The perfect square polynomial is x² - 32x + 256 and the factored form is (x - 16)(x - 16)
How to factor perfect square polynomials?A perfect square trinomial is defined as an algebraic expression that is obtained by squaring a binomial expression.
A perfect square polynomial can be represented as follows;
ax² + bx - c = 0
Hence, the perfect square trinomial is x² - 32x + 256.
Now, let's factorise it.
x² - 32x + 256.
x² - 16x - 16x + 256
x(x - 16) -16(x - 16)
Therefore,
(x - 16)(x - 16)
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Answer: x²-32x+16²
Step-by-step explanation:
(x-a)²=x²-32x+a² where .2ax=-32x so, 2a=32 then a=16
then (x-16)²=x²-32x+16²
if f(x) is discontinuous, determine the reason. f of x equals the quantity x squared plus 4 for x less than 1 and equals x plus 4 for x greater than 1
The two equations for f(x) are not equal at x = 1 and f(x) is therefore discontinuous at this point
f(x) is discontinuous at x = 1 because when x = 1, the two separate equations for f(x) do not have the same output. For x < 1, [tex]f(x) = x^2 + 4[/tex], so when x = 1, [tex]f(1) = 1^2 + 4 = 5. For x > 1, f(x) = x + 4[/tex] , so when x = 1, f(1) = 1 + 4 = 5. The output of f(1) is different on each side of the discontinuity. This can be seen in the following calculation:
For x < 1,
[tex]f(x) = x^2 + 4f(1) = 1^2 + 4 = 5For x > 1,f(x) = x + 4f(1) = 1 + 4 = 5[/tex]
Since f(1) is 5 for x < 1 and f(1) is also 5 for x > 1, the two equations for f(x) are not equal at x = 1 and f(x) is therefore discontinuous at this point.
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¿Como se resuelve este problema? 184=5y-y
Answer:
pls mark brainliest
Step-by-step explanation:
it is 8
Determine whether each statement is always true, sometimes true, or
never true.
1. Every square is a rhombus.
2. Every rhombus is a parallelogram.
3. Every rectangle is a parallelogram.
4. The diagonals of a square are perpendicular.
5. If the diagonals of a quadrilateral bisect each other, then the
quadrilateral is a square.
6. If the diagonals of a quadrilateral are perpendicular, then the
quadrilateral is a rhombus.
7. The diagonals of a rectangle are congruent.
8. The diagonals of a rhombus bisect the vertex angles.
9. Some rectangles are rhombi.
10. Some rhombi are squares.
Here the statements 1, 2, 3, 4, 5, 7, 8, 10 are correct according to the rules of the shapes.
1: A rhombus is a quadrilateral with four equally sized sides. Each square is a rhombus since they all have four sides that are the same length. 2: Due to the parallel alignment of its opposing sides, every rhombus is a parallelogram. 3: It is true that all rectangles are parallelograms since they have two sets of parallel sides and two pairs of equal opposing sides. 4: The other is split into two equal halves by each bisector. 5: If a quadrilateral's diagonals are equal and bisect one another at right angles, it is a square. 7: Since the diagonals themselves are congruent, each bisected line segment is also congruent. 8: The diagonals split a rhombus's vertex angles into equal halves. The diagonals of a rhombus are at right angles to one another. 10: A square is a rhombus. Sometimes, this is accurate. When a rhombus has four right angles, it is true. So the statements 1,2,3,4,5,7,8,10 are correct.
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Rationalize the numerator
[tex]\frac{\sqrt{3} -5}{\sqrt{2} +5 }[/tex]
(Simplify your answer. Type an exact answer, using radicals as needed.)
The surd is rationalized to give √6 - 5√3 + 5√2 - 25/2 + 25
How to rationalize the fractionIt is important to note that fractions are a part of whole number or element.
The different types of fraction includes;
Simple fractionsComplex fractionsProper fractionsImproper fractions, etcGiven the expression;
√3 - 5/√2 + 5
√3 - 5/ √2 + 5 ×√2 - 5/√2 - 5
Multiply the values
√6 - 5√3 + 5√2 - 25/√4 - 5√2 + 5√2 + 25
Add the like surds and find the square roots, we get
√6 - 5√3 + 5√2 - 25/2 + 25
Hence, the expression is √6 - 5√3 + 5√2 - 25/2 + 25
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15 bakers comple an order in 24 hrs how much time would it take for 18 bakers to complete same order
Answer:
15×24
times 15and24
giving you this answer
120
then divide 120 by 18
=20hrs would take the Baker
Answer:
28.8 hours
Step-by-step explanation:
[tex]\frac{24 .hours}{15 .bakers}[/tex] = 1.6 hours per baker
1.6 x 18 = 28.8 hours for 18 bakers to complete that order
Let AA be the event that a randomly selected IRSC student is an Associate of Arts student and
P(AA) = 0.41. Let the event PM be the event that a randomly selected IRSC student is on the pre-med
degree track and P(PM) = 0.38. Finally, the probability that a randomly selected IRSC student is an AA degree seeker and on the pre-med degree track is 0.05. Use this information to calculate the following
probability.
Answer:
P(AA) = 0.41
P(PM) = 0.38
P(AA and PM) = 0.05
As you are finding P(AA or PM), you can apply the formula:
P(A U B) = P(A) + P(B) - P( A ∩ B)
U = Union P( A U B) = P (A or B)
∩ = And
From the formula, you can find out the answer:
P(AA or PM) = P(AA) + P(PM) - P(AA and PM)
= 0.41+0.38-0.05
= 0.74
hope this helps!!!!
How do you find the asymptotic complexity of a function?
To find the asymptotic complexity of a function, you need to analyze the behavior of the function as the size of the input grows. You need to determine the number of operations that are performed by the algorithm, and express this as a function of the size of the input.
What is the asymptotic complexity?
Asymptotic complexity is a measure of the growth rate of the running time of an algorithm as the size of the input grows towards infinity. It is expressed using big O notation, which provides an upper bound on the growth rate of the running time.
Here are the steps to find the asymptotic complexity of a function:
Identify the dominant operation: Identify the operation in the algorithm that takes the most time, and consider only this operation for analyzing the asymptotic complexity.Express the dominant operation as a function of the size of the input: Express the number of times the dominant operation is performed as a function of the size of the input. This function will represent the running time of the algorithm.Simplify the function: Simplify the function by ignoring lower order terms and constant factors. The goal is to express the running time in terms of a basic mathematical function that grows at the same rate as the original function.Express the simplified function using big O notation: The big O notation provides an upper bound on the growth rate of the running time. The simplified function can be expressed using the big O notation, which expresses the running time in terms of the size of the input, 'n', and a basic mathematical function.To learn more about asymptotic complexity, Visit
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Find the following F distribution values from the F distribution table. (Round your answers to two decimal places.)
(a) F0.05 with degrees of freedom 6 and 15
(b) F0.025 with degrees of freedom 30 and 25
(c) F0.01 with degrees of freedom 8 and 12
(d) F0.10 with degrees of freedom 10 and 20
To find the F0.10 with degrees of freedom 10 and 20, first you need to locate the row with 10 degrees of freedom, then you need to find the column with 20 degrees of freedom. The intersection of these two values is 1.86.
(a) 2.45
(b) 2.75
(c) 2.82
(d) 1.86
(a) To find the F0.05 with degrees of freedom 6 and 15, first you need to locate the row with 6 degrees of freedom, then you need to find the column with 15 degrees of freedom. The intersection of these two values is 2.45.
(b) To find the F0.025 with degrees of freedom 30 and 25, first you need to locate the row with 30 degrees of freedom, then you need to find the column with 25 degrees of freedom. The intersection of these two values is 2.75.
(c) To find the F0.01 with degrees of freedom 8 and 12, first you need to locate the row with 8 degrees of freedom, then you need to find the column with 12 degrees of freedom. The intersection of these two values is 2.82.
(d) To find the F0.10 with degrees of freedom 10 and 20, first you need to locate the row with 10 degrees of freedom, then you need to find the column with 20 degrees of freedom. The intersection of these two values is 1.86.
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paula lives 1/9/10 from school. Nate lives 1/3/4 miles from school. Cristian lives 11/8 miles from school. who lives closest to school?
The distance from the school to Cristian home is least which is 1.375 miles.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
Paula lives 1 ⁹/₁₀ from school. Nate lives 1 ³/₄ miles from school. Cristian lives 11/8 miles from school.
Convert the mixed fraction and fraction number into a decimal number. Then we have
1 ⁹/₁₀ = 1.90 miles
1 ³/₄ = 1.75 miles
11/8 = 1.375 mies
The distance from the school to Cristian home is least which is 1.375 miles.
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Explain how to use the distributive property to create
an expression that is equivalent to 2b + 5b.
Answer:
Step-by-step explanation:
The variable b is common to each expression.
Take the b out and put the remaining numbers in a parenthesis:
b ( 2 + 7)
b (9)
9b
100 points!!!
There is a pic if you click on it
Here is a graph that shows the water height of the ocean between September 22 and September 24, 2016 in Bodega Bay, CA.
1. The water's height at 12 pm on September 22 was given as follows: 3.5 feet.
2. The number of times that the water's height was of 5 feet is of: 4 times.
3. The lowest rate the water got during this time period was of: 0.5 feet at 12 pm on 09/24.
4. The water never reaches a height of 6 feet.
How to make the estimates?The estimates are made considering the graph of the function.
The input and the output of the graph are given as follows:
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If the size of one object is 8.5*10^-4 meters and the size of a second object is 3.7*10^6, how many times bigger is the second object compared to the first object?
The second object is approximately 4.4 * 10^9 times bigger than the first object.
Division of numbers involving Scientific Notation.The division of the value of the second scientific notation from the first scientific notation is the precise and accurate way with which we can determine many many times bigger is the second object compared to the first object.
To do so, group coefficients together and exponents together to divide numbers in scientific notation. i.e.
= (3.7/8.5) * ((10^6)/(10^−4))
= 0.43529411 × ((10^6)/(10^−4))
Subtract the exponent from the denominator from the exponent of the numerator for the same base 0.43529411 ⋅ 10^(6 −4*−1)
= 0.43529411 × ((10^6+4)
= 0.43529411 × 10^10
= 4.3529411 × 10^9
≅ 4.4 × 10^9
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What is the measure of the angle formed by Main Street and Park Street?
Answer:
90°
Step-by-step explanation:
they are forming a right angle (90°).
Given the table find f(1)
The table of linear function shows that f(1) is equal to -3
What is a linear functionA linear function is a mathematical function of the form f(x) = mx + b, where m and b are constants and x is the input variable. This function produces a straight line on a graph, with a constant slope (m) and a y-intercept (b) where the line intersects the y-axis.
The slope (m) of a linear function represents the rate of change of the function, or the steepness of the line, while the y-intercept (b) represents the value of the function when x=0.
In the function table given, we can find f(1) when we look at the table.
This shows that f(1) is equal to -3
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You are going to a restaurant, and the subtotal
is $80.00, there is a 6.5% sales tax.
What will the total bill come to?
How much are you paying in sales tax? If you tip a 15% before tax, how much will be
the tip?
How much are you paying in total?
Answer:587
Step-by-step explanation:
Ok so it’s 587 I’m jp
Que es más frío -2 °F o -1 °F y por qué
Answer:-2 °F
Step-by-step explanation:
Este numero es mas frio porque es de menos valor y lo mas bajo que es el numero lo mas frio que se siente.
84 is 99 fewer than a number c .
Answer:
c is -15
Step-by-step explanation:
minus 84 from 99 then add a minus onto it or just take away 84 from 99
There will be 1,825 campers at a state summer camp this year. If each cabin has 2 counselors for every 25 campers, what prediction can you make about the number of counselors who will be at the state camp?
A There will be about 23 counselors there.
B There will be about 146 counselors there.
C There will be about 900 counselors there.
D There will be about 913 counselors there.
Answer: B
Step-by-step explanation:
1825/25=73
73*2=146
146
Cx=2x-15 and C E=2x-8. Find CX
the value of EX will be 8x -23 in the form of variable x.
What are Systems of equations?Simultaneous equations, Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given, Cx = 2x-15 and CE=2x-8 these are the measurement of the distance Of points E and x from the point c
Distance between two points is the length of the line segment that connects the two points in a plane.
Thus the total distance = CE + CX = 2x -15 + 2x -8
Total distance (EX) = 4x - 23
Therefore, the value of EX will be 8x -23 in the form of variable x.
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m/1 and m/2 are vertical
angles. If m/1 = 3x + 21
and m/2 = 5x-35, find the
measures of both angles.
The measure of both the angles is equal and it is of 105 degrees.
Vertical Angles:
The opposing angles created when two lines cross one another. They are always equal.
The vertex, not up or down, where they meet, is the term understood by the phrase "vertical."
In the given question,
m/1 = 3x+21
m/2 = 5x-35
it is also given that, both angles are vertical angles,
therefore,
m/1 = m/2
3x + 21 = 5x - 35
2x = 56
x = 28
Now, place the value of x in given angles,
m/1 = 3 (28) + 21
m/1 = 84 + 21
m/1 = 105
Similarly,
m/2 = 5 (28) - 35
m/2 = 140 - 35
m/2 = 105
Therefore, both the given angles are of 105 degrees.
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let y1,y2 be independent random variables both having the uniform(0,1) distribution. re- call that the density function and distribution function of a uniform random variable y
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function.
A uniform random variable's density function is f(y) = 1 for y 1 and 0 otherwise. Accordingly, the likelihood of any specific outcome of y is the same, and the likelihood of any range of outcomes is equal to the length of the range. F(y) = 0 for y 0, F(y) = y for 0 y 1, and F(y) = 1 for y > 1 define the distribution function. Accordingly, the length of the range multiplied by the likelihood of any specific occurrence yields the cumulative probability of any range of outcomes. Since the likelihood of any specific result in that range is 1 and the range's length is 0.5, for instance, the cumulative probability of 0 y 0.5 is 0.5. Since the likelihood of any given result within that range is still 1, but the range's length is 0.5, the cumulative probability of 0.5 y 1 is 0.75. The chance of any range of outcomes for y1 and y2 if they are independent random variables both having the uniform(0,1) distribution is just the sum of their respective cumulative probabilities.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).
Jason and Mark have volunteered to fill water into the two dunk tanks for their scout field days. The amount of water in Jason's dunk tank is represented by the equation below, where W represents the amount of water, in gallons, x minutes after he began to fill.
The amount of water in Mark's dunk tank is represented by the equation below, where W represents the amount of water, in gallons, x minutes after he began to fill.
w=2x+1 w=10x+5
Using graphing technology, complete the statements.
After
minutes, the total amount of water in both dunk tanks will be the same.
The total amount of water at that minute will be
gallons.
2 minutes of time both the tanks have same amount of water and total amount of water at that minute will be 25 gallons.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The amount of water in Jason's dunk tank is represented by the equation below, where W represents the amount of water, in gallons, x minutes after he began to fill.
w=2x+1
The amount of water in Mark's dunk tank is represented by the equation
w=10x+5
The total amount of water in both dunk tanks will be the same.
2x+1=10x+5
8x=-4
Divide both sides by 4
x=-2
So at 2 minutes of time both the tanks have same amount of water.
Now plug in 2 value in any of equation
W=25
Hence, at 2 minutes of time both the tanks have same amount of water and total amount of water at that minute will be 25 gallons.
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Simplify-(-5) and -|-2|
(I don’t understand the steps)
Answer: -(-5) =5
-|-2| = -2
Step-by-step explanation:
Two negatives = positives
Glad to help do you mind clicking the crown for me it would really help please and thank you have a blessed day!
y = 2x + 3
y = 8/4 x - 1/4
how many solutions
Answer: The number of solutions for the system of linear equations depends on whether the lines are parallel or intersect at a single point. If the lines are parallel, there are no solutions, as they never meet. If the lines intersect at a single point, there is exactly one solution.
To determine the number of solutions, we need to find the point of intersection of the two lines. We can do this by solving for x in one equation and substituting it into the other equation:
2x + 3 = 8/4 x - 1/4
8x + 12 = 2x - 1/2
6x = - 12.5
x = -2.08
Then, substituting this value of x back into either equation to find the corresponding value of y:
y = 2 * (-2.08) + 3 = 0.16
So, the two lines intersect at the point (-2.08, 0.16), which means there is exactly one solution to the system of linear equations.
Step-by-step explanation:
A college finds that 8% of students have taken a distance learning class and that 30% of students Part (e) Are D and E mutually exclusive? Explain.are part-time students. Of the part-time students, 20% have taken a distance learning class. Let D = event that a student takes a distance learning class and E = event that a student is a part-time student. Part(a) Find P(D AND E )Part (b) Find P(EID). Part (c) Find P(D OR E). Part (d) Are D and independent?
(a) P(D and E) is equal to 0.06.
(b) P(E | D) is equal to 0.75.
(c) P(D or E) is equal to 0.32.
(d) D and E are not independent.
(e) D and E are not mutually exclusive.
The solution has been obtained using probability.
What is probability?
Probability is a mathematical concept used to determine the likelihood of an event. It merely allows us to calculate the probability or possibility that an event will occur. The range of probabilities lies between 0 and 1, where 1 signifies a certain event and 0 denotes an impossibility.
We are given the following:
No. of students that have taken a distance learning class = 8%
No. of students that are part-time students = 30%
No. of part-time students that have taken a distance learning class = 20%
Let D = event that a student takes a distance learning class and E = event that a student is a part-time student.
(a) Since, 20% of the part times students are taking distance learning classes (D and E) so,
P(D and E) = 0.3 * 0.2 = 0.06
(b) P (E | D) = P (D and E) / P (D)
P (E | D) = 0.06 / 0.08
P (E | D) = 0.75
(c) P (D or E) = 0.3 + 0.08 - 0.06 = 0.32
(d) For events to be independent, probability of D and E must be equal to P(D) x P(E).
But, P(D and E) ≠ P(D) x P(E)
So, D and E are not independent.
(e) Events are considered mutually exclusive if they do not occur at the same time.
But, D and E can occur at the same time.
So, D and E are not mutually exclusive.
Hence, the solutions have been obtained.
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The radius of a circle is 4.5 cm.find the circumference to the nearest tenth
Answer:
28.26cm
Step-by-step explanation:
The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle.
Plugging in r = 4.5 cm, we get:
C = 2π * 4.5 = 9π cm
To find the value of C to the nearest tenth, we can approximate π to 3.14:
C = 9 * 3.14 = 28.26 cm
2. A student receives test scores of 62, 83, and 91. The student's term project score is 88 and her homework score
is 76. Each test is worth 20% of the final grade, the term project is 25% of the final grade, and the homework
grade is 15% of the final grade. What is the student's mean score in the class?
3. The median for the given set of six ordered data values is 27.5. What is the missing value? ______
5 12 23 ______ 41 51
4. For the following data, approximate the mean number of emails received per day
Answer:
Step-by-step explanation:
75
use newton's method to find all real roots of the equation correct to six decimal places. (enter your answers as a comma-separated list.) 4 x = 1 + x3
Using newton's method to find all real roots of the equation, 4x = 1+ x³ is
x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.
We have the equation,
4x = 1+ x³
To find the real roots of equation we have,
x1 = -2.11491, x2 = 0.2541, x3 = 1.86081.
The cubic equation formula in mathematics is how the cubic equation is represented. An equation with degree three is said to be cubic. In nature, the roots of all cubic equations are either one real root and two real roots or three real roots. Cubic polynomials are the name given to three-degree polynomials.
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In this polygon, all angles are right angles.
What is the area of this polygon?
Enter your answer in the box.
ft²
Polygon in the shape of a letter L, which could be formed by a horizontal rectangle attached along the bottom part of a vertical rectangle. The left side of the figure is 18 ft, the bottom side of the figure is 21 ft, the right side of the figure is 8 ft, and the top part of the horizontal rectangle to the right of the vertical rectangle is 12 ft.
On solving the provided question, we can say that the area of the rectangle polygon is 474 ft².
What is rectangle?A rectangle in Euclidean geometry is a parallelogram with four slight angle. It may alternatively be described as a hexagon that is basic rule, or one in which all of the angles are equal. A straight angle is another another option for the parallelogram. In a square, four of the vertices are the same length. A quadrilateral with a rectangle-shaped cross section has four 90 ° angle vertices + equal parallel sides. As a result, it is sometimes referred to as a "equirectangular rectangle". Due to such equal and parallel dimensions of its two sides, a rectangle is occasionally referred to as parallelogram.
The left rectangle has a height of 18 ft and a width of 21 ft, so its area is:
[tex]18 ft x 21 ft = 378[/tex] ft²
The right rectangle has a height of 12 ft and a width of 8 ft, so its area is:
[tex]12 ft x 8 ft = 96[/tex] ft²
Therefore, the total area of the polygon is:
378 ft² + 96 ft² = 474 ft²
So the area of the polygon is 474 ft².
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Which supplementary angles can prove
that lines L and M are parallel?
A
L-
+
M-
A. 3 and 4
B. 3 and 5
C. 7 and 8
2
3 4
5 6
78
3 and 5 supplementary angles can prove that lines L and M are parallel. The solution has been obtained by using the properties of parallel lines.
What are parallel lines?
In a plane, lines that are parallel to one another do not meet or overlap at any point. They are always parallel and equally spaced apart. Parallel lines are non-intersecting lines. Infinity is another place where parallel lines are believed to meet.
We are given a set of parallel lines and various angles are marked on the lines.
Angles 3 and 4 can not prove that the lines are parallel because they lie on the same line.
Similarly, angles 7 and 8 can also not prove.
But, angles 3 and 5 can prove this because they lie on different lines i.e. they belong to both the lines.
Hence, 3 and 5 supplementary angles can prove that lines L and M are parallel.
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Complete question:
\Which supplementary angles can prove that lines L and M are parallel?
A. 3 and 4
B. 3 and 5
C. 7 and 8