Resonance causes the amplitude of vibrations to increase.
This statement is correct because resonance is the phenomenon that occurs when an object is vibrating at its natural frequency and it is in phase with an external force, such as a sound wave. When this happens, the amplitude of the vibrations increases and the object can reach a large amplitude of oscillation. Resonance can be observed in many physical systems such as bridges, musical instruments, mechanical systems and electrical circuits.
I hope this helps :)
determine the total number of roots of eat polynomial function using the factored form
As long as there are x powers, there are an equal number of roots. The polynomial in this instance has 4 roots because there are 4 x's.
When given a polynomial's factored form, how do you discover its roots?The polynomial equation can be solved by locating its roots. Set each factor to 0 and then solve for x to obtain P(x) = 0. Make use of factoring to solve the polynomial equation. 0 should be entered for each factor. 2x4 = 0; (x - 6) = 0; (x + 1) = 0 For x, find the solution.
Though there are only 2 true roots, it is significant to notice this. Since the integer I appears in both of the last two roots of this equation, they are not real.
As long as there are x powers, there are an equal number of roots. The polynomial in this instance has 4 roots because there are 4 x's.
The complete question is,
Utilizing the factored form, ascertain the overall quantity of roots for each polynomial function. f (x) = (x + 2)(x - 1) (x - 1) [x - (4 + 3i)] [x - (4 - 3i)].
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Two teams A & B participated in a competition. 2 points were awarded for every goal and 1 point is deducted as a penalty for foul. If team A did 13 goals and 5 penalties and team and by how much? B scored 18 goals and 12 penalties, who won the competition.
Team A won the competition by a narrow margin of 13 points.
What is points in math?Points in math are locations in the coordinate plane that can be described by an ordered pair of numbers. Points are often used to graph equations, draw diagrams, and find the solution to problems. Points can also be used to measure distances, angles, and other geometric objects. Points are an essential part of geometry, algebra, and other math topics.
Team A scored 13 goals and incurred 5 penalties, giving them a total of 8 points. On the other hand, team B scored 18 goals and incurred 12 penalties, giving them a total of 6 points. Therefore, team A won by a difference of 8-6=2 points.
It is important to note that any competition should be based upon fair play and sportsmanship. Foul play should not be allowed and all teams should be equally and fairly judged. Furthermore, proper rules and regulations should be implemented to ensure a fair and level playing field. The competition between teams A and B was a good example of how a competition should be conducted in a fair manner.
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Drag each graph to show if the systemn of linear equations it represents will have no
solutions, one solution, or infinitely many solutions.
No Solutions
One Solution
Infinitely many solutions
The number of solutions for the graphs are - for graph 1 and graph 4 there are infinite solutions, for graph 3 there is no solution and unique solution for graph 2.
What is the equation for a straight line?
A straight line can be written in the form of equation as, y = mx + c. Two straight lines intersect each other only at one point. When two straight lines are parallel to each other the angle between them is zero.
The graphs of a pair of lines for different cases are given.
Since, two equations have a unique solution for intersecting lines, infinite solutions for coinciding lines and no solution for parallel lines.
Given graphs can be considered as per the above rule as follows -
For graph 1 -
The pair of lines are coinciding. So, it has infinitely many solutions.
For graph 2 -
The pair of lines are intersecting each other. So it has a unique solution.
For graph 3 -
The pair of lines are parallel to each other. So, it has no solutions.
For graph 4 -
The pair of lines are coinciding. So, it has infinitely many solutions.
Therefore, the number of solutions for the given graphs are given as infinitely many solutions, unique solution, no solutions, and infinitely many solutions respectively.
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What is the graph of inverse relation?
If an equation describes the relation in the variables x and y, the equation of the inverse relation is obtained by replacing every x in the equation with y and every y in the equation with x. Their graphs are mirror images over the line of reflection y = x.
Now, According to the question:
What is graph of inverse relation?
The inverse of a relation is a relation obtained by interchanging or swapping the elements or coordinates of each ordered pair in the relation. Inverse relation in sets can be defined using the ordered pairs. The domain and range of an inverse relation can be written by swapping the domain and range of that relation.
If an equation describes the relation in the variables x and y, the equation of the inverse relation is obtained by replacing every x in the equation with y and every y in the equation with x. Their graphs are mirror images over the line of reflection y = x.
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options.
m∠5 + m∠3 = m∠4
m∠3 + m∠4 + m∠5 = 180°
m∠5 + m∠6 =180°
m∠2 + m∠3 = m∠6
m∠2 + m∠3 + m∠5 = 180°
Answer:
a d e
Step-by-step explanation:
How do you construct a 15 degree angle without a protractor?
A 15 degree angle can be created by using a compass or a straightedge.
1) Using a compass: Set the compass to the length of the angle's ray, and draw an arc that intersects the angle's vertex. Repeat the process with a second arc, and the point of intersection between the two arcs is the endpoint of the angle's ray.
2) Using a straightedge and 30-60-90 triangles: You can use a straightedge to bisect a 30-degree angle, then use the bisector to construct a 15-degree angle.
These are just a few ways to construct a 15-degree angle without a protractor, and there might be other methods as well.
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How do you graph a quadratic form?
The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.
The graph of quadratic functions is a technique to study the nature of the quadratic functions graphically. The shape of the parabola is determined by the coefficient 'a' of the quadratic function f(x) = ax2 + bx + c, where a, b, c are real numbers and a ≠ 0.
the vertex of a quadratic function is. [tex]f(x)=a(x-h)^2+k, where (h,k)[/tex] is the vertex of parabola. When a>0 then function will be open upward if a<0 then function will be opens downward.
Steps to plot graph of quadratic function.
a[tex]x^2[/tex] is imply a vertical scaling of the parabola, if a<0 the parabola will also flip its mouth from the positive to negative side.
[tex]a(x+\frac{b}{2a} )^2[/tex] This is a horizontal shift of magnitude |[tex]\frac{b}{2a}[/tex]| units. The direction of the shift will be decided by the sign of b/2a. The new vertex of the parabola will be at (-b/2a,0).
This transformation is a vertical shift of magnitude |[tex]\frac{D}{4a}[/tex]| units. The direction of the shift will be decided by the sign of [tex]\frac{D}{4a}[/tex]. The final vertex of the parabola will be at ([tex]\frac{-b}{2a} ,\frac{-D}{4a}[/tex]).
So, The Graph of quadratic functions gives parabolas that are U-shaped, and wide or narrow depending upon the coefficients of the function.
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The population P (in thousands) of a certain city from 2000 through 2014 can be modeled by
P = 160.2ekt,
where t represents the year, with
t = 0
corresponding to 2000. In 2006, the population of the city was about 165,050.
The value of {k} is equivalent to k = 0.51 {approx.}.
What are functions?In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y.The set X is called the domain of the function and the set Y is called the codomain of the function.Functions whose domain are the non - negative integers, known as sequences, are often defined by recurrence relations.Given a function as [tex]${\displaystyle f\colon X\to Y}[/tex] its graph is, formally, the set -[tex]${\displaystyle G=\{(x,f(x))\mid x\in X\}.}[/tex]
Given is the population {P} (in thousands) of a certain city from 2000 through 2014 can be modeled by {P} = 160.2[tex]$e^{kt}[/tex], where {t} represents the year, with {t} = 0 corresponding to 2000. In 2006, the population of the city was about 165,050.
The exponential function is a mathematical function denoted by : f(x) = eˣ.We have the function -
{P} = 160.2[tex]$e^{kt}[/tex]
For 2006, t = 6 years. So -
165050 = 160.2[tex]$e^{6k}[/tex]
[tex]$e^{6k}[/tex] = (165050)/(160)
[tex]$e^{6k}[/tex] = (16505)/(16)
[tex]$e^{6k}[/tex] = 1,031.5625
log([tex]$e^{6k}[/tex]) = log(1031.5625)
6k = 3.01349554601
k = (3.01349554601/6)
k = 0.5022492576683333
k = 0.51 {approx.}
Therefore, the value of {k} is equivalent to k = 0.51 {approx.}.
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Can someone help me, please? 10 POINTS
The triangle with the side lengths 2 ft, 3ft, and 5 ft is not the right triangle.
What are Pythagorean triplets?In a right-angled triangle, its sides, such as hypotenuse, and perpendicular, and the base is Pythagorean triplets.
Here,
Given sides,
2ft, 3ft, 5ft
Now,
perpendicular p = 2 ft
base b = 3 ft
hypotenuse h = 5 ft
According to Pythagoras' theorem
h² = p² + b²
5² = 2² + 3²
25 ≠ 13
Thus, the triangle with the side lengths 2 ft, 3ft, and 5 ft is not a right triangle.
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Please help me i don't understand this
The best describe Maria's solution to the equation is Maria incorrectly applied the associative property in going from the line(1) to line(2).
What is associative property?
Rearranging the parenthesis in an expression will not change the outcome since some binary operations in mathematics have the associative feature. Associativity is a legitimate rule of replacement for expressions in logical proofs in propositional logic.
Here, we have
Given: The equation -2(3x - 5) = 40
-2(3x - 5) = 40
-6x + 10 = 40
-6x = 40 - 10
-6x = 30
x = -5
The solution to the equation is -5 instead of -25/3.
Hence, the best describe Maria's solution to the equation is Maria incorrectly applied the associative property in going from the line(1) to line(2).
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A chef used 0.28 pounds of flour to make a batch of chicken nuggets. If he has used 1/7th of the pack of flour, what is the weight of the pack?
(PLEASE SHOW WORK)
The weight of the flour pack used by the chef to make chicken nuggets is 0.04 pounds.
what is the weight of the pack?Quantity of flour used to make chicken nuggets by the chef = 0.28 pounds
If the chef used 1/7th of the pack of flour;
Quantity of flour used by the chef = 1/7 of 0.28 pounds
= 1/7 × 0.28
= 0.04 pounds
Therefore, the chef used 0.04 poundsof the flour pack
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HELP IM ON A TIMER WILL GIVE BRAINLISTEST AND 5 STAR REVIEW
Answer:
Step-by-step explanation:
angle ACD is corresponding to the angle BCE, hence the line DE is congruent to line AB
Which of the following types of polynomials is 2x3 − 3x2 x 5?
The polynomial 2x^3 - 3x^2 x 5 is known as a cubic polynomial.
A cubic polynomial is a polynomial of degree 3, or a polynomial with the highest power of x being 3. This means that the formula for a cubic polynomial can be written as ax^3 + bx^2 + cx + d, where a, b, c, and d are all constants.
In the example of 2x^3 - 3x^2 x 5, the coefficients are 2, -3, 0, and 5 respectively. To calculate the value of the cubic polynomial, one must substitute a value of x into the equation. For example, if x = 2, then the equation would be 2(2^3) - 3(2^2) x 5, which simplifies to 32 - 24 x 5, or 32 - 120, which equals -88.
Therefore, when x = 2, the polynomial 2x^3 - 3x^2 x 5 equals -88. This can be further verified by graphing the polynomial and observing the point (2, -88).
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Complete question: What type of polynomial is 2x3 − 3x2 x 5?
Let's look at a bunch of equations in Desmos to make predictions and patterns.
Now, predict what these will look like...
y = 10(.5)*
y = 16(3) *
y = - 4(3)*
In this activity, students write and solve a system of two linear equations to explore the numerical and graphical meaning of "solution.
What is linear equations?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.Linear Equation Definition: A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.There are linear equations in one variable and linear equations in two variables.To learn more about algebraic equation refer to:
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14 in
Use the Pythagorean
Theorem to determine if
this is a right triangle.
12 in
15 in
A Yes
B No
2
Using the Pythagorean Theorem we can see that, the sides 9 in, 12 in and 15 in can form a right angle triangle.
In the given question, using the Pythagorean Theorem we have to determine if this is a right triangle.
The given sides are 12 in and 15 in.
A key concept in mathematics is the Pythagorean Theorem, which describes the relationship between the sides of a right-angled triangle.
To check the given sides form a right triangle or not. We have to check that the sum of the square of the sides given a proper square root.
We can also check using the triplet. As we know that 3, 4 and 5 is the triplet that can form a right angle triangle.
The multiple of these triplet also can from a right angle triangle.
So a right angle triangle can be formed by 9 in, 12 in and 15 in.
Using the Pythagorean theorem;
[tex]15^2 = 9^2+12^2[/tex]
225 = 81 + 144
225 = 225
Hence, Using the Pythagorean Theorem we can see that, the sides 9 in, 12 in and 15 in can form a right angle triangle.
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The polynomial is missing the coefficient of the third and last terms.
8x³ - 144x²y + __xy²-__y^3
In order to be factorable using the binomial theorem, the coefficient of xy² is
and the coefficient of y3 is __
Answer:
coefficient of xy^2 is : 864 and that of y^3 is 1728
Step-by-step explanation:
Using binomial theorem,
1st term is 1 (ax)^3 = 8x^3 from which a = 2
2nd term is 3(ax)^2(by) = -144x^2y from which b = -12
3rd term is 3(ax)(by)^2 = 3(2x)(-12y)^2 = 864
4th term is 1(by)^3 = 1(-12y)^3 = -1728y^3
What are the vertex focus and directrix of the parabola with equation y=x^2-6x+15.
The vertex focus of the parabola is (3,15) and the directrix is x=3.
1. Rewrite the equation in the form y = a(x - h)^2 + k
y = x^2 - 6x + 15
y = 1(x - 3)^2 + 15
2. The vertex focus is (h, k) = (3, 15)
3. The directrix is x = h = 3
By rewriting the equation in the form of y = a(x - h)^2 + k, we can find the vertex focus and directrix of the parabola. The vertex focus of a parabola is the point at which the graph changes direction, and is equal to (h, k). The directrix is the line at which the vertex focus is located, and is equal to x = h. For this equation, h = 3 and k = 15, so the vertex focus is (3, 15) and the directrix is x = 3.
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What is the value of log 1 to base 7?
0 is the value of log 1 to base 7.
The inverse of an exponential function is named a logarithm. That means the logarithm of a number y to the base b is the exponent to which b must be raised, to produce y. For example, since 100 = 10², the logarithm base 10 of 100 is 2, or log₁₀ (100) = 2. The logarithm of x to base a is denoted as logₐ (x), or without parentheses, logₐ x, or even without the explicit base, log x.
As we know,
aˣ = N ⇔ [tex]log_{a}N[/tex] = x
Let log₇1 = x
⇒7ˣ = 1
⇒7⁰ = 1
Equating powers on both sides, we get
x = 0
⇒log₇1 = 0
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The door to Sophia’s room is 0. 9 m wide and 2. 06 m tall in order to buy paint To paint it she needs to know the area of one side of the door what is the area of one side of the door
The area of the Sophia's room door from one side with the given dimensions is equal to 1.854 square meters.
As given in the question,
Dimensions of the door of Sophia's room is given by :
Width of the door = 0.9m
Door Height = 2.06m
Doors are always in rectangular shape.
Area of the one side door = Length × Width
Substitute the values we get,
⇒ Area of the one side door = 2.06 × 0.9
⇒ Area of the one side door = 1.854 square meters
Therefore, the area of the one side door of the Sophia's room is equal to 1.854 square meters.
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I need help ASAP 15 POINTS!!!!!
Therefore , the solution of the given problem of function comes out to be x =15/2 and x = -4/3.
What is meant by the word function?A science called mathematics studies numbers, their variants, mathematical and the local structures, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function variable . A function is a collection of inputs that together produce a single, recognisable output by each input.
Here,
Given :
=> 2x = 15x²
=> 2 = 15x
=> x =15/2
=> -6x =8x²
=> -6 = 8x
=>x = -4/3
thus , x =15/2 and x=-4/3
Therefore , the solution of the given problem of function comes out to be x =15/2 and x = -4/3.
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at a depth of x metres, the temperature of the water in an ocean is T°C. At depths below 900 metres, T is inversely proportional to x. T is given by T=4500 divided by x. Work out the difference in the temperature of the water at a depth of 1200 meters and the temperature of the water at a depth of 2500 meters
Step-by-step explanation:
the temperature of the water is always inversely proportional to the depth x. the larger the depth the lower the temperature.
just the rate of change changes at certain levels.
so, below 900 meters the relation is defined as
T = 4500/x
at 1200 m this means
T = 4500/1200 = 45/12 = 15/4 = 3.75°C
at 2500 m this means
T = 4500/2500 = 45/25 = 9/5 = 1.8°C
the difference in temperature at these 2 levels is
3.75 - 1.8 = 1.95°C
Morty wants to buy candy from the candy shop. The candy is buy...
any 5 for $3.00 or
any 10 for $6.00.
Which equation below best represents the relationship between the number of candy purchased, c, and the cost T?
The equation which represents the relationship between the number of candy purchased, c, and the cost T is,
⇒ T = 3/5c - 3
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
Morty wants to buy candy from the candy shop.
The candy is buy any 5 for $3.00 or any 10 for $6.00.
Now, Find the equation which represents the relationship between the number of candy purchased, c, and the cost T as;
Let two points for candy and its cost as;
⇒ (5, $3.00) and (10, $6.00)
Hence, The equation is,
⇒ T = (6 - 3) / (10 - 5) (c - 5)
⇒ T = 3/5 (c - 5)
⇒ T = 3/5c - 3
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The table shows the cost of several bunches of bananas. What equation can be used to represent the cost C of a bunch that weights P pounds?
From the table that shows the cost of several bunches of bananas , the equation that is used to represent the cost "C" for "p" pounds is [tex]C=0.42\times p[/tex].
For 2.5 pounds of bunches of bananas the cost is = $1.05 ;
and the cost for 3.5 pounds of bananas , the cost is $1.47 ;
we can calculate the rate of 1 pound of bananas as : [tex]\frac{1.47-1.05}{3.5-2.5}[/tex] ;
On simplifying the above fraction ,
we get ;
⇒ 0.42 ;
the per pound cost for bananas is $0.42 ;
let the number of pounds of bananas be = p ; and
let the cost for p pounds of bananas be = C ;
Therefore, the equation for cost "C" can be represented as : [tex]C=0.42\times p[/tex].
The given question is incomplete , the complete question is
The table shows the cost of several bunches of bananas. What equation can be used to represent the cost C of a bunch that weights P pounds ?
Number of pounds 2.5 3.5 4 4.5
Cost($) 1.05 1.47 1.68 1.89 .
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How do you simplify y=23x+68?
The simplest form of the equation, y = 23x + 68, is the same equation of y = 23x + 68, as this is the simplest form.
How to simplify the equation ?y = 23x + 68 is a linear equation that it in the slope - intercept form which means that there is no need to simplify it further.
The slope - intercept form is:
y = mx + b
Where:
m = slope of the line
b = y - intercept of the line
The equation shows that the slope is 23 and that the y - intercept is 68. This means therefore , that the equation is as simple as it can be.
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Mr.Elms Can run 20 miles per hour; but he can only run for 4 hours. What’s the domain and range?
Mr. Elms can only run for four hours, his range and domain are each set at 20 miles per hour.
what is domain ?A function's acceptable range of values is referred to as its domain. These numbers serve as representations of the x-values of a function like f. (x). The set of potential values that a function can be applied to is known as its domain. When the x value is inserted, the method returns the value that is contained in this set. A function's definition is Y = f, where x is the independent variable and y is the dependent variable (x). If it is possible to successfully use a value of x to generate a single value of y using the value of x, that value of x is said to be in the domain of the function.
given
Graphs can be used as a second method to define the domain and range of functions.
A graph's domain is the entire set of input values represented on the x-axis because the term "domain" refers to the set of potential input values. The various output values are displayed on the y-axis and make up the range.
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Really need help asap on this one
a) 7x
b) 2a + 6b
c) -3b + 7d + 3bd
d) 7ab - 2ac - c
e) 16a + 6
f) 26x - 2
g) 4b + 1
h) -5j - 10
i) 2g + 7
Target sells skateboards for $35. To make a profit in the Spring and Summer months,
Target increases the price with a 42% markup. How much is the markup?
The markup price of the skateboards is equal to $49.7.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that Target sells skateboards for $35. To make a profit in the Spring and Summer months, Target increases the price with a 42% markup.
The markup price will be calculated as,
Markup price = $35 x 1.42
Markup price = $49.7
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What is distance Class 4?
The physical distance they need to travel to get to school, or the distance they need to measure in math class.
Distance for a student of Class 4 would likely refer to the physical distance they need to travel to get to school, or the distance they need to measure in math class. Without more context, it is difficult to provide a specific answer.
In mathematics, distance refers to the measurement of the difference between two points in a space or a geometric figure. It can be represented by a numerical value and is often used to determine the shortest path between two points. The most common distance formula used in Euclidean geometry is the distance between two points (x1, y1) and (x2, y2) is the square root of ((x2 - x1)^2 + (y2 - y1)^2). This is known as the Euclidean distance.
Therefore, The physical distance they need to travel to get to school, or the distance they need to measure in math class.
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if you are dealt 5 cards from a 52-card deck, what is the probability of getting a three of a kind? please provide a decimal answer (e.g. 0.0034), with a leading zero.
The percentage takes at least one science or math course is 73%.
62% of the students take math
so,
n(m)=62
49% take science
n(s)=49
38% take both science and math
n(M∩S)=38
now, we can use union formula
n(M∪S)=n(M)+n(S) -n(M∩S)
now, we can plug values
and we get
n(M∪S)=62+49 -38
n(M∪S)=73
so,
the percentage takes at least one science or math course is 73%.
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what is the null hypothesis in words? group of answer choices the (population) mean amount of time reading and sending e-mails daily is greater than 60 minutes. the (population) mean amount of time reading and sending e-mails daily is equal to 60 minutes the (sample) mean amount of time reading and sending e-mails daily is equal to 60 minutes. the (sample) mean amount of time reading and sending e-mails daily is greater than 60 minutes.
The null hypothesis is a common statistical theory that contends that there is no statistically significant association between any two sets of a single observed variable.
The hypothesis suggests no two given sets make any significance meaning until and unless they are proven wrong.
As given in the example,
The group of answer choices the (population) mean amount of time reading and sending e-mails daily is greater than 60 minutes and the (population) mean amount of time reading and sending e-mails daily is equal to 60 minutes.
You can see in one set the amount of reading and sending e-mails is more than 60 minutes and in other one the amount of time reading and sending e-mails is equal to 60 minutes which doesn't make any sense if you consider them both in a single set of information.
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