Answer:
The roots are;
x = (2 + i)/5 or (2-i)/5
where the term i is the complex number representing the square root of -1
Step-by-step explanation:
Here, we want to use the completing the square method to solve the quadratic equation;
f(x) = -5x^2 + 4x -1
Set the function to zero
0 = -5x^2 + 4x - 1
So;
-5x^2 + 4x = 1
divide through by the coefficient of x which is -5
x^2 - 4/5x = -1/5
We now take half of the coefficient of x and square it
= -2/5^2 = 4/25
add it to both sides
x^2 - 4x/5 + 4/25= -1/5 + 4/25
(x- 2/5)^2 = -1/5 + 4/25
(x - 2/5)^2 = -1/25
Take the square root of both sides
x - 2/5 = √( -1/25
x - 2/5 = +i/5 or -i/5
x = 2/5 + i/5 or 2/5 - i/5
pls help i need asap
Translate the following word phrase into an algebraic equation.
“4 times a number increased by 7 is 27”
4(x + 7)=27
(x – 4) + 7=27
4x + 7=27
x ÷ 4 + 7=27
i think its 4+7=27
Answer:
4x+7=27
Step-by-step explanation: The answer you think is correct ! So the 4 times a number is 4x the four being a coefficient and X being the unknown number( variable ) and increase is adding so its +7 and is is just an another word for equal =
Seth built a wooden step stool out of two rectangular prisms and two cubes. Before fastening the components together, he stained each component to give it its final color.
To completely stain the bottom rectangular prism, Seth had to cover
square inches of wood. For one of the cubes to be completely stained, he had to cover
square inches of wood. To completely stain the top rectangular prism, he had to cover
square inches of wood.
Once the stool was fastened together, he applied a coat of sealant to all exposed surfaces of the stool, including the bottom, to cover a total of
square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
What is surface area?A solid object's surface area is a measurement of the overall space that the object's surface takes up.
Given that:
Bottom rectangular prism:
Length = 22 in
Width = 8 in
Height = 6 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((22)(6) + (8)(6) + (22)(6))
SA= 624 square inches.
To complete stain the bottom rectangular prism, he needs to cover 624 square inches.
Square:
Side = 4 in
The surface area of the cube is:
\(SA = 6a^2\)
\(SA = 6 (4)^2\\\\SA= 96\)square inches.
To completely stain two squares, he needs to cover 96 * 2 = 196 square inches.
Top rectangular prism:
Length = 18 in
Width = 5 in
Height = 2 in
The surface area of the rectangular prism is:
SA = 2( lh + wh + lw)
SA = 2((18)(2) + (5)(2) + (18)(5))
SA = 136 square inches
Hence to completely stain top rectangular prism, he needs to cover 136 square inches.
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The function g(x) is defined as g(x) = 7x2 + 1. What is g(–2) ?
Answer:
-27
Step-by-step explanation:
7(-2)*2+1 = -27
Find the perimeter of the shape shown below.
perimeter = turn of the figure
P = 6 + 3 + 4 + 4 + 3 + 6 + 3 + 4 + 3 = 36
the triangle has 2 équal sides => isosceles
and 1 angle is 60° so the triangle is equilateral
For a material with a half-life of 4 years, the amount remaining in a sample after t
years can be found with the equation f (t) = A(1), where A is the amount of
f(t) = A(b)¹.
material in the original sample. This function can be rewritten as
What is the value of b?
The exponential function that models the amount of material after t years is \(A(t) = A(0)(0.5)^{\frac{t}{4}}\), and the value of b is of 0.5.
How to model an exponential function?The standard definition of an exponential function is given as follows:
\(A(t) = A(0)b^{\frac{t}{n}}\)
The parameters of the exponential function are given as follows:
A(0) is the initial amount.b is the rate of change.n is the time needed for the rate of change.The material has a half-life of 4 years, hence the parameter values for b and n are given as follows:
b = 0.5, n = 4.
Then the function is given as follows:
\(A(t) = A(0)(0.5)^{\frac{t}{4}}\)
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How many miles pls help me!!!
PLEASE ANSWER I WILL MARK BRAINLIST
Answer:
1.1/8
2.because multiply the numerator by the reciprocal of the denominator
Step-by-step explanation:
i think the answer is 4 x 2. i hope its right
The sum of 3 times a number and
twice the same number
is less than 45.
a) 3n + 2n < 45
b) 3n + 2 > 45
c) 3(n + 2) < 45
d) 2(n + 3) < 45
Answer:
poop
Step-by-step explanation:
poop
Ruth packs 2 muffins into a gift box. She has 3 flavors of muffins to choose from: lemon,
apple, and blueberry. How many combinations of two different muffins can she pack into
the box?
Answer:
6
Step-by-step explanation:
Answer:
6 i re-assured
Step-by-step explanation:
Using the CPT manual, code the following: Five MeV of radiation treatment delivery to a single area for primary breast cancer, right female breast
According to the CPT manual, the appropriate code for the treatment for primary breast cancer, would be 77427.
In medical coding, it is important to assign the correct CPT code to accurately describe the provided medical service. For the described scenario of delivering five MeV of radiation treatment to a single area for primary breast cancer, the appropriate code is 77427. This code specifically represents the radiation treatment delivery for breast cancer.
The CPT manual is a widely used resource that provides a comprehensive list of medical procedures and services, each assigned a specific code. These codes help healthcare providers communicate and document the services rendered to patients, as well as facilitate accurate billing and reimbursement. The codes in the CPT manual are regularly updated to reflect advancements in medical technology and practices.
By referencing the CPT manual, healthcare professionals can ensure that the services they provide are accurately coded, allowing for consistent and standardized communication across the healthcare industry. This helps in maintaining proper documentation, tracking patient care, and facilitating efficient billing processes.
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The CPT manual provides specific codes for radiation treatment delivery, including those for breast cancer. The appropriate code for the given treatment would depend on the specific technique used and can be found in the CPT manual.
In order to code the radiation treatment delivery for primary breast cancer, right female breast, we need to refer to the CPT manual. The CPT manual provides specific codes for different types of radiation treatment delivery. In this case, the treatment involves the delivery of Five MeV of radiation to a single area.
Based on the information provided, the appropriate CPT code for this treatment would be determined by the specific technique used for radiation delivery. The CPT manual provides codes for different techniques, such as external beam radiation therapy (EBRT) and brachytherapy.
Since the question does not specify the technique, we cannot provide a specific CPT code. However, a healthcare professional would consult the CPT manual and select the appropriate code based on the specific details of the treatment.
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(X²-3x-1)²-12(x²-3x-1)+27
Answer:
Step-by-step explanation:
x^4 - 6x^3 -5x^2 +42x +40
Answer:
Step-by-step explanation:
(x²-3x-1)² = (x²)² + (-3x)² + (-1)²+ 2(x²)(-3x)+2*(-3x)(-1)+2*(-1)(x²)
= x^4 +9x² +1 -6x³ +6x -2x²
=x^4 - 6x³ + 9x² -2x² + 6x + 1
=x^4 - 6x³ + 7x² + 6x + 1
(x²-3x-1)²-12(x²-3x-1)+27 = x^4 - 6x³ + 7x² + 6x + 1 - 12x² + 36x + 12 + 27
=x^4 - 6x³ + 7x² - 12x² + 6x +36x + 1 + 12 +27
=x^4 - 6x³ - 5x² + 42x + 40
PLEASE HELP ASAP!!!!
Use the graph of ƒ to find x if ƒ(x) = 2.
x = –0.5
x = –8
(–∞, –0.5)
x = 0.5
Answer:
\({ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}\)
A beehive contains 5 gallons of honey. A beekeeper removes 4 gallons, 1 pint, and 2 ounces. How much honey remains in the beehive?
Answer: 3 quarts and 14 ounces
Step-by-step explanation:
1 gallon = 4 quarts = 128 ounces,
1 quart = 2 pints,
1 pint = 16 ounces.
Therefore:
5 gallons - ( 4 gallons 1 pint 2 ounces ) =
= 5 * 128 - ( 4 * 128 + 1 * 16 + 2 ) = 640 ounces - 530 ounces = 110 ounces
110 ounces = 3 * 32 + 14
ABC is the image of ABC under a translation
How many sides does a rectangular pyramid
Answer:
Step-by-step explanation:
A rectangular pyramid has five sides. It consists of a rectangular base and four triangular faces that meet at a common vertex or apex.
≧◉◡◉≦
13. Erica has a home that is appreciating in value over the past 4 years. The data for the growth of her home'svalue is shown below.lifelongAlgebra 1BCredit 5L4L - Algebra 1B (2020) Page 51YearAmount2016$400,0002017I$420,0002018$441,00020195463,050What kind of function can be used to best represent this data linear, quadratic or exponential? Explain yourreasoning (2 points)
Mathematical Models
Given a set of two-variable data, we can tell if there is a linear relationship between them by analyzing the change of values of y with respect to the change of values of x.
If the relationship was linear, the change in values of y should be the same when the change in x is equal.
Note that between 2016 and 2017 there was only one year and the value of the house increased by $20,000.
For the next two years, the value increased by $21,000. This means the relationship is not linear.
The possible exponential relationship is also easy to spot. If the ratio between the values of y is constant, then it's an exponential function.
Testing the ratios:
420,000 / 400,000 = 1.05
441,000 / 420,000 = 1.05
463,050 / 441,000 = 1.05
Since the ratio is constant, the growth can be modeled with an exponential function.
consider the following regression equation: y = 30 8x. if sse = 980 and ss total = 1,400., then the correlation coefficient is _______.
In this case, we are given the regression equation y = 30 + 8x, the sum of squared errors (SSE) as 980, and the total sum of squares (SS_Total) as 1,400. Our goal is to find the correlation coefficient.
To find the correlation coefficient (r), we need to first calculate the coefficient of determination (R^2). R^2 is the proportion of the total variation in the dependent variable (y) explained by the independent variable (x) and can be found using the formula:
R^2 = 1 - (SSE / SS_Total)
Plugging in the values given:
R^2 = 1 - (980 / 1,400) = 1 - 0.7 = 0.3
Now that we have the coefficient of determination (R^2 = 0.3), we can find the correlation coefficient (r) by taking the square root of R^2 and determining the appropriate sign. The sign of the correlation coefficient will be the same as the sign of the slope (8) in the regression equation. Since the slope is positive, the correlation coefficient will also be positive.
r = ±√(R^2) = ±√(0.3) ≈ ±0.5477
Since the slope is positive, we choose the positive value for r:
r ≈ 0.5477
Therefore, the correlation coefficient for this regression equation is approximately 0.5477.
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What is the equation of a line that contains the points (5, 0) and (5, −2)? (1 point)
Answer: \(x=5\)
Step-by-step explanation:
Because the \(x\) coordinate of both of the points is 5, the equation is \(x=5\).
Help with geometry on equations of circles. What would be the center of the circle and what is the length of the radius of this circle?
The coordinates of the center is (32, 40.5).
length of the radius of the circle is 73 units.
How to find the center coordinatesThe coordinates of the center is solved using the formula for midpoints expressed as
Midpoint x-coordinate = (x₁ + x₂) / 2
Midpoint y-coordinate = (y₁ + y₂) / 2
Plugging in the values:
x₁ = 8 and y₁ = 13
x₂ = 56 and y₂ =68
Midpoint x-coordinate
= (8 + 56) /2
= 64/2
= 32
Midpoint y-coordinate
= (13 + 68) /2
= 81/ 2
= 40.5
distance formula will be used to find the length of the radius of the circle
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
Plugging in the values:
= √[(56 - 8)² + (68 - 13)²]
= √(48² + 55²)
= √(2304 + 3025)
= √5329
= 73
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20
Select the correct answer.
What is this expression in simplified form?
2√2-7√18
O A. 84√2
OB. 18√5
O c. 14sqrt6
O D.
D. 84
The Question is based on concept of Simplification and answer to this question is -19√2
What is Simplification?
Simplification is the process of making a task, problem, or system easier to understand and manage. It involves breaking down a concept or problem into simpler parts in order to better understand the whole. Simplification can help streamline a process, making it more efficient and easier to complete. It can also help to make complex topics more accessible to a wider audience. Simplification can also be used to make a difficult problem more manageable, allowing for easier solutions.
Here we are given question 2√2 - 7√8 we can do some simplifications like:
but we know we can write √8 = 3√2
hence putting back in original eqn
2√2 - 7(3√2)
2√2 - 21√2
-19√2
Hence required answer is -19√2 by simplification
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Figure R S T U V is reflected across a point of reflection n to form R prime S prime T prime U prime V prime. Figure R prime S prime T prime U prime V prime is rotated 270 degrees about point P to form R double-prime S double-prime T double-prime U double-prime V double-prime
Which composition of transformations maps figure RSTUV to figure R"S"T"U"V"?
a reflection across line n followed by a translation down and to the right
a reflection across line n followed by a 270° rotation about point P
a translation down followed by a 270° rotation about point P
a translation down followed by a reflection across line n
The first transformation for this composition is a reflection across line n followed by a 270° rotation about point P.
When we convert a point across a line y = x then x-coordinate and y-coordinate change.
Also when we reflect a point across the line y = -x then signs exist changed and both coordinates change places.
When transformation maps X"Y" Z" .Then the first transformation for this composition exists, and the second exists at 90° rotation about point X'.
Therefore, the correct answer is option B. first transformation across the line n.
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Need answer ASAP! Question in picture
Answer:
b
Step-by-step explanation:
hope this helps
Help help help help help
My song has put off her adornments. She has no pride of dress and decoration. Ornaments would mar our union; they would come between thee and me; their jingling would drown thy whispers. My poet’s vanity dies in shame before thy sight. O master poet, I have sat down at thy feet. Only let me make my life simple and straight, like a flute of reed for thee to fill with music. –"Song VII," Rabindranath Tagore Which line contains an example of personification? "O master poet, I have sat down at thy feet. " ". . . Like a flute of reed for thee to fill with music. " "My poet’s vanity dies in shame before thy sight. " "Only let me make my life simple and straight. . . ".
The passage does not contain any examples of personification. Personification is a figure of speech in which non-human things or ideas are given human attributes or qualities.
What is Personification?
Personification is a literary device in which non-human objects or concepts are given human-like qualities or characteristics, such as emotions or actions. For example, a common example of personification is when we describe the wind as "howling" or "whistling", which are human actions, even though the wind is not capable of producing those sounds on its own.
In the given passage, there are no instances of non-human objects or concepts being given human-like qualities or characteristics. Instead, the passage contains examples of metaphor and symbolism. For instance, the line "Like a flute of reed for thee to fill with music" is a metaphor comparing the speaker's life to a simple and straight flute that can be filled with music by the master poet. The line "My poet's vanity dies in shame before thy sight" is a symbolic expression of humility, as the speaker is expressing how he feels in the presence of the master poet.
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a group of 268 students are surveyed about their ability to speak mandarin, korean, and japanese. there are 37 students who do not speak any of the three languages surveyed. mandarin is spoken by 174 of the students, japanese is spoken by 139 of the students, and korean is spoken by 112 of the students. the survey results also reflect that 102 students speak both mandarin and japanese, 81 students speak both mandarin and korean, and 71 students speak both japanese and korean. how many students speak all three languages?
There are 99 students who speak all three languages: Mandarin, Japanese, and Korean. The minimum number of students who speak all three languages is 99.
The method used to solve this problem is based on set theory, which is a branch of mathematics that deals with the study of sets, their properties, and their relationships with one another. Specifically, the principle of inclusion-exclusion, which is used in this problem, is a counting technique that is often used in combinatorics and probability theory, which are also branches of mathematics.
Let X be the number of students who speak all three languages.
Then we have:
Number of students who speak only Mandarin = 174 - 102 - 81 - X = -9 - X (since there cannot be a negative number of students)
Number of students who speak only Japanese = 139 - 102 - 71 - X = -34 - X (since there cannot be a negative number of students)
Number of students who speak only Korean = 112 - 81 - 71 - X = -40 - X (since there cannot be a negative number of students)
Number of students who speak only one language = -9 - X + (-34 - X) + (-40 - X) = -83 - 3X (since there cannot be a negative number of students)
Total number of students who speak at least one language = 268 - 37 = 231
Therefore, the number of students who speak all three languages is:
Total number of students who speak at least one language - Number of students who speak only one language - Number of students who do not speak any of the three languages
= 231 - (-83 - 3X) - 37
= 297 + 3X
Since the number of students who speak all three languages cannot be negative, we have:
297 + 3X ≥ 0
3X ≥ -297
X ≥ -99
Therefore, the minimum number of students who speak all three languages is 99.
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PLEASE HELP ASAP!!! i’ll mark brainlessly
1.5 km per hour
ngl i could be wrong :/
PLEASE HELP!!!
what is the value of the expression 2/5m−1/3 when m = 3?
Answer:
13/15
Step-by-step explanation:
I took the quiz and solved it out. I would give further explaination but it is kinda hard to do that in text form. Have a nice day!
The value of the expression if m = 3 is 13/15
Given the expression as shown below:
2/5 m - 1/3If the value of m = 3, hence the expression will become;
2/5(3) - 1/3
6/5 - 1/3
Find the LCM
6/5 - 1/3 = 3(6)-5/15\
6/5 - 1/3 = 18-5/15
6/5 - 1/3 = 13/15
Hence the value of the expression if m = 3 is 13/15
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Customers arrive at the CVS Pharmacy drive-thru at an average rate of 5 per hour. What is the probability that less than 4 customers will arrive at the drive-thru during a randomly chosen hour? 0.600
The probability that less than 4 customers will arrive at the CVS Pharmacy drive-thru during a randomly chosen hour is 0.600.
Given, the average rate of arrival of customers at the CVS Pharmacy drive-thru = λ = 5 per hour. We need to find the probability of less than 4 customers arriving in a randomly chosen hour.Using Poisson's probability distribution formula,P (x < 4) = e⁻ᵩ [ 1/0! + ᵩ/1! + ᵩ²/2! + ᵩ³/3!]where ᵩ is the expected number of customers arriving during a randomly chosen hour,= 5 since the average rate of arrival of customers at the CVS Pharmacy drive-thru = 5 per hour= e⁻⁵ [1/0! + 5/1! + 5²/2! + 5³/3!] = e⁻⁵ [ 1 + 5 + 12.5 + 20.83]= e⁻⁵ × 39.33= 0.674Thus, the probability that less than 4 customers will arrive at the CVS Pharmacy drive-thru during a randomly chosen hour is 0.674.
The given value of the average rate of arrival of customers at the CVS Pharmacy drive-thru = λ = 5 per hour
Therefore, the expected number of customers arriving during a randomly chosen hour = ᵩ = 5.
Using Poisson's probability distribution formula,P (x < 4) = e⁻ᵩ [ 1/0! + ᵩ/1! + ᵩ²/2! + ᵩ³/3!]P (x < 4) = e⁻⁵ [ 1 + 5 + 12.5 + 20.83]P (x < 4) = e⁻⁵ × 39.33= 0.674
Therefore, the probability that less than 4 customers will arrive at the CVS Pharmacy drive-thru during a randomly chosen hour is 0.674.
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Can someone help me with this Question.
The formula we need to use is given above. In this formula, we will substitute the desired values. Let's start.
\(P=3W+D\)A) First, we can start by analyzing the first premise. The team has \(8\) wins and \(5\) losses. It earned \(8 \times 3 = 24\) points in total from the matches it won and \(1\times5=5\) points in total from the matches it drew. Therefore, it earned \(24+5=29\) points.
B) After \(39\) matches, the team managed to earn \(54\) points in total. \(12\) of these matches have ended in draws. Therefore, this team has won and lost a total of \(39-12=27\) matches. This number includes all matches won and lost. In total, the team earned \(12\times1=12\) points from the \(12\) matches that ended in a draw.
\(54-12=42\) points is the points earned after \(27\) matches. By dividing \(42\) by \(3\) ( because \(3\) points is the score obtained as a result of the matches won), we find how many matches team won. \(42\div3=14\) matches won.
That leaves \(27-14=13\) matches. These represent the matches team lost.
Finally, the answers are below.
\(A)29\)
\(B)13\)
Answer:
a) 29 points
b) 13 losses
Step-by-step explanation:
You want to know points and losses for different teams using the formula P = 3W +D, where W is wins and D is draws.
A 8 wins, 5 drawsThe number of points the team has is ...
P = 3W +D
P = 3(8) +(5) = 29
The team has 29 points.
B 54 pointsYou want the number of losses the team has if it has 54 points and 12 draws after 39 games.
The number of wins is given by ...
P = 3W +D
54 = 3W +12
42 = 3W
14 = W
Then the number of losses is ...
W +D +L = 39
14 +12 +L = 39 . . . substitute the known values
L = 13 . . . . . . . . . . subtract 26 from both sides
The team lost 13 games.
__
Additional comment
In part B, we can solve for the number of losses directly, using 39-12-x as the number of wins when there are x losses. Simplifying 3W +D -P = 0 can make it easy to solve for x. (In the attached, we let the calculator do the simplification.)
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Determine whether each expression is monomial right yes or no explain your answer 2a - 2b
The expression 2a - 2b has two terms: 2a and -2b. Therefore, it is a binomial.
Is the expression 2a - 2b monomial?No, the expression 2a - 2b is not a monomial because a monomial is a single term consisting of a product of numbers and variables with non-negative exponents.
The expression 2a - 2b has two terms: 2a and -2b. Therefore, it is a binomial.
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