y = (x - 4) (x - 4) The factored quadratic function (x - 2) has a vertex with an x-coordinate of 3, and two unique roots.
what is function ?The study of mathematics covers numbers and their variations, equations and related structures, shapes and their locations, and locations where they can be found. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Each function is assigned a domain and a codomain, or scope. Typically, the symbol f is used to represent functions (x). input consists of an x. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.
given
Two distinct roots means two real solutions for x (the parabola needs to cross the x-axis twice)
Vertex form of a quadratic equation: (h,k) is vertex
y = a(x-h)^2 + k
The x of the vertex needs to equal 3
y = a(x-3)^2 + k
y = (x-3)^2 - 1
y = x^2 -6x + 8
y = (x - 4) (x - 4) The factored quadratic function (x - 2) has a vertex with an x-coordinate of 3, and two unique roots.
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Which of the following triplets are Pythagorean ?(3,4,5),(6,7,8),(10,24,26),(2,3,4).
The Pythagorean Triplets states that in any right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two legs of the right triangle. The Pythagorean Triplets is (3,4,5).
Pythagorean triplets:
The Pythagorean numbers consist of three positive integers a, b, and c such that a2 + b2 = c2. Such triples are usually written as (a, b, c), with a familiar example being (3, 4, 5). If (a, b, c) are Pythagorean numbers, then (ka, kb, kc) for all positive integers k. A primitive Pythagorean number is one in which a, b, and c are relatively prime (that is, they have no common divisors greater than 1). For example, (3, 4, 5) is a primitive Pythagorean number, but (6, 8, 10) is not. A triangle whose sides form a Pythagorean triple is called a Pythagorean triangle and is always a right triangle.
Based on the Question:
Let the smallest even number be 2m
(i) (3,4,5)
2m = 4
⇒ m = 2
⇒ m² −1 = 4−1 = 3
⇒ m² +1 = 4+1 = 5
∴(3,4,5) is a Pythagorean triplet.
(ii) (10,24,26)
2m = 10
⇒ m = 5
⇒ m²−1 = 25−1 = 24
⇒ m²+1 = 25+1 =26
∴(10,24,26) is not a Pythagorean triplet.
(iii) (6,7,8)
2m = 6
⇒ m = 3
⇒ m² −1 = 9−1 = 8
⇒ m² +1 = 9+1 = 10
∴(6,7,8) is not a Pythagorean triplet.
(iv) (2,3,4)
2m=2
⇒m=1
m² −1 = 1−1 = 0
m²+1 = 1+1 = 2
∴(2,3,4) is not a Pythagorean triplet.
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Bike sprockets and chain.
A gear ratio is the ratio of the teeth on the front sprocket and the teeth on the rear sprocket. If a bike has 36 teeth on the front sprocket and 12 teeth on the rear sprocket, what is the gear ratio for the bike?
1
The gear ratio for the bike based on the information is 3:1.
How to illustrate the ratio?Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).
From the information, the gear ratio is the ratio of the teeth on the front sprocket and the teeth on the rear sprocket. If a bike has 36 teeth on the front sprocket and 12 teeth on the rear sprocket,
The gear ratio for the bike will be:
= 36 / 12
= 3 / 1
= 3:1
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The function f(x) is shown on the graph.
The graph shows three pieces of f of x. One piece is curved in quadrant three increasing from the left and turning at approximately negative 3.8 comma negative 5.5 to then decreases and is asymptotic to the line x equals negative 2. Another piece is an upward opening u-shaped curve, which is asymptotic to the line x equals negative 2 and x equals 2 with a minimum at approximately negative 0.3 comma 2.4 3.24. Another piece is asymptotic to the line x equals 2 and is increasing from the left and passes through the point 3 comma 2 and continues to increase in quadrant one.
Which type of function describes f(x)?
Exponential
Logarithmic
Polynomial
Rational
Answer:
The answer is rational.
I just got it right on the test.
The table of values of the function f(x) = 5x³ + 2x² - 6x + 7 are illustrations of polynomial functions
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
The values on the table can be represented as:
(x, g(x)) = (-3, 0.375) (-1, 0.75) (1, 1.5) (3, 3) (5, 6) (7,12) (9, 24)
The above values show that as the values of x increases by 2, the values of function g(x) doubles.
Only an exponential function has this property.
Hence, the table of values represents an (a) exponential function.
3. Example of a polynomial function
A polynomial function is represented as:
y = ax^n + bx^n-2 + .......... + d
Using the above format, the function that is a polynomial function is (a) f(x) = 5x3 + 2x2 – 6x + 7
4. Key features in the functions
The functions are given as,
f(x) = 2x² + 7x + 6
g(x) = 2x + 5
Set x to 0 to calculate the y-intercept
f(0) = 2(0) + 7(0) + 6 = 6
g(x) = 2⁰ + 5 = 6
Hence, both functions have the same (c) y-intercept
Questions 1 and 5 are not properly presented
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tiana cells 47 boxes of orders for a fundraiser Tim cells to a few boxes them Tiana how many more boxes of oranges does Tim need to sell in order to sell 60 boxes
The boxes of oranges that Tim need to sell in order to sell 60 boxes will be 13 oranges.
How to illustrate the expression?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.
In this situation, Tiana sells 47 boxes of orders for a fundraiser. Therefore, the boxes of oranges that Tim need to sell in order to sell 60 boxes will be:
= 60 - 47
= 13
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Which relation is a function?
Every possible input value results in exactly one output value in a function. "The output is a function of the input," we state. The domain is made up of the input values, while the range is made up of the output values.
What do you mean by relation of a function?
A relation that states that there should be only one output for each input is known as a function. Alternatively, we could say that a special sort of relation (a set of ordered pairs) that adheres to the rule that every X-value should be associated with only one y-value is known as a function.
To ascertain whether a graph accurately depicts a function, use the vertical line test. If there are multiple points where the vertical line intersects the graph, the graph is not a function.
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On the school playground, the slide is 16 feet due west of the tire swing and 12 feet due south of the monkey bars. What is the distance between the tire swing and the monkey bars?
Answer:
20 feet
Step-by-step explanation:
Using the Pythagorean theorem, the distance is [tex]\sqrt{12^2+16^2}=20[/tex] feet.
There are 40 students in the
classroom. If 25 are boys, what
percent are girls?
Answer:
The answer is 37.5%
Step-by-step explanation:
Answer:
37.5
Step-by-step explanation:
1% of 40= 0.4
0.4 x 25 = 62.5
100-62.5 = 37.5
Can anybody help me solve this
Answer: (5x^2-7)(x-4)
Step-by-step explanation:
5x^2(x-4)-7(x-4)
= (5x^2-7)(x-4)
Drag each equation to show if it could be a correct first step to solving the equation 3(6+x)=24 3(6+x)=24.
Answer:
2
Step-by-step explanation:
3(6+x) = 24
18 + 3x = 24
3x = 24 - 18
3x = 6
x = 6/3
= 2
Xavier's mother has a large collection of shoes. the table shows flip flop 8, boots 4, and clogs 6. if xavier mother chose a pair of shoes at random, what is the probability that the shoes would be a flip flop, write your answer is a fraction.p(flip flop)
The probability of having a flip flop is 4/9.
What is the probability of flip flops?In the question, we can see from the data that we have that Xavier's mother has a large collection of shoes. the table shows flip flop 8, boots 4, and clogs 6.
Recall that probability deals with the possibility that an event may occur or not occur under a given circumstance. We know that;
Total number of the shoes = 4 + 6 + 8 = 18
Probability of a flip flop = 8/18 = 4/9
This is the possibility that what would be picked is a flip flop.
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Use your calculator to find the approximate value of e^7. (Round to 4 decimal places)
Answer:1096.6332
Step-by-step explanation:
Answer: Use
1096.6332
Step-by-step explanation:
I=$180
P=___
r=4.5%
t=3 years
what’s p?
Using the formula of Simple Interest, the value for the principal amount is obtained to be P = $1333.33.
What is Simple Interest?
Simple interest is a way to figure out how much interest will be charged on a sum of money at a specific rate and for a specific duration of time. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
The value for Simple Interest is given as = $180
The value for rate is given as = 4.5%
The value for time is given as = 3 years
To find the value for Principal amount, follow the formula for Simple Interest -
SI = P R T/100
Where P is the principal amount, R is the rate and T is the time.
Substitute the values in the equation -
180 = (P × 4.5 × 3)/100
180 = 13.5P / 100
P = (180 × 100) / 13.5
P = 18000 / 13.5
P = 1333.33
Therefore, the value for principal amount is $1333.33.
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A number, c , rounded to 1 d. P. I 47. 3
A number , d , rounded to 1 d. P. I 4. 6
What are the lower and upper bound of c-d?
The lower bound of c-d is 42.70 and the upper bound of c-d is 42.69.
In the given question, a number, c, rounded to 1 d.P. is 47.3.
A number, d, rounded to 1 d.P. is 4.6.
We have to find the lower and upper bound of c-d.
The maximum and smallest values that a number may have before it was rounded are known as upper and lower limits. They are also known as accuracy limits.
Error intervals are a useful tool for expressing the upper and lower bounds.
This is the lower bound for c; the smallest integer that will round to 47.3 is 47.25.
47.33999... is the highest number of c that may be rounded down to 47.3. Therefore, we define 47.34 as the upper bound.
This is the lower bound for d; the smallest integer that will round to 4.6 is 4.55.
4.64999... is the highest number of c that may be rounded down to 4.6. Therefore, we define 4.65 as the upper bound.
So, the lower bound of c-d = 47.25-4.55 = 42.70
So, the upper bound of c-d = 47.34-4.65 = 42.69
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The value of which of these expressions is closest to e?
(¹+4)*
B. (1+²
OC. (¹+1)
OD. (1++)"
OA.
Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.
What does expression mean?An algebraic expression must be checked by replacing each variable with a number and performing arithmetic operations. In the example above, the answer variable is identical to 6, since 6 + 6 = 12. If we know the values of the variables, we can replace them with those values and evaluate the expression.
Here,
Assumed: expressions
Finding the expression with a value that is closest to e
Solution:
e is worth 2.718, which equals (1 + 1/19).
(1 + 1/19)^19
=> (20/19)^19 = 2.65
=> (1+ 1/22)^22
= >(23/22)^22 = 2.659
=> (1 + 1/20)^20
= >(21/20)^20 = 2.653
=>(1 + 1/21)^21
= > (22/21)^21 = 2.656
As a result, the value of e is closest to the value of 2.659.
Option B is hence the appropriate choice.
Therefore ,the solution of the given problem of expression comes out to be Option B is hence the appropriate choice.
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Do sides 10 cm 24cm 26cm from a right-angled triangle justify?
As the sides of the triangle 10 cm, 24 cm and 26 cm are triplets, the triangle will be a right angle triangle with side having length 26 cm as hypotenuse.
What is meant by triangle?
A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.The triangle is referred to as being equilateral when each of its three sides is the same length. Isosceles triangle: An isosceles triangle is one in which each of its sides are equal.Having three sides, three angles, and three vertices, a triangle is a closed, two-dimensional object. A polygon also includes a triangle.An angle is a figure in plane geometry that is created by two rays or lines that have a shared endpoint.To learn more about triangle refer to
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A 9,000-gallon pool is being filled at a rate of 40 gallons per minute. At this rate, how many minutes will it take to fill this pool?.
Answer:
225 minutes
Step-by-step explanation:
[tex]\displaystyle \frac{40\text{ gallons}}{\text{min}}=\frac{9000\text{ gallons}}{\text{x min}}\\\\x=\frac{9000\text{ gallons}}{40 \text{gallons}}=225\text{ min}[/tex]
What is 6 with exponent of 2?
6 with an exponent of 2 is 36. 6 with an exponent of 2 means 6 multiplied by 6.
When a number is raised to a certain power, it means that the number is multiplied by itself that many times.
6^2 = 6 x 6 = 36Exponents are a way of shorthand for repeated multiplication. When a number has an exponent of 2, it means that the number is multiplied by itself once. When a number has an exponent of 3, it means the number is multiplied by itself twice.
In this case 6 with exponent of 2, means 6 multiplied by itself twice, which is equal to 36.
It's important to note that the exponent is also known as the power, so 6^2 is also read as 6 to the power of 2.
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Find the square root of the following fraction correct to two decimal numbers 5 5/11
By square root 5 this we get the value √5 = 2.2360…Or √5 ≈ 2.24 with correct two decimal number fraction .
What is Division Method to Find the Value of Root 5 ?Using the long division approach, it is feasible to calculate the value of any number's roots. The following list of instructions will help you determine the value of root 5:1. First, the number 5 can be expressed as 5.00000000, or 5 = 5.00 00 00 00.
2.Take the number whose square is less than five. The perfect square of the number 2 is 4, which comes after the number 5.
3..Enter 2 in both the divisor and quotient places so that it may be multiplied by 2 to get the answer 4. Add 4 to 5 to obtain the answer, which is 1.
4.Write two zeros after one and add them to the quotient. Add the decimal point after the first zero.
5.Now multiply by 2 to make 4 in the divisor. Pick a number that will go next to 4, ensuring that the result of multiplying the combination with that number will be less than or equal to 100. In order to make 42 times 2 equal 84, which is less than 100, we shall use 2 in this instance. To get the remainder, take 100 out of it immediately. The remainder is therefore 16.
6.Repetition of Step 5 up to 4 places of decimals with the addition of two more zeros.
7.Ultimately, you arrive at the quotient value, which is 2.2360, or around 1.236.
In light of this, the value of root 5 is, √5 = 2.2360… Or √5 ≈ 2.24
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What is the formula of image in straight line?
The formula of an image in a straight line is y = mx + c, where m is the slope of the line, x is the x-coordinate of the point and c is the y-intercept.
What is straight line?A straight line is a line whose points all lie in the same plane and all have the same distance from each other, making them all equidistant. The line does not curve or bend in any way, and can extend infinitely in either direction. Straight lines are the most basic form of geometric shape and are the foundation of all other shapes. The line is defined by two points, known as its endpoints, and any point that lies on the line is called a point on the line. Straight lines are important in mathematics, as they are used to describe relationships between points on a graph, and they can also be used to define equations and boundaries.
The y-intercept is the point at which the line crosses the y-axis. The slope of the line is determined by the ratio of the change in the y-coordinate to the change in the x-coordinate. To calculate the slope of a line, the formula m = (y2 - y1)/(x2 - x1) is often used, where (x1, y1) and (x2, y2) are two points on the line. Using the slope and the y-intercept, the formula can be used to plot the points of the image along a straight line.
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Determine the equation of the inverse for f(x)=7x2
The inverse of the equation f(x) = 7x -2 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex].
What is inverse of an equation?A function that can reverse into another function is known as an inverse function or anti function. In other words, the inverse of a function "f" will take y to x if any function "f" takes x to y. The inverse function is denoted by f-1 or F-1 if the function is represented by [tex]f^{-1}(x)[/tex].
The given function is:
f(x) = 7x -2
Write the function in the form of a function:
y = 7x - 2
Interchange the variables in the equations:
x = 7y - 2
Isolate the value of y:
y = x/7 + 2/7
Replace y with [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex]
Hence, the inverse of the equation f(x) = 7x -2 is [tex]f^{-1}(x) = \frac{x}{7} + \frac{2}{7}[/tex].
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A cylinder with a height of 9cm. And a width of 10cm. Find the exact volume.
A. 90pi cm^3
B. 45pi cm^3
C. 900pi cm^3
D. 225pi cm^3
Answer:
The correct answer is D. 225pi cm^3.
To find the volume of a cylinder, you use the formula:
V = πr^2h
Where V is the volume, π is pi, r is the radius of the base, and h is the height of the cylinder.
In this case, the height is 9cm, and the width is 10cm. To find the radius, we divide the width by 2:
r = 10cm / 2 = 5cm
Now we can plug in the values into the formula:
V = πr^2h
V = π(5cm)^2(9cm)
V = π(25cm^2)(9cm)
V = 225π cm^3
So the volume of the cylinder is 225π cm^3
Step-by-step explanation:
Answer: D) 225pi cm^3.
Step-by-step explanation:
A culptor need to move a piece of marble. It i a cuboid with dimenion 1m by 0. 6m by 0. 3m. Marble ha denity of 2. 7g/cm cubed. What i the ma of the cuboid in kg
The mass of the marble in kg is 486 kg .
Now, According to the question:
A sculptor needs to lift a piece of marble.
It is a cuboid with dimensions 1 m by 0.6 m by 0.3 m.
Marble has a density of 2.7 g/cm³.
We need to find what is the mass of the marble in kg .
Let's find out :
Volume of Cuboid = Length × Width × Height
Volume = (1m)(0.6m)(0.3m)
Volume = 0.18[tex]m^3[/tex]
Also , We know that
Density = [tex]\frac{Mass}{Volume}[/tex]
Density = 2.7[tex]\frac{g}{cm^3}[/tex]
Density = 2.7 [tex]\frac{10^-^3kg}{(10^-^2m)^3}[/tex]
Density = 2.7[tex]\frac{10^-^3kg}{(10^-^6m)}[/tex]
Density = 2.7[tex](10^-^3^+^6)kgm^-^3[/tex]
Density = 2.7[tex](10^6)kgm^-^3[/tex]
Now, Density = [tex]\frac{Mass}{Volume}[/tex]
2.7[tex](10^6)[/tex] = [tex]\frac{Mass}{0.18}[/tex]
Mass = [tex]2.7(10^6)[/tex] × 0.18
Mass = 486kg
Therefore , the mass of the marble in kg is 486 kg .
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What is the value of base 2?
Binary is also known as Base 2. This means it is composed of only 0's and 1's. For example 9 in binary/base 2 is 1001.
About binary number systemThe binary number system or base two number system is a system of writing numbers using two symbols, namely 0 and 1.The modern binary number system was discovered by Gottfried Wilhelm Leibniz in the 17th century. This number system is the basis of all digital-based number systems. From the binary system, we can convert it to the Octal or Hexadecimal number system. We can also refer to this system as Bits, or Binary Digits. Binary groupings on a computer always add up to 8, with the term 1 Byte/byte. In computer terms, 1 Byte = 8 bits. Computer design codes, such as ASCII, American Standard Code for Information Interchange use a 1 Byte coding system.
In modern digital communication systems, where data is transmitted in the form of binary bits, a system is needed that is resistant to noise contained in the transmission channel so that the transmitted data can be received correctly. Errors in sending or receiving data are fundamental problems that have a very significant impact on communication systems.[2] The commonly used binary has 8 digit numbers and only contains the numbers 1 and 0, no other numbers. Base-2 ; Position Value: 2 · 2 ; Digit Value: 128s. 64s ; Binary Number: 1. 1.
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in a video game players Form teams and work together to earn as many points as possible for their team each team can have between two and four players each player can score up to 20 points in each round of the game Han and three of his friends decided to form a team and play around.
a. the number of players in a game with six different teams of different sizes: two teams have 4 players each and the rest have 3 players each
b. the possible number of players in a game with eight teams
Therefore , the solution to the given problem of expression comes out to be 80.
What does expression mean?Math allows for addition, subtraction, multiplication, and division. Following is the structure of an expression: Calculator, number or variable, and expression The components of a mathematical expression include numbers, variables, and operations (such as subtraction, multiplication , addition, or division etc.) You can contrast phrases and expressions.
Here,
The formula for the number of points Han's team scores in a single round if each player has a perfect score is 20 4.
Each player is limited to a maximum of 20 points.
Han's team has four members.
Thus, assuming each participant receives a perfect score, the expression that will indicate the total points that Han's team receives in one round is:
= 20 × 4
= 80
Therefore , the solution to the given problem of expression comes out to be 80.
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I need this ASAP
Pleaseee 50 points!!!
choose 50 distinct numbers between 0 and 99. For starlings and geese, follow the same procedure.
what is probability ?Measurement of the likelihood that an event will occur or a claim is true is done via probability theory, a branch of mathematics. The probability of an occurrence is a number between 0 and 1, with 1 denoting certainty and 0 roughly indicating how likely it is that the event will occur. A probability is a numerical representation of how likely it is that a certain occurrence will take place. Probabilities can also be expressed as ranges of 0% to 100% or 0 to 1. the proportion of occurrences in a whole set of equally likely options that lead to a particular event relative to the entire number of outcomes.
given
All of the blackbirds were numbered and tagged from 00 to 99. With a random number generator,
choose 50 distinct numbers between 0 and 99. For starlings and geese, follow the same procedure.
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the correct question is :- In search of a mosquito repellent that is safer than the ones that are currently on the market, scientists have developed a new compound that is rated as less toxic than the current compound, thus making a repellent that contains this new compound safer for human use. Scientists also believe that a repellent containing the new compound will be more effective than the ones that contain the current compound. To test the effectiveness of the new compound versus that of the current compound, scientists have randomly selected 100 people
Fully simplify 5√/20 - 4√5
Is it possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm which result did you use to verify this?
It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are greater than three sides.
In the given question, we have to check that it is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm.
The sum of the two sides must always be greater than the third side in order to determine whether or not the given sides may form a triangle.
To check this we firstly add the 10.2 and 5.8
10.2 + 5.8 > 4.5
16 > 4.5
Now we add 5.8 and 4.5
5.8 + 4.5 > 10.2
10.3 > 10.2
Now we add 10.2 and 4.5
10.2 + 4.5 > 5.8
14.7 > 5.8
It is possible to construct a triangle whose sides are 10.2 cm 5.8 cm and 4.5 cm because the sum of two sides are greater than three sides.
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Why is 180 degree longitude considered to be an important meridian?
The meridian at 180° longitude is commonly known as the International Date Line. As you pass the International Date Line, you either add a day (going west) or subtract a day (going east.)
The prime meridian and the International Date Line create a circle that divides Earth into the Eastern and Western Hemispheres.
The prime meridian has been set up in Greenwich, UK. It is an imaginary line that represents O degrees of longitude. This line, like all other meridians, runs from the North Pole to the South Pole and has the same length as all of the other meridians.
From the prime meridian, there are 180 degrees west and 180 degrees east. This is the line that divides the world in the Western and Eastern Hemispheres. The prime meridian is also the line from which time is counted either plus or minus, as it is at 0+ time zone, and everything east of it is plus, while everything west is minus. On the opposite side of the world of the prime meridian, we have the line that represents the start of time.
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Which of the following angles are supplementary to ∠1? Select all that apply.
∠6 and ∠7 are the angles which are supplementary to ∠1.
What are Angles?An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.
Supplementary angles are those angles that sum up to 180 degrees.
In the given figure lines l and m are parallel lines.
A transversal passed through parallel lines.
∠1+∠2=180 degrees
∠1+∠3=180 degrees.
∠2 is corresponding angle of ∠6.
∠1+∠6=180 degrees.
∠3 is corresponding angle of ∠7.
∠1+∠7=180 degrees.
Hence, ∠6 and ∠7 are the angles which are supplementary to ∠1.
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What does the mark of the angles and sides of the triangle indicate?
The mark of the angles and sides of the triangle indicate that they are congruent.
What is congruence of triangle ?Triangle diagram with side and angle indicators. To demonstrate if two or more sides are congruent, indicator marks are utilized (equal in measure).
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, twist, flip, and turn these triangles to create a similar appearance.
When two angles and the included side of one triangle are equal to two angles and the included side of another triangle, two triangles are said to be congruent. PB = DE. The matching triangle portions are equal since the triangles are congruent.
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