After answering the presented question, we can conclude that As a function result, f(x) = [tex]x^4 - 2x^3 + 37x^2 - 72x + 36[/tex] is the polynomial with real coefficients of degree 4 and zeros 1 (multiplicity 2) and 6i.
what is function?Mathematicians research numbers and their variants, equations or related structures, structures and their locations, and prospective locations for these things. The noun "function" describes the connection that exists among a set of inputs, each of which has a corresponding output. A function is an input-output connection where each input results in a single, separate output. A domain, codomain, or scope is assigned to each function. Functions are usually denoted by the letter f. (x). An x is used for entry. On functions, one-to-one skills, multiple capabilities, in skills, and on functions are the four major types of accessible functions.
If a polynomial has a multiplicity 2 root, it can be factored as the product of two linear factors, each containing that root once. In this situation, the factorization of f(x) is:
(x - 1)2 (x - 6i) (x + 6i) f(x)
Where z = a + bi, z* = a - bi.
[tex](x - 1)2 (x - 6i) (x + 6i) = f(x) (x - 1)\\a^2 ((x - 6i)(x + 6i))\s= (x - 1) (x - 1)\\a^2 (x^2 - (6i)^2)\s= (x - 1)^2 (x^2 + 36)\\[/tex]
Extending this expression yields:
f(x) = x4 minus 2x3 + 37x2 minus 72x + 36
As a result, f(x) = [tex]x^4 - 2x^3 + 37x^2 - 72x + 36[/tex] is the polynomial with real coefficients of degree 4 and zeros 1 (multiplicity 2) and 6i.
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X^2+4÷3_x÷7 write in standard form
The expression [tex]x^2 + 28 / (3x)[/tex] can be written in standard form as [tex](3x^2 + 28x) / 3[/tex].
To write the expression in standard form, we need to simplify it and arrange it in a specific order.
First, let's simplify the expression:
[tex]x^2 + 4 / (3x/7)[/tex]
To simplify the expression, we need to multiply the numerator and denominator of the fraction by the reciprocal of the denominator, which is 7/3x. This gives us:
[tex]x^2 + 4 * 7 / (3x)[/tex]
Simplifying the fraction gives:
[tex]x^2 + 28 / (3x)[/tex]
Now, to write the expression in standard form, we need to arrange it in the order [tex]ax^2 + bx + c[/tex], where a, b, and c are constants. To do this, we need to simplify the expression further:
[tex]x^2 + 28 / (3x)[/tex]
= [tex]3x(x^2 / 3x + 28 / (3x^2))[/tex]
= [tex]3x(x + 28/3x)[/tex]
Therefore, the expression in standard form is:
[tex](3x^2 + 28x) / 3[/tex]
Standard form of a linear equation in two variables is represented as Ax + By = C, where A, B, and C are constants, and x and y are variables.
Standard form of a complex number is represented as a + bi, where a and b are real numbers, and i is the imaginary unit, which satisfies the equation [tex]i^2 = -1[/tex].
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Mr.bakers yard has an area of 1,472 square feet. The width of the yard is 32 feet. What is the length of mr.bakers yard?
Help me i pay you ;)
Answer:
a) x = 90°
b) The angle between the tangent and the radius at a point on a circle is 90°.
[tex]\hrulefill[/tex]
Step-by-step explanation:
The radius of a circle is the distance from the center of the circle to any point on its circumference.
The tangent of a circle is a straight line that touches the circle at exactly one point, called the "point of tangency".
The given diagram shows circle O along with a tangent line. The radius of the circle intersects the tangent at the point of tangency.
The tangent of a circle is always perpendicular to its radius.
Therefore, the size of angle x is 90°.
Therefore, the circle theorem that allowed us to work out the size of angle x is:
The angle between the tangent and the radius at a point on a circle is 90°.Gage buys a bag of cookies that contains 6 chocolate chip cookies, 8 peanut butter cookies, 5 sugar cookies and 9 oatmeal cookies.
What is the probability that Gage reaches in the bag and randomly selects a chocolate chip cookie from the bag, eats it, then reaches back in the bag and randomly selects a peanut butter cookie?
The prοbability that Gage randοmly selects a chοcοlate chip cοοkie frοm the bag, eats it, then reaches back in the bag and randοmly selects a peanut butter cοοkie is 2/63.
What is Prοbability?Prοbability is a measure οf the likelihοοd οr chance οf an event οccurring. It is a number between 0 and 1, with 0 indicating impοssibility and 1 indicating certainty.
The tοtal number οf cοοkies in the bag is:
6 + 8 + 5 + 9 = 28
The prοbability οf Gage randοmly selecting a chοcοlate chip cοοkie frοm the bag is: 6/28 = 3/14
After Gage eats the chοcοlate chip cοοkie, there will be 27 cοοkies left in the bag, including 8 peanut butter cοοkies. Sο, the prοbability οf Gage randοmly selecting a peanut butter cοοkie frοm the bag is: 8/27
The prοbability οf bοth events οccurring is the prοduct οf the individual prοbabilities: (3/14) * (8/27) = 2/63
Therefοre, the prοbability that Gage randοmly selects a chοcοlate chip cοοkie frοm the bag, eats it, then reaches back in the bag and randοmly selects a peanut butter cοοkie is 2/63.
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An ice cream shop sells small and large sundaes. One day, 30 small sundaes and 50 large sundaes were sold for $420. Another day, 15 small sundaes and 35 large sundaes were sold for $270. Sales tax is included in all prices. If x is the cost of a small sundae and y is the cost of a large sundae, write a system of equations to represent this situation.
Peyton thinks that small sundaes cost $2.75 and large sundaes cost $6.75. Is Peyton correct? Justify your answer?
Using your equations, determine algebraically the cost of one small sundae and the cost of one large sundae?
The cost of small sundae = 4 dollars
cost of large sundae = 6 dollars
What is the cost price?
The precise value that corresponds to the unit price paid is represented by the cost price. In some stock market theories, this value is utilized to establish the value of stock holdings and is used as a key determinant of profitability.
Here, we have
Given: An ice cream shop sells small and large sundaes. One day, 30 small sundaes and 50 large sundaes were sold for $420. On another day, 15 small sundaes and 35 large sundaes were sold for $270.
let
x = cost of each small sundae
y = cost of each large sundae
30x + 50y = 420...(1)
15x + 35y = 270...(2)
multiply equation(ii) by 2
30x + 50y = 420
30x + 70y = 540
subtract equation(i) from equation(ii)
20y = 120
y = 120 / 20
y = 6
Now, put the value of y in equation(1) and we get
30x + 50(6) = 420
30x + 300 = 420
30x = 420 - 300
30x = 120
x = 120 / 30
x = 4
Hence, the cost of small sundae = 4 dollars
cost of large sundae = 6 dollars
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1/2xh=10
what is the value of h?
Answer:
20
Step-by-step explanation:
divide 10 by 1/2
How many unique codes are possibly formed from two characters, where the first character can be 2 to 7, and the second character can be A to C?
Using the Multiplication Principle of Counting, 18 unique codes can be formed.
EquationThere are 6 possible choices for the first character (2, 3, 4, 5, 6, or 7) and 3 possible choices for the second character (A, B, or C). Therefore, by the multiplication principle of counting, there are 6 × 3 = 18 unique codes that can be formed from two characters where the first character can be from 2 to 7 and the second character can be from A to C.
What is Multipliplication Principle of Counting?The multiplication principle of counting is a basic principle in combinatorics that states that if there are k ways to do one thing and m ways to do another thing, then there are k × m ways to do both things together. In other words, if there are a ways to choose the first element of a sequence and b ways to choose the second element of the same sequence, then there are a × b ways to choose the two elements together. This principle can be extended to more than two choices as well.
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PLEASE HELP ME ANSWER THIS QUESTION ASAP!!
Answer:
7z + 17
Step-by-step explanation:
Like terms
All the numbers without letters are like terms
All the numbers with letters are like terms
Since we have 2 numbers without letters, we'll combine those.
15 + 2 = 17
Since there's only one number with letters, we can keep it the same since there's no others to combine it with
7z + 17
Are these triangles similar if so tell how you know and complete the similarity statement
Answer: Two triangles are similar if they have the same ratio of corresponding sides and equal pair of corresponding angles .
Two increased by the product of a number and 7 is at most -29
The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.
The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.
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The number that satisfies the equation is x = -31/7. This means that if we increase two by the product of a number and 7, the result is at most -29 if the number is -31/7.
The expression we need to solve is "Two increased by the product of a number and 7 is at most -29". We can express this as 2 + x × 7 ≤ -29 where x is the number we need to find.In order to solve this equation, we need to start by isolating the variable x. We can subtract 2 from both sides of the equation to get x × 7 ≤ -31. Then, we divide both sides of the equation by 7 to get x ≤ -31/7.Therefore, the number that satisfies the equation is x = -31/7. This means that if we two by the product of a number and 7, the result is at most -29 if the number is -31/7.
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In the figure, mZ1= (3x)° and mZ2 = (x+14)°. 2 1 (a) Write an equation to find x. Make sure you use an Equation: (b) Find the degree measure of each angle. m 41= m / 2 = 0 = " sign in your answer. = X X Ś 5
a) Equation is: (3x)° + (x + 14)° = 90° and value of x = 19°
b) ∠1 = 57° and ∠2 = 33°
Define right angle triangle?A right angle triangle is a geometric form with a single angle that is precisely 90 degrees in length. A right angle is another name for this angle. The other two angles are acute, which means that they have a degree value below 90. The hypotenuse, which is the triangle's longest side, is the side that faces the right angle.
Given a right angle of ∠1 and ∠2:
a) So, ∠1 + ∠2 = 90°
(3x)° + (x + 14)° = 90°
4x + 14° = 90°
x = 19°
b) ∠1 = (3x)°
∠1 = (3*19)°
∠1 = 57°
and, ∠2 = (x+14)°
∠2 = (19+14)°
∠2 = 33°
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Please help, it shouldent take too much time
The sum of angles in a triangle is always 180 degrees. Therefore, the angle C measures 60 degrees.
In triangle ABC, we know that angle A measures 75 degrees, and angle B measures 45 degrees.
To find the measure of angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees:
Angle A + Angle B + Angle C = 180
Substituting the values we know:
75 + 45 + Angle C = 180
Simplifying:
120 + Angle C = 180
Subtracting 120 from both sides:
Angle C = 60
Therefore, angle C measures 60 degrees.
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please help me with this test im smart js not at the right mind
Answer:
sal-43 mins
elena-45 mins
Step-by-step explanation:
cant be bothered to type explanation
Quality assurance or trusted answerer pls help me!
I'll will give my whole points, 5 star and crown.
The factored versions of the expressions are:
(x + 3) ( x - 3)4 (3x + 1) ( 3x -1)3 (5x + 1) (5x - 1)(4x + 7) ( 4x- 7)(7x + 2) (7x - 2)(8 + x) (8 - x) (3 + x) (3 - x)(10x + 7) (10x - 7)9 (10x + 1) (10x - 1)5x ( 2x + 1 ) ( - 2x + 1)(11 + 4x) (11 - 4x)10x ( 5x + 1 ) ( - 5 x + 1 )6x (x - 2) (x + 2)What is factorization ?Factorization is the process of breaking down a mathematical expression into simpler components. It is useful in simplifying algebraic expressions, solving equations, and understanding the behavior of mathematical functions.
Let's consider the first problem: x² - 9. We can observe that this expression can be written as the difference of two squares: x ² - 3².
Using the formula for the difference of squares, we can factor this expression as (x + 3)(x - 3).
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Please give simple answers ! Will rate good.
Step-by-step explanation:
16. 2/8 and 12/32
Common denominator is 32
8/32 and 12/32
17. 10/100 and 12/50
Common denominator is 100
10/100 and 24/50
18. 24/16 and 3/4
Common denominator 16
24/16 and 12/ 16
10000 truncated to the hundreds
Answer: 10,000
Step-by-step explanation:
Polygraph tests have an accuracy rate of about 90%. This means that it will detect 90% of people who lie and 90% of people who are telling the truth. A company of 4000 employees has everyone submit to a polygraph test. It turns out there are 40 employees who will lie during their polygraph. (Hint: Tests Positive means they are lying!) Complete a table as in your course materials and use it to answer the given question.
If someone does pass their polygraph test, what is the probability they told the truth?
The probability of someone telling the truth if they pass their polygraph test is 3960/4000, which is 99%.
Polygraph tests are used to detect deception by monitoring physiological responses, such as changes in blood pressure and heart rate, while the subject is asked a series of questions. The accuracy rate of a polygraph test is typically around 90%, meaning that it will detect 90% of people who are lying and 90% of people who are telling the truth. In the given scenario, there is a population of 4000 employees and it is known that 40 of them will lie during their polygraph test. This means that there are 3960 people who will tell the truth. The probability of someone telling the truth if they pass their polygraph test is 3960/4000, which is 99%. This means that if someone passes their polygraph test, there is a 99% probability that they are telling the truth. It is important to note that the accuracy rate of polygraph tests is not 100%, so it is still possible for someone to lie and pass their test. However, the probability of a truthful person passing the test is much higher than the probability of a liar passing the test.
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One angle of a triangle measures 75°. The other two angles are in a ratio of 10:11. What are the measures of those two angles?
One angle of a triangle measures 75°. The other two angles are in a ratio of 10:11. What are the measures of those two angles?
One angle measures = 75°
Ratio of other 2 angles = 10 : 11
Let the number be x
So, 10x : 11x
Sum of interior angles of a triangle = 180°
Now,
[tex]75 + 10x + 11x = 180[/tex]
[tex]10x + 11x = 180 - 75[/tex]
[tex]10x + 11x = 105[/tex]
[tex]21x = 105[/tex]
[tex]x = 105\div21[/tex]
[tex]x = 5[/tex]
So,
Second angle = 10x = 10 × 5 = 50° ans
Third angle = 11x = 11 × 5 = 55° ans
I'LL MARK THE BRAINLIEST!
This figure consists of a rectangle and a quarter circle.
What is the perimeter of this figure?
Use 3.14 for π.
Enter your answer as a decimal in the box.
Answer:
Step-by-step explanation:
The perimeter of a figure be 27.85 ft .
Answer:
27.85
Step-by-step explanation:
I done the test.
can someone please help me
-Solve each triangle. Round to the nearest tenth, if necessary.
show work
Answer:
T = 20°t = 29.0u = 17.7Step-by-step explanation:
You want the solution to triangle TUV, given U=12°, V=148°, v=45.
Triangle solutionSolving a triangle generally means finding the measures of all sides and angles. When two angles and one side are given, and that side is opposite the largest angle, there is one solution. It can be found using the Law of Sines.
Missing angleThe Angle Sum theorem tells you the sum of angles in a triangle is 180°. This means ...
T +U +V = 180°
T +12° +148° = 180°
T = 20° . . . . . . . . . . . . subtract 160°
Missing SidesThe Law of Sines tells you the side lengths are proportional to the sine of the opposite angle:
t/sin(T) = u/sin(U) = v/sin(V)
t = v/sin(V)·sin(T) = 45/sin(148°)·sin(20°) ≈ 29.0 . . . . multiply by sin(T)
u = v/sin(V)·sin(U) = 45/sin(148°)·sin(12°) ≈ 17.7 . . . . . multiply by sin(U)
__
Additional comment
There may be two solutions if the given side is not opposite the largest angle.
please help! , 2(3x+1) QUICK PLS
Answer:
6x+2
Step-by-step explanation:
We can use the distributive property.
2(3x+1) is the problem
The distributive property means you distribute what is outside the parenthesis to every term that is in the parenthesis.
So we get this:
3x(2) + 1(2)
Which leads to this
6x+2
6x+2 cannot be simplified, so that is our answer.
a board is 23.5 inches long. how long is the board in centimeters? use the following conversion: 1 inch is 2.54 centimeters
Answer:
59.69cm
Step-by-step explanation:
23.5
x 2.54
-----------
59.69
A small theater had 9 rows of 24 chairs each. An extra 8 chairs have just been brought in. How many chairs are in the theater now?
Answer:224 SILLAS HAY AHORA
YA QUE ANTES HABIAN 216
Step-by-step explanation:
There are 224 chairs in the theater now.
Given:
9 rows
1 row = 24 chairs
8 extra chairs
9 x 24 = 216 chairs
216 chairs + 8 chairs = 224 chairs in all.
Find the value of x using trigonometry. Round your answer to the nearest tenth.
The required value of x is 16.1 units.
What is right angled triangle?Right-angle triangles are formed when the angle formed by two of their edges is exactly 90 degrees. Obtuse angle triangle: An obtuse angle triangle is one in which the angle formed by two sides is larger than 90 degrees.
According to question:We have;
∅ = 49°, Base = 14, perpendicular = x
To find value of x.
Then,
tan∅ = perpendicular/Base
tan(49°) = x/14
Here tan(49°) = 1.15
x = 1.15(14)
x = 16.1 units
Thus, required value of x is 16.1 units.
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can someone help? I completely forgot how to find the answer when they only give us one angle
Answer:
a=70
Step-by-step explanation:
please mark as brainliest
Please show work.
Charles has six songs on a playlist. Each song is by a different artist. The artists are Jennifer Lopez, Nick Carter, Shania Twain, Shakira, Michael Jackson, and Mariah Carey. He programs his player to play the songs in a random order, without repetition. What is the probability that the first song is by Mariah Carey and the second song is by Shania Twain? Write your answer as a fraction or a decimal, rounded to four decimal places.
After answering the presented question, we can conclude that As a result, the probability is 0.0333. (rounded to four decimal places).
What is probability?
Probabilistic theory is a branch of mathematics that calculates the likelihood of an event or proposition occurring or being true. A risk is a number between 0 and 1, with 1 indicating certainty and a probability of around 0 indicating how likely an event appears to be to occur. Probability is a mathematical expression for the likelihood or likelihood that a certain event will occur. Probabilities can also be expressed as numbers ranging from 0 to 1 or as percentages ranging from 0% to 100%. the proportion of occurrences among equally likely events
There are six options for the first song, but we want Mariah Carey to be the first song, so there is only one option.
There are 5 songs left after Mariah Carey's, but we want Shania Twain's song to be second, so there is only one option for the second song.
As a result, the likelihood of the first song being Mariah Carey and the second song being Shania Twain is:
1/6 * 1/5 = 1/30
As a result, the probability is 0.0333. (rounded to four decimal places).
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Solve for x: 2|2x-4|-5=-3
The expression 2|2x-4|-5=-3 is the value of x=5/2 or x=3/2.
The act of expressing something involves making your ideas, sentiments, etc. known through voice, writing, or another means. Algebraic expressions fall into three main kinds, including: Numeral Expression. Binary Expression. Expression of a polynomial.
Exponential equations to solve
The standard exponential equation is expressed as y = ab^x
Given the expression
2|2x-4|-5=-3
Rearrange the terms.
2|2x-4|=-3+5
Reduce.
2|2x-4|=2
Divide the both.
|2x-4|=1
Separate into possible cases.
2x-4=1 or 2x-4=-1
Show more steps.
x=5/2 or x=3/2.
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a tower leans at an angle of about 84.7°. the figure shows that 185 feet from the base of the tower the angle of elevation to the top is 47.4°. find the distance to the nearest foot from the base to the top of the tower
After answering the presented question, we can conclude that As a trigonometry result, the distance from the tower's base to its peak is roughly 660 feet to the nearest foot.
what is trigonometry?Trigonometry is the field of mathematics that explores the relationship amongst triangle side angles. The issue first originated in the Hellenistic era, during the third century BC, as a consequence of the usage of geometry in astrological investigations. The subject of algebra known as exact techniques is concerned with certain trigonometric factors and their practical benefits in computations. Trigonometry has six commonly used trigonometric functions. Their separate names and initials are sine, arc, tangent, coordinate geometry, secant, and cosecant (csc). Basic arithmetic is the study of geometric properties, specifically those of trigonometry. As a result, geometry is the analysis of the properties of all shapes.
tan(84.7°) = h/x (since the tower is leaning at an angle of 84.7°, the opposite side is "h," and the neighbouring side is "x").
tan(47.4°) = h/(185+x) (Since the elevation angle to the top of the tower is 47.4°, the opposing side is "h," and the neighbouring side is 185+x.)
first equation yields h = x*tan(84.7°), which we can substitute for h in the second equation:
x*tan(84.7°)/(185+x) = tan(47.4°)
xtan(84.7°) = (185+x)tan(47.4°).
x(tan(84.7°) - tan(47.4°) = 185tan(47.4°)
x = 185*tan(47.4°)/(tan(84.7°) minus tan(47.4°))
659.5 feet = h*tan(84.7°) (rounded to the nearest tenth).
As a result, the distance from the tower's base to its peak is roughly 660 feet to the nearest foot.
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It is possible to find the rate of change for an interval between two points of a function by finding the slope between the points. Use the
graph to find the y-value for each x-value. Then find the rate of change for each interval.
(0.2) and (1)
(0.2) and (1.blank)
The rate of change between the points (0.2) and (1) is 6.25.
What is rate of change?Rate of change is a measure of how quickly the value of a function is increasing or decreasing at a given point. It is calculated by taking the difference between two points on the function and dividing it by the change in the independent variable, usually time. This allows us to measure how quickly the function is changing over time. Rate of change is a key concept in calculus and can help us to understand how different functions behave.
To find the rate of change between the two points (0.2) and (1), we must first find the y-values of each x-value. On the graph, this is done by drawing a vertical line from the x-value to the graph, and then drawing a horizontal line from that point to determine the y-value. Thus, the y-value at x-value 0.2 is 3, while the y-value at x-value 1 is 8.
Now we can use the slope formula to find the rate of change between the two points. The slope formula is given as (y2 - y1) / (x2 - x1). Plugging in the values we got from the graph yields (8 - 3) / (1 - 0.2) = 5 / 0.8 = 6.25.
Therefore, the rate of change between the points (0.2) and (1) is 6.25.
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which one is it
A
B
C
D
Answer:
Step-by-step explanation:
If you substitute the values x = −3 and y = 2 into the first equation, you get a false statement: 2(2) = −3 + 9. To solve this system, try rewriting the first equation as x = 2y − 8. Then substitute 2y − 8 in for x in the second equation, and solve for y. The correct answer is x = −2, y = 3.
