With the decimal point in the proper place, dividing decimals is equivalent to dividing entire numbers.
How to Divide Decimals?While dividing decimals, we must remember to place the decimal point correctly in the quotient. This is similar to how we divide whole numbers. The decimal point, which separates a decimal number's whole number and fractional parts, is a dot. A value less than 1 can be found in the digits following the decimal point. 24 is a good example. A decimal number, 15, has a fractional component of 15 and a whole number component of 24. There are two situations in which dividing decimal numbers might occur: the first calls for dividing decimals by whole numbers, and the second requires dividing decimals by decimals.To Learn more About dividing decimals refer To:
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8. Solve the equation 1/4-2x-7/8=x/2 .
9. Dicson pays $610 for 3 DVDs and 2 blue-ray discs. If the price of each blue-ray disc is $10 less than 2 times that of a DVD, find the price of
(a) a DVD,
(b) 3 blue-ray discs.
The value of x in the algebraic equation is -1/2 and using system of linear equation to solve the problem, the cost of DVD and blue-ray are 84.3 and 178.6 respectively
Linear EquationThis is a mathematical statement that represent an algebraic problem. It often two expression equating with one another.
8)
1/4 [(-2x - 7) / 8] = x / 2
Multiply through by 1/4
(-2x - 7) / 32 = x / 2
Cross multiply both sides
2(2x - 7) = 32x
4x - 14 = 32x
collect like terms
32x - 4x = - 14
28x = -14
x = -14 / 28
x = - 1/2
9)
To solve this problem, we should write a system of linear equations;
Let;
x = DVDy = blue - ray3x + 2y = 610 ...eq(i)
y - 10 = 2x ...eq(ii)
From equation (ii)
y = 2x + 10 ...eq(iii)
Put eq(iii) into equ(i)
3x + 2(2x + 10) = 610
3x + 4x + 20 = 610
x = 590/7 = 84.3
Put x = 84.3 into equ(ii)
y - 10 = 2(84.3)
y = 1250 / 7
y = 178.6
The cost of DVD is 84.3 and the cost of blue-ray is 178.6
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Use the Divergence Test to determine whether the following series diverges or state that the test is inconclusive. Select the correct answer below and fill in the answer box to complete your choice. O A. According to the Divergence Test, the series converges because lim ak = k- 00 (Simplify your answer.) OB. According to the Divergence Test, the series diverges because lim ax = kos (Simplify your answer.) OC. The Divergence Test is inconclusive because lim ak (Simplify your answer.) OD. The Divergence Test is inconclusive because lim ak does not exist.
The Divergence Test is inconclusive because lim ak = ∞
The Divergence Test is used to determine whether a given infinite series converges or diverges.
In order to use the Divergence Test, we must examine the limit of the terms of the series as n approaches infinity.
In the given series, the limit of the terms as n approaches infinity is not defined. Therefore, the Divergence Test is inconclusive.
The Divergence Test is inconclusive because lim ak = ∞
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A company offers cable television at $29.95 per month plus a one-time installation fee. The total cost for the first six months of service is $214.70
The linear equation that represent the total cost after x month is y = 35 + 29.95x.
What is linear equation?
A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the y-intercept, and only a constant and a first-order (linear) term are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Given that, a cable operator offer at $29.95 per month plus a one-time installation fee.
Assume that, a be one time installation fee.
After x month, they need to pay without one-time installation fee is 29.95x.
The total amount that need to pay after x month is a + 29.95x
The linear equation that represents total cost after x month is
y = a + 29.95x
Putting y = 214.70 and x = 6
214.70 = a + 29.95 × 6
214.70 = a + 179.70
a = 35.
Putting a = 35 in y = a + 29.95x
y = 35 + 29.95x
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Consider the reaction: SO2(g) + 1/2 O2(g)SO3(g) Write the equilibrium constant for this reaction in terms of the equilibrium constants, and , for the reactions below: 2 S(s) + 3 O2(g) 2 SO3(g) S(s) + O2(g) SO2(g) For answers with both a subscript and a superscript, enter the subscript first. For example, enter K12 if the first equilibrium constant should be squared. K =
the equilibrium constant for this reaction in terms of the equilibrium constants is Knet = √Ka/Kb
and for the reactions below:
2 S(s) + 3 O2(g) 2 SO3(g) is √Ka
S(s) + O2(g) SO2(g) is 1/Kb
A reversible reaction mechanism progresses from initial conditions to chemical equilibrium at a constant temperature, with all reactants and products present in constant non-zero amounts. At this temperature, an equilibrium constant "K" exists. It is frequently followed by a subscript to indicate the type of equilibrium constant that it considers depending on the phases of reaction species that it considers. The expression for each type of equilibrium constant differs with the direction and stoichiometry of the balanced reaction equation. This enables existing equations with known "K" values to be exploited in order to derive new "K" values for related systems.
SO2(g) + 1/2 O2(g)SO3 (g) is the desired reaction equation
We consider the first given reaction system at the bottom. We divide its coefficients by two to get the square root of the initial equilibrium constant: 2 S(s) + 3 O2(g) (g) 2 SO3(g) = √Ka
Then we reverse the second given reaction system at the bottom. Its current equilibrium constant is the reciprocal of the predecessor: S(s) + O2(g) SO2(g) is 1/Kb
The above two equations total to yield our target equation. The product of the two values obtained above yields the target equilibrium constant: Knet = √Ka/Kb
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find a polynomial function whose graph passes through (7,11) (11,-12) and (0,4)
The polynomial function whose graph passes through (7,11) (11,-12) and (0,4) will be y = -0.614x² + 5.295x + 4.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
Assume the polynomial function is quadratic. Then the equation is given as,
y = ax² + bx + c
At (0, 4), we have
4 = a(0)² + b(0) + c
c = 4
Then the equation is written as,
y = ax² + bx + 4
At (7, 11), we have
y = ax² + bx + 4
11 = 49a + 7b + 4 ...1
At (11, -12), we have
- 12 = 121a + 11b + 4 ...2
Equations 1 and 2 are solved by a calculator. Then we have
a = - 0.614 and b = 5.295
The polynomial capability whose diagram goes through (7,11) (11,- 12) and (0,4) will be y = - 0.614x² + 5.295x + 4.
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At a movie theater, one group of people spent $54 on 3 large popcorns and 6 sodas.
Another group spent on $77 on 4 large popcorns and 9 sodas. Determine the cost of a
large popcorn and the cost of a soda
Answer: 54
Step-by-step explanation: bc ? you just divid 54 by 3 and 6 then you divid 77 by 4 and 9 then divide them both tada
Answer:
sodas cost $5 and a large popcorn costs $8
create formulas out of the situations making the variable p=popcorn and s=soda
so,
3p + 6s = 54
and
4p + 9s = 77
then choose one variable to solve for
3p = 54 - 6s
divide both sides by 3
p = 18 - 2s
then plug your answer for p into the other equation:
4(18 - 2s) + 9s = 77
finally, solve for s
72 - 8s + 9s = 77
s = 5
if s=5 then
3p + 6(5) = 54
p = 8
Determine the population mean, variance, and standard deviation for the set of data. (Round your answers to two decimal places.)
3, 6, 8, 12, 13, 15
mean variance standard deviation
Given the set of data, we can calculate that the mean is 9.5, the variance is 17.58 and the standard deviation is 4.19
Mean, variance, and standard deviation
The concepts of mean, variance and standard deviation are very basic but very important in statistics.
Mean is the average of all data in a sample group, which is obtained by adding up all the data values, then dividing by the number of samples.
[tex]mean = \frac{sum all of the data}{size of data}[/tex]
Variance is a value that describes the variation of data, by measuring how far each piece of data is spread from the average of a data set.
[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]
Standard Deviation is a measure of the spread of observations in a data set relative to their mean. it measures how many observations in a data set differ from the mean and is the square root of the variance.
σ = [tex]\sqrt{variance}[/tex]
Now we can calculate the mean of the given data as follows:
[tex]mean = \frac{sum all of the data}{size of data}[/tex]
= (3 + 6 + 8 + 12 + 13 + 15) / 6
= 57 / 6
= 9.5
Then we can calculate the variance as follows:
[tex]variance = \frac{sum (x_{i} - mean)^{2} }{n}[/tex]
= [tex]\frac{((3-9,5)^{2} + (6-9,5)^{2} + (8-9,5)^{2} + (12-9,5)^{2} + (13-9,5)^{2} + (15-9,5)^{2} )}{6}[/tex]
= (42,25 + 12,25 + 2,25 + 6,25 + 12,25 + 30,25) / 6
= 105.5 / 6
= 17.58
Standard deviation can be calculated from the variance:
σ = [tex]\sqrt{variance}[/tex]
= [tex]\sqrt{17.58}[/tex]
= 4.19
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Use the scale to help you solve the equation and find the value of x. Enter the
value of x below.
x+ 5 = 12
X =
Answer: 7
Step-by-step explanation:
x=12-5
x=7
Answer:
x=7
Step-by-step explanation:
12-5=7 or 7+5=12
PLEASE HELP ME
Can someone please explain how the "-6000(1+1.1+1.1^2+...+1.1^7)" became "-6000(1.1^8/0.1)"????
Thank you very much
The answer of the given pattern is 38564.11
What are exponents?The exponents of a number are defined as the representation of a number that shows how many times a number is multiplied by itself.
If we have a^b then 'a' is called base and 'b' is called power or exponent and we call it "a is raised to the power b" (this statement might change from text to text slightly).
We are given the expression as
"-6000(1+1.1+1.1^2+...+1.1^7)"
Using the power series we get;
= -6000(1.1^8/0.1)
After the complete solution the answer is 38564.11
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A realtor makes 4% commission on the sale of a home. If she sold a home for $250,000, how
much will she make in commission?
commission = 250,000×4/100
commission = $10,000
Answer:
$10,000
Step-by-step explanation:
because of acom by Jill one GB cb to be yes we will i you and the ward off Luth you sir ma we have in mind the customer service is not available for is it possible to you IJN you and the ward screen shot of a quick response because I am not you sir I am not sure if my proposal sounds interesting for you ma I will send it to u the picture
For each of these lists of integers, find a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.
f ) 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, . . .
The simple formula or rule that generates the terms of an integer sequence that begins with the given list is given below.
What is sequence?Sequence is the order in which elements, such as numbers, letters, or symbols, follow one another in a specific order. It is a fundamental concept in mathematics and computer science, and is used in many other areas including music, language, and art. In mathematics, it is often used to describe patterns or to represent numerical values. In computer science, it is used to represent data structures, such as lists and arrays.
a. The sequence can be expressed as 3x2^n, where n is the position of the number in the sequence. The next three terms are 127, 162, and 201.
b. The sequence can be expressed as 4n+3, where n is the position of the number in the sequence. The next three terms are 47, 51, and 55.
c. The sequence can be expressed as 2^n+n-1, where n is the position of the number in the sequence. The next three terms are 1111, 10000, and 10011.
d. The sequence can be expressed as the number of times the previous value is repeated, starting with 1. The next three terms are 5, 5, and 8.
e. The sequence can be expressed as 4x3^n, where n is the position of the number in the sequence. The next three terms are 5906, 17718, and 53154.
f. The sequence can be expressed as (n+1)!+(n-1)!+2, where n is the position of the number in the sequence. The next three terms are 27027025, 94594500, and 34459425.
g. The sequence can be expressed as the number of times the previous number is repeated, starting with 1. The next three terms are 0, 0, and 1.
h. The sequence can be expressed as 4^n, where n is the position of the number in the sequence. The next three terms are 4294967296, 17179869184, and 68719476736.
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Complete questions as follows-
For each of these lists of integers, provide a simple formula or rule that generates the terms of an integer sequence that begins with the given list. Assuming that your formula or rule is correct, determine the next three terms of the sequence.
a. 3, 6, 11, 18, 27, 38, 51, 66, 83, 102, . . .
b. 7, 11, 15, 19, 23, 27, 31, 35, 39, 43, . . .
c. 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1011, . . .
d. 1, 2, 2, 2, 3, 3, 3, 3, 3, 5, 5, 5, 5, 5, 5, 5, . . .
e. 0, 2, 8, 26, 80,242,728,2186,6560,19682, . . .
f. 1, 3, 15, 105, 945, 10395, 135135, 2027025, 34459425, . . .
g. 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, . . .
h. 2, 4, 16, 256, 65536, 4294967296, . . .
Tom weighs 5kg more than Harry. Harry weighs 3kg more than Freddie who, in turn weighs
2 kg less than Alfie. What is the difference, in kilograms, between Tom and Alfie?
The difference between Tom and Alfie is 1 kg
Let's call the weight of Tom T, the weight of Harry H, the weight of Freddie F, and the weight of Alfie A. We are given that T = H + 5, H = F + 3, and F = A - 2.
Substituting the second and third equations into the first equation gives us:
T = (A - 2) + 3 + 5
T = A - 2 + 3 + 5
T = A + 1
So the difference between Tom and Alfie is T - A = A + 1 - A = 1 kg.
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a) What is 10% of 40 ?
b) What number is 10% more than 40 ?
The expression 10% of 40 is 4 and 10% more than 40 is 44
(a) What is 10% of 40?From the question, we have the following parameters that can be used in our computation:
10% of 40
Express "of" as products
So, we have
10% of 40 = 10% * 40
Evaluate
10% of 40 = 4
b) What number is 10% more than 40?In this case, we have:
10% more than 40
This means that
10% more than 40 = 40 * (1 + 10%)
Evaluate
10% more than 40 = 44
Hence. 10% more than 40 is 44
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Can someone please solve this problem for me.
The cost of one chair is [tex]x=54.75[/tex] $ and the cost of one table is [tex]y=49.5[/tex] $.
What is the total cost?
The total cost formula is used to combine the variable and fixed costs of providing goods to determine a total. The formula is:
Total cost = (Average fixed cost x average variable cost)
Let cost of one chair is [tex]x[/tex]
Let cost of one table is [tex]y[/tex]
So,
[tex]5x+3y=31[/tex] ...(1)
[tex]2x+6y=52[/tex] ......(2)
Solving equation (1) and (2) we get
[tex]a_1x+b_1y+x_1=0\\\\a_2x+b_2y+c_2=0[/tex]
[tex]\frac{x}{b_1c_2-b_2c_1}=\frac{y}{c_1a_2-c_2a_1}=\frac{1}{a_1b_2-a_2b_1}\\\\\frac{x}{3(31)-6(52)}=\frac{y}{31(2)-52(5)}=\frac{1}{5(2)-2(3)}\\\\\frac{x}{93-312}=\frac{y}{62-260}=\frac{1}{10-6}\\\\\frac{x}{-219}=\frac{y}{-198}=\frac{1}{-4}\\\\x=54.75,y=49.5[/tex]
Hence, the cost of one chair is [tex]54.75[/tex] $ and the cost of one table is [tex]49.5[/tex] $.
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Cindy is a travel agent. She receives a 9% commission based on the value of the trips she books. Today she spent eight hours arranging a $9,300 cruise for a newlywed couple. 19. How much commission did she earn? 20. What was her mean hourly pay for the work she did?
Cindy was able to make $837 in commission thanks to her commission rate, which equates to $104.62 per hour.
What is the explanation?Cindy is a travel agent. She receives a 9% commission based on the value of the trips she books. Today she spent eight hours arranging a $9,300 cruise for a newlywed couple
The commission that Cindy received can be determined by:
= Commission % x Price of booked trip
= 9% x 9,300
= $837
Consequently, the following is her hourly wage:
= Commission received / Hours worked
= 837 / 8
= $104.62
The bottom line is that made $104.62 per hour plus $837 in commission.
Cindy was able to make $837 in commission thanks to her commission rate, which equates to $104.62 per hour.
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Suppose that there are two types of tickets to a show: advance and same-day. Advance tickets cost $30 and same-day tickets cost $35. For one performance, there were 55 tickets sold in all, and the total amount paid for them was $1825. How many tickets of each type were sold?
Answer:
sorry i messed up my first calculations, currently recalculating
Step-by-step explanation:
Answer:
35 same-day tickets20 advance ticketsStep-by-step explanation:
You want the number of $30 advance tickets and $35 same-day tickets sold, when a total of 55 tickets were sold for $1825.
SetupLet s represent the number of same-day tickets sold. Then 55-s is the number of advance tickets sold, and total revenue is ...
35s +30(55 -s) = 1825
Solution5s = 175 . . . . . . Simplify, subtract 1650
s = 35
55-s = 30
35 same-day and 30 advance tickets were sold.
What is as a fraction?
A fraction means a part of something or a number of parts of something. The number on the bottom shows how many parts something has been divided into ½ means 1 part of something that has been divided into 2 parts. We call this a half. If you add two halves together you get one.
Answer: A fraction is a numerical quantity that is not a whole number
Step-by-step explanation:
PLS HELP
Select the correct answer.
A museum curator estimates that 85% of people who attend the museum would return a second time. She randomly surveys
50 people and finds that only 75% indicate that they would return a second time. So she decides to randomly survey an additional
100 people.
if her model is valld, what could she expect from the 150 total survey results?
The difference between the data and the model will get larger.
The difference between the data and the model will stay the same.
O it is impossible to predict how the difference between the data and the model will change
The difference between the data and the model will get smaller.
O
Submit
The difference between the model and the data will get smaller.
What is the sample size?A sample is a percentage of the total population in statistics. You can use the data from a sample to make inferences about a population as a whole.
Given here, she 50 people and finds that only 75% and additional 100 people hence changing the sample size
As our sample size increases, the confidence in our estimate increases, our uncertainty decreases and we have greater precision. Thus with the increase in sample size, the data would move closer to the estimated probability.
Hence The difference between the model and the data will get smaller.
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Answer:
The difference between the data and the model will get smaller.
Step-by-step explanation:
Plato/Edmentum
Find the volumes of the solid generated by revolving the regions bounded by the graphs of the graphs of the equations about the given lines:
y=5x2y=0x=3
a) on the y-axis.
b) on the x-axis.
c) on the line y = 45.
d) on the line x = 3.
Volume of solid generated by revolving the region bounded by the graph is 3817.53 unit
What do you mean by volume of revolution?A volume is created while a plane figure rotating about an axis or around any straight line situated on the same plane.
How to calculate volume of solid generated by revolving the region?We apply definite integration to calculate the required volume.
we are given the equation y = 5x² and y =0, x= 3
volume is calculated by using the formula, V = ∫π y² dx
V = ∫₀³π (5x²) ² dx
On the y-axis x = 0 so upper limit x = 3 and lower limit x= 0
V= π × 25/5 [x⁵] ³₀
V = 15.71 [3⁵- 0]
hence, the volume of solid = 3817.53 unit
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Find the slope from the line of best fit y = 5 - 3x.
Answer:
slope = -3
Step-by-step explanation:
⭐ What is the equation of a line in slope intercept form?
[tex]y = mx+b[/tex]m is the slope. It is always multiplied with the variable (x)b is the y-intercept. It is always the term without a variableThe given line of best fit is written in slope-intercept form. All we have to do is identify which term is the slope.
[tex]y = -3x + 5[/tex]
-3 is the coefficient of x. Therefore, -3 is the slope.
Mr. Muehlenweg S class used 1 3/4 cups baking soda for an experiment. If his students performed the experiment 6 1/2 times, how much baking soda did they use?
Total no. of cups of baking soda used for the experiment in improper fraction is [tex]\frac{91}{8}[/tex].
How much baking soda was used?Initial no. of cups of baking soda used for an experiment = [tex]1\frac{3}{4}[/tex]
Converting mixed fraction to improper fraction,
[tex]1\frac{3}{4}=\frac{7}{4}[/tex]
No. of times the experiment performed by students = [tex]6\frac{1}{2}[/tex]
Converting mixed fraction to improper fraction,
[tex]6\frac{1}{2} = \frac{13}{2}[/tex]
Total no. of cups of baking soda =(Initial no. of cups)* (No. of times)
[tex]=\frac{7}{4} *\frac{13}{2} \\\\=\frac{91}{8} \\\\[/tex]
= 11.4 (decimal form)
What is a mixed fraction?A mixed fraction is one that has both its quotient and remainder represented. A mixed fraction like [tex]1\frac{3}{4}[/tex] is one where the remainder is 3 and the quotient is 1. Therefore, a mixed fraction is made up of both a full number and a correct fraction. A whole number and a legal fraction are both expressed together as a mixed number.A number between any two whole numbers is typically represented by it. Any fraction whose numerator exceeds or is equal to its denominator is considered improper. When the numerator value is less than the denominator, the fraction is said to be proper.To learn more about improper fraction, refer:
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Dr. Bert Vogelstein and his partners study the causes of cancer. In 2017, they published a study of 32 types of cancer. The study concluded that most cancer cases are caused by DNA replication errors. In fact, 66% of the cancer cases they studied were caused by random DNA replication errors. Environmental factors such as diet, sunburns, and smoking caused 29% of the cancers. The last 5% of cancers in the study were caused by inherited factors. What happens as a result of DNA replication? 0
A. A blueprint is transferred from the nucleus to the ribosome.
B. mRNA encodes a message from DNA. O
C. A chromosome with two identical DNA strands is formed. O
D. A protein is formed.
The result of DNA replication, given the fact that most cancer cases came as a result of DNA replication errors, is C. A chromosome with two identical DNA strands is formed.
What is a DNA replication ?The biological process of creating two identical copies of DNA from a single original DNA molecule is known as DNA replication.
After this process is complete and all the DNA has been copied, the cell actually has twice as much DNA as it needs, which it can then divide and parcel into the daughter cell, resulting in the daughter cell and the mother cell being nearly genetically identical in many cases.
Sometimes however, there will be errors in DNA replication, and this can lead to things like cancer as shown by Dr. Bert Vogelstein.
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when finding 6.1/0.1, how is the decimal point moved?
The decimal point can be removed by dividing 10 with each numerator and denominator of 6.1/0.1
(61/10)/(1/10) = 61/10 x 10 = 61
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
6.1/0.1
We will remove the decimal point by dividing 10 with both the numerator and denominator.
(61/10)/(01/10)
= 61/10 x 10/1
= 61/1
= 61
Thus,
The value of 6.1/0.1 is 61.
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4. Give a brief summary (two or three sentences) of what you think the Chorus is talking about overall on pages 10, 11 and 12. (3 points)
Chorus over all view is about love, magic and war and following is the summary of his theme.
What does Chorus says in Antigone?In the chorus, it is stated that "everything but death" has been vanquished by man, hinting at what Antigone will experience. Additionally, they sing of "unsavory ambition," or inordinate pride, which alludes to Creon's terrible fault, or hamartia.
What about Chorus in Oedipus?The chorus in "Oedipus Rex" serves as the voice of the common people and offers perspective that the other characters in the play are unable to express. The chorus advances the plot by introducing new characters and providing answers to issues that arise.
The chorus declares that this play will not be about love, war, or valiant acts. Instead, it will detail the successes and failures of Dr. John Faustus, a German native of humble origins who attends the University of Wittenberg to study philosophy and divinity. He is so good at theology that he finally gets haughty, which is what brings him to ruin. In the end, Faustus decides to research necromancy, or magic.
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HELP!! Drag the tiles to the correct boxes to complete the pairs.
Match each rational expression to its simplest form.
Answer:
Step-by-step explanation:
6 minus radical 2 over 4 simplified
The response will be -10 if the stated statement is accurate.
What radicals are most prevalent?This same square root and cubed root are the two radicals we see most frequently. Since the square root is so often employed, it is customary to presume that any radical written without the need for an index is a square root. The figure above constitutes a radical taken as a whole.
What does a math radical mean?An phrase that has a root, often a square or cube root, is referred to as a radical. A radical is made up of three main parts, namely: It expresses the degree of radicand multiplication. If the root symbol's numeric component is absent, it is assumed as 2 (square root). The symbol √ means “root of”.
Briefing:= 6 - 4²
= 6 - 16
= - 10
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The correct questions are-
6 - 4²
A line with a slope of 4 and passes through (2, 4) What is the equation of the line in slope intercept form (y = mx + b) ?
The equation of line in slope in intercept form will be equal to y = 4x - 4.
What is slope?It is possible to determine a line's direction and steepness by looking at its slope. Finding the slope between lines inside a coordinate plane can aid in anticipating if the lines are perpendicular, parallel, or none at all without physically using a compass.
As per the data provided in the question,
The formula for a line is y = mx + b, where m denotes the slope and b the y intercept.
So,
The equation can be written as,
y = 4x + b
As per the given point (2, 4),
4 = 4(2) + b
b = 4 - 8
b = -4
So, the final equation will be,
y = 4x - 4
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Based on the figure given below.
AC = 20cm
BC = 24Cm
AB = 16cm
CD = 15Cm and CE = 18cm then
a) Show that triangle ABC sim triangle DEC
b) How long is DC ?
Answer:
Step-by-step explanation:
A.) To show that triangle ABC is similar to triangle DEC, we need to prove that the ratios of the sides of the two triangles are equal.
First, we can write the ratios of the sides of triangle ABC as follows:
AC/AB = 20/16 = 5/4
BC/AB = 24/16 = 3/2
Now, we can write the ratios of the sides of triangle DEC as follows:
CE/CD = 18/15 = 6/5
AC/CD = 20/15 = 4/3
Since the ratios of the sides of the two triangles are equal, it follows that triangle ABC is similar to triangle DEC.
B.) To find the length of DC, we can use the fact that triangle ABC is similar to triangle DEC. Since the ratios of the sides of the two triangles are equal, we can set up a proportion to solve for DC.
First, we can write the ratio of the sides of triangle ABC as follows:
AC/AB = DC/CE
Then, we can substitute the known values for AC, AB, and CE:
20/16 = DC/18
Then, we can cross-multiply to solve for DC:
DC = (20/16) * 18
= (5/4) * 18
= 45/4
= 11.25 cm
Therefore, the length of DC is approximately 11.25 cm.
Answer:
Step-by-step explanation:
To show that triangle ABC is analogous to triangle DEC, we need to prove that the rates of the sides of the two triangles are equal.
First, we can write the rates of the sides of triangle ABC as follows
AC/ AB = 20/16 = 5/4
BC/ AB = 24/16 = 3/2
Now, we can write the rates of the sides of triangle DEC as follows
CE/ CD = 18/15 = 6/5
AC/ CD = 20/15 = 4/3
Since the rates of the sides of the two triangles are equal, it follows that triangle ABC is analogous to triangleDEC.
B.) To find the length of DC, we can use the fact that triangle ABC is analogous to triangle DEC. Since the rates of the sides of the two triangles are equal, we can set up a proportion to break for DC.
First, we can write the rate of the sides of triangle ABC as follows
AC/ AB = DC/ CE
also, we can substitute the known values for AC, AB, and CE
20/16 = DC/ 18
also, we cancross-multiply to break for DC
DC = (20/16) * 18
= (5/4) * 18
= 45/4
= 11.25 cm
Thus, the length of DC is roughly11.25 cm.
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Solve for x (9x-16) (3x+11) (7x-5)
9x²-16x(3x+11)(7x-5)
9x²-48x²-176x(7x-5)
9x²-48x²-1232x²+880
-1271x²+880
Write an equation for the parabola when the x intercepts are (-2,0) and (-4,0)
Answer:
[tex]y = x^2 + 6x + 8[/tex]
Step-by-step explanation:
⭐What is the equation of a parabola in standard form?
[tex]y = ax^2 + bx + c[/tex]⭐Whenever you factorise a quadratic (parabola), you are writing the parabola in terms of its x-intercepts.
⭐ Therefore, the expressions of the x-intercepts are the factors of your quadratic.
⭐What are factors of a number?
factors are 2 or more numbers or expressions that multiply together to become a numberWe have to reverse-engineer this problem to find the quadratic by:
re-writing the quadratic in terms of its factors (the x-intercepts)multiplying the factorssimplifying the product from step #21. Re-write the quadratic in terms of its factors
If one of the x-intercepts is -2, then the expression for said x-intercept is: [tex](x+2)[/tex]
If one of the x-intercepts is -4, then the expression for said x-intercept is:
[tex](x+4)[/tex]
2. Multiply the factors
[tex]y = (x+2)(x+4)[/tex]
[tex]y = x^2 + 4x + 2x + 8[/tex]
3. Simplify the products
[tex]y = x^2 + 6x + 8[/tex]