For corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock
The consolidated tax return is defined as a single income tax return filed by an affiliated group of corporations that combines their tax liability.
The percentage is the ratio that can be represented as the fraction of hundred.
The voting stock is defined as the shares that give the stockholder, that is the right to vote on the policymaking of the corporation
Here, p must own 80% of s's voting stock
Hence, for corporation p to file a consolidated tax return with corporation s, p must own 80% of s's voting stock
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After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?.
After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large, the best recommendation is c. Increase the sample size.
What is a confidence interval?A confidence interval is a range of estimates for an unknown parameter in frequentist statistics. A confidence interval is calculated at a specific confidence level; the 95% confidence level is the most commonly used, but other levels, such as 90% or 99%, are also used.
Confidence intervals are used by statisticians to quantify uncertainty in a sample variable. A researcher, for example, may randomly select different samples from the same population and compute a confidence interval for each sample to determine how well it may represent the true value of the population variable. The resulting datasets are all unique, with some intervals containing the true population parameter and others not.
In this case, the sample size should be increased when the results are meaningless because the width of the interval is too large.
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Complete questions
After computing a confidence interval, the user believes the results are meaningless because the width of the interval is too large. Which one of the following is the best recommendation?
a. Increase the level of confidence for the interval
b. Decrease the sample size
c. Increase the sample size
d. Reduce the population variance
Cuánto es el resultado de 1326 dividido entre 41
1326 divided by 41 is equivalent to 32.35.
What is Equation Modelling?
Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is 1326 divided by 41.
Assume that 1326 divided by 41 is equivalent to [x].
[x] = 1326/41
[x] = 32.35
Therefore, 1326 divided by 41 is equivalent to 32.35.
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[Question translation in english -
How much is the result of 1326 divided by 41.]
the tortoise and the hare are in a race. The hare has run 315 feet, while the tortoise has traveled 70 feet.
(a) what is the ratio of the distance the hare traveled to that of the hare? express as a unit rate.
The ratio of the distance the hare traveled to that of the tortoise is 9 : 2 and expressing it in the unit rate it will be 4.5 miles per miles
What is unit rate?
A unit rate is a cost for only one of anything. Unit rate is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.
Solution Explained:
For the ratio of the distance:
Try to reduce the ratio further with the greatest common factor (GCF).
The GCF of 315 and 70 is 35
Divide both terms by the GCF, 35:
315 ÷ 35 = 9
70 ÷ 35 = 2
The ratio 315 : 70 can be reduced to lowest terms by dividing both terms by the GCF = 35 :
315 : 70 = 9 : 2
Now, to express it as a unit rate
This is a fraction equal to
315 miles ÷ 70 miles
We want a unit rate where
1 is in the denominator,
so we divide top and bottom by 70
[tex]\frac{315}{70} / \frac{70}{70}[/tex]
= 4.5 miles per miles
Therefore, in unit rate the ratio of the distance the hare traveled to the tortoise is 4.5 miles per miles.
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PLEASE HELP!!!!
Evaluate f(x)=5x−8 when x=−3,0, and 4.
f(−3)=
f(0)=
f(4)=
Hey scale drawing of an nfl goal post uses a scale of 2 inches equal 5 feet if the actual width of the goalposts is 18 1/2 feet what is the width of the goal post on the drawing
A scale drawing of an NFL goal post uses a scale of 2 inches equal 5 feet if the actual width of the goal posts is 18 1/2 feet what is the width of the goal post on the drawing.
If 3 inches on the scale drawing represents 5 feet in actuality, determine the actual area of a kitchen if the area of the scale drawing is 45 inches 3 inches to 5 feet is 1:20
From the question asked you cannot determine the area. (No width given) You state the measurement is 45 inches (not square inches) 45 inches at 20:1 = 900 inches or 75 feet (linear)
Hence the answer is 75 ft.
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Answer:
75 ft
Step-by-step explanation:
The coordinates of a point are given. What is its line of reflection?
(7,−7)⟶(7,7)
Answer:
reflection over the y-axis
Step-by-step explanation:
formula for reflection over y is (x,y) -> (x,-y)
What is the solution set of the inequality for X?.
The solution set of the inequality |x-1| ≤ 5 is found to be [-4,6] by simplifying the inequality.
What do math inequalities mean?An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The most frequent application is to size-compare two numbers on a number line.Relationships between two expressions that aren't equal to one another are known as inequalities. Inequalities are represented by the symbols <, >, ≤, ≥ and ≠.Given inequality is given as:
|x-1| ≤ 5
Simplifying this inequality we get,
-5 ≤ x-1 ≤ 5
Adding 1 on both sides, we get,
-5+1 ≤ x-1 ≤ 5+1
-4 ≤ x ≤ 6
Therefore, the solution set of the inequality |x-1| ≤ 5 is found to be [-4,6] by simplifying the inequality.
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NOTE: The given question is incomplete on the portal. Here is the complete question.
QUESTION: What is the solution set of the inequality |x-1| ≤ 5?
Express 2x² + 12x + 8 in the form a(a + b)² + c, where a, b and c are
numbers.
What are the values of a, b and c ?
We can write given quadratic expression 2x² + 12x + 8 as 2(x + 3)² - 10
And a = 2, b = 3, c = -10
We have been given an expression 2x² + 12x + 8
We need to write given expression in the form a(a + b)² + c, where a, b and c are numbers.
2x² + 12x + 8
= 2x² + 12x + 18 - 18 + 8
= (√2x + 3√2)² - 10
= (√2)² (x + 3)² - 10
= 2(x + 3)² - 10
Comparing with a(a + b)² + c, where a, b and c are numbers.
a = 2, b = 3 and c = -10
Therefore, we can write given quadratic expression 2x² + 12x + 8 as 2(x + 3)² - 10
And a = 2, b = 3, c = -10
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Find the perimeter and area of the rectangle with coordinates (3,7), (3,-2), (-6.-2) and (-6,7)
The area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.
In this question, we have been given the rectangle with coordinates (3,7), (3,-2), (-6.-2) and (-6,7)
We need to find the perimeter and area of the rectangle.
Using distance formula we find the length and width of the rectangle.
d1 = √(-2 - 7)² + (3 - 3)²
d1 = √(-9)²
d1 = 9
And d2 = √(-2 + 2)² + (-6-3)²
d2 = √(-9)²
d2 = 9
d3 = √(7 + 2)² + (-6 + 6)²
d3 = 9
This means, the length and width of rectangle are equal i.e., 9 units.
So, perimeter would be,
P = 4 * 9
P = 36 units
And the area would be,
A = 9 * 9
A = 81 square units
Therefore, the area of the rectangle 81 square units and the perimeter of the rectangle is 36 units.
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what is X,Y, and Z, show work if possible
The values of x, y and z are 74°, 37° and 17° respectively
What is Angles?
An angle is a figure in Euclidean geometry made up of two rays that share a common endpoint and are referred to as the angle's sides and vertex, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles. Dihedral angles are these.
Given,
x°, (4z + 6)°, 2y° and 106°
Lets solve,
x° and 106°
From the co-interior angle
x + y = 180°
x° + 106° = 180°
x = 180 - 106
x = 74°
by alternate exterior angle
x = 2y
Since we know about the value of x
we can write it as
74 = 2y
y = 74/2
y = 37°
Now by alternate interior angles
(4z + 6) = x
(4z + 6) = 74
4z = 74 - 6
4z = 68
z = 68/4
z = 17°
Hence, Value of x, y and z is 74°, 37° and 17° respectively
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Explain how to make a standard form parabola equation into vertex form
We can convert a parabola equation from standard form to vertex form. This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)
Standard Form
A parabola's standard form is: y = ax2 + bx + c
Here, a, b, and c are real numbers (constants), with a = 0. x and y are variables, with (x, y) representing a parabola point.
Vertex Form
A parabola's vertex form is: y = a (x - h)2 + k
Here, a, h, and k are real numbers, with a = 0. x and y are variables, with (x, y) representing a parabola point.
There is a "whole square" in the vertex form, y = a (x - h)2 + k. To convert from standard to vertex form, we simply need to complete the square. Aside from that, we have a formula method for doing this. Let us investigate both methods.
By Finishing the Square
Consider the following standard-form parabola: y = -3x2 - 6x - 9 and complete the square to get the vertex form. First, we must ensure that the x2 coefficient is 1. If the coefficient of x2 is NOT 1, the number will be placed outside as a common factor. We'll get: y = 3x2 6x 9 = 3 (x2 + 2x + 3).
Now, the coefficient of x2 is 1. Here are the steps to convert the above expression into the vertex form.
Determine the x coefficient. 3 (x2 + 2x + 3)
Divide it in half and square the result.
(2/2)^2 = 1^2 = 1
Y= -3(x2+2x+1-1 +3)
Using the appropriate identity, factor the perfect square trinomial formed by the first three terms.
We can use x2 + 2xy + y2 = (x + y) in this case.
x2 + 2x + 1 = (x + 1) in this case.
The preceding expression becomes:
Y= -3 (x2 + 2x + 1-1 +3)
Y= -3(x+1)^2 – 1 +3
The last two numbers should be simplified, and the outside number should be distributed.
Here, -1 + 3 = 2. As a result, the preceding expression becomes:
Y= -3(x+1)^2 + 2
Y = -3(x+1)^2 - 6
This is in the vertex form and has the formula y = a (x - h)2 + k. The vertex, in this case, is (h, k)=(-1,-6)
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A colony of bacteria double every half hour. How many
new bacteria would there be after 4 hours if there are
60 bacterium to start?
Can you factor [tex]12x^{2} -8x+1=0[/tex]?
Answer:
Yes
Step-by-step explanation:
You must use the quadratic formula
-b√b^2 -4ac/2a --> -8√-(-8)^2 -4(12)(1)/2(12)
8 +/- 4/24
(1/2, 1/6)
Yes, we can factor 12x²-8x+1=0 and the factors are x=1/6 and x= 1/2.
What is factor?
A factor in maths is one of two or more numbers that divides into a number without a remainder, making it a whole number.
In other words, a factor is a number that divides another number evenly.
12x² -8x +1=0
⇒ 12x² -2x- 6x+1=0
⇒ 2x (6x-1) -1 (6x-1)=0
⇒ (2x-1) (6x-1)=0
⇒ 2x-1 = 0, 6x-1 = 0
⇒ x=1/2, x=1/6
Therefore, the factors of 12x²-8x+1=0 are 1/2, 1/6.
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What amount is 20 more than 70?.
The amount is 20 more than 70 that will be 90.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A numerical expression is an algebraic information stated in the form of numbers and variables that are unknown. Information can is used to generate numerical expressions.
We have been given that the statement is "20 more than 70"
WE are asked to find the amount of the given statement.
More means addition therefore,
20 more than 70 = 20 + 70
= 90
Therefore, the amount is 20 more than 70 that will be 90.
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A baseball team sells for two games. the ratio of sold tickets to unsold tickets for the first game was 7 : 3. for the second game, the ratio was 13 : 2. there were 24 unsold tickets for the second game. how many tickets were sold for the first game?
1260 tickets were sold on the first game
For the second game, the ratio of the number of sold tickets to number of unsold tickets is 13:2
Total ratio = 13+2 = 15
There were 240 unsold tickets for the second game. Let total number of tickets for the second game be x
This means that
240 = 2/15 × x
2x/15 = 240
2x = 15 × 240= 3600
x = 3600/2 = 1800
1800 tickets were sold for the second game. Assuming total number of tickets for the first game is equal to total number of tickets for the second game. Therefore,
Total number of tickets sold for the first game is 1800
The ratio of sold tickets to unsold tickets for the first game was 7:3.
Total ratio = 7+3 = 10
Number of sold tickets for the first game would be
7/10 × 1800 = 12600/10
= 1260 tickets
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Identify the domain of the function shown in the graph -6 < x < 6
The domain of the function shown on the graph is given by the following option:
B. All real numbers.
What is the domain of a function?The domain of a function is the set composed by all the input values that are assumed by the function.
On a graph, the meaning of each variable is given as follows:
Values of x -> horizontal axis -> input values.Values of y -> vertical axis -> output values.Hence, considering the graph of the function, the domain of the function is the set that contains all the values of x of the function.
From the image given at the end of the answer, the line continues to left and to right, meaning that it has no spaces in it's definition, and thus the function is defined for all real values and the correct option is given by option b.
Missing InformationThe problem containing the graph of the function and the options is given by the image presented at the end of the answer.
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Thaddeus wants to attend a sports camp this spring that costs $170.00 for the week. He rakes leaves during the fall and earns $58.35 . He shovels snow during the winter and earns $58.35 . How much more money does Thaddeus need to earn to pay for the sports camp? Write your answer as a decimal.
Thaddeus needs to earn $blank.
Cost of Thaddeus camp is $170.00 and total money earned by Thaddeus in raking leaves and shovels snow is $58.35 each then total amount of money Thaddeus required to earn to pay sports camp fee is equal to $53.3.
As given in the question,
Cost of Thaddeus sports camp is equal to $170.00
Money earned by Thaddeus while raking leaves = $58.35
Money earned by Thaddeus while shovels snow = $58.35
Total amount of money Thaddeus required to earn to pay sports camp fee
= $170 - $(58.35 + 58.35)
= $(170 - 116.7)
= $53.3
Therefore, cost of Thaddeus camp is $170.00 and total money earned by Thaddeus in raking leaves and shovels snow is $58.35 each then total amount of money Thaddeus required to earn to pay sports camp fee is equal to $53.3.
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You bought 5 tickets for $30. How many tickets could you purchase for $90?
15
5 t = 30$
1t = 30/5
= 6$ per ticket
then, 90$/6 = 15 tickets
9)Two boys age 12 years and 7 years shared 108 naira in the ratio of their age .how much will each get of them receive??
Answer:
68.21 and 39.79
Step-by-step explanation:
When it says that they are going to "share" it means that the number (108) is going to be divided amongst the two of them. So you are going to do an addition problem which is 12+7=19. So you are going to do 12/19*108=68.21. Then to find the second number it's 7/19*108=39.79.
9
7. The ratio of blue cars to red cars in the parking lot is 3 to 5. If there are 60 red cars, how many
blue cars would there Be
The number of blue cars is 375.
What is a ratio?
Ratio is a relationship between two values, represented by numbers or percentage Which expresses which of the two value are bigger. And to find that we cancel the common factor between them.
We are given that the ratio of blue cars to red cars is 3:5
Also there are 600 cars in the parking lot
Now, Let the common factor between them be 'x'
Hence the number of red cars is 3x and number of blue cars is 5x
Hence the equation can be given as
3x+5x = 600
8x = 600
Dividing both sides by 8 we get
x= 75
Hence the number of blue cars is 5(75)= 375
The number of blue cars is 375
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Can someone help me really quick
(Please Explain how you know this is correct.)
The price per gallon will be 2.4 at Miguel's gasoline center.
What is the slope of the line?The slope of the line is represented as the rise of the line.
Here the price per gallon is equal to the slope of the given points
Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates (x₁,y₁) and Point 2 has coordinates (x₂, y₂)
we take the two points (4, 10) and (9, 22)
Let
x₁ = 4, y₁ = 10
x₂ = 9, y₂ = 22
∵ Slope m = (y₂ - y₁)/(x₂ -x₁ )
Substitute values in the formula
m = (22 - 10) / (9 - 4)
m = (12)/(5)
m = 2.4
Thus, the price per gallon will be 2.4 at Miguel's gasoline center.
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people with type o- blood are universal donors. that is, any patient can receive a transfusion of o- blood. only 7.2% of the american population has o- blood. if 10 people appear at random to give blood, what is the probability that at least 1 of them is a universal donor?
The probability that at least 1 of them is a universal donor 20.1%
What is a probability simple definition?A probability is a numerical representation of the possibility or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
What are probability and types?Mathematics' study of random events is known as probability, and there are four primary forms of probability: axiomatic, classical, empirical, and subjective. Since probability is the same as possibility, you might argue that it is the likelihood that a specific event will occur.
According to the given equation:-
The probability that at least one of every three is O-negative is 20.1%
Note that the question is unfinished. The following question is similar:
Type O-negative individuals can donate blood to anyone. In other words, O-negative blood can be transfused to any patient. Only 7.2% of Americans have blood that is O-negative. What is the likelihood that at least one of the ten Americans we randomly choose donating blood is a universal donor?
Detailed explanation:
7.2%, or 0.072, of the population has O-negative blood.
Probability of not being O-negative is equal to 1 - P(O-negative), which is 1 - 0.072, or 0.928.
Using the multiplication rule, calculate the likelihood that 10 persons are O-negative.
Probability that 10 is not zero = (P (not O-negative) ¹⁰ = (0.928) (0.928) ¹⁰ =0.4737
Therefore, the probability that at least one is O-negative is given by the formula: 1 - P(not O-negative) = 1 - 0.4737 = 0.5263.
P(at least 1 in 10 being O-negative) = 52.63% in percentage
to 3 arbitrary donors
likelihood of 3 not - (P) negative (not O-negative) ³ = (0.928) (0.928) ³ = 0.7991
As a result, the likelihood that at least 1 is O-negative is equal to 1 - P(3 not O-negative) = 1 - 0.7991 = 0.2009.
P(at least 1 out of 3 being O-negative) = 20.1% in percentage
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Given a∥b , and c is not parallel to a or b, which statements must be true?
Select each correct answer.
Responses
m∠1=m∠8
m∠1=m∠12
m∠3=m∠7
m∠5=m∠9
Answer: first one
Step-by-step explanation:
Elliot takes a roast out of the oven when the internal temperature of the roast is 165°F. After 12 minutes, the temperature of the roast
drops to 140°F.
The temperature of the room is 70°F.
How long does it take for the temperature of the roast to drop to 125°F?
Use the Newton's Law of Cooling equation, T(t)=TA+ (To-TA) e-kt
Enter your answer in the box. Round your answer to the nearest minute.
minutes
Answer:
21.475 minutes
(Rounded) 21 minutes
Step-by-step explanation:
T(t) = TA + (T0 - TA)e^(-kt)
We know that after 12 minutes...
140 = 70 + ( 165 - 70)e^(-k* 12)
1 ) Simplify and subtract 70 from both sides
70 = ( 95)e^(-12k)
2 ) Divide both sides by 25
70/95 = e^(-12k)
3 ) Take the Ln of both sides
Ln (70/95) = Ln e^(-12k)
and we can write Ln (70/95) = (-12k) Ln e
[ Ln e =1, so we can ignore this ]
4 ) Divide both sides by -12
Ln (70/95) / -12 = k ≈ .02545
So...
5 ) We want to find this 125 = 70 + ( 165 - 70)e^(-.02545t)
6 ) 55 = (95)e^(-.02545*t)
7 ) 55/95 = e^(-.02545*t) take the Ln of both sides
8 ) Ln (55/95) = Ln e ^(-.02545 *t)
9 ) Ln (55/95) = (-.02545 * t) * Ln e
10 ) Ln (55/95) = -.02545 * t
11 ) Ln (55/95) / (-.02545) = t ≈ 21.475 minutes
12 ) If we are rounding then it would be 21 minutes
Hope this helps! :)
avery sets up a passcode on her tablet, which allows only nine-digit codes. a spy sneaks a look at avery's tablet and sees her fingerprints on the screen over nine numbers. what is the probability the spy is able to unlock the tablet on his first try? express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
The probability to unlock the tablet on his first try is [tex]P=\frac{1}{10^{9} }[/tex].
According to the statement
We have to find that the probability to unlock the tablet on his first try.
For this purpose, we know that the
Probability is the the ratio of the number of outcomes to the total number of possible outcomes.
And
The desired outcomes is the 1 because only 1 password is the correct.
And the total outcomes is the
Nine-digit codes.so,
[tex]T=10^{9}[/tex]
Because For each digit, there are 10 possible outcomes.
And the probability is the
[tex]P=\frac{1}{10^{9} }[/tex].
So, The probability to unlock the tablet on his first try is [tex]P=\frac{1}{10^{9} }[/tex].
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the number defects per part from an aging machine is shown below. number of defects (x) per part 0 1 2 3 4 5 probability p(x) 0.15 0.20 0.30 0.10 0.20 0.05 what is the mean of the data?
The mean of the following data is 0.1800
What is mean?In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "expected value."There are different ways of measuring the central tendency of a set of values. There are multiple ways to calculate the mean. Here are the two most popular ones:Arithmetic mean is the total of the sum of all values in a collection of numbers divided by the number of numbers in a collection.acc to our question-
100C5 * .05^5 *.95^95 ~ 18.00%hence,The mean of the following data is 0.1800
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if using the method of completing the square to solve the quadratic equation x2-9x-26=0, which number would have to be added to complete the square (pls quickkkk!!)
The numbers would have to be added to complete the square is x = [tex]\frac{9+\sqrt{185} }{2}[/tex] and x = [tex]\frac{9-\sqrt{185} }{2}[/tex]
The quadratic equation is
[tex]x^2[/tex] - 9x - 26 = 0
Add both side of the equation by 26
[tex]x^2[/tex] - 9x - 26 + 26 = 26
[tex]x^2[/tex] - 9x = 26
[tex]x^2[/tex] - 2(9/2)x = 26
Take the coefficient of x and take square of the term and add both side of the equation
[tex]x^2[/tex] - 2(9/2)x + 81/4 = 81/4 + 26
Add the terms
[tex]x^2[/tex] - 2(9/2)x + 81/4 = 185/4
Form the left side of the equation in the form of [tex](a-b)^2[/tex]
Then the equation will be
[tex](x-\frac{9}{2} )^2[/tex] = 185/4
x - 9/2 =± [tex]\frac{\sqrt{185} }{2}[/tex]
x = [tex]\frac{\sqrt{185} }{2}[/tex] + 9/2
x = [tex]\frac{9+\sqrt{185} }{2}[/tex]
Then
x = - [tex]\frac{\sqrt{185} }{2}[/tex] + 9/2
x = [tex]\frac{9-\sqrt{185} }{2}[/tex]
Hence, the numbers would have to be added to complete the square is x = [tex]\frac{9+\sqrt{185} }{2}[/tex] and x = [tex]\frac{9-\sqrt{185} }{2}[/tex]
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Solve for x
x =
A
C
E
4
D
3
x
B
4
A
After solving the value of x = 1/2.
From the figure:
AB = 4 ,BD = 3,DE = 4
AD = AB + BD
= 4+3
= 7
ADE is a right angle triangle.
AE^2 = AD^2+DE^2
= 7^2 + 4^2
= 49 + 16
= 65
AE = [tex]\sqrt{65}[/tex]
AC = AE/2
= [tex]\sqrt{65}[/tex]/2
ABC is a right angle triangle.
AC^2 = AB^2+BC^2
[tex](\sqrt{65}/2)^2[/tex]= 4^2+x^2
65/4 = 16 + x^2
65/4 - 16 = x^2
65 - 16*4 / 4 = x^2
1/4 = x^2
x = [tex]\sqrt{1/4}[/tex]
x = 1/2
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A roofer charges $60 for the first hour of a service call and $20 per hour for each additional hour, as shown on the graph below.
Look at the above Roofer’s Prices graph and then answer the following questions.
Part A What is the slope of a line joining the points on this graph? Show your work or explain your answer.
Part B What does the slope represent?
Slope of line will be 2 and both the variable quantity charge and time are positively related that means if time will increase cost will also increases.
Slope for two points:
P(x1,y1) and Q(x2,y2)
slope of line PQ,
[tex]m_{pq}[/tex] = [tex]\frac{y2 - y1}{x2 - x1}[/tex]
while calculating the slope it may comes positive or negative,
A positive slope means that two variables are positively related to each other.
while,
A negative slope means that two variables are negatively related.
from the given graph,
Part A :
we have two points
A(1 , 60)
B(3,100)
slope of AB will be,
[tex]m_{AB}[/tex] = [tex]\frac{100 - 60 }{3 - 1}[/tex]
= 40 / 2
= 2
slope of line in graph will be 2
Part B:
Here slope of line is 2 which is positive, means both the variables charges and hours are positively related.
that means, if time will increase the cost will also increases.
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2log (10/9) + 3log(81/30)= 2log(25/24)+log 2 give answers after solving
After solving the equation we get to know LHS = RHS
What is an equation ?
An equation is a mathematical statement that proves two mathematical expressions are equal in algebra, and this is how it is most commonly used. In the equation 3x + 5 = 14, for instance, the two expressions 3x + 5 and 14 are separated by the symbol "equal."
LHS
7 log(10/9) - 2log(25/24) + 3 log( 81/80)
= 7log{(2*5)/3²} - 2log{5²/ (2^3 *3)} + 3log{(3^4/(2^4*5)}
= 7( log 2 + log5 - 2log3) -2 (2log 5- 3log2-log3) + 3(4log3 - 4log2–log5)
= 7log2+ 7log5- 14log3 - 4log5 + 6log2 + 2log 3 + 12log3 - 12log2 - 3log 5
= (7log2+ 6log2 -12log2 ) + (7log5 - 4log5–3log5)
= 13log2 - 12 log2 + 3log5 - 3log5
= log2
= RHS
∴ LHS = RHS
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