Answer:
66
Step-by-step explanation:
22 per minute
? Per 3 minutes
22 x 3 = 66
Answer: The position of the whale relative to the surface of the water can be determined by multiplying the rate at which it descends (22 feet per minute) by the amount of time it has been descending (3 minutes).
Position = Rate x Time
Position = 22 feet/minute x 3 minutes = 66 feet
So, after diving for 3 minutes, the position of the whale relative to the surface of the water is 66 feet.
It means the whale descended for 66 feet from the surface level of the water.
Please keep in mind that this information is assuming a linear motion, without taking into account any other factors that could affect the whale's descent such as currents or obstacles in the water.
Step-by-step explanation:
In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology. All the students do at least one of the three subjects. 3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only. Find the number of numbers of students that do two subjects only exactly one subject at least two of the subjects Represent the information on a complete Venn diagram.
Number of students that do two subjects are 12.
Number of students that do only exactly one subject are;
For Art;
⇒ 14
For Chemistry;
⇒ 11
For Bio;
⇒ 8
Number of students that do at least two of the subjects are 15.
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;
In a class of 48 students, 24 of them do Arts, 22 do Chemistry and 20 do Biology.
All the students do at least one of the three subjects.
3 do all three subjects while 4 do Arts and Biology only, 3 do Arts and Chemistry only and 5 do Chemistry and Biology only.
Here,
Total students = 48
So, Number of students that do two subjects are = 4 + 3 + 5
= 12
And, Number of students that do only exactly one subject are;
For Art;
⇒ 24 - (3 + 4 + 3)
⇒ 14
For Chemistry;
⇒ 22 - (3 + 5 + 3)
⇒ 11
For Bio;
⇒ 20 - (3 + 4 + 5)
⇒ 8
Number of students that do at least two of the subjects are;
⇒ 3 + 3 + 4 + 5
⇒ 15
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Please help I have a learning disability and this is due today
Determine whether the two expressions are equivalent. If so, tell what property is applied. If not, explain why.
0 + 32 and 0
yes, it uses the Commutative Property
No they are not equivalent. The first expression is equal to 32, not 0.
yes, it uses the Associative Property
yes, it uses the Identity Property
Answer:
yes, it uses the Commutative Property
Step-by-step explanation:
What are the three types of dilation?
Enlargements of the picture or reductions of the image are both types of dilations.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.
The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.
Even in the enlarged picture, parallel and perpendicular lines are still discernible.
A dilated image's side's midway matches the pre-exactly. image's
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which is the functions for increases 8.3%
Answer:
The US Consumer Price Index (CPI) increased 8.3% in the 12 months through August, with rent, food and healthcare accounting for the rise Excluding volatile food and gas prices, inflation climbed 6.3% year-on-year in July and 8.2% in September. US inflation ticked back up in August despite plunging gas prices.
citations: https://nypost.com/2022/10/13/inflation-hits-8-2-in-september-as-core-prices-surge/Step-by-step explanation:
When a problem is said to be decidable or undecidable give an example of an undecidable problem?
Example of an undecidable problem is given by the problems in the system created by computer viruses.
What is decidable and undecidable problems?According to the computability theory, the problems that needs either yes or no answer, but it is not possible by any computer programming languages to create exact answer then this computational problem is termed as undecidable problems.
A decidable problem is a decision problem in the computer system that can be solved by an algorithm correctly.
When is a problem said to be decidable or undecidable?
whenever we find a problem for which there is no algorithm available for solve and we are also unable to create any program that can solve the problem exactly in finite time are declared as undecidable problems.
If we find a problem that ask yes or no question about some input and there is programming language available for responding correctly then this particular problem is declared as decidable.
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What are the 3 types of terms in quadratic equation?
The 3 types of terms in quadratic equation:
1) quadratic term,
2) linear term,
3) constant term.
We know that the second degree algebraic equation in x is a quadratic equation.
The standard form of quadrtic equation is ax^2 + bx + c = 0, where a, b, c are integers.
As thise is a quadratic equation, the value of a can not be zero. a ≠ 0
The term ax^2 is called the quadratic term.
From this term, the name given to the equation(quadrtic equation)
The term bx is called the linear term.
And the term c is called the constant term.
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(100 points)A catering company offers meal pairings that include an appetizer of either salad or soup and an entree of either chicken or fish. At one event, they serve a total of 78 meals. Of the 46 meals that include salads, 21 also include fish. There are 35 meals with fish as the entree. Determine which two-way frequency table represents this situation. Jk
Two-way table showing meal pairings with frequency of salad, soup, chicken and fish.
Meal Pairing Salad Soup Chicken Fish
Frequency 46. 32. ?. 35
To calculate the frequency of chicken, subtract the frequency of salad and fish from the total of 78 meals.
Frequency of chicken
= 78 - 46 - 35
= 27.
Meal Pairing Salad Soup Chicken Fish
Frequency 46. 32. 27. 35
The total number of meals served is 78. Of the 46 meals that included salads, 21 also included fish. This means that the frequency of fish is 35. The frequency of chicken can be calculated by subtracting the frequency of salad and fish from the total number of meals. The frequency of chicken is 27. The two-way frequency table representing this situation is as follows: Meal Pairing, Salad, Soup, Chicken, Fish; Frequency, 46, 32, 27, 35. This table shows that there were 46 meals with salad, 32 meals with soup, 27 meals with chicken, and 35 meals with fish.
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In AABC, AB = AC and AP 1 BC. If AB= (2x + 3) cm, AC = (3y-1) cm, BP = (y + 1) cm and PC = (x + 2) cm find the values of x and y.
Answer:
x = 1y = 2Step-by-step explanation:
Given isosceles triangle ABC with AB≅AC, altitude AP, and AB=(2x+3), AC=(3y-1), BP=(y+1), and PC=(x+2), you want the values of x and y.
Isosceles triangleCorresponding parts of ∆ABP and ∆ACP are congruent, so we have ...
2x +3 = 3y -1
x +2 = y +1
SolutionSubtracting twice the second equation from the first gives ...
(2x +3) -2(x +2) = (3y -1) -2(y +1)
-1 = y -3 . . . . simplify
2 = y . . . . . . add 3
Substituting into the second equation, we have ...
x +2 = 2 +1
x = 1 . . . . . . . .subtract 2
The values of x and y are 1 and 2, respectively.
Find the missing length and area of each figure
LM = √(8² + 6²) = √(64 + 36) = √100 = 10 yd
Area = 2 × (1/2) × 6 × 8 = 48 yd²
Which expression is the factored form of X^3 2x^2 5x 6?
The factors of the given equation x³ - 2x² - 5x + 6 is (x - 1)(x + 2)(x - 3) with the help of synthetic division.
Let f(x) = x³ - 2x² - 5x + 6
Substitute x = 1
f(1) = (1)³ - 2(1)² - 5(1) + 6
⇒ f(1) = 1 - 2 - 5 + 6
⇒ f(1) = -1 + 1
⇒ f(1) = 0
As x = 1 is the root of the given equation therefore one of the factor of the given equation is (x-1)
Now use long division method, we get (x² - x - 6) as another factor.
⇒ f(x) = (x - 1)(x² - x - 6)
⇒ f(x) = (x - 1)(x² - 3x + 2x - 6)
⇒ f(x) = (x - 1)(x(x-3) + 2(x-3))
⇒ f(x) = (x - 1)(x - 3)(x + 2)
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Solve for x in the equation 2^(2x-1)x[1/8]^(1-x)=4^(3x+1)
Answer: x=-6
Step-by-step explanation:
[tex]\displaystyle\\2^{2x-1}*(\frac{1}{8} )^{1-x}=4^{3x+1}\\\\2^{2x-1}*8^{(-1)(1-x)}=(2^2)^{3x+1}\\\\2^{2x-1}*(2^3)^{x-1}=2^{2*(3x+1)}\\\\2^{2x-1}*2^{3*(x-1)}=2^{6x+2}\\\\2^{2x-1}*2^{3x-3}=2^{6x+2}\\\\2^{2x-1+3x-3}=2^{6x+2}\\\\2^{5x-4}=2^{6x+2}\\\\Hence,\\\\5x-4=6x+2\\\\5x-4-2=6x+2-2\\\\5x-6=6x\\\\5x-6-5x=6x-5x\\\\-6=x\\\\Thus,\ x=-6[/tex]
Answer:
Step-by-step explanation:
We have:
2^(2x-1) x [1/8]^(1-x) = 4^(3x+1)
2^(2x-1) x [1/2³]^(1-x) = 2²^(3x+1)
2^(2x-1) x 2^-3+3x = 2^6x+2
2^5x-4 = 2^6x+2
on comparing both sides we get :
5x-4 = 6x +2
x = -6
a pair of sneakers in on sale as shown the sale price is $51. This is 75% of the original price. what was the original price of the shoes
pls help explanation required
Answer:
$68
Step-by-step explanation:
Let x = original price.
The sale price is 75% of the original price, so the sale price is 75% of x.
75% as a decimal is 75/100 = 0.75
75% of is the same as 0.75x
We are told the sale price is $51, so 0.75x must equal $51.
0.75x = 51
Divide both sides by 0.75 to find the value of x.
x = 51/0.75
x = 68
Answer: $68
Answer:
Step-by-step explanation:
$51 is 75% of 100%
75% = 3/4
51 / 3 = 17
17 = 1/4
51 + 17 = 68
$68 is the original price of the shoes
if pam makes 250 dollars from making 15 pots, what is her piece rate?
Pam's piece rate is $16.67 for every pot she produces.
What is the rate?A rate is a type of ratio that compares two values with distinct units. A rate is expressed as a fraction.
Pam's piece rate is the amount of money she earns for each pot she makes. In this case, she earned $250 for making 15 pots, so her piece rate is:
$250 ÷ 15 pots = $16.67 per pot
Therefore, Pam earns $16.67 for each pot she makes. This is a way of calculating her pay based on the number of units she produces, rather than by the hour.
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How do you know if it is a linear exponential or quadratic graph?
Linear graphs have the following form: y = mx + b, where m is the slope of the line and b is the y-intercept.
To calculate the slope, you can use the formula m = (y2 - y1)/(x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.
Exponential graphs have the following form: y = ab^x, where a and b are constants. To calculate the constants, you can use the formula y = a + b^x, where (x, y) are two points on the graph and a is the y-intercept.
Quadratic graphs have the following form: y = ax^2 + bx + c, where a, b, and c are constants. To calculate the constants, you can use the formula y = ax^2 + bx + c, where (x, y) are two points on the graph and c is the y-intercept.
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What is equivalence and example?
Equivalence Relation is a type of Relation that satisfies the property of Reflexive , Symmetric and Transitive , and an example of such relation is [tex][(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (4, 4)][/tex] .
What is an Equivalence Relation ?
A relation R on a set A is can be called as an equivalence relation if and only if the relation is reflexive, symmetric and transitive.
It is a relationship on the set which is represented by symbol “∼”.
(i) Reflexive: A relation is termed as reflexive, if [tex](a, a) \in R[/tex], for every [tex]a \in A[/tex].
(ii) Symmetric: A relation is termed as symmetric, if [tex](a, b) \in R[/tex] , then [tex](b, a) \in R[/tex] .
(iii) Transitive: A relation is termed as transitive if [tex](a, b) \in R[/tex] and [tex](b, c) \in R[/tex], then [tex](a, c) \in R[/tex] .
An Example of Equivalence Relation is [tex][(1, 1), (1, 3), (2, 2), (2, 4), (3, 1), (3, 3), (4, 2), (4, 4)][/tex] because ;
(i) [tex][ (1, 1),(2, 2), (3, 3), (4, 4) ] \in R[/tex] , So , R is Reflexive .
(ii) [tex](2,4) \in R[/tex] and [tex](4,2)\in R[/tex] , Thus , relation given by R is Symmetric .
(iii) [tex](3,1) \in R[/tex] and [tex](1,3) \in R[/tex] ⇒ [tex](3,3) \in R[/tex] , So R is Transitive .
Therefore , the Relation given by R is Equivalence Relation .
The given question is incomplete , the complete question is
What is Equivalence Relation and its Example ?
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The price of a notebook has risen to $3.80 today. Yesterday's price was $3.30 . Find the percentage increase. Round your answer to the nearest tenth of a percent.
The percentage increase in the price of the notebook is 15%.
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100.
The proportion, therefore, refers to a component per hundred. Per 100 is what the term percent signifies. The letter "%" stands for it.
Finding the increase in the price of the notebook:
$3.80 - $3.30 = $0.50
Dividing the increase by the original amount:
0.50 / 3.30 = 0.1515
To change to a percent multiply by 100 and round off to significant numbers:
0.1515 *100 = 15.15% or, 15%.
Thus, the percentage increase in the price of the notebook is 15%.
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(a) What is the probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50
Using the normal distribution and the central limit theorem, it is found that there is a 0.0901 = 9.01% probability that the proportion of voters in the sample of Region A who support the ballot measure is greater than 0.50.
What is probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one. Probability has been introduced in Maths to predict how likely events are to happen. The meaning of probability is basically the extent to which something is likely to happen. This is the basic probability theory, which is also used in the probability distribution, where you will learn the possibility of outcomes for a random experiment. To find the probability of a single event to occur, first, we should know the total number of possible outcomes.To learn more about distribution refer to:
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How do you solve this? 11t-t^2=30
Answer:
t = 5, 6
Step-by-step explanation:
Given the equation:
[tex]\displaystyle{11t-t^2=30}[/tex]
First, arrange the expression in the standard quadratic form ax² + bx + c = 0
[tex]\displaystyle{t^2-11t+30=0}[/tex]
Then factor the expression, find two numbers that add up which result in -11 and multiply which result in 30 - that two numbers are -6 and -5
[tex]\displaystyle{(t-6)(t-5)=0}[/tex]
Solve like a linear equation
[tex]\displaystyle{t=5,6}[/tex]
Therefore, the solutions to the equation are t = 5, 6
Answer:
The solution set is {5, 6}.
Step-by-step explanation:
11t-t^2=30
t^2 - 11t + 30 = 0
(t - 5)(t - 6) = 0
t = 5, 6.
What is the volume of the rectangular prism?
^answer:^
~10 cubic feet~
^step by step explanation:^
first, calculate the volume of the front “panel” of the shape. (5 cubic centimeters because 5 times 3 is 15 and 15 times 1/3 is 5. 5 times 2 is 10.
gary has two ladders for a project one reaches 16 3/7 while the other reaches 12 /5/7 how much higher can the longer ladder reach
The longer ladder can reach 3 8/7 feet higher than the shorter one.
The Proportionality Theory.The longer ladder can reach 4 2/7 feet higher than the shorter ladder. To calculate this, we need to subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet).We can represent this calculation with a fraction equation, as follows:[tex]\frac{16 \frac{3}{7}}{12 \frac{5}{7}} - 12 \frac{5}{7} = \frac{4 \frac{2}{7}}{1}[/tex]To solve this equation, we first need to convert the fractions into equivalent fractions with a common denominator. In this case, the denominator is 7. This means that the first fraction becomes 16 3/7, the second fraction becomes 12 5/7, and the third fraction becomes 4 2/7.Once we have the fractions in the same denominator, we can now subtract the shorter ladder's height (12 5/7 feet) from the taller ladder's height (16 3/7 feet). This gives us a result of 4 2/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To put this into perspective, if we were to use the ladders to reach a height of 16 3/7 feet, the shorter ladder would only reach 12 5/7 feet, while the longer ladder would reach 16 3/7 feet. This means that the longer ladder can reach 4 2/7 feet higher than the shorter ladder.To learn more about The Proportionality Theory refer to:
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Why are the acute angles of an isosceles right triangle always 45?
An isosceles right triangle has two sides that are equal in length; this means that the angles opposite the sides must also be equal. Since the triangle is a right triangle and the sum of angles of a triangle is 180 degrees, the angles must each be 45 degrees.
The acute angles of an isosceles right triangle are always 45 because of the Pythagorean Theorem. This theorem states that in a right triangle the sum of the squares of the two sides adjacent to the right angle (the legs) is equal to the square of the hypotenuse. Since an isosceles right triangle has two equal legs, and the hypotenuse is the longest side, the two legs must both have the same length, and the angles opposite from these sides must also be the same. This means that the two acute angles in an isosceles right triangle must both be 45 degrees.
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please help: solve for x
Step-by-step explanation:
in an isoceles triangle (both legs have identical length) the height from the top corner to the baseline shots the baseline into 2 identical halves.
so,
6x + 6 = 9x - 15
6 = 3x - 15
21 = 3x
x = 21/3 = 7
many greetings to your teacher from me : he/ she made a formal mistake. the angles at Y have to be indicated as right angles. because if the line WY is not the height but could have any angle with the baseline, this cannot be solved.
A seventh grade class and 7 adults go on a field trip. Two-thirds of the people ride on a bus.
Everyone else rides in vans. If 54 people ride on the bus, how many seventh graders go on the
field trip?
54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.
what is expression ?A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.
given
To find P P, divide P
P by the total number of participants (students and chaperones), which is 81.
Seventh graders totaling 81 - 7 =
74 participated in the field trip.
54 individuals take the bus while the remaining 74 seventh graders ride in vans for the field trip.
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par teme
d
Bookwork code, 021
Cessss chance Review your workings and see if you can comes your make
Ria buys 19 textbooks, which cost £6.82 each,
By first rounding both numbers to 1 significant figure, estimate the total
amount of money Ria spends,
Give your answer in pounds (L),
Answer?
Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.
Define unitary method.By multiplying the value about one unit by the quantity of units required, one can apply the unit technique to solve a problem. The unit procedure is used to separate a single entity integer from a given many, to put it simply. One pen, or 400 rupees, would be needed to purchase 40 needle. There might be a common way to verify this. only one nation. Anything has a unique feature. Algebra, grid logic, and its laminates and reverse are all identical terms used to describe mathematical analysis.
Here,
Given : Ria purchases 19 books for £6.82 apiece.
Thus,
Total cost of book = 19 * 6.82
=> 129.58
Therefore , the solution of the given problem of unitary method comes out to be total amount spent by Ria £129.58.
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The age at which small breed dogs are fully housebroken follows a Normal distribution with mean ms = 6 months and standard deviation ss = 2. 5 months. The age at which large breed dogs are fully housebroken follows a Normal distribution with mean mL = 4 months and standard deviation sL = 1. 5 months. Let xS – xL represent the sampling distribution. Be sure show all work and conditions. Let the sample size for both sets be 25 dogs. Should we be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs? Explain your answer
The answer is no, we would not be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs, as the probability of this happening is very small, 2.28%.
HOUSEBROKEN AGE PROBABILITYThe sampling distribution for the difference in sample means, xS - xL, is also normally distributed with a mean of ms - mL = 6 - 4 = 2 months.The standard deviation of √((ss²/nS) + (sL²/nL)) = √((2.5²/25) + (1.5²/25)) = 0.5 months, where nS and nL are the sample sizes for the small and large breed dogs, respectively.Using a z-score, we can calculate the probability of observing a sample mean difference of at least 3 months between the small and large breed dogs, given that the true difference in population means is 2 months. This probability can be found using the standard normal table or calculator.The z-score formula is (x - mu) / sigma, where x is the observed sample mean difference, mu is the population mean difference, and sigma is the standard deviation of the sampling distribution.z = (3-2) / 0.5 = 2
The probability of observing a z-score of 2 or greater is approximately 0.0228, or 2.28%. This is a small probability, so we would be surprised if the sample mean housebroken age for small breed dogs was at least 3 months more than the sample mean housebroken age for the large breed dogs.So, the answer is no. Not be surprised if the sample mean housebroken age for the small breed dogs is at least 3 months more than the sample mean housebroken age for the large breed dogs, as the probability of this happening is very small, 2.28%.Learn more about Probability here:
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Three line segments have measures of 18 units, 12 units, and 10 units. Will the segments form a triangle?
Does it form a triangle?
No, the segments will not form a triangle based on the line segments provided.
For three line segments to form a triangle, they must satisfy the triangle inequality theorem. The triangle inequality theorem states that for any triangle, the sum of the lengths of any two sides of the triangle must be greater than the length of the third side.
This is because if the sum of the lengths of any two sides is less than or equal to the third side, it would not be possible to form a triangle with those side lengths, as the two shorter sides would not be able to reach the longer side to form the triangle.
In this case, the sum of the two shorter segments (12 units + 10 units) is 22 units, which is less than the measure of the longest segment (18 units). Therefore, the three segments will not form a triangle.
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Please help me with my HW
Answer:
Step-by-step explanation:
(9a⁴b⁷) x (6a³b⁸)
(9 x 6) x (a⁴ x a³) x (b⁷ x b⁸)
54 x a⁷ x b¹⁵ = 54a⁷b¹⁵
Answer:
(9a⁴b⁷).(6a³b⁸)
=54a⁷b¹⁵
Why can't the sine of an angle be greater than 1?
Therefore, the sine of any angle can also only be between -1 and 1, inclusive.
What is an angle?An angle is a shape created by two rays that share a terminus and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are on the plane where the rays are located.
Define sides and vertices.Lines (line segments) and points make up the forms we perceive (vertices). To create a shape, these line segments are connected at their vertices. These lines' sides are what they are known as. The line segment that connects two vertices of a form or two-dimensional object is referred to as a side in geometry.
The sine of an angle can never be greater than 1 because the sine function maps an angle to the y-coordinate of the point on the unit circle that corresponds to that angle. The y-coordinate of any point on the unit circle is always between -1 and 1, inclusive. Therefore, the sine of any angle can also only be between -1 and 1, inclusive.
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Translate the triangle.
The enter the new coordinates.
A (-2,4)
C
(-3,2)
B
(1,1)
<-4, -1 >
A'(-6, [?])
B'([ ], [ ])
C'([], [])
Therefore , the solution of the given problem of triangle comes out to be A'(1, 0) (1, 0) , B'(1, 2) (1, 2) and C'(3,-2) (3,-2).
Explain the triangle.The fact that a triangle has four segments or vertices qualifies it as a polygon. It is an elementary geometric form. The name given to a triangle with endpoints A, B, then C is Triangle ABC. A singular plane and square are obtained in Euclidean geometry when the edges are not collinear. Any triangle that has three sides and three corners is a polygon. The triangle's corners are the spots at which its three sides intersect. 180 degrees is the result of three triangle angles.
Here,
The image A'B'C' is formed by our transformation rule, (+3,y-2)
So:
1. Describe the updated coordinates for points A', B', and C'?
In order to locate these new positions, we have:
A' (-23, 2-2) => A'(1, 0) (1, 0)
B' => (-23, 4-2) => B'(1, 2) (1, 2)
C'=> (0+3,0-2) => C'(3,-2) (3,-2)
2. Explain the qualities that would emerge if the respective vertices were linked together by lines.
We can notice the two triangles on the First Figure if we look closely. The green one is A'B'C, while the red one would be the triangle ABC.
The equivalent vertices with in second figure have been joined together by line segments, as shown by the green lines.
Two things can be said about those three lines: first, they are parallel, and second, they are all the same length.
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Why do 3 points make a plane?
In mathematics, a plane is a two-dimensional surface that can be enlarged indefinitely. In order to make a plane we need at least 3 points.
Why do 3 points make a plane?In order to make a plane we need at least 3 points. Let A, B and C are three points which can be defined by two particular vector AB and AC.
As the two vectors is located on the plane, we can use their cross product to define a normal vector on the plane.
As we see a triangle which is a two-dimensional geometric figure that is developed based on 3 points. Triangle is the smallest polygon. The other polygon needs more point for creation.
Therefore, it is proved that minimum three points is mandatory for plane formation.
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