Trigonometry is the study of relationships between angles and sides of a triangle.
The six trigonometric functions—sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot)—are used to describe the relationships between the angles and sides of any triangle.
The unit circle is a circle of radius one centered at the origin of a Cartesian coordinate system. When we determine the coordinates of points on the unit circle, we are using the six trigonometric functions. The unit circle is used to find the values of the trigonometric functions for angles of measures 0°, 30°, 45°, 60°, and 90°.
In the interval [0, 2π], we can use the unit circle to calculate the trigonometric functions of the angles in both degrees and radians. For example, sin 0° = 0, cos 0° = 1, tan 0° = 0, csc 0° = undefined, sec 0° = 1, cot 0° = undefined. The corresponding values in radians are sin 0 = 0, cos 0 = 1, tan 0 = 0, csc 0 = undefined, sec 0 = 1, cot 0 = undefined.
By using the unit circle, we can find the value of all six trigonometric functions for any angle in the interval [0, 2π], given in degrees or radians. We can also use the unit circle to find the trigonometric functions for any angle in any interval.
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2x+y=32
x+3y=36
solve the equation by elmination method
Answer: (x,y)=(12,8)
Step-by-step explanation:
. let x denote the annual salary of scientists in the united states, measured in thousands of dollars. suppose that e[x]
The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8. and The mean is the average. So the average, measured in thousands of dollars, is 56.
Average salary: 56
Standard deviation of the salary: 8
$56,000 dollars is 56 thousand dollars.
$8,000 is 8 thousand dollars.
The mean is the average. So the average, measured in thousands of dollars, is 56.
The standard deviation is $8,000. So, the standard deviation measured in thousands of dollars, is 8.
complete question
Let X denote the average starting salary for 2014 U.S. college graduates, measured in dollars. Suppose that the average annual salary is $56,000 dollars, with a standard deviation of 8,000. Find the mean and standard deviation when salary is measured in thousands of dollars.
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state whether the standardized test statistic t indicates that you should reject the null hypothesis. explain.
No, the standardized test statistic t does not indicate that you should reject the null hypothesis.
The value of the test statistic t only tells you how much of an effect the independent variable has on the dependent variable. To determine whether to reject the null hypothesis, you must compare the value of t to a critical value based on the sample size, the level of significance, and the degrees of freedom.
The standardized test statistic t does not indicate whether you should reject the null hypothesis. To determine this, you must compare the value of t to a critical value based on the sample size, level of significance, and degrees of freedom.
No, the standardized test statistic t does not indicate that you should reject the null hypothesis.
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At an amusement park, guests have to take either a train or a boat 22 miles from the parking lot to the front entrance and then back when they leave the park. The train goes 10 mph faster than the boat . Abdul takes the train into the park and the boat on his way back. The boat goes an average speed of 20 mph. How long did the round trip take?
Answer:
1 hour 50 minutes
Step-by-step explanation:
Total distance from parking lot to entrance = 22 miles
We will assume that the total distance from entrance to lot is also 22 miles
The average speed of the boat = 20mph
The average speed of the train is 10 mph faster = 20 + 10 = 30 mph
Time taken for travel from parking lot to park by train = 22/30 hours
22/30 hours = 22/30 x 60 minutes = 44 minutes
On the way back, the boat was taken
Distance = 22 miles, speed = 20 mph
Time taken = distance/speed = 22/20 hours
22/20 hours = 22/20 x 60 minutes = 66 minutes
Total round trip time taken = 44 + 66 = 110 minutes
110 minutes = 110/60 hours
= 1 50/60 = 1 hour 50 minutes
Let f: X - Y, where X and Y are the set of all real numbers, and x and h are real numbers. a. Find a function f such that the equation / (x + h) = / (x) + f (h) is not true for all values of x and h. Justify your reasoning. b. Find a function / such that equation / (x + h) = / (x) + / (h) is true for all values of x and h. Justify your reasoning. c. Let /(x) = 2*. Find a value for x and a value for h that makes f(x + h) = f(x) + / (h) a true number sentence.
Answer:
a. A function f such that the equation f(x + h) = f(x) + f(h) is not true for all values of x and h is a function that is not linear. For example, a function f(x) = x^2 is not linear because it does not satisfy the equation f(x + h) = f(x) + f(h).
b. A function f such that the equation f(x + h) = f(x) + f(h) is true for all values of x and h is a linear function. For example, a function f(x) = mx + b, where m and b are constants, is a linear function because it satisfies the equation f(x + h) = f(x) + f(h).
c. Let f(x) = 2x. If we choose x = 3 and h = 2, then f(x + h) = f(3 + 2) = f(5) = 2(5) = 10, and f(x) + f(h) = f(3) + f(2) = 2(3) + 2(2) = 6 + 4 = 10. Therefore, the equation f(x + h) = f(x) + f(h) is true in this case.
Which graph has infinite solutions
The graph that shows a system of equations with infinite solutions is graph C.
Which graph has infinite solutions?Here we have some systems of equations graphed.
A system of equations has infinite solutions when both equations are equivalent (in this case, both equations represent the same line)
Then we we look at the graph of the system of equations we will see a single graph instead of two, like what we can see on option C.
The graph that shows infinite solutions is graph C (the one in the top right side).
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If (5,-4) is a point on f(x), write an ordered pair that must be on the graph of y=f(x-2)-3
I already tried plugging 5 and -4 in for x, but that didn't work.
Answer:
(3,0)
Step-by-step explanation:
x - 2
5 - 2 = 3
3 would be our x value or our input value.
When the input is 3, the output is
3 - 3 = 0
This gives us the ordered pair
(3,0)
A student is trying to identify the composition of a pure metal block by determining its density. The student records the mass to be 20.0g. The rectangular block is 3.00cm x 4.00cm x 1.40cm. Calculate the density (in g/cm^3). Express your answer to the correct number of significant figures.
The block's density can be calculated using the equation d=25g/8.4 cm.
What are equations?Two things are equal, according to an equation.
For instance, 10 + 2 equals 6 + 6.
Simply put, this means that 10 plus 2 equals or is the same as 6 plus 6.
In an equation, the unknown could be present, as in 10 + x = 6 + 6.
So, find the block's volume first:
= Length * Width * Height
= 2 x 3 x 1.4
= 8.4 cm
Now that you know the volume and the mass, you can add them to the density formula, which is as follows:
= Mass / Volume
Assuming density is represented by the symbol b, the formula would be:
d = 25 g / 8.4 cm
Therefore, the block's density can be calculated using the equation d=25g/8.4 cm.
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Correct question:
A student is trying to identify the composition of a pure metal block by determining its density. The student records the mass of the sample to be 25.00 g. The rectangular block is 2.0 cm x 3.0 cm x 1.4 cm.
Which equation is necessary to determine the density sample?
What is one plus sixety-four
Answer:
65
Step-by-step explanation:
Answer:
like 149
Step-by-step explanation:
big brain
50 POINTS!!! Simplify each expression by combining like terms. NO SPACES in your answer.
−5.2t+8.2−7.8t
What is the answer in simpelest form?
Answer: -13t+8.2
Step-by-step explanation:
When combining like terms, only the same terms can be combined. In this case, it is -5.2t and -7.8t are the same. If we add them together, we got -13, unfortunately, 8.2 is different, so our simplest form is
-13t+8.2.
Write an equation in the form y = a(x-r)(x-s) to represent the parabola shown.
On solving the provided question, we can say that from the graph we have a equation [tex]y = x^2 - 3x - 4[/tex] => y= x(x+1) - 4(x+1) => y = (x+1)(x-4)
What is graphs?Mathematicians use here graphs to logically convey facts or values using visual representations or charts. A graph point will typically reflect a relationship between two or more things. Nodes, or vertices, and edges make form a graph, a non-linear data structure. Glue together the nodes, often referred to as vertices. This graph has vertices V=1, 2, 3, 5, and edges E=1, 2, 1, 3, 2, 4, and (2.5), (3.5). (4.5). Statistical charts (bar charts, pie charts, line charts, etc.) graphical representations of exponential growth. a logarithmic graph in the shape of a triangle
from the graph we have a equation
[tex]y = x^2 - 3x - 4[/tex]
y= x(x+1) - 4(x+1)
y = (x+1)(x-4)
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6.
Simplify. Write in scientific notation. (9 × 10-3)2
08.1 x 10-5
081 x 104
081 × 10-3
08.1 x 10-6
[tex]$\left(9 \times 10^{-3}\right)^2$[/tex] can be wrltten in sclentlflc notation as[tex]$8.1 \times 10^{-5}$[/tex]
What is scientific notation?If a number is too big or too small to be conveniently represented in decimal form, it can be expressed using scientific notation. It might also be known as standard form in the UK, scientific form, or standard index form. A simple approach to write numbers is in scientific notation. Since it is shorter, more efficient, and clearly indicates magnitude, it is particularly helpful when expressing extremely big or extremely small values. Every real number can be expressed as the product of two elements, a decimal portion and an integer power of ten. The default base value ought to be 10. The exponent must be an integer that is not zero; therefore, it may be either positive or negative.A number is written in scientific notation if it can be written as [tex]$p \times 10^x$[/tex]where p has value greater than or equal to 1 and less than 10 and x is an integer.
Given[tex]- $\left(9 \times 10^{-3}\right)^2$[/tex]
Flrst applying [tex]$(a b)^2=a^2 b^2$[/tex]
We get, [tex]$\left(9 \times 10^{-3}\right)^2=9^2 \times\left(10^{-3}\right)^2$[/tex]
using property of exponents [tex]$\left(a^n\right)^m=a^{n m}$[/tex]
[tex]$9^2 \times\left(10^{-3}\right)^2=81$[/tex] times [tex]$10^{-6}$[/tex]
Thus, we have to write 81 times[tex]$10^{-6}$[/tex]In scientific notation,
Multiply and divide by 10 , we get
81 times [tex]$10^{-6}=8.1 \times 10^{-5}$[/tex]
Thus, [tex]$\left(9 \times 10^{-3}\right)^2$[/tex]can be written in scientific notation as [tex]$8.1 \times 10^{-5}$[/tex]
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GRADES On his first five quizzes, Percy has earned scores of 24, 27, 22, 21, and 18 points. What score must Rachael earn on her sixth and final quiz so that both the mean and median of her quiz scores is 23?
Answer:
26
Step-by-step explanation:
To find the mean score of all six quizzes, you add all the scores and divide by the number of examinations. So if Percy's first five quiz scores are 24, 27, 22, 21, and 18, the total is 112. To find the mean score of all six quizzes, add Rachael's sixth quiz score to the total and divide by 6.
If the mean score of all six quizzes is 23, then the total score of all six examinations is 138 (23 x 6).
To find the score Rachael needs on her sixth quiz, you subtract Percy's score (112) from the total score of all six examinations (138)
Rachael needs to score 26 on her sixth quiz (138 - 112) for the mean and median of her quiz scores to be 23
in one or two well-crafted paragraphs, summarize how neurons communicate at the synapse. your paragraph must include each of the following terms. underline each term in your paragraph. synapse action potential neurotransmitters vesicles axon dendrites axon terminal receptors
Dendrites first receive electrical signals from other neurons, after which an action potential is sent down the axon until it reaches the axon terminal. The vesicles then set the neurotransmitters in motion. Neurotransmitters will then travel to the synapse, where receptors will begin to transmit the signal.
What is neurotransmitters?A neurotransmitter is a signaling molecule that a neuron secretes to affect another cell across a synapse. The cell receiving the signal, which could be any major body part or target cell, could be another neuron or a gland or muscle cell. Neurotransmitters are chemical messengers required by your body to function. They are in charge of moving chemical signals (called "messages") from one neuron (nerve cell) to the next target cell. The next target cell might be another nerve cell, a muscle cell, or a gland.
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brainstorm consider what kind of program you would like to build. as you do, think about how your program can fulfill the coding requirements the college board outlines. remember, you need a list, an algorithm that uses sequencing, selection and iteration and a procedure that uses parameters.
The total score will be used to determine the student’s final admissions status.
I would like to build a program that calculates a student's score for a college admissions test. The program will be based on the coding requirements outlined by the college board, which include a list, an algorithm that uses sequencing, selection and iteration and a procedure that uses parameters.
The list will contain the student’s scores for each section of the admissions test. The algorithm will use sequencing to add the scores of each section together. Selection will then be used to determine whether the student has met the minimum requirements, and iteration will be used to keep track of any sections that were not completed. The procedure will be used to calculate the student’s total score, using parameters such as the number of sections completed and the scores for each section. The total score will be used to determine the student’s final admissions status.
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show that the least squares cost function for linear regression written compactly as in section 3.1.3
The cost function is minimized when the predicted values are as close as possible to the actual values, which is achieved by finding the optimal values of the parameters θ.
What is the least squares cost function?
The least squares cost function for linear regression is used to measure the difference between the predicted values and the actual values of the target variable. It is defined as the sum of the squared differences between the predicted values and the actual values.
The compact form of the cost function is given by:
J(θ) = (1/2m) * Σ(i=1 to m) (hθ(x^i) - y^i)^2
where:
hθ(x^i) is the predicted value of the target variable for the ith sample, given by the hypothesis function hθ(x^i) = θ^T * x^i
y^i is the actual value of the target variable for the ith sample
θ is the vector of parameters for the linear regression model
m is the number of samples in the dataset
Hence, The cost function is minimized when the predicted values are as close as possible to the actual values, which is achieved by finding the optimal values of the parameters θ.
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Cola Root Beer Lemon-line
Under 21 years of age 40 25 20
Between 21 and 40 35 20 30
Over 40 years of age 20 30 35If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.
The probability of the person over 40 years of age who drinks root beer is equal to 0.1176.
As given in the question,
Total number of people is equal to 255
From the given table :
Number of people who drinks root beer and over 40 years of age is
= 30
Required probability who drinks root beer and over 40 years of age is given by :
= ( Number of favourable outcomes ) / ( total number of outcomes )
= ( 30 / 255 )
= 0.1176
Therefore, the required probability of the people over the age of 40 years and drinks root beer is given by 0.1176.
The above question is incomplete , the complete question is :
Cola Root Beer Lemon-line
Under 21 years of age : 40 25 20
Between 21 and 40 : 35 20 30
Over 40 years of age : 20 30 35 If one of the 255 subjects is randomly selected, find the probability that the person is over 40 years of age or that they drink root beer.
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John Corporation produces widgets. The fixed expenses are $45,000,
and the variable expenses are $9 per widget. Express the total expense E
in terms of q, where q is the quantity of widgets produced. (Hint: E = V + F).
The total cost E expressed as a function of q, wherein q is the number of widgets manufactured= E = 9q + 45,000.
What is fixed expenses?Changes in sales or production volume have no effect on costs or expenses that are constant. They cover costs like rent, insurance, membership dues and subscriptions, equipment leases, loan payments, depreciation, management salaries, and advertising.
What exactly are variable expenses?Variable costs are expenses that alter as the volume of a product or service that a company produces fluctuates. The total of marginal costs over all units produced is what is referred to as variable costs. They may also be regarded as ordinary expenses. The two parts of total cost are fixed costs as well as variable costs.
According to the given information:The fixed expenses = $45,000,
The variable expenses = $9
E = V + F
E = 9q + 45,000
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In the figure below, the segments HI and HJ are tangent to the circle centered at O. Given that OI=8 and OH=11.6, find HJ.
Answer:
HJ = 8.4
Step-by-step explanation:
tangents to a circle from an external point are congruent , then
HJ = HI
the angle between a tangent and a radius of the circle at the point of contact is a right angle.
so Δ OHI is right with ∠ OIH = 90°
using Pythagoras' identity in the right triangle
HI² + OI² = OH² , that is
HI² + 8² = 11.6²
HI² + 64 = 134.56 ( subtract 64 from both sides )
HI² = 70.56 ( take square root of both sides )
HI = [tex]\sqrt{70.56}[/tex] = 8.4
Then
HJ = HI = 8.4
There are 80 pupils in a group. The only languages available for the group to study are Russian and Spanish. 50 pupils study Russian. 31 pupils study Spanish. 23 pupils study neither Russian nor Spanish. Find the probability to select a pupil that studies Spanish and Russian. Probability
3/10
Explanation
The total number of people that are studying neither Russian nor Spanish will be subtracted from the total number of people
i.e 80-23=57
Now let's calculate those that studies both languages (x)
50+31-x=57
-x=57-50-31
-x=-24
x=24
probability of choosing those that studies both Spanish and Russian is
24/80=3/10
Answer:
33 out of 80 pupils
Step-by-step explanation:
Total = 80 pupils
Studying Russian and Spanish = 80 - 23;
= 57 pupils
Out of 57 pupils, 50 pupils study Russian = 7 diff.
Out of 57 pupils 31 pupils study Spanish = 26 diff.
show that the least squares residuals e are heteroskedastic and correlated, even if the disturbance vector e is homoskedastic and uncorrelated.
The least squares residuals e are heteroskedastic and correlated, even if the disturbance vector e is homoskedastic and uncorrelated.
The least squares residuals e are heteroskedastic and correlated even if the disturbance vector e is homoskedastic and uncorrelated because the variance of the observed errors, Var(e) = Var(X'e) = X'Var(e)X. As X'e is not a vector of independent random variables, the variance-covariance matrix of the errors is not diagonal and therefore the errors are correlated and heteroskedastic. This can be calculated by the formula Var(X'e) = X'Var(e)X. This formula shows that the variances of the least squares residuals e depend on the parameters of the model, and that the errors are therefore correlated and heteroskedastic.
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What is BD?
In triangle ABC, the length of side AB is 12 and the length of side AD is 27. The line AC started from point A and cuts the side BD a point C. The length of BC is x and the length of CD is x + 5.
The procedures below can be used to determine a triangle's length BD.
In th that is presented;
The holding ratio is, therefore, as follows:
12 : x = 27 : x + 5
12 / x = 27 / (x + 5 )
When we cross multiply these, we obtain:
12 ( x + 5 ) = 27x
12x + 60 = 27x
Taking the x values on one side, we obtain:
27x - 12x = 60
15x = 60
x = 60/15
x= 4
The length of line BD is:
= BC + CD
= x + x + 5
After entering the value of x, we get
= 4 + 4 + 5
= 13
As a result, the length of the line BD is 13.
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Sample surveys show that fewer people enjoy shopping than in the past.
A recent survey asked a nationwide random sample of 2577 adults if they agreed or disagreed that "I like buying new clothes, but shopping is often frustrating and time-consuming."
The population that the poll wants to draw conclusions about is all U.S. residents aged 18 and over.
Suppose that in fact 62% of all adult U.S. residents would say "Agree" if asked the same questions.
What is the probability that 1610 or more of the sample agree?
The likelihood that at least 1610 members of the sample agree is 0.3385.
What is meant by probability?How likely something is to occur is known as its probability. We can discuss the probabilities of various outcomes how likely they are when we aren't sure how a particular event will turn out. Statistics describes the examination of events subject to probability. The quantity of possible outcomes is known as probability. all events that could possibly occur. For instance, there is a 1 in 2 chance of receiving a head when flipping a coin, and there are 2 possible outcomes overall (a head or tail). P(heads) = 12 is the formula.Probability is a measure of how likely it is for a given event to take place.Given,
sample std = sqrt[0.62 × 0.38/2577]
= 0.0096
sample proportion = 1610/2577
= 0.6240
z(0.6240) = (0.6240-0.62)/0.0096
= 0.4167
P(x >= 1610) = P(z >= 0.4167)
Then we get,
= 0.3385
Hence, The likelihood that at least 1610 members of the sample agree is 0.3385.
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دین
-10
26. The drama club is selling tickets for the upcoming play. Each student ticket costs $5.50 and each adult
ticket costs $9.50. If the Drama Club sold 98 tickets and raised $703, write a system of equations to figure out
how many of each ticket was sold. Find how many of each ticket was sold.
A total of 57 student tickets and a total of 41 adult tickets were sold to generate a total revenue of $703.
What is the definition of an equation?A mathematical statement known as an equation is composed of two expressions joined together with the equal sign. A formula would've been 3x - 5 = 16, for illustration.. When this equation is solved, we discover that the quantity of the variables x is 7.
The following response has been produced in a straightforward, step-by-step manner.
Step: 1
Price of each student ticket = $ 5.50
Price of each adult ticket = $ 9.50
If x Equals the quantity of student tickets sold
If y Equals the quantity of adult tickets sold,
Step: 2
(i). It is given that a total of 98 tickets were sold.
Therefore, we can write as -
(Number of student tickets sold) + (Number of adult tickets sold) = 98
x+y =98 -----------equation (1)
Step: 3
(ii). The total revenue earned from the sale of tickets was $703.
Therefore, we can write as -
(Revenue earned from selling student tickets) + (Revenue earned from selling adult tickets) = 703
(Price of each student ticket×Number of student tickets sold) + (Price of each adult ticket ×Number of adult tickets sold) = 703
(5.50 × x)+ (9.50 × y) =703
5.50x+9.50y =703 ----------equation 2
Step: 4
System of Equations :
1) x+y =98
2) 5.50x + 9.50y =703
On performing (eq 2) - 5.50(eq 1), we get -
(5.50x +9.50y) - 5.50(x+y)=703-5.50(98)
5.50x + 9.50y - 5.50x-5.50y=703-539
4y=164
y=164/4
y=41
The operation was performed to reduce the equation in a single variable.
Step: 5
On substituting the value of y=41 in eq 1 , we get-
x+41 =98
x= 98-41
x=57
Thus, a total of 57 student tickets and a total of 41 adult tickets were sold to generate a total revenue of $703.
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Then Venn diagram shows sets shade (A n B) ‘U C’
Venn diagram you mentioned illustrates the connection between A, B, and C, three sets. set (A n B), which is the intersection of two sets, is represented as region where A and B overlap. Scroll down for more detail.
What Is A Venn Diagram?A Venn Diagram is a pictorial representation of the relationships between sets.
The relationship between the three sets A, B, and C is depicted in the Venn diagram you are referring to. The set (A n B), which is the intersection of the two sets, is represented as the region where A and B overlap. The set (A U C) or the union of the sets A and C is represented by the region outside of this intersection but inside the larger circles. In the universal set, this is sometimes referred to as the complement of (A n B).
The following figures show how to shade regions of Venn Diagrams for two sets:
A intersect B, A union B, A’, A intersect B’, A’ intersect B, A union B’,
A’ union B, A’ union B’ = (A intersect B)’, A’ intersect B’ = (A union B)’.
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create the following tables and calculate the average: mean use the additional column to caculate the frequency subtotal
To create the tables and calculate the average mean, we need to have a set of data that we want to organize in a tabular form. The table should have columns for the data values, frequency, and frequency subtotal. The frequency column will show how many times a particular data value appears in the set.
The frequency subtotal column will be used to find the sum of the product of each data value and its corresponding frequency.
The average mean can be calculated by dividing the sum of the frequency subtotal by the total frequency.
Mean = ([tex]f_{1}x_{1}[/tex] + [tex]f_{2}x_{2}[/tex]+ [tex]f_{3}x_{3}[/tex]+ ... + [tex]f_{n}x_{n}[/tex]) / ([tex]f_{1}[/tex]+[tex]f_{2}[/tex]+[tex]f_{3}[/tex]+...+[tex]f_{n}[/tex])
By creating this table, we can easily see the distribution of the data and can calculate the average mean. This method of organizing data in tabular form is commonly used in statistics and data analysis, and it is an efficient way of summarizing and understanding large sets of data.
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When we have a distribution of a variable, we know or have a sense of two qualities. Select the two qualities: How often we observe each of the possible values of a variable. - The experimental units involved in the study.- The explanatory and response variables of a study. - The possible values the variable can take on.- The observational units involved in the study
The possible values the variable can take on and how often we observe each of the possible values of a variable.
The possible values the variable can take on and how often we observe each of the possible values of a variable.
A distribution of a variable describes the possible values the variable can take on and how often we observe each of the possible values of a variable. It does not describe the experimental units involved in the study or the explanatory and response variables of a study, nor does it describe the observational units involved in the study. The possible values the variable can take on and how often we observe each of the possible values of a variable.
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Neeedd helpppp !!!! I only have a little bit of time
The value of m∠1 is 50°. The solution is obtained using properties of angle and triangle.
What is an angle?
When two rays are brought together at a single point, an angle is created. The two rays in this instance are referred to as the arms of the angle, while the common point is known as the node or vertex. The symbol "∠" stands for an angle. Angle is a derivative of the Latin word "Angulus."
In the figure, we are given a right-angled triangle which means that one angle in the triangle measures 90°.
We are given an exterior angle equal to 140°.
We know that angles on a straight line form a linear pair which means that their sum is 180°.
Let the angle on the straight line be 'x'.
So, we get
⇒x + 140° = 180°
⇒x = 40°
Now, we know that in a triangle, the sum of all the angles is 180°.
Therefore,
⇒m∠1 + 90° + 40° = 180°
⇒m∠1 + 130° = 180°
⇒m∠1 = 50°
Hence, the value of m∠1 is 50°.
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you are given a vector in the xy plane that has a magnitude of 90.0 units and a y component of -45.0 units. there are two possibilities for the x component - one positive and one negative. please provide the positive possibility.
The positive possibility of the [tex]x[/tex] component in a vector in the XY plane that has a magnitude of 90 units and the [tex]y[/tex] component is -45 units is [tex]+77.94[/tex].
Given,
The magnitude of the vector, [tex]M[/tex] = 90 units
The y component of the vector, [tex]y[/tex] = -45 units
We know that,
The magnitude of the vector can be expressed as:
[tex]M^{2} = x^{2} +y^{2}[/tex]
[tex]x^{2} =M^{2} -y^{2}[/tex]
Substitute the values in the above equation, and we get :
[tex]x^{2} = (90)^{2} - (-45)^{2}[/tex]
[tex]x^{2} = 8100 - 2025[/tex]
[tex]x^{2} = 6075[/tex]
[tex]x=[/tex] ±[tex]77.94[/tex]
Hence, the Positive possibility of [tex]x[/tex] the component is 77.94
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Two times the interior angle of a regular polygon is equal to seven times is exterior angle. Find the interior angle of the polygon and the number of sides in it.
The interior angle of a regular polygon with n sides is (n-2) times 180 degrees divided by n.
The exterior angle of a regular polygon with n sides is 360 degrees divided by n.
A polygonal shape is what?
A polygon is a two-dimensional, closed form that is flat or planar and is limited by straight sides. Its sides are not curled. A polygon's edges are another name for its sides. The vertices (or corners) of a polygon are the places where two sides converge.
Given that 2 * interior angle = 7 * exterior angle, we can set up the following equation:
2 * ( (n-2) * 180 / n ) = 7 * ( 360 / n )
Solving for n, we get:
n = (1440 / (2*(7-180)) ) = 9
So the polygon has 9 sides. To find the interior angle, we substitute n back into the formula:
(n-2) * 180 / n = (9-2) * 180 / 9 = 160
So the interior angle of the polygon is 160 degrees.
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