The vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4). The vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). Which conclusion is true about the quadrilaterals? (5 points)

The measure of their corresponding angles is equal.
The ratio of their corresponding angles is 1:2.
The ratio of their corresponding sides is 1:2
The size of the quadrilaterals is different but shape is same.

Answers

Answer 1

The measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4). This can be obtained by plotting the quadrilaterals on a graph paper and comparing the figures.

Which conclusion is true about the quadrilaterals?

Given that,

vertices of quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4)

vertices of quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4)

(x,y) ; (x, y-8)

ABCD is reflected across the line y=4 to get the quadrilateral EFCD.

Reflection means the size and shape of the quadrilaterals is same ⇒quadrilateral ABCD and quadrilateral EFCD are congruent.

Thus corresponding parts of congruent triangles are equal, corresponding angles will be equal.

Hence the measure of their corresponding angles is equal the vertices of a quadrilateral ABCD are A(4, 8), B(10, 10), C(10, 4), and D(4, 4) and the vertices of another quadrilateral EFCD are E(4, 0), F(10, -2), C(10, 4), and D(4, 4).

Learn more about quadrilaterals:

brainly.com/question/22763917

#SPJ1

The Vertices Of A Quadrilateral ABCD Are A(4, 8), B(10, 10), C(10, 4), And D(4, 4). The Vertices Of Another

Related Questions

3x^2 - 5x -1 =0
Quadratic Equation
please explain step by step

Answers

Answer:

Step-by-step explanation:

Solving 3x2-5x-1 = 0 by the Quadratic Formula .

According to the Quadratic Formula, x, the solution for Ax2+Bx+C = 0, where A, B, and C number, often called coefficients, is given by :

- B ± √ B2-4AC

x = ————————

In our case, A = 3

B = -5

C = -1

B2 - 4AC =

25 - (-12) =

Applying the quadratic formula :

5 ± √ 37

x = —————

√ 37, rounded to 4 decimal digits, is 6.0828

So now we are looking at:

x = ( 5 ± 6.083 ) / 6

Two solutions:

x =(5+√37)/6= 1.847

x =(5-√37)/6=-0.180

a group of young women decided to raise 480000 to start a business after some time 4 women pulled outand they had to pay additional 20000 . determine the original number of women

Answers

Answer:

96 is the number of original women investors.

Step-by-step explanation:

Let X be the number of young women in the initial group. They raised 480000, so the average payment per person was (480000/X).

When 4 pull out, the new average is (480000/(X-4)). We are told that this new average required the remaining women (X-4) to add another 20000.

The four women therefore had contributed 20000 in total, making their average 20000/4 = 5000 each.

This would have been the same amount contributed by all X women. Thus, we can set the average (480000/X) equal to 5000

(480000/X) = 5000

(480000) = 5000X

(480000)/5000 = X

X = 96

The original number of women was 96.

===

Check

(96 Women)(5000/Woman) = 480000 CHECKS

(4 Women pull out)*(5000) = 20000 that needs to be added to stay at 480000. CHECKS

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothesis test to determine if the population mean time on death row could likely be 15 years, what would the null and alternative hypotheses be

Answers

The null hypothesis be is =15 and the alternative hypothesis be is ≠15

According to the statement

Mean length of time on death row is 17.4 years

Standard deviation of 6.3 years.

Now we determine the hypothesis with mean time 15 years then

P value outcome is 0.00015

So, The null hypothesis be is =15 and the alternative hypothesis be is ≠15

Learn more about HYPOTHESIS here https://brainly.com/question/12416923

#SPJ4

A rectangular closet has a perimeter of 18 feet and an area of 20 square feet. What are the dimensions of the closet.

Answers

Answer:

The width can either be 4 or 5 feet.

Step-by-step explanation:

Assuming the length is x and the width is y.2x+2y=18xy=202y=18−2xy=9−xx(9−x)=209x−x2=200=x2−9x+200=(x−5)(x−4)x=5and4 The width can either be 4 or 5 feet

Help pls

Use the data from the table to create a scatter plot. Plot all the data points from the table.

Variable A 1 4 2 3 5 1 3 7 6 6 2 9 7 5 8
Variable B 6 6 1 6 7 4 4 7 5 3 5 25 21 4 4

Answers

The attached graph represents the scatter plot of the table of values

How to create the scatter plot?

The table of values is given as:

Variable A 1 4 2 3 5 1 3 7 6 6 2 9 7 5 8

Variable B 6 6 1 6 7 4 4 7 5 3 5 25 21 4 4

Rewrite the table as:

x 1 4 2 3 5 1 3 7 6 6 2 9 7 5 8

y 6 6 1 6 7 4 4 7 5 3 5 25 21 4 4

Next, we plot the values on a graph

See attachment for the scatter plot

Answers

Answer:

972π or 3052.08 if π=3.14(remember to label the answer with your units)

Step-by-step explanation:

The formula for the volume of a sphere is [tex]\frac{4}{3}\\[/tex]π[tex]r^{3}[/tex]. So, just plug the radius into the formula. [tex]r^{3}[/tex] in this case is [tex]9^{3}[/tex] which is 729. For, [tex]\frac{4}{3}[/tex]×729, the 3 and 729 cancel out to create 4×243 which is 972. Just add π to this and you get 972π. If π is 3.14 just multiple 972 and 3.14 to get 3052.08.

#12Writethe converse, inverse, and contrapositive of the following statement. Find the truth value of each.“If Brielle drives at exactly 0 mi/h, then she travels 10 mi in 0 mins

Answers

See below for the converse, inverse, and contrapositive of the statement

How to write the conditional statements?

The statement is given as:

If Brielle drives at exactly 30 mi/h, then she travels 10 mi in 20 mins

The speed is calculated as:

Speed = Distance/Time

So, we have:

Speed = 10 mi/20 mins

This gives

Speed = 10 mi/1/3 h

Speed = 30 mi/h

The converse

To do this, we simply switch the hypothesis and the conclusion

So, the converse is:

If Brielle travels 10 mi in 20 mins, then she drives at exactly 30 mi/h

The above statement is true

The inverse

To do this, we simply negate the hypothesis and the conclusion

So, the inverse is:

If Brielle did not drive at exactly 30 mi/h, then she did not travel 10 mi in 20 mins

The above statement is false

The contrapositive

To do this, we simply negate the hypothesis and the conclusion, and then switch them

So, the contrapositive is:

If Brielle did not travel 10 mi in 20 mins, then she did not drive at exactly 30 mi/h

The above statement is false

Read more about conditional statements at:

https://brainly.com/question/18152035

#SPJ1

We can learn a lot about a population if we select a ______ of it. Group of answer choices population subset data set case

Answers

We can learn a lot about a population if we select a subset of it.

What is a subset?

One kind of set is a sample space. It is a clear listing of every event that could occur in a statistical experiment. A statistical experiment's events are a subset of the sample space.

A subset is a smaller group of results that are part of the bigger group.

Subsets are events, and events are subsets. A subset is an event of a sample space, and an event is a potential result of an experiment. A random experiment's sample space is a set (S) that contains all of the experiment's potential outcomes.

Learn more about subsets here:

https://brainly.com/question/20509970

#SPJ4

solve each equation round to the nearest ten-thousandth in (x+21)=7

Answers

The solution to the equation (x+21)=7 is x = -14

How to solve the equation?

The equation is given as:

(x+21)=7

Remove the brackets

x + 21 = 7

Subtract 21 from both sides

x + 21 - 21 = 7 - 21

Evaluate the expression

x = -14

Hence, the solution to the equation (x+21)=7 is x = -14

Answers

Answer:

5:9

Step-by-step explanation:

So since 18 chose to do oral report, that means (28-18) or 10 students decided to do a written report.

To find the written to oral report ration, we need to find for each student that did a written report, how many did an oral report? We can express this as a fraction and simplify to get the simplified ratio. So the the written will be the numerator and the oral will be the denominator: 10/18, to simplify this simply divide both sides by 2, to get 5/9 which gives us the simplified ratio of 5:9 meaning that for every 5 students who decided to do a written report 9 students decided to do an oral report.

Model the situation with the sun of the polynomials. Then simplify their sum.

A rectangular picture frame has the dimensions shown in the figure. Write a polynomial that represents the perimeter of the frame.

Answers

Answer: 16x - 2

Step-by-step explanation:

The perimeter of a figure is the total length of all sides of the figure. Since this figure is a rectangle, opposite sides have the same length.

Therefore, the perimeter of the picture frame can be modeled by

[tex]6x+3+2x-4+6x+3+2x-4[/tex]

Moving all like terms together, we get

[tex]6x+2x+6x+2x+3-4+3-4[/tex]

Finally, combining these terms, we get

[tex]16x -2[/tex]

A group of Advanced Open Water Divers plans to make two dives. The first dive is on a reef in 22 metres of water for 20 minutes. The group then remains on the surface for 1 hour. The second dive is on a wreck in 16 metres of water, with a planned bottom time of 30 minutes. What will be the ending pressure group after the second dive

Answers

The ending pressure group after the second dive is R.

According to the statement

We have given that the

The first dive is on a reef in 22 metres of water for 20 minutes and The second dive is on a wreck in 16 metres of water, with a planned bottom time of 30 minutes.

And we have to find the pressure group after second dive.

So, For this purpose, we know that the

Recreational scuba diving (R) – this diving has prescribed limits, including a depth no greater than 130 fsw, using only compressed air, and never requiring a decompression stop.

From the above situation, we could note that there was a prescribed limit 18m/60ft of water with a bottom time of 30 minutes.

And due to its the ending pressure becomes R.

So, The ending pressure group after the second dive is R.

Learn more about Pressure here

https://brainly.com/question/5018408

#SPJ1

To find the 95% confidence interval for the population standard deviation using the bootstrap method. You repeatedly sample with replacement from the sample, tens of thousands of times. For each sample, you compute the sample standard deviation. What is the next step?.

Answers

The next line after computing the sample standard deviation is to; determine the 2.5th and 97.5th percentiles of the values.

How can the 95% confidence interval be determined?

It follows from the task content that the 95% confidence interval for the population standard deviation using the bootstrap method in which case, after numerous sampling, the 2.5th and 97.5th percentiles of the standard deviations are determined.

Answers

Answer:

856.5ft^2

Step-by-step explanation:

I took the test.

Select the equivalent expression. (Please Help!!!)
(a/b^3)^4 = ?
Choose 1 answer:
A. a^8/b^8
B. a^4/b^12
C. a/b^81
D. a^5/b^7

Answers

Answer: B. a^4/b^12

Step-by-step explanation:

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{a}{b^{3} }\right)^{4} \end{gathered}$}[/tex]

Use the rules of exponents to simplify the expression.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \left(\frac{a^{1} }{b^{3}}\right)^{4} \end{gathered}$}[/tex]

To raise the quotient of two numbers to a power, raise each power to the power and then divide it.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{(a^{1})^{4} }{(b^{3})^{4} } \end{gathered}$}[/tex]

To raise a power to another power, multiply the exponents.

[tex]\large\displaystyle\text{$\begin{gathered}\sf \frac{a^{4} }{b^{3\times4} } \end{gathered}$}[/tex]

Multiply 3 by 4.

[tex]\boxed{\large\displaystyle\text{$\begin{gathered}\sf \frac{a^{4} }{b^{12} } \end{gathered}$}}[/tex]

We conclude that: the correct option is "B".

Which side lengths form a right triangle?
Choose all answers that apply:
A:
11,13,√290
B:
7, 24, 25
C: 2, 5, 7

Answers

The side lengths that forms a right triangle are as follows:

11, 13 √2907, 24, 25

What is a right angle triangle?

A right angle triangle has one of its angle as 90 degrees. The sides of the triangle follows Pythagoras theorem.

Therefore,

c² = a² + b²

where

a and b are the legsc is the hypotenuse

The hypotenuse is the longest side of the right triangle.

Therefore, the side lengths that forms a right triangle are as follows:

11, 13 √2907, 24, 25

learn more on right triangle here: https://brainly.com/question/14593341

#SPJ1

Go to a clothing store with
your parent/guardian and
pick out one item that you
would like to purchase. How
much of a discount would
you have if the item had
25% off sale? What would
a
the sale price be?

Answers

Answer:

original price $75

discount $18.75

sale price $56.25

Step-by-step explanation:

I found a pair of dress pants for $75.

Since the discount is 25%, then the discount is

25% of $75 = 0.25 × $75 = $18.75

The sale price is the original price, $75, minus the discount, $18.75.

$75 - $18.75 = $56.25

I enter the mall with dollars. I spend dollars at American Eagle, which is more than the amount I spent at Banana Republic. I also spent less at American Eagle than I spent at Cole Haan. How much money do I have left after shopping at these three stores

Answers

The correct answer is 64 - 3 a.

What is a linear equation in math?

A linear equation only has one or two variables. No variable in a linear equation is raised to a power greater than 1 or used as the denominator of a fraction. When you find pairs of values that make a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.

I spent a dollars at American Eagle, which is 4 more than the amount I spent at Banana Republic ( b ).

a = b + 4. Therefore: b = a - 4

Also I spent 15 less at American Eagle than I spent in Cole Haan ( c ).

a = c - 15, or: c = a + 15.

75 - a - ( a - 4 ) - ( a + 15 ) = 75 - a - a + 4 - a - 15 =

= 64 - 3 a

Therefore, I have 64 - 3a dollars left after shopping at these three stores. Now we just have to know how much dollars I spent at American Eagle and we will have the amount in dollars.

Learn more about linear equation

brainly.com/question/387530

#SPJ4

The complete question is -

I enter the mall with $75 dollars. I spend a dollars at American Eagle, which is 4 more than the amount I spent at Banana Republic. I also spent 15 less at American Eagle than I spent at Cole Haan. How much money do I have left after shopping at these three stores?

Se vendieron un total de 430 boletos para la obra de teatro escolar. Los boletos eran o de adulto o de estudiante. Se vendieron 70 boletos de estudiante menos que boletos de adulto. ¿Cuántos boletos de adulto fueron vendidos?

Answers

Resolviendo un sistema de ecuaciones, veremos que se vendieron 250 boletos de adulto.

¿Cuántos boletos de adulto fueron vendidos?

Definamos las variables:

x = boletos de adulto vendidos.y = boletos de estudiantes vendidos.

Se vendieron un total de 430 boletos, entonces:

x + y = 430

Y se vendieron 70 boletos de estudiante menos que boletos de adulto:

y = x - 70

Tenemos el sistema de ecuaciones:

x + y = 430

y = x - 70

Para resolverlo, podemos reemplazar la segunda ecuación en la primera:

x + y = 430

x + (x - 70) = 430

2x = 430 + 70 = 500

x = 500/2 = 250

Se vendieron 250 boletos de adulto.

Sí quieres aprender más sobre sistemas de ecuaciones:

https://brainly.com/question/13729904

#SPJ1

9 boys can paint a basketball court in 3 hours how long should 5 boys take working at the same rate

Answers

Answer:

100 minutes

Step-by-step explanation:

3 hours= 180 min

180/9 = 20

20 x 5 =100 min

3\sqrt(6)*6\sqrt(6)
Please quick reply!

Answers

Answer: 3

Step-by-step explanation:

Multiply the numerator to get 3 x 6 is 18

Multiply the denominator to get √6 x √6 = 6

Divide 18 by 6 to get the answer is 3

Kelly is 5'4" tall. She measured her shadow one morning to be 8'7". She then measured the shadow of her house. The house shadow was 42'3". How tall is the
actual house? (inches rounded to the hundredths.)

Answers

The height of the actual house is 26'.26" .

How to find the height of the house using ratio?

A ratio indicates how many times one number contains another.

Therefore, the heights will form a similar length. Therefore, the corresponding length have the same ratios.

Therefore,

height of Kelly / x = height of Kelly shadows / height of house shadow

Hence,

where

x = actual height of the house

5.4 / x = 8.7 / 42.3

cross multiply

42.3 × 5.4 = 8.7x

Therefore,

228.42 = 8.7x

divide both sides by 8.7

228.42 / 8.7 = 8.7x / 8.7

x = 26.2551724138

Therefore, the height of the actual house is 26'.26"

learn more on ratio here: https://brainly.com/question/20849502

#SPJ1

I dont know this. pls help

Answers

Answer:

28, 4 or 4, 28 (order doesn't matter, both are true answers)

Step-by-step explanation:

l + w = 32

l*w = 112

l = 112/w

112/w + w = 32

w = 28 or 4

l = 28 or 4

Answer:

4,28

Step-by-step explanation:

So let's look at the sentence to take any necessary information out. It says the length of a rectangle plus it's width is 32. Since we do not know what the length and width are, let's just represent them as L (length) and W (width). Using this information we get the equation: [tex]L + W = 32[/tex] and since we're given the area of the rectangle, we can also define another equation which is: [tex]LW = 112[/tex] since the length * width = area.

So now all we have is a systems of equations. We can solve for L or W in the area equation and plug it into the addition equation. We can also solve for L or W in the addition equation and then plug it into the area equation, either should work, but in this example I'll solve for L in the addition equation:

Original Equation:

[tex]L + W = 32[/tex]

Subtract 32 from both sides

[tex]L = 32-W[/tex]

Now let's use this definition of L to plug into the second equation:

[tex]LW = 112 \implies (32-W)W = 112[/tex]

Distribute the W

[tex]-W^2+32W=112[/tex]

Now if you notice, we simply have a quadratic equation and we can subtract 112 from both sides and then use the quadratic formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Subtract 112 from both sides

[tex]-W^2+32W-112=0[/tex]

Use quadratic formula

[tex]W = \frac{-32\pm\sqrt{32^2-4(-1)(-112)}}{2(-1)}[/tex]

Simplify stuff in radical

[tex]W = \frac{-32\pm\sqrt{576}}{-2}[/tex]

Calculate the square root

[tex]W=\frac{-32\pm24}{-2}[/tex]

Use positive sign:

[tex]W=\frac{-32+24}{-2}[/tex]

Simplify numerator

[tex]W = \frac{-8}{-2}[/tex]

Simplify fraction

[tex]W=4[/tex]

Take negative sign
[tex]W = \frac{-32-24}{-2}[/tex]

Simplify numerator

[tex]W=\frac{-56}{-2}[/tex]

W = [tex]28[/tex]

So we have two solutions, and the reason for this is because had we solved for W in the original equation and substituted that into here, there would be no different, it's not bound by some variable name. So these are actually the two sides of the rectangles

4 + 28 = 32

4 * 28 = 112

4, 28

Use the drop-down menus to complete the proof. by the unique line postulate, you can draw only one segment,

Answers

The reflection of BC over I is shown below.

What is reflection?A reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is known as the reflection's axis (in dimension 2) or plane (in dimension 3). A figure's mirror image in the axis or plane of reflection is its image by reflection.

See the attached figure for a better explanation:

1. By the unique line postulate, you can draw only one line segment: BC

Since only one line can be drawn between two distinct points.

2. Using the definition of reflection, reflect BC over l.

To find the line segment which reflects BC over l, we will use the definition of reflection.

3. By the definition of reflection, C is the image of itself and A is the image of B.

Definition of reflection says the figure about a line is transformed to form the mirror image. Now, the CD is the perpendicular bisector of AB so A and B are equidistant from D forming a mirror image of each other.

4. Since reflections preserve length, AC = BC

In Reflection the figure is transformed to form a mirror image.Hence the length will be preserved in case of reflection.

Therefore, the reflection of BC over I is shown.

Know more about reflection here:

https://brainly.com/question/1908648

#SPJ4

The question you are looking for is here:

C is a point on the perpendicular bisector, l, of AB. Prove: AC = BC Use the drop-down menus to complete the proof. By the unique line postulate, you can draw only one segment, Using the definition of, reflect BC over l. By the definition of reflection, C is the image of itself and is the image of B. Since reflections preserve , AC = BC.

Firm valuation schultz industries is considering the purchase of arras manufacturing. arras is currently a supplier for schultz, and the acquisition would allow schultz to better control its material supply. the current cash flow from assets for arras is $8 million. the cash flows are expected to grow at 9 percent for the next five years before leveling off to 6 percent for the indefinite future. the cost of capital for schultz and arras is 13 percent and 11 percent, respectively. arras currently has 3 million shares of stock outstanding and $25 million in debt outstanding. what is the maximum price per share schultz should pay for arras? (do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) price per share $

Answers

Based on the calculations, the maximum price per share that Schultz should pay for Arras is approximately equal to $53.00.

How to calculate the maximum price per share?

First of all, we would determine the cash flows for the company until the growth rate changes at a constant perpetual rate:

Year 1: $8,000,000(1 + 0.09) = $8,720,000.

Year 2: $8,720,000(1 + 0.09) = $9,504,800.

Year 3: $9,504,800(1 + 0.09) = $10,360,232.

Year 4: $10,360,232(1 + 0.09) = $11,292,652.88.

Year 5: $11,292,652.88(1 + 0.09) = $12,308,991.6392.

Year 6: $12,308,991.6392(1 + 0.06) = $13,047,5311.137552.

Next, we would calculate the terminal value in Year 5:

TV₅ = CF₆/(RWACC - g)

TV₅ = CF₆/(0.11 - 0.06)

TV₅ = $12,308,991.6392/0.05

TV₅ = $246,179,832.784.

By using Arras' cost of capital, we would determine its present value:

V₀ = $8,720,000/(1 + 0.11) + $9,504,800/(1 + 0.11)² + $10,360,232/(1 + 0.11)³+ $11,292,652.88/(1 + 0.11)⁴+ ($12,308,991.6392 + $246,179,832.784)/(1 + 0.11)⁵.

V₀ = $8,720,000/(1.11) + $9,504,800/(1.11)² + $10,360,232/(1.11)³+ $11,292,652.88/(1.11)⁴+ ($12,308,991.6392 + $246,179,832.784)/(1.11)⁵.

V₀ = 7,855,855.8559 + 7,714,308.9035 + 7,575,312.3467 + 7,438,820.2323 + 153,400,536.1422.

V₀ = $183,984,855.4806.

For the market value of the equity, we have:

S = 183,984,855.4806 - 25,000,000

S = $158,984,855.4806.

Now, we can find the maximum price per share:

Maximum price per share = 158,984,855.4806/3,000,000

Maximum price per share = $52.9949 ≈ $53.00.

Read more on maximum price per share here: https://brainly.com/question/15404593

#SPJ1

What is the solution for the compound 5/2+x>1/3 or x+2 < -29/6

Answers

Answer:

x < -41/6 or x > -13/6.

Step-by-step explanation:

5/2+x>1/3

x > 1/3 - 5/2

x > 2/6 - 15/6

x > -13/6

x+2 < -29/6

x < -29/6 - 2

x < -41/6

The answer is x < -41/6 or x > -13/6.

Answer:

x > -13/6 or x < -41/6

Step-by-step explanation:

5/2+x>1/3 or x+2 < -29/6

x > 1/3 - 5/2 or x < -29/6 - 2

x > 2/6 - 15/6 or x < -29/6 - 12/6

x > -13/6 or x < -41/6

The table gives an inequality and a number to multiply both sides of the inequality by. Identify the new, true inequality.
A: (-16 > -4) (-16 < -4) (-16 = -4)
B: (40 > 8) (40 < 8) (40 = 8
C: (-45 > 15) (-45 < 15) (-45 =15)
D: (35 > -20) (35 < -20) (35 = -20)
Multiplying both sides of an inequality by a negative number (does not change) (reverses) the inequality symbol.

Answers

Multiplying both sides of an inequality by a negative number reverses the inequality symbol.

How to determine the true inequalities?

The table of values is given as:

A: (-16 > -4) (-16 < -4) (-16 = -4)

B: (40 > 8) (40 < 8) (40 = 8

C: (-45 > 15) (-45 < 15) (-45 =15)

D: (35 > -20) (35 < -20) (35 = -20)

In the above list of inequalities, the true inequalities are

-16 < -4 --- because -16 is less than -4

40 > 8 --- because 40 is greater than 8

-45 < 15 --- because -45 is less than 15

35 > -20 --- because 35 is greater than -20

Lastly, when an inequality is multiplied or divided by a negative number, the inequality sign changes

Answers

The logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]

How to determine the logarithmic equation?

The exponential equation is given as:

8^x = 64

Take the logarithm of both sides

xlog(8) = log(64)

Divide both sides by log(8)

x = log(64)/log(8)

Apply the change of base rule

[tex]x = \log_8(64)[/tex]

Hence, the logarithmic equation of 8^x = 64 is [tex]x = \log_8(64)[/tex]

Read more about logarithmic equation at:

https://brainly.com/question/3181916

#SPJ1

what is the probability that random permutation of n numbers gets sorted after 1 pass of bubble sort

Answers

It means the probability of a random permutation of n numbers gets sorted after 1 pass of bubble sort is n!

According to the statement

we have to find the probability of random permutation of the N numbers.

So, according to the definition of A random permutation is a random ordering of a set of objects, that is, a permutation-valued random variable.

In this we order of select the objects randomly.

So, Let There are n−1 comparisons, so 2n−1 possible sequences of actions - swap or don't swap.

To find the permutations, start with 1,2,3,4,5 and undo a sequence.

For example, if let n=5, there are 24=16 out of 5!

which is 5! =120 that end after one round of bubble sort.

So, It means the probability of a random permutation of n numbers gets sorted after 1 pass of bubble sort is n!

Learn more about probability of a random permutation here https://brainly.com/question/14615273

#SPJ4

Pentagon ABCDE ~ LMNOP. Find the value of x and the measure of Lc.

Answers

The value of x is 6 and the measure of ∠C is 86 degrees

How to solve for x and the measure of c?

The complete question is added as an attachment

Given that:

ABCDE ~ LMNOP

It means that we have the following equivalent ratio

ED : BC = PO : MN

This gives

8 : 6 = 12 : x

Express as fraction

6/8 = x/12

Multiply both sides by 12

12 * 6/8 = x

Evaluate

9 = x

Rewrite as

x = 9

Also

ABCDE ~ LMNOP implies that the corresponding angles are equal

The corresponding angle of C is N

And, we have:

N = 86

This implies that

C = 86

Hence, the value of x is 6 and the measure of ∠C is 86 degrees