The probability that a randomly chosen family with two or more children has children of the same gender is 1/2
To find the probability that a randomly chosen family with two or more children has children of the same gender, we can use the following information:
The probability of having a boy is 1/2 and the probability of having a girl is 1/2
The number of children is 2 or more
The sample space is all possible families with two or more children.
We can use the formula of conditional probability:
P(A|B) = P(A and B) / P(B)
Where A is the event of having children of the same gender, and B is the event of having two or more children.
We can use the formula of conditional probability to find the probability of having children of the same gender given that they have two or more children.
P(A and B) = P(A) * P(B|A)
Where P(A) is the probability of having children of the same gender, which is 1/2.
P(B|A) is the probability of having two or more children given that they have children of the same gender, which can be found using the formula of conditional probability as well.
P(B|A) = 1 - P(not B|A)
Where P(not B|A) is the probability of having less than two children given that they have children of the same gender.
Given that the family has children of the same gender, the probability of having less than two children is 0, because if the family has children of the same gender, it implies that the family has at least two children.
So, P(B|A) = 1- 0 = 1
Now we can substitute these values to the first equation:
P(A|B) = P(A) * P(B|A) / P(B) = (1/2) * 1 / P(B)
The only thing left to find is P(B) which is the probability of having two or more children. We don't have the exact number, but we know that the number of children is 2 or more, so P(B) is greater than 0.
We can say that P(A and B) = P(A) * P(B|A) = (1/2) * 1 = 1/2
Thus, the probability that a randomly chosen family with two or more children has children of the same gender is 1/2.
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a series of items that are associated with each other in a set
What are the term associated with set?
Sets.Universal Set.Venn Diagrams.Intersection of Sets.Union of Sets.Disjoint Sets.Difference of Sets.Sub Sets.Now, According to the question:
Let's know:
What are Sets?
A set is a well-defined collection of objects. Sets are named and represented using a capital letter. In the set theory, the elements that a set comprises can be any kind of thing: people, letters of the alphabet, numbers, shapes, variables, etc.
Any collection of objects (elements), which may be mathematical (e.g., numbers and functions) or not. A set is commonly represented as a list of all its members enclosed in braces. The intuitive idea of a set is probably even older than that of number.
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The table shows how many pizzas Antonio’s pizza shop can make in an hour. Complete the table. Write a function to represent the number of pizzas Antonio’s pizza shop can make in \displaystyle xx hours using function notation. What is a reasonable domain and range for the number of pizzas Anotonio’s can make? On your paper, create a coordinate plane and graph the relationship.
A function to represent the number of pizzas Antonio’s pizza shop can make in x hours using function notation is y = 13x + 5.
A reasonable domain and range for the number of pizzas Antonio’s can make include the following:
Domain = [1, 5].Range = [18, 85].How to write a function to represent the number of pizzas?In order to write a function to represent the number of pizzas Antonio’s pizza shop can make in x hours using function notation, we would have to determine the slope and y-intercept by using the point-slope form equation;
Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁) or y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
Where:
m represents the slope.x and y are the points.The table representing the number of pizzas Antonio’s pizza shop can make in x hours should be completed as follows;
Hours, x 1 2 3 4 5
# of pizzas, y 18 31 49 67 85
Next, we would determine the linear equation representing the line which passes through the points (1, 18) and (2, 31) by using the point-slope form as follows:
y - y₁ = (y₂ - y₁)/(x₂ - x₁)(x - x₁)
y - 18 = (31 - 18)/(2 - 1)(x - 1)
y - 18 = 13/1(x - 1)
y = 13x - 13 + 18
y = 13x + 5
Therefore, a reasonable domain and range for y = 13x + 5 is given by:
Domain = 1 ≤ x ≤ 5 or [1, 5]
Range = 18 ≤ y ≤ 85 or [18, 85]
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use f(x) = 1/2x and f-1(x) =2x to solve the problems
f(2) = __
f-1(1) = __
f-1(f(2)) = __
Answer:
f(2)=1/4 f-1(1)=2 f-1(f(2))=1/2Step-by-step explanation:
f(x)=1/2xf(2)=1/2(2)f(2)= 1/4f-1(x)=2xf-1(1)=2(1)f-1(1)=2f-1(f(x))= 2(1/2x)f-1(f(2))=2(1/2(2))f-1(f(2))=1/2absolute value 2xt5 =11
The solutions to the given absolute value equation as required in the task content are; x = 3 and x = -8.
What are the solutions for the value of x in the absolute value equation?It follows from the task content that the given absolute value equation which is to be solved for the value of x as required is; | 2x + 5 | = 11.
Hence, the equation can be solved as;
2x + 5 = 11
2x = 11 - 5; 2x = 6
x = 3
OR
2x + 5 = -11
2x = -11 - 5
2x = -16
x = -8.
Ultimately, the possible values of x which represents the solution to the absolute value equation are; x = 3 and x = -8.
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4. The navigator of a ship on a N44°E course sights a buoy with a bearing of S46°E. After the ship sails 15 km
along the same course, the navigator sights the same buoy with a bearing S12°E. Find the distance between the
ship and the buoy at the time of each sighting.
5. The angle of depression from a helicopter to its landing port is 64º. If the altitude of the helicopter is 1600
meters, find the direct distance from the helicopter to the landing port.
The correct answer for the given questions is 26.82 km and 780.372 km respectively.
4. To find the distance between the ship and the buoy at the time of each sighting, we can use the principle of non-collinearity of the ship, buoy, and observer.
Let x be the distance between the ship and the buoy at the time of the first sighting and y be the distance between the ship and the buoy at the time of the second sighting.
The angle of bearing from the ship to the buoy is S46°E, which is equivalent to (180 - 46) = 134° from the North.
The angle of bearing from the ship to the buoy at the second sighting is S12°E, which is equivalent to (180 - 12) = 168° from the North.
Therefore, the angle between the two lines of bearing is 168 - 134 = 34°.
Thus, 15/x= tan 34°
=> x= 15/tan 34°
=>x= 22.28 m
And, 15/y= sin 34°
=> y= 15/sin 34°
=> y= 26.82 km
5. To find the direct distance from the helicopter to the landing port, we can use the tangent function.
Let d be the direct distance from the helicopter to the landing port.
The angle of depression is 64°, and the altitude of the helicopter is 1600 meters.
tan(64) = 1600/d
d = 1600 / tan(64) = 780.372 km
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Write the expanded form of the expression. y(3.05x−3.75)−2.25y
The expanded form for given expression y(3.05x−3.75)−2.25y will be in form of a linear equation = 3.05yx - 6y.
What is linear equation?
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.
Now
By Solving y(3.05x−3.75)−2.25y
=3.05yx -3.75y - 2.25y
=3.05yx - 6y
Hence,
expanded form will be in form of a linear equation = 3.05yx - 6y.
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Copy and complete the table for the graph
y = -2x - 3.
What values should replace A, B and C?
X
Y
-2 −1
1
A
0 1
B
-5
2
C
The values of A and B are 1 , 5 from the given equation y=2x+1.
What is linear Equation ?
linear equation can be defined as the equation in which the highest degree is one .
Given Equation ,
y = 2x+1
The values of x are -1,0,1,2,3
The values of y are -1,A,3,B,7.
put x= 0 and y = A in the equation
we get,
A = 2*0 + 1
A =1
put x = 2 and y = B
we get,
B = 2*2 +1
B = 4+1
B = 5
Hence, The values of A and B are 1 , 5 from the given equation y=2x+1.
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Problem No. 4
300 is divided into 4 parts such that the first integer number is twice the second, three times the third
and four times the fourth. What is the value of the largest of these numbers?
Answer:
x = 144
Step-by-step explanation:
300 = x + [tex]\frac{1}{2}[/tex]x + [tex]\frac{1}{3}[/tex]x + [tex]\frac{1}{4}[/tex]x
300 = [tex]\frac{12}{12}x+\frac{6}{12}x+\frac{4}{12}x+\frac{3}{12}x[/tex]
300 = [tex]\frac{25}{12} x[/tex]
[tex]x=(300)(\frac{12}{25} )[/tex]
x = 144
To check if the answer is right:
300 = 144 + [tex]\frac{1}{2}[/tex](144) + [tex]\frac{1}{3}[/tex](144) + [tex]\frac{1}{4}[/tex](144)
300 = 144 + 72 + 48 + 36
300 = 216 + 84
300 = 300
Which lines are positive and negative?
A positive line is a line that has a positive slope, meaning it rises from left to right. A negative line is a line that has a negative slope, meaning it falls from left to right.
The formula for a positive line is y = mx + b, where m is the slope, x is the x-intercept, and b is the y-intercept. The calculation for a positive line is the slope multiplied by the x-value, plus the y-intercept. For example, if the slope is 4 and the y-intercept is -2, the equation would be y = 4x - 2. If the x-value is 1, then the y-value would be 2 (4x – 2 = 4 * 1 – 2 = 2).
The formula for a negative line is y = mx + b, where m is the slope, x is the x-intercept, and b is the y-intercept. The calculation for a negative line is the slope multiplied by the x-value, minus the y-intercept. For example, if the slope is -4 and the y-intercept is -2, the equation would be y = -4x - 2. If the x-value is 1, then the y-value would be -6 (-4x – 2 = -4 * 1 – 2 = -6).
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In a class with 45 pupils, 20 are girls. What is the ratio of the number of boys to the number of girls? please include explanation not only answer
Answer: 25;20
Step-by-step explanation:
40-25=20
It ask for ratio of boys TO girls. So you put amount of boys then girls.
It is multiple choice.
The expressions that are equivalent to 25 + 3(a-5) + 7a are:
10a + 10, 5(2a + 2) and 2(5a + 5)
How to determine the equivalent expressions?
Equivalent expressions are expressions that work the same even though they look different. If two algebraic expressions are equivalent, then the two expressions have the same value when we substitute the same value(s) for the variable(s).
The expression 25 + 3(a-5) + 7a can be written as follow:
25 + 3(a-5) + 7a = 25 + 3a -15 + 7a
= 10a + 10
Thus, 10a + 10 is equivalent to 25 + 3(a-5) + 7a
Since 5(2a + 2) = 10a + 10. Thus, 5(2a + 2) is equivalent to 25 + 3(a-5) + 7a
Also, 2(5a + 5) = 10a + 10. Thus, 2(5a + 5) is equivalent to 25 + 3(a-5) + 7a
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V = 37° W= 3n+8° U= 69⁰
I need to know m < UWV
it's not 180
n=22
From the given triangle, The value of angle ∠VWU = 74.
No matter what kind of triangle it is, all triangles have internal angles that sum to 180°. Two of the angles in an isosceles triangle will be of equal size. All angles in an equilateral triangle will be 60 degrees. In a right-angled triangle, one of the angles will be 90°, making the sum of the other two angles also 90°.
A triangle's three inside angles will always add up to 180 degrees. Since the other two angles (180°+0°+0°) would not exist, a triangle cannot have a single angle of 180°. A triangle's three angles must add up to 180 degrees.
Sum of the angles of triangle = 180°
⇒ 3n + 8 + 37 + 69 = 180°
⇒ 3n + 114 = 180°
⇒ 3n = 180 - 114
⇒ 3n = 66
⇒ n = 22
The measure of ∠VWU = 3 × 22 + 8 = 74
Checking the results = 74 + 37 + 69 = 180°
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which graph shows a quadratic function
what is the probability that the mean mcat score of 100 randomly selected people will be more than 510?
The probability of selecting 100 randomly selected people with an average MCAT score of more than 510 is essentially zero. The maximum MCAT score is 528, so it is impossible for the mean of 100 randomly selected people to exceed 510.
Furthermore, the average MCAT score nationally is 500, meaning that it is highly unlikely that the mean of 100 randomly selected people would be more than 510.
To determine the probability of selecting 100 randomly selected people with an average MCAT score of more than 510, we would need to know the distribution of MCAT scores among the population. For example, if we knew that the population had a normal distribution with a mean of 510, we could calculate the probability of selecting 100 people with a mean of more than 510. However, without this information, it is impossible to calculate the probability.
Overall, it is highly unlikely that the mean of 100 randomly selected people will be more than 510, and the mean can't be higher than the maximum MCAT score. Therefore, the probability of selecting 100 randomly selected people with an average MCAT score of more than 510 is essentially zero.
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What are the 11 identities of polynomials Class 9?
The following are the most significant algebraic identities, or polynomial identities, in mathematics:
(a+b)2 = a2+b2+2ab
(a-b)2 = a2+b2-2ab
(a+b)(a-b) = a2-b2
(x+a)(x+b) = x2+ x(a+b)+ab
(a+b)3 = a3+3a2b+3ab2+b3
(a-b)3 = a3-3a2b+3ab2-b3
a3+b3 = (a+b)(a2-ab+b2)
a3-b3 = (a-b)(a2+ab+b2)
(a+b+c)2 = a2+b2+c2+2ab+2bc+2ca
An equation that makes it simple to solve expressions with greater exponents and integers is a polynomial identity. Typically, polynomial identities are employed to expand the equation by dividing it into smaller, more manageable components.
A polynomial identity is an equation that holds true regardless of the values of the variables. When factorizing or expanding a polynomial, we apply polynomial identities. It is crucial to grasp some of the significant polynomial identities that are listed in order to solve the polynomial equation quickly.
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A scientist is working with 11 meters of gold wire. How long is the wire in millimeters?
Answer:
11000
Step-by-step explanation:
1 meter = 1000 millimeter
11x1000
11000
Answer:
Step-by-step explanation:
11,000
for each single Meters its a thousand Millimeters
What are 2 examples of parallel lines?
Real-world instances of parallel lines:
1. Tracks for a railroad.
2. Walls that are in direct opposition.
Parallel lines are a grouping of two or more lines that all lie in the same plane but never cross. Both of them have the same slope and are equally spaced apart.
No matter how far we extend them, parallel lines are straight lines that never intersect. Numerous pairs of angles are created whenever any two parallel lines are intersected by a third line known as a transversal. The other angles are supplementary while some are congruent (equal).
Real-world instances of parallel lines:
1. Tracks for a railroad.
2. Walls that are in direct opposition.
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(SAT Prep) Find the value of x. x 35° 60°
Answer: 180.
Step-by-step explanation: x + 35 + 60 = 180.
Sue downloads music videos on her phone.
The cost of the video downloads (in dollars) is given by the equation c = 2v, where c is the total cost of the videos and v is the number of videos. The constant of proportionality in the equation in terms of cost per video is (1/2, 1, 2, 4) In this example, the constant of proportionality is also the (total price, unit price) of the videos.
The constant of proportionality in the equation in terms of cost per video is 2.
Option C is the correct answer.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 4 is an equation.
We have,
The cost of the video downloads (in dollars) is given by the equation.
c = 2v
where c is the total cost of the videos and v is the number of videos.
Now,
c = 2v can be written as,
c ∝ v
This means,
2 is the constant of proportionality.
Thus,
The constant of proportionality is 2.
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which is NOT a zero of the following functions. f(x)= x^3+3x^2-x-3 A.1 B.-1 C.3 D.-3
The value x = 3 is not a zero of polynomial f(x) = x³ + 3 · x² - x - 3. (Correct choice: C)
What value of x is not a zero of a polynomial?
Let p(x) be a polynomial, a value x is a zero of polynomial p(x) when p(x) = 0. Now we need to determine a value x such that polynomial f(x) = x³ + 3 · x² - x - 3 ≠ 0. The procedure is shown below:
Case A: x = 1
f(1) = 1³ + 3 · 1² - 1 - 3
f(1) = 1 + 3 - 1 - 3
f(1) = 4 - 4
f(1) = 0
Case B: x = - 1
f(- 1) = (- 1)³ + 3 · (- 1)² - (- 1) - 3
f(- 1) = - 1 + 3 + 1 - 3
f(- 1) = 0
Case C: x = 3
f(3) = (3)³ + 3 · (3)² - (3) - 3
f(3) = 27 + 27 - 3 - 3
f(3) = 48
Case D: x = - 3
f(- 3) = (- 3)³ + 3 · (- 3)² - (- 3) - 3
f(- 3) = - 27 + 27 + 3 - 3
f(- 3) = 0
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What is the factored form of 12x2 8x 4?
The factored form of the given equation as found by calculating is known to be, (12x + 4)(x - 1) .
The given equation is 12x² - 8x - 4 , now in order to get the factors we will factorize the expression.
12x² - 8x - 4
= 12x² -12x + 4x -4
= 12x( x - 1) +4( x - 1 )
= (12x + 4)(x - 1)
Therefore, the factors of the given equation is found to be as ,
x = 1 or -4 / 12.
Factorizing is a process by which we find the factors of a given number. The factor of a number is made up of prime numbers . Prime numbers are the numbers which are only divisible by 1 or by the number itself.
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Which expression is equivalent to 8-4(x-6) divided/over 4?
Answer:
-x+8
Step-by-step explanation:
8-4(x-6)=8-4x+24=-4x+32
(-4x+32)/4=-x+8
You are taking a multiple-choice test that has 5 questions. Each of the questions has 5 answer choices, with one correct answer per question. If you select one of these choices for each question and leave nothing blank, in how many ways can you answer the questions?
The number of ways the questions can be answered is given by the equation A = 5⁵ ways = 3125 ways
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the number of ways the questions can be answered be A
Now , the equation will be
The total number of questions in the test = 5 questions
The total number of choices for each question = 5 choices
And , each choice of the question has been answered
So , the number of ways the questions can be answered A = choices ^ questions
Substituting the values in the equation , we get
The number of ways the questions can be answered A = 5⁵ ways
The number of ways the questions can be answered A = 3,125 ways
Therefore , the value of A is 3,125 ways
Hence , the number of ways is 3,125 ways
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5 people of different ages are sitting around a table what is the probability they are sitting in age order
The probability of 5 people of different ages are sitting in age order is 1/12.
Let the youngest individual take a seat first. If the seats are not designated, this person may occupy any of the five available seats, and each one is equally valuable.
The next senior citizen must then be placed. For this reason, there are two possible placements for the second person: either to the left of the first person or to the first person's right. The two options, ascending order and descending order, are matched by this.
We are unable to place the additional individuals after the second person is set because there is only one spot available adjacent to the first person.
There are only two methods to arrange five persons of different ages sitting at a round table in ascending or descending order.
The number of ways in which we can arrange are 5 people at a round table without any restriction is 4!.
Probability of 5 people in around table is 2/4! = 1/12.
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The sum of the reciprocals of two consecutive odd integers is 12/35. Find the two integers.
The two consecutive odd integers are 9 and 11. 1/8 plus 1/11 equals 12/35.
The sum of the reciprocals of two consecutive odd integers is 12/35.
1/x + 1/(x+2) = 12/35
(x+2)/(x*35) + (x/35) = 12/35
x + 2 + x = 12
2x = 10
x = 5
5 and 7 are the next two odd numbers.
The sum of the reciprocals of two consecutive odd integers is 12/35. To find the two integers, we need to solve for x. Since the two integers are consecutive and odd, the equation
1/x + 1/(x+2) = 12/35
can be used to find x. We can then multiply both sides of the equation by x*35 and simplify it to (x+2)/(x*35) + (x/35) = 12/35.
By subtracting x/35 from both sides and then adding 2 to both sides, we can get the equation
x + 2 + x = 12.
By solving the equation 2x = 10, we find that x = 5. This means that the two consecutive odd integers are 5 and 7. This can also be verified by checking that 1/5 + 1/7 is equal to 12/35.
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A term is a constant, a variable, or a ___ of numbers and variables.
A term is a constant, a variable, or a number-variable product.
What exactly is a variable?In algebra, a symbol (usually a letter) used to indicate an unknown numerical value in an equation or algebraic statement. A variable is a quantity that is changeable rather than fixed. In mathematics, a variable is an alphabet or phrase that represents an unknown amount, unknown value, or unknown number. Variables are very useful in algebraic expressions or algebra. As an example, the variables x and 9 are constants in the linear equation x+9=4.
A term can be a number, a constant, a variable, or the product of a number and a variable in this context.
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Select from the drop-down menus to correctly complete the proof using rational or irrational for your answers
To prove that 4π is irrational, assume the product is rational and set it equal to a/b, where b is not equal to 0: 4π = a/b. Isolating π gives π=a/4b. The right side of the equation is _______(rational or irrational).
Because the left side of the equation is ________(rational or irrational)
, this is a contradiction.
Therefore, the assumption is wrong, and the number 4π is
________(rational or irrational).
To prove that 4π is irrational, assume the product is rational and set it equal to a/b, where b is not equal to 0: 4π = a/b. Isolating π gives π=a/4b.
The right side of the equation is rational.
Because the left side of the equation is irrational, this is a contradiction.
Therefore, the assumption is wrong, and the number 4π is irrational.
What are rational and irrational numbersRational numbers refers to a numbers that can be represented as a fraction say a/b where a and b are integers
Irrational numbers refers to numbers that cannot be represented as a fraction
π is an irrational number often used 3.142, the number cannot be accurately represented as a fraction.
In the proof, a/b and a/4b are rational and this is contradictory to π which is irrational. The contradiction completes the proof as required.
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PLEASE HELP!!! Geometry similar triangle proofs! please!!!
The angles R and U of the two triangles are equal, the ratio of the sides is RS/UW = RT/UV.
What is triangle?A triangle is a three-sided polygon which is one of the basic shapes in geometry. It is a closed figure formed by three line segments which are connected end-to-end. Each side of a triangle is called an edge, and each corner is called a vertex. The angles of a triangle are the interior angles which are formed by the intersection of two edges. Triangles come in many different types depending on the length of the sides and the size of the angles. The three most common types of triangles are equilateral, isosceles, and scalene.
Proof:
The two triangles, RST and UWV, are similar triangles because the angles R and U are equal. According to the similarity theorems, if two angles of one triangle are equal to two angles of a second triangle, then the two triangles are similar.
Since the two triangles are similar, their sides are proportional. The proportionality can be expressed as:
RS/UW = RT/UV
The proof is completed by applying the Angle-Angle Similarity Postulate which states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
This implies that the proportionality of the sides of the two triangles can be expressed as a ratio of the sides. Since the angles R and U of the two triangles are equal, the ratio of the sides is RS/UW = RT/UV.
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solving quadratics by factoring worksheet answer key
Factorization is a step in the process of locating the roots of a quadratic equation.
Why is quadratic equation by factoring?Finding the roots of a quadratic equation involves the process of factorization. When factoring quadratic equations, the original quadratic expression is changed into the product of two linear factors.
A quadratic function has the formula f(x) = ax² + bx + c, with a, b, and c being integers and a not equal to zero. A parabola is a curve that represents the graph of a quadratic function. Parabolas can have openings that are upward or downward, different "widths" or "steepnesses," but they all share the same fundamental "U" shape.
Breaking down the factors, or numbers, that multiply to create another number is a frequent mathematics operation known as factoring. Various things affect some figures.
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if the diameter of a circle is 13 cm, what is the circumference of the circle?
A.
39 cm
B.
26 cm
C.
13 cm
D.
42.25 cm
The circumference of the circle is 40.84cm.
What is the circumference of the circle?
The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more often referred to as the perimeter.
Here, we have
Given: the diameter of a circle is 13 cm.
We have to find the circumference of the circle.
C = 2.π.r
where,
r is the radius of the circle.
r = diameter/2
r = 13/2
r = 6.5
then,
C = 2.π.6.5
C = 40.84cm
Hence, the circumference of the circle is 40.84cm.
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