To see if the two triangles are similar, you first have to get them both in the same direction. You do this by rotating (turning) one shape to align with the other. Such a transformation is called a rotation.
Geometry transformations are movements of two-dimensional shapes in two dimensions, or within their plane. Like restricted game pieces on a game board, you can move two-dimensional shapes in only three ways:
Rotation -- Shapes are rotated or turned around an axisReflection -- Shapes are flipped across an imaginary line to make mirror imagesTranslation -- Shapes are slid across the planeTransform one of the triangles such that the orientation of the triangles is the same.
Identify the corresponding sides of the triangles and write each set of corresponding sides as a ratio. If the ratios of the side lengths are the same for all 3 sides, then the triangles are similar.
Hence, by performing two rigid motions, we can prove the congruence between these two triangles. Now once the triangles are superimposed, we can identify the corresponding parts by checking which side and angle of the initial triangle is superimposed on the transformed triangle.
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Question : A good practice when using credit cards is to routinely
A: take advantage of major sales.
B: use one credit card to pay debt on another credit card.
C: pay the complete balance each month.
D: accept all pre-approved credit card offers.
Answer: C: pay the complete balance each month
Math work-related tasks
Francine can make a dress in 18 hours.Her mother can make a dress in 6 hours. They decide to work together . How long will it take them to make a dress ? Choose from the answers below .
A.4 hours
B. 4 hours and 30 minutes
C. 5 hours
D. 12 hours
Answer:
D. 12 hours
Step-by-step explanation:
I am guessing that they want you to find the average time together, or the mean.
Add 18 hours and 6 hours together to get 24 hours.
To get the average, you have to divide the total hours by the amount people involved.
Since there are 2 groups (2 people) that have an outcome of 18 hours and 6 hours, 24 hours/2 people is a 12 hour average.
1: The drama department sold a total of 360 tickets to there Friday and Saturday night shows. They Sold three times as many tickets for Saturday's show than for Fridays show.
A: Write a system of equations to represent this scenario
B: How many tickets were sold for Friday, and Saturday? Is there more than one solution?
C: Graph the system of equations on a coordinate plane. Label the axes.
D: Justify algebraically that your solution is correct.
(A) Given question can be represented in the system of linear equations as x + y = 360,
y =3x
(B) 90 tickets were sold on Friday and 270 tickets were sold on Saturday.
There will be only one solution to this question.
(C) We have drawn the graph for the solution.
(D) We have justified our answers by using the substitution method.
What is a linear equation in two variables?
An equation is said to be a linear equation in two variables if it is written in the form of ax + by + c=0, where a, b & c are real numbers and the coefficients of x and y, i.e a and b respectively, are not equal to zero.
Let x number of tickets sold on Friday and y number of tickets sold on Saturday.
By using the given condition,
x + y = 360 ----------(I)
y =3x -------(II)
Put y = 3x in equation (I), we get
x + 3x = 360
4x = 360
x = 90
Now put x = 90 in equation (I), and we get
90 + y = 360
y = 270
Hence, 90 tickets were sold on Friday and 270 tickets were sold on Saturday.
There will be only one solution to this question.
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Please help with this geometry problem and explain it step by step
Answer:
x = 8
Step-by-step explanation:
In a triangle, if two angles are congruent, then the opposite sides are congruent.
Since you are told that angles A and C are congruent, then their opposite sides, BC and AB are congruent.
That makes BC = AB.
3x - 3 = 2x + 5
x = 8
How do you read X sets?
The elements in sets are separated by commas so they can be read easily.
Define set builder notation.Instead of describing the constituents of a set, a set-builder notation describes them. The elements are listed, for instance, in the set {5, 6, 7, 8, 9}. We interpret the collection of all x such that x is a counting number between 4 and 10 as the collection of all x.
Define set.In mathematics, a set is a logically arranged group of items that can be represented in either set-builder or roster form. Sets are typically denoted by curly brackets {}; for instance, A = {1, 2, 3, 4} is a set.
The sequence of elements (separated by commas) between the curly braces " and "in mathematics form an unordered group of elements known as a set. For instance, the domesticated animals {cat, cow, dog} , the odd numbers {1, 3, 5, 7, 9} and the alphabets {a, b, c, d, e} are all sets. So they can be read or interpreted easily.
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What is the sample space of rolling a 6 sided number cube?
The sample space of rolling a 6 sided number cube is the set of all possible outcomes of rolling the number cube. The sample space for a 6 sided number cube is the set of numbers 1,2,3,4,5, and 6.
When rolling a 6 sided number cube, the sample space is the set of all possible outcomes, which are the numbers from 1 to 6. This means that the sample space includes each of the six numbers, with no bias towards any particular number. Each of the six numbers has an equal chance of being obtained when rolling the number cube.
The sample space of a 6 sided number cube is also known as a discrete sample space, since all of the possible outcomes are predetermined and known. The sample space of a 6 sided number cube is finite and can be easily calculated by listing all the possible outcomes. Since there are 6 possible outcomes, the sample space consists of 6 elements.
The sample space of a 6 sided number cube can be easily visualized by imagining a six-sided die being rolled and each side being labeled with a number from 1 to 6. This demonstrates that the sample space of a 6 sided number cube is a discrete sample space, and each of the six numbers has an equal chance of being obtained.
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Help with special right triangles rounding
Answer:
9.8 units-----------------------------------
Hypotenuse of an isosceles triangle is √2 times the leg:
x = √12 × √2 = √24 = 4√6 ≈ 9.8 units (rounded to the nearest tenths)How do you find the inverse of a 2x2 matrix on a calculator?
We find the inverse of a 2x2 matrix on a calculator using formula
A⁻¹ = Adjoint of A / determinant of A
Where, adjoint of A = [ d -b]
[-c a]
and, determinant of A = 1/ ad - bc
What is inverse of a 2X2 matrix?A real number's inverse is a number that, when multiplied by the inputted number, yields the multiplicative identity, which is 1, or 1. A matrix's inverse, represented by A⁻¹ in matrices, is a matrix that, when multiplied by A, yields the identity matrix I, or A.A⁻¹ = A⁻¹.A = I
The formula (adj A)/(det A) can be used to determine the inverse of a matrix A, where "adj A" stands for "adjoint of A" and "det A" for "determinant of A".
Let A is a 2x2 matrix such that, A = [a b]
[c d]
then, A⁻¹ = Adjoint of A / determinant of A
Where, adjoint of A = [ d -b]
[-c a]
and, determinant of A = 1/ ad - bc
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The longest ladder on the fire truck reaches 95 feet. A building has 20 stories, and each story is 18 feet high. what is the highest story that the ladder can reach?
(A) 5th story
(B) 6th story
(C) 10th story
(D) 18th story
(Somebody please help me answer this question I rlly need help with this!)
Answer:
Rounding down to the nearest whole number, we get 5 stories. The correct answer is, therefore (A) the 5th story.
Step-by-step explanation:
To solve this problem, we need to find the number of stories the ladder can reach by dividing the length of the ladder by the height of each story.
The longest ladder on the fire truck reaches 95 feet, and each story is 18 feet high, so the highest story that the ladder can reach is:
95 feet / 18 feet/story = <<95/18=5.28>>5.28 stories
10. A new bank customer with $3,000
a money market account. The
wants to open
simple interest rate of 1.1%.
bank is offering a
a. How much interest will the customer earn in
20 years?
b. What will be the account balance after
20 years?
Answer:
a. $660
b. $3660
Step-by-step explanation:
a. 1.1% = 1 years
22% = 20 years
22% = 0.22
Take 3000 times 0.22 = $660
So, they will earn $660 interest in 20 years
b. $3000 + $660 = $3660
$3660 is their account balance after 20 years
According to the rational root theorem, the following are potential roots of f(x) = 6x4 + 5x3 – 33x2 – 12x + 20. negative five-halves, –2, 1, ten-thirds which is an actual root of f(x)?
As per the rational root theorem, the actual root of the polynomial is - 5/2
The term polynomial refers the algebraic expression in which the exponents of all variables should be a whole number
Here we have given that f(x) = 6x⁴ + 5x³ – 33x² – 12x + 20. and we need to find which is an actual root of f(x).
In order to find the root for the polynomial we have to apply each value as the replacement of x in the polynomial.
And then we have to find in which one makes the polynomial result as zero.
First we have to take the value of x as -5/2, then the polynomial equation be like,
Here we have to substitute x=-5/2, then we get
=> f(-5/2) = 6(-5/2)⁴ + 5(-5/2)³ - 33(-5/2)² - 12(-5/2) + 20
=> f(-5/2) = 6(625/16)-5(125/8)-33(25/4)+30+20
when we simplify this one then we get,
=> f(-5/2)=(1,875-625-1,650+400)/8
=> f(-5/2)=0/8
Here we know that if we zero by any number we get the result as zero.
Therefore, f(-5/2)=0 then x=-5/2 is a root of f(x)
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Answer:
its A
Step-by-step explanation:
Just took the test
what is the sign of f on -5/2 < x < 4
Answer:
f is negative
I almost thought that this had no solutions, but I'm not sure, could anyone help me on this? I would deeply appreciate it!
Consider the equation 2x = 3x. Does this equation have one solution, no solution, or infinite solutions? Explain your reasoning
Answer:
one solution because when you isolate the x terms:
2x-3x=0 and you combine like terms
-x=0
and divide by negitive one because -x is (-1)(x)
you get x=0
Step-by-step explanation:
Answer:
One solution
Step-by-step explanation:
It appears this problem has no solution, buttt let's look closer.
2x and 3x are like terms, meaning they can be added and subtracted because they both have x!
So let's combine these like terms and see what we get...
2x = 3x
0 = 3x -2x
0 = 1x
x = 0 / 1
x = 0
The only solution is 0! No other number is possible.
what values for m and n that make this number sentence true: 1/2+9/10+m+n=2.
1/2+9/10+m+n=2 is true when m and n have values { (m, n) : m = 3/5 - n, ∀ n and m ∈ R }.
What is number?
An arithmetic value known as a number is used to calculate and represent a quantity.
Given, 1/2+9/10+m+n=2
m+ n = 2 - 1/2 - 9/10
m+ n = 3/5
m = 3/5 - n
So, If n= 0, m = 3/5
Hence, we can define as { (m, n) : m = 3/5 - n, ∀ n and m ∈ R }
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6 less than a number in algebraic expression
Answer:
Step-by-step explanation: Let x represent the number in the algebraic expression, then 6 less means the following:
x-6
What are the 3 parameters used in a for loop in Python?
Range with three parameters: start, end, step.
Now, According to the question:
What are the 3 loops in Python?
The three types of loop control statements are:
break statement.continue statement.pass statement.What are the three parameters in range in Python?
The range() function in Python works by taking three inputs as parameters which are start_value, stop_value, and step value. The range() function returns an immutable sequence of numbers starting from the start_value, and increments the values by the value given in the step_value, and stops at the stop_value.
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1)No regime de juros composto, encontre as taxas trimestral e anual equivalentes à taxa de 1,05% ao mês
2)Calcule a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês, nos períodos a seguir:
a)ao semestre;
b)ao ano.
alguém pode me ajudar a entender como fazer esses tipos de exercícios? estive tentando aprender a um tempo mas não to conseguindo e o livro não ajuda muito.
Answer:
Para encontrar a taxa trimestral equivalente à taxa de 1,05% ao mês, basta dividir a taxa mensal por 3, pois um trimestre é composto por 3 meses. Portanto, a taxa trimestral equivalente à taxa de 1,05% ao mês é de 1,05% / 3 = 0,35%.
Para encontrar a taxa anual equivalente à taxa de 1,05% ao mês, basta multiplicar a taxa mensal por 12, pois um ano é composto por 12 meses. Portanto, a taxa anual equivalente à taxa de 1,05% ao mês é de 1,05% x 12 = 12,6%.
2)a) Para calcular a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao semestre, basta multiplicar a taxa mensal por 6, pois um semestre é composto por 6 meses. Portanto, a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao semestre é de 1% x 6 = 6%.
b) Para calcular a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao ano, basta multiplicar a taxa mensal por 12, pois um ano é composto por 12 meses. Portanto, a taxa de juros compostos equivalente a uma taxa efetiva de 1% ao mês ao ano é de 1% x 12 = 12%.
For a certain oscillator the net force on the body with mass m is given by fx = -cx^3. One-quarter of a period is the time for the body to move from x=0 to x=A. Calculate this time and hence the period. Express your answer in terms of the variables A, m, and c.
The time period is T = √[(4π^2mA^2)/mw^2A^2].
In the given question, we have to calculate this time and hence the period.
By conservation of energy :
1/2*mw^2A^2 = 1/2*mv^2+1/2*mw^2x^2
V^2 = w^2(A^2−x^2)
V = w√(A^2-x^2)
dx/dt = w√(A^2-x^2)
[tex]\frac{dx}{\sqrt{A^2-x^2}}[/tex] = w*dt
[tex]\frac{dx}{A\sqrt{(1-(x/A)^2}}[/tex] =w*dt
put (x/A)^2 = v
dx/A=dv
[tex]\int_{0}^{1} \frac{dv}{\sqrt{1-v^2}} = \int_{t=Io}^{t=t}w\times dt[/tex]
[tex][sin^{-1}(1)-sin^{-1}0]=wt[/tex]
π/2=wt
t= π/2w
[∴w=2π/T]
t= πT/2*2* π
t=T/4
Where T is time period
F = -kx
a = -k/m*x
ma = -kx
a = -w^2x
(standard equation of S.H.H)
w = √(k/m)
T = 2π/w
T = 2π√(m/k)
[k = mw^2]
T = √[(4π^2mA^2)/mw^2A^2]
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What are the dimensions (in cm) of the enlarged picture?
A teacher is showing a picture on a screen.
The picture is 12cm by 8cm.The screen is 2.4m by 2m
The teacher enlarges the image on the screen so it is as big as possible without distorting its proportions.
Answer:
Below
Step-by-step explanation:
Picture is .12 x .08 m
2 m / .08 m = 25
2.4 m / .12 m = 20 <===== limiting factor ( 20 is less than 25)
so it would be 20 * (.12) X 20(.08) = 3.84 m^2
How do you find the height and area of an isosceles triangle?
To find the height of an isosceles triangle, we square the length of one of the equal sides and subtract the square of half the base, and the area can be easily calculated if the height and the base are known. Multiplying the height with the base and dividing it by 2, results in the area of the isosceles triangle.
isosceles triangle
an isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length.
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Calculate the perimeter of the irregular shape please show ur work Bc I have too
Answer:
34 cm
Step-by-step explanation:
the gap in the middle is 2 cm because 9 - ( 4 + 3 ) = 2
4 + 2 + 2 + 3 + 3 + 6 + 9 + 5 = 34
How do you find the largest and smallest number in an unsorted integer array Python?
There are 3 methods to find the largest and smallest number in an
unsorted integer array Python.
How do you find the largest and smallest number in an unsorted integer array Python?Method 1 : Using Iteration.Method 2 : Using Sort() function.Method 3 : Using max() and min() functionMethod 1:
Take a variable say mini to store the smallest element of the array and maxi to store the largest element.Set mini = arr[0] and maxi = arr[0]Check if(arr[i]<mini) then set mini = arr[i]Also check if(arr[i]>maxi) then set maxi = arr[i]After complete iteration print mini and maxi.Method 2:
Sort the array using inbuilt sort()functionSmallest element is at index 0 and largest is at index -1So, print(arr[0])And, print(arr[-1])Method 3:
Using inbuilt function min(arr) , it return smallest element of the array.Similarly max(arr) return the largest element of the array.There are 3 methods to find the largest and smallest number in an
unsorted integer array Python.
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How do you find the multiplicity of roots?
The multiplicity of a root of a polynomial can be determined by the factorization of the polynomial.
If a root is repeated multiple times, then this root is said to have a higher multiplicity. For example, if a polynomial has the form a(x-r)^2, then the multiplicity of root r is 2. This is because the polynomial can be written as a(x-r)(x-r), and the root r is repeated twice.
To calculate the multiplicity of a root, the polynomial must be factored into its linear factors. The multiplicity of each root is then equal to the power of the corresponding linear factor. For example, if a polynomial is factored into (x-r)^3(x-s), the multiplicity of root r is 3 and the multiplicity of root s is 1.
In general, if a polynomial is written in the form [tex]a*(x-r1)^k1*(x-r2)^k2*...*(x-rn)^kn[/tex], then the multiplicity of root ri is ki. Therefore, the multiplicity of the roots can be calculated by factoring the polynomial and finding the power of the linear factors.
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What is integration in simple words?
Regional economic integration has facilitated trade among neighbors while allowing nations to concentrate on issues pertinent to their stage of development. Four forms of regional economic integration are possible. Zone of unrestricted trade. The most basic form of economic cooperation is this one.
Worldwide integration of the markets. global integration of the economy. On the financial markets, the effects of globalization are being assessed. More than ever, people, companies, and sectors are linked. This facilitates linkages, which encourages specialization, innovation, and economic expansion.
These accords have made it possible for nations to trade successfully with one another today by removing trade and financial restrictions. actions taken to lower prices for consumers in the member countries of the bloc when tariffs are decreased
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please help me with this question it is urgent
Answer:
4 1/3, 4.337, 35/8, 4.44
Step-by-step explanation:
4.337, 4 1/3, 35/8, 4.44
4 1/3 = 13/3 = 4.333
35/8 = 4.375
So, the order from least to greatest is: 4 1/3, 4.337, 35/8, 4.44
Answer:
4 1/3, 4.337, 35/8, 4.44
Step-by-step explanation:
"order from least to greatest" means put the smallest first and each next one bigger and the biggest one last.
Change everything to decimals to compare.
A fraction bar is just a division symbol.
1/3 means 1÷3 which is .33333...
4 1/3 = 4.33333...
35/8 means 35÷8
= 4.375
Smallest is 4.333...
So 4 1/3 goes first.
Then 4.337 and next 35/8 (bc 4.375)
Last is biggest 4.44 so it goes last.
In order from least to geatest is:
4 1/3, 4.337, 35/8, 4.44
What is the example of linear inequality in two variables?
4x + 8y ≤ -24 is the example of linear inequality in two variables.
What is a linear inequality equation?Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.
The graph of a two-variable inequality is the set of points that describe all solutions to the inequality. The coordinate plane is split in half by a boundary line created by a linear inequality, with one-half representing the solutions to the inequality.
It's a line with a shaded side on one side to show which xy pairings are the inequality's solutions.
For example -
Let us take a equation, 4x + 8y ≤ -24
Now, solve the above equation in the form of slope-intercept.
4x + 8y ≤ -24
or, 8y ≤ - 4x - 24
or, y ≤ -(1/2)x - 3
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What is the factor of 2x³ 3x² 17x 30?
Therefore, the solution to this problem is (x - 2)(x + 3) are the factors of p(x) (2x - 5).
Examine the equation.An equation is a mathematical statement that is created by connecting two expressions using the equivalent sign. An example of an equation is 2x - 5 = 15. By resolving this equation, we may ascertain that the variable x has a value of 5.
Here,
Given, the polynomial in this case is 2x3 - 3x2 - 17x + 30.
It is necessary to factor the polynomial.
Let p(x) equal 2x3, 3x2, 17x, and 30.
P(xconstant )'s term is 30.
Factors of 30 are equal to 1, 2, 3, 5, 6, 10, 15, and 30.
Consider x = 2.
Replace x = 2 in p. (x),
2(2)³ - 3(2)² - 17(2) + 30 =p(2)
=> 2(8) - 34 - 3(4) + 30
= >16 - 16
= 0
So, x - 2 is a factor of 2x³ - 3x² - 17x + 30.
Now splitting the x² and x terms,
2x³ - 4x² + x² - 2x - 15x + 30= 2x³ - 3x² - 17x + 30
=> x(x - 2) - 15(x - 2) + 2x²(x - 2)
= > (x - 2) * (2x² + x - 15)
factoring 2[tex]x^{2}[/tex] + x - 15
= 2[tex]x^{2}[/tex] + 6x - 5x - 15
= - 5(x + 3) + 2x(x + 3)
= (x + 3)(2x - 5)
Therefore, the solution to this problem is (x - 2)(x + 3) are the factors of p(x) (2x - 5).
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How do you represent three consecutive odd integers?
You represent three consecutive odd integers with x, x + 2 and x + 4
How to determine the representation of odd integersFrom the question, we have the following parameters that can be used in our computation:
Three consecutive odd integers
As a general rule
Odd integers are integers that cannot be divided by 2
Consecutive odd integers have a difference of 2
This means that the three consecutive odd integers are
x, x + 2 and x + 4
Where the least of the integers is x
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Which of these is, or describes, a geometric sequence with a common ratio of 2? select two answers that are correct.
A geometric sequence with a common ratio of 2 is E . F( n ) = 5 * 2^n where n = 1 , 2 , 3 .
Given :
A. -5 , -3 , -1 , 1 , 3
common ratio r = -3/-5
it is not the option
B . 0.0625 , 0.125 , 0.25 , 0.5 , 1
Common ratio :
r = 0.125 / 0.0625
= 0.5
it is not the option .
C. a[tex]_n[/tex] = 1/2 * [tex]a_{n-1}[/tex] where a1 = 2
a2 = 1/2 * a1
= 2/2
= 1
common ratio = 1/2
it is not the option
D. a[tex]_n[/tex] = [tex]a_{n-1}[/tex] + 2 where a1 = 3
a2 = a1 + 2
= 3 + 2
= 5
common ratio = 5/3
it is not the answer
E. F( n ) = 5 * 2^n where n = 1 , 2 , 3
a1 = 5 * 2^1
= 10
a2 = 5 * 2^2
= 20
common ratio = 20 / 10
r = 2
It is the correct option.
F. f ( n ) = n^2 where n = 1 , 2 , 3
a1 = 1^2
a2 = 2^2
= 4
common ratio = 4/1 = 4
it is not the correct option.
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Full question :
Which of these is, or describes, a geometric sequence with a common ratio of 2? select two answers that are correct.
A. -5 , -3 , -1 , 1 , 3
B . 0.0625 , 0.125 , 0.25 , 0.5 , 1
C. a[tex]_n[/tex] = 1/2 * [tex]a_{n-1}[/tex] where a1 = 2
D. a[tex]_n[/tex] = [tex]a_{n-1}[/tex] + 2 where a1 = 3
E. F( n ) = 5 * 2^n where n = 1 , 2 , 3
F. f ( n ) = n^2 where n = 1 , 2 , 3
a political scientist investigated the effect of political advertisements on the way that people voted in the presidential election. they want to do a hypothesis test to determine if political advertisements influenced the vote of less than 31% of all voters. the political scientist randomly surveyed 2509 voters and asked if political advertisements influenced the way the person voted. 709 said the advertisements did influence their vote. calculate the test statistic. round your final answer to two decimal places.
The probability of the influenced voters, if The political scientist randomly surveyed 2509 voters, 709 said the advertisements did influence their vote, is 0.283.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a value between 0 and 1.
Given:
The political scientist randomly surveyed 2509 voters, n = 2509,
709 said the advertisements did influence their vote, S = 709,
Calculate the probability of influenced voter as shown below,
[tex]Probability = S / n[/tex]
Probability = 709 / 2509
Probability = 0.283
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