by-step explanation:

Diagonals of rectangle are congruent and bisect each other

Therefore, OB = OA

   5x + 4 =  3x + 8

    5x = 3x + 8 -4

    5x = 3x + 4

5x - 3x = 4

      2x =  4

      x = 4/2

      x =2

What is the slope of the line? x + 3 y = 10 x+3y=10x, plus, 3, y, equals, 10 Choose 1 answer: Choose 1 answer: (Choice A) A 1 3 3 1 ​ start fraction, 1, divided by, 3, end fraction (Choice B) B 1 10 10 1 ​ start fraction, 1, divided by, 10, end fraction (Choice C) C − 1 10 − 10 1 ​ minus, start fraction, 1, divided by, 10, end fraction (Choice D) D − 1 3 − 3 1 ​

Answers

Answer:

-1/3

Step-by-step explanation:

The standard from of equation of a line written in slope-intercept format is expressed as y = mx+c where c is the slope of the line and c is the y-intercept.

Given the equation of the line x+3y = 10, to get the slope of the line, we need write he equation in standard from first by making y the subject of the formula as shown;

[tex]x+3y = 10\\\\subtract\ x \ from \ both \ sides\\\\x+3y-x = 10 -x\\\\3y = -x+10\\\\Divide \ through\ by \ 3\\\\\frac{3y}{3} = -\frac{x}{3} +\frac{10}{3} \\\\[/tex]

[tex]y = -\frac{1}{3}(x) +\frac{10}{3} \\[/tex]

Comparing the resulting equation with y = mx+c, the slope 'm' of the equation is -1/3

The slope of the line is -1/3.

the correct option is D.

To find the slope of the line given by the equation x + 3y = 10, we need to rewrite it in slope-intercept form, which is y = mx + b, where m represents the slope.

Let's rearrange the equation to solve for y:

x + 3y = 10

3y = -x + 10

y = (-1/3)x + 10/3

Comparing this equation to the slope-intercept form, we can see that the coefficient of x (-1/3) represents the slope.

Therefore, the slope of the line is -1/3.

Learn more about Slope here:

https://brainly.com/question/17158875

#SPJ6

-The pendulum would accelerate to the right.
-The pendulum would accelerate downward.
-The pendulum would accelerate to the left.
-The pendulum would accelerate to the upward. help needed ASAP will give brainliest

Answers

Answer:

The pendulum would accelerate to the left.

Step-by-step explanation:

Because the force pushing it left is greater than the force pushing it right, it would go to the left.


[tex] \frac{15x - 8 }{3} + \frac{9x - 3}{2} [/tex]

Answers

Greetings from Brasil...

Here is the problem:

[(15X - 8)/3] + [(9X - 3)/2]

Let's multiply everything by 6

[6.(15X - 8)/3] + [6.(9X - 3)/2]

[2.(15X - 8)] + [3.(9X - 3)]

30X - 16 + 27X - 9

57X - 25

The mean number of people per day visiting an art show in July was 110. If
20 more people each day visited the museum in August, what was the mean
number of people per day visiting in August?
A. 130
B. 620
C. 640
D. 110

Answers

Answer:

I believe the answer is A. 130

Answer:

A 130

Step-by-step explanation:

Ruben goes to a shop to buy 24.5m of cloth and 13.5m ribbon. The cloth costs Rs.85.40 per metre and the ribbon costs Rs.8.5 per metre. If he pays Rs. 2300 to the shopkeeper, how much money will he get back?

Answers

Answer:

Rs.92.95

Step-by-step explanation:

Given the following :

Metres of cloth purchased = 24.5m

Metres of ribbon = 13.5m

Cost of cloth per metre = Rs.85.40

Cost of Ribbon per metre = Rs.8.50

Total amount given to shopkeeper = Rs. 2300

how much money will he get back?

Total cost of cloth:

Cost per metre * number of metres

85.40 * 24.5 = Rs. 2092.30

Total cost of Ribbon :

Cost per metre * number of metres

8.50 * 13.5 = Rs. 114.75

Total cost of goods purchased :

Rs. (2092.30 + 114.75) = Rs. 2,207.05

Amount of change :

Rs. (2300 - 2207.05) = Rs.92.95

Aisha saves 2 Dhs on first week of the month of June, 4Dhs on second week of the month, 8 Dhs on third week of the month and so on. What will be her saving at the end of second week of July? What value is being shown by Aisha? Is saving is a good habit? How often do you save money? What are the different ways of saving money?

Answers

Answer:

she is saving in an exponential way, that is an amazing habit that will multiply her savings over time. At the end of the second week of July she will have 126 if she kept multiplying the amount every week from June into July but she will  have 38 if she starts over with saving 2 on the 1st week of the second month. I save money often, my way of saving is only spending the money i have on things I need rather than want. I also save in a linear way buy saving five dollars every month which is slower than aishas way in the long run but it is easy for me. There are so many different ways of saving money but some are slower than others and some are faster.

Step-by-step explanation:

Hope this helps, please give brainliest, i never got it before

Find a101 of the sequence 5,8,11,

Answers

Answer:

305

Step-by-step explanation:

This sequence es the sum of 3

5+3 =8

8+3 = 11

then

101 = 100 + 1

the fisrt date is 5

the another 100:

100*3 = 300

300 + 5 = 305

Interior angles are located on the a. Inside b. Outside of a polygon. Exterior angles are located on the a. Inside b. Outside of a polygon.

Answers

Answer:

Interior angles are inside. Exterior angles are outside.

Step-by-step explanation:

"Interior" means inside. "Exterior" means outside.

Answer:

inside, outside

Step-by-step explanation:

Please help! Find the surface area of the composite figure

Answers

Answer:

Step-by-step explanation:

area of base=6×6=36 m²

surface area of four walls=4×6×12=144 m²

area of top= area of four triangles=4×1/2×6×5=60 m²

total surface area=36+144+60=240 m²

HELP ME ASAP I DONT UNDERSTAND

Answers

Answer

False

Step-by-step explanation:

3 is an element of A but {3} is not so it is false.

Which value of x makes the following matrix equation true?

Answers

Answer:

[tex]\large \boxed{{x=-3}}[/tex]

Step-by-step explanation:

[tex]{\mathrm{view \ attachment}}[/tex]

40. Which families of plane figures given below are NOT always similar?
A. Squares
C. Equilateral triangles
B. Circles
D. rectangle​

Answers

Answer:

Rectangle

Explanation:

Rectangles can be oblong, and square is also a rectangle.

6x^2+12x=5x-2
solve the quadratic by factoring

Answers

[tex]6x^2+12x=5x-2\\6x^2+7x+2=0\\6x^2+3x+4x+2=0\\3x(2x+1)+2(2x+1)=0\\(3x+2)(2x+1)=0\\x=-\dfrac{2}{3} \vee x=-\dfrac{1}{2}[/tex]

What are the possible steps involved in solving the equation shown? Select three options. 3.5 + 1.2(6.3 – 7x) = 9.38 Add 3.5 and 1.2. Distribute 1.2 to 6.3 and –7x . Combine 6.3 and –7x . Combine 3.5 and 7.56. Subtract 11.06 from both sides. Mark this and return Save and Exit Next Submit

Answers

Answer:

1) Distribute 1.2 to 6.3 and -7x

2)Combine 3.5 and 7.56

3)Subtract 11.06 from both sides

Step-by-step explanation:

3.5 + 1.2(6.3 - 7x) = 9.38

Distribute 1.2 to 6.3 and -7x

3.5 + 1.2* 6.3 - 1.2 * 7x = 9.38

        3.5 + 7.56 - 8.4x = 9.38

Combine 3.5 and 7.56

11.06 - 8.4x = 9.38

Subtract 11.06 from both sides

11.06 - 8.4x -11.06 = 9.38 - 11.06

                    -8.4x = -1.68

To find solution:

Divide both sides by (-8.4)

-8.4x/-8.4 = -1.68/-8.4

 x = 0.02

Answer:

B, D, and E

its right cus i took the test soo..

solve for x 3x - 4 = 3x - 10

Answers

Answer:

no solution

Step-by-step explanation:

3x - 4 = 3x - 10

Subtract 3x from each side

3x-3x - 4 = 3x-3x - 10

-4 = -10

This is never true so there is no solution

Answer:

Step-by-step explanation:

I think you might have copied down the problem incorrectly.

If you try and solve this problem by moving the variables onto one side and the constants onto the other, you get:

3x-4=3x-10

   +10    +10

3x+6=3x

-3x     -3x

6=0 (which is FALSE)

Hope this helps!

P.S. Please give me brainliest. Thanks :)

Solve A=1/2(bh) for h

Answers

Answer: 2A/b = h

Step-by-step explanation: First, get rid of the fraction by multiplying both sides of the equation by 2. That gives us 2A = bh.

Don't be thrown off by the capital A in this problem.

Just treat it like any other variable.

To get h by itself on the right side of the equation, we now simply

divide both sides of the equation by b and our answer is 2A/b = h.

Take a look back at the formula now in the

original problem, A = 1/2bh, does that look familiar?

How do I solve for x.

Answers

Answer:

x = 17

Step-by-step explanation:

(whole secant) x (external part) =  (whole secant) x (external part)

(x+7) * 7 = ( 13+8) *8

(x+7) * 7 = ( 21) *8

Divide each side by 7

x+7 = 21/7 *8

x+7 = 3*8

x+7 = 24

Subtract 7

x = 17

Answer:

The answer is x = 17

Though I think the other guy explained it better

I am a 2 dimensional shape that has four sides. I have two obtuse angles and two acute angles. I have two different sets of parallel sides. I also have two sides that are one length, and my other two sides are a different length.

Answers

Answer:

Quadrilateral

Step-by-step explanation:

what is the value of F? (ap physics summer hw) show work

Answers

See the attached picture.

A line passes through point (4,-3) and has a slope of 5/4. Write an equation in Ax + By = C

Answers

Answer:

The answer is

5x - 4y = 32

Step-by-step explanation:

To write an equation of a line using a point and slope use the formula

y - y1 = m(x - x1)

where

m is the slope

(x1 , y1) is the point

So we have

Equation of the line using point (4 , -3) and slope 5/4 is

[tex]y + 3 = \frac{5}{4} (x - 4)[/tex]

Multiply through by 4

4y + 12 = 5(x - 4)

4y + 12 = 5x - 20

5x - 4y = 20 + 12

The final answer is

5x - 4y = 32

Hope this helps you

The angles of a triangle are in the ratio 11 : 5 : 2. The side opposite the largest angle is 5.5 centimeters. The length of the side opposite the smallest angle of the triangle is centimeters.

Answers

Answer:

  2.0 cm

Step-by-step explanation:

The sum of ratio units is 11 +5 +2 = 18, so each one stands for 10° of angle. Then the largest angle is 110°, and the smallest is 20°. The law of sines can help us find the smallest side (x):

  x/sin(20°) = 5.5/sin(110°)

  x = 5.5·sin(20°)/sin(110°) ≈ 2.00

The side opposite the smallest angle is 2.0 cm.

Answer:

the anser is 2

Step-by-step explanation:

Other Questions
answer it answer it answer it A research center poll showed that % of people believe that it is morally wrong to not report all income on tax returns. What is the probability that someone does not have this belief? 78 The probability that someone does not believe that it is morally wrong to not report all income on tax returns is . (Type an integer or a decimal.) que sentimientos experimentan el coronel, Isabel y el nio frente al cuerpo muerto del medico en la novela hojarasca Write the form of the partial fraction decomposition of the rational expression. Do not solve for the constants. 5x 4 x(x2 + 7)2 A box contain 12 balls in which 4 are white 3 are blue and 5 are red.3 balls are drawn at random from the box.find the chance that all three are selected Identify the sentence in which an adverb clause is underlined. Much of the desert has a scattered, indigenous population, which explorers sometimes encounter. Nomads continue to wander the desert in search of water and food. Many animals are raised in captivity because the conditions are not as harsh. Although people live in the desert, they are still limited by its harsh climate. Which part of an I-statement involves a description of your needs or feelings? What type of triangles has no equal sides and one right angle? To warm up before a run David begins by completing quad and hurdlers stretches. Which of these accurately evaluates his choice of warm up activities?A. These activities are appropriate because they prepare muscles for intense movementB. These activities are not appropriate because the muscles stretched are not warm yet.C. These activities are appropriate because they make the leg muscles more flexibleD. These activities are not appropriate because they stretch muscles not used in the exercise Find the product of the first 3 positive integers and then the first 5 negative integers. How did war and diplomacy change the United States and people's lives in theearly 1800s? "A broker-dealer who acted as financial advisor to a municipality in structuring a new issue now wishes to act as underwriter in a negotiated offering. Which statement is TRUE?" o prepare vegetables for finishing by grilling, sauting, pan frying, deep frying, or stewing, you should _______ them to cook them to partial doneness To whom is he addressing his speech? In sonnet 18 by William Shakespeare. Predatory pricing is considered an anti-competitive practice, and is considered illegal under competition laws. Which of the following best describes predatory pricing?A. Predatory pricing requires one company to aquire the assets of another.B. One business chooses to put another out of business by pricing its product below the level another competing business must be at to make a profit.C. Predatory pricing occurs when a firm colludes with one or more firms to fix prices or output.D. Predatory pricing is when a business sends someone out to change the price of another company's product so it is higher than its own. Fly High Co. is expanding and expects operating cash flows of $65,000 a year for four years as a result. This expansion requires $105,000 in new fixed assets. These assets will be worthless at the end of the project. In addition, the project requires $7,000 of net working capital, which will be recovered at the end of the project. What is the net present value of this expansion project at a required rate of return of 15 percent Which term best describes the difference in colors of the birds below? 4 birds are shown. One has light brown feathers with darker wings. One has very dark feathers with lighter wings. Another has medium brown feathers with light wings. The last one has medium brown feathers with very dark wings. natural selection reproductive maturity genetic variation genetic drift Mark this and return A project will reduce costs by $38,500 but increase depreciation by $18,300. What is the operating cash flow if the tax rate is 35 percent? Importance of strategic planning Prepare journal entries to record each of the following four separate issuances of stock. A corporation issued 10,000 shares of $20 par value common stock for $240,000 cash. A corporation issued 5,000 shares of no-par common stock to its promoters in exchange for their efforts, estimated to be worth $45,500. The stock has a $1 per share stated value. A corporation issued 5,000 shares of no-par common stock to its promoters in exchange for their efforts, estimated to be worth $45,500. The stock has no stated value. A corporation issued 2,500 shares of $50 par value preferred stock for $170,500 cash.