By using the Pythagorean identities we can find the sine of an acute angle.
What is angle ?
An angle is a measure of rotation about a point or a line. It is a geometric concept that describes the amount of rotation between two lines or planes. Angles are typically measured in degrees or radians.
What is acute angle ?
An acute angle is an angle that measures less than 90 degrees. It is an angle that is smaller than a right angle. Acute angles are commonly found in triangles and other geometric shapes. They are represented by the symbol "α" (alpha) in trigonometry.
What is Pythagorean identities?
The Pythagorean identities are a set of trigonometric identities that are based on the Pythagorean theorem. They relate the sine, cosine, and tangent of an angle to the ratios of the sides of a right triangle. The Pythagorean identities can be used to find the sine of an acute angle by relating it to the ratio of the opposite side to the hypotenuse of a right triangle.
Specifically, the identity [tex]sin^2(x) + cos^2(x) = 1[/tex] can be used to find the sine of an acute angle x by first finding the cosine of x and then subtracting it from 1.
The equation becomes [tex]sin(x) = \sqrt{1 - cos^2(x)}[/tex].
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Joseph wants to earn $850 this summer in order to pay for a down payment on a car. His summer break is 6 weeks. He has been offered 3 different jobs.
Which job should he take to earn the $850 quickest? Explain your response.
Working as a cashier in a bookstore that pays $7.50 an hour and he is expected to work 25 hours per week
Working at a summer camp as a camp counselor for a flat rate of $175 per week (the camp is only 4 weeks)
Working as a sales associate at a department store that pays $7.25 an hour with 5% commission on all sales (he is expected to work 20 hours per week and projected to sell $1,350 per week)
B. Which job will not help him get to his goal of $850?
Answer:
A - Sales associate
B - Summer Camp Counselor
Step-by-step explanation:
First, lets look at how much Joseph would averagely earn from each job.
Cashier in bookstore: in 6 weeks he will earn 900
Summer camp counselor: in 4 weeks 700
Sales associate: in 4 weeks he will earn 850
Overall, becoming a Sales associate will allow Joseph to earn his $850 quicker.
B - the Summer Camp Counselor job will not allow Joseph to make $850 because Summer Camp only lasts 4 weeks.
What are the 4 system of equations?.
There are four systems of equations in mathematics, namely linear equations, quadratic equations, polynomial equations, and exponential equations.
Each has its own unique properties that can be exploited for solving problems. Linear equations are the simplest system of equations and are the basic building blocks of more advanced systems of equations. Quadratic equations use the product of two terms to solve one equation. For example, 5x + 6y = 20 can be rewritten as 2x + 5y = 20. Polynomial equations use the power of a term squared to solve one equation. For example, x^2 + 7x + 12 = 55 can be written as x2 + 9x + 22 = 55. Exponential equations use the power to the base to solve one equation. For example, x^3 + 3x^2 - 10x - 16 = 0 can be written as x^3 + 3x^2 - 10x - 16 = 0e^-3 = e. These systems can be used to represent real world scenarios such as population growth,
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How do you find the nth term of Class 10?.
The nth term of an arithmetic sequence is given by aₙ = a + (n – 1).
A series in which the differences between each pair of following terms are the same is known as an arithmetic progression (AP). A formula for the nth term of the AP could be derived from this kind of progression. Because it follows a pattern where each number is acquired by adding 4 to the preceding term, the sequence 2, 6, 10, 14,... is an example of an arithmetic progression (AP). In this series, the nth term equals 4n-2. By changing the nth term to n=1,2,3,..., the sequence's terms can be obtained. i.e.,
First term when n = 1 is 4n-2 = 4. (1)
-2 = 4-2=2
second term = 4n-2 = 4 when n = 2 (2)
-2 = 8-2=6
The third term is 4n-2 = 4 for n = 3. (3)
-2 = 12-2=10
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What is the formula of sum of series?.
In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.
Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.
Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.
So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.
If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:
S
3
=2+4+6
S3=12.
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Answer:
Step-by-step explanation:
In the context of mathematics, a series has a stagnant difference between terms. Therefore , we can find out the sum of the terms in arithmetic series by multiplying the number of times the average of the very last and first terms.
Thus we can observe that series and knowing the sum of the terms of series is a very crucial task in mathematics. In this head, we will talk about some very known series and series formulas with instances.
Actually, a series in math is very easy the sum of the different numbers or elements of the series. For instance, to make a series from the channel of the first five positive integers 1, 2, 3, 4, 5 we will simply sum them up. Therefore 1 + 2 + 3 + 4 + 5 is a series.
So, the series of a sequence is the sum of the sequence to some given number of terms, or occasionally til infinity. It is frequently written as S_n.
If the series is 2, 4, 6, 8, 10, … , then the sum of the first 3 terms:
S
3
=2+4+6
S3=12.
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A fair six-sided number cube has the following faces: 1, 1, 2, 2, 5, 6. This number cube is rolled 50 times. What is the
probability that fewer than 30% of the rolls result in a two?
Find the z-table here.
O 0. 309
O 0. 421
O 0. 450
O 0. 691
The probability that fewer than 30% of the rolls result in a two is 0.450.
What is probability ?
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
To find the probability that fewer than 30% of the rolls result in a two, we can use a normal distribution to model the number of twos rolled in 50 rolls.
Let's assume that the mean number of twos rolled in 50 rolls is μ = 50 * (2/6) = 16.67 (since the probability of rolling a two is 2/6). The standard deviation can be calculated as σ = sqrt(50 * (2/6) * (4/6)) = 2.94.
Now, we can use the normal distribution to find the probability that the number of twos rolled is less than 15 (30% of 50 rolls), which is P(X < 15) = P((X - μ) / σ < (15 - 16.67) / 2.94). We can use a standard normal table (z-table) to find this probability, which is approximately 0.450.
Therefore , the probability that fewer than 30% of the rolls result in a two is 0.450.
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There is a 0.450 percent probability that fewer than 30% of rolls will produce a two.
The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.
We can predict the frequency of twos rolled in 50 rolls using a normal distribution to determine the likelihood that less than 30% of the rolls produce two.
Given that the probability of rolling a two is 2/6, let's assume that the mean number of twos rolled in 50 rolls is = 50 * (2/6) = 16.67.
Calculating the standard deviation is as follows:
sqrt(50 * (2/6) * (4/6) = 2.94.
The chance that the number of twos rolled is less than 15 (30% of 50 rolls) can now be calculated using the normal distribution, and it is given by P(X 15) = P((X - ) / (15 - 16.67) / 2.94). It is possible to determine this probability, which is around 0.450, using a common normal table (z-table).
As a result, 0.450 represents the likelihood that fewer than 30% of rolls will produce a two.
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The length of a rectangle is three meters less than four times its width. If the perimeter of the rectangle is 74 meters, what is the length of the rectangle?
The length of the rectangle is L = 29 meters
What is the Perimeter of a Rectangle?The perimeter P of a rectangle is given by the formula, P=2 ( L + W) , where L is the length and W is the width of the rectangle.
Perimeter P of rectangle = 2 ( Length + Width )
Given data ,
Let the length of the rectangle be represented as L
Let the width of the rectangle be represented as W
Now , Perimeter P of rectangle = 2 ( Length + Width ) = 74 meters
And , length of a rectangle is three meters less than four times its width
Substituting the values in the equation , we get
L = 4W - 3
And , 74 = 2 ( 4W - 3 + W )
Divide by 2 on both sides of the equation , we get
37 = 5W - 3
Adding 3 on both sides of the equation , we get
5W = 40
Divide by 5 on both sides of the equation , we get
W = 8 meters
Now , the length of the rectangle L = 4 ( 8 ) - 3
Length of the rectangle L = 32 - 3 = 29 meters
Hence , the length of the rectangle is 29 meters
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5. Nina is reselling t-shirt and pants, to avail a discount she to order at least 30 t-shirts. If the
discounted price of t-shirt is Php 150. 00 and the price of pant Php 600. 00, at least how many parts
she can buy with Php8. 0. 00?
a. At least 5 b. At least 6
c. At least 8
d. At least 10
The correct option is a. At least 5 which indicates the number of pants that can be bought.
To avail discount Nina needs 30 shirts. So, calculating the cost on buying minimum required number of t-shirts.
So, 150 × 30 = php 4,500
Total php available with Nina = 8,000
Now, leftover money for pants = total money - money spent on t-shirts
Leftover money for pants = 8000-4500
Leftover money for pants = 3500
Now, total pants Nina can buy = leftover money divided by php for pants
So, 3500/600=5
Thus Nina should buy atleast 5 pants.
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Work out the value of 3 2/5 × 10
Give your answer as a whole number or as a
fraction in its simplest form.
To work out the value of 3 2/5 × 10, we need to first convert the mixed number 3 2/5 into an improper fraction. To do this, we multiply the whole number (3) by the denominator (5) and add the numerator (2) to get:
3 2/5 = (3 x 5) + 2 / 5 = 15 + 2 / 5 = 17/5
Now that we have the improper fraction, we can multiply it by 10:
17/5 x 10 = (17 x 10) / (5 x 10) = 170 / 50 = 34 / 10
The answer is 34/10, which can be simplified to 17/5. Therefore, the value of 3 2/5 × 10 is 17/5.
Yu Yan make a wall hanging from a piece of fabric. For the firt part, he cut off 1/3 of the length of the original piece of fabric. For the next two part, he cut off 10 inche and 5 inche from the length of the remaining fabric. In total, he cut 35 1/2 inche from the length of the original piece of fabric. How long wa the original piece of fabric? Write and olve an equation. Check your olution.
The length of the original piece of fabric is 61 1/2 inches.
Let x be the length of the original piece of fabric.
If the first cut is 1/3 of the length of the original fabric, then we can express that as an algebraic expression 1/3x.
The next two cuts made from the remaining fabric is 10 inches and 5 inches.
10 + 5 = 15 inches
Therefore, the total length that was cut off was 1/3x + 15 inches = 35 1/2 inches.
With the algebraic equation written, solve for x.
1/3x + 15 = 35 1/2
To solve for x, isolate the terms containing the variable x on one sie and the constant terms on the other side.
1/3x = 35 1/2 - 15
1/3x = 20 1/2
Multiply both sides by 3 to get x.
1/3x = 20 1/2
x = 61 1/2 inches
Therefore, the original length of the fabric was 61 1/2 inches.
We can check our solution by adding the length of the cuts off to the original length:
1/3(61 1/2 inches) + 10 inches + 5 inches = 20 1/2 + 10 + 5 = 35 1/2
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pls hell i’m stuck on this it’s hypotenuse leg theorem
By solving a system of equations we will see that:
t = 33 and u = 308
Which values of t and u make the triangles congruent?
The two triangles will be congruent if the correspondent sides have the same measure, then we can write two equations (or a system of equations) like the one below:
16t = 6u
20t -44 = 2u
So we have a little system of equations to solve.
We can isolate u on the second equation to get:
u = (20t - 44)/2
u = 10t - 22
Now we can replace that on the other equation to get:
16t = 6*( 10t - 22)
16t = 60t - 132
We can solve this for t to get:
132 = 60t - 16t
132 = 44*t
132/44 = t
33 = t
And the value of u is:
u = 10t - 22
u = 10*33 - 22 = 308
The values are t = 33 and u = 308
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Determine which function(s) are exponential. Select all that apply.
A.
x 0 1 2 3 4
y 0 1 4 9 16
B.
x 0 1 2 3 4
y 13
1 3 9 27
C.
x 0 1 2 3 4
y 5 52
54
58
516
D.
x 0 1 2 3 4
y 4.5 4 3.5 3 2.5
Only table {1} represents a exponential function.
What is exponential function?The exponential function is a mathematical function denoted by the expression as - f(x) = eˣReal exponential function is commonly defined by the following power series as -[tex]$e^{x} =\sum _{k=0}^{\infty }{\frac {x^{k}}{k!}}=1+x+{\frac {x^{2}}{2}}+{\frac {x^{3}}{6}}+{\frac {x^{4}}{24}}+\cdots }[/tex]
Given are the function tables as shown in the question.
For the table {1}, we have -{x} → 0 1 2 3 4
{y} → 0 1 4 9 16
The value of {y} varies with respect to {x} as : y = x². This is an exponential function.Therefore, only table {1} represents a exponential function.
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What is the product of 3 fractions?.
The product of three fractions is acquired by multiplying the numerators and then multiplying the denominators of the three fractions to get the product fraction.
To find the product of any 3 fractions, multiply the three numerators. After that, multiply the three denominators. After the product of numerators and denominators, write them as fractions. This method will provide the product of 3 fractions in fractional form. To obtain this fraction in decimal form, divide the numerator of the fractional product by its denominator.
For example, consider the fractions 1/5 × 2/5 × 3/5.
In this, first multiply all the numerators: 1×2×3 = 6
Similarly, multiply all the denominators: 5×5×5 = 125
Now, the product of the three fractions is 6/125.
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Write A Exponential growth model
inital value 2,000 growth rate 6%
The exponential growth model is given by the equation y = 2000(1.06)ˣ
What is an equation?An equation is an expression showing the relationship between numbers and variables.
An exponential function is in the form:
y = abˣ
a is the initial value and b is the multiplication factor. if b > 1, it is an exponential growth whereas if b < 1, it is an exponential decay.
A Exponential growth model initial value 2,000 growth rate 6%, hence a = 2000, b = 100% + 6% = 1.06
The exponential model becomes y = 2000(1.06)ˣ
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compute the limit of the given trigonometric function
lim x→0 x csc x =
Answer:8u6
Step-by-step explanation:
8+9_rjs_+5
Question What is the value of x? Enter your answer in the box. x = Two intersecting lines. The angle formed at the top is labeled 3 x plus 50 degrees. The angle formed at the bottom directly opposite it is labeled 6 x minus 10 degrees.
The value of x when solving for the alternate angles is; x = 20 degrees
How to solve alternate angles?Alternate angles are defined as angles that occur on the opposite sides of the transversal line and thus have the same size. There are two different types of alternate angles namely alternate interior angles and alternate exterior angles 3x + 50 degrees and 6x - 10 degrees are alternate angles and as such;
3x + 50 = 6x - 10
Rearrange to collect like terms to get;
6x - 3x = 50 + 10
3x = 60
x = 60/3
x = 20 degrees
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X and Y are 2 sets such that X has 15 elements, Y has 25 elements and X (union) Y has 40 elements.
Find the number of elements in X (intersection) Y
The number of elements in the set that represents the intersection of X and Y is given as follows:
Zero.
How to obtain the number of elements in the intersection of X and Y?The number of elements in the intersection of X and Y is obtained according to the rule presented as follows:
n(X or Y) = n(X) + n(Y) - n(X and Y).
The parameters for this problem have the values given as follows:
n(X) = 15.n(Y) = 25.n(X or Y) = 40.Hence the number of elements in the intersection set is given as follows:
n(X or Y) = n(X) + n(Y) - n(X and Y).
40 = 15 + 20 - n(X and Y)
n(X and Y) = 0.
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please help me- speed
Answer:
4 km per hour
Step-by-step explanation:
Use the point (15,1) Since the line is proportional, the slope is y/x or 1/15
1/15 this is in minutes
1/15 x 60/1 To convert to hours
4 km per hour
Answer:
4 Km per hour
Step-by-step explanation:
average speed (S) is calculated as
S = [tex]\frac{D}{T}[/tex] ( D is distance and T is time, in hours )
the distance ( vertical axis ) from her home to the newspaper shop is 1 Km
time ( horizontal axis )
from 09 00 to 09 30 has 6 divisions
then 1 division = 30 minutes ÷ 6 = 5 minutes
time to walk to the shop is 3 divisions = 3 × 5 = 15 minutes
15 minutes = [tex]\frac{15}{60}[/tex] of an hour = [tex]\frac{1}{4}[/tex] hour
then average speed from home to newspaper shop is
S = [tex]\frac{1}{\frac{1}{4} }[/tex] = 4 Km per hour
How do you find the domain and range given points on a graph?.
To find the domain and range from given points on a graph: the set of all x-coordinates is the input and the set of all y-coordinates is the output.
We know that the domain of function is the set of all possible input values for which the function is well defined.
And the range of function is the set of all possible output values for given input.
To find the domain and range of function we can graphical methhod.
We know that the input values of function are shown on the x-axis and the output values of the function are shown on the y-axis.
This means, the domain of a graph shown on the x-axis. Whereas the range is shown on the y-axis.
To find the domain and range when points on a graph are given:
the set of all x-coordinates would be the domain and the set of all y-coodinates is the range of function.
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The movie starts at 1:40 pm and ends at 6:03 pm. How long is the movie?
Answer:4 hours and 23 minutes
Step-by-step explanation:1:40-5:40 is 4 hours. Then add 20 minutes and you get to 6 o'clock. Then finally add 3 minutes and you get to 6:03. When you add 4 hr + 20 min + 3 min you get 4 hours and 23 minutes.
prove that:cosA/sinA -sinA/cosA=2cos^2A-1/sinA cosA
Answer:
To prove that cosA/sinA -sinA/cosA=2cos^2A-1/sinA cosA, we can start by multiplying both sides of the equation by sinA cosA:
cosA/sinA -sinA/cosAsinA cosA = (2cos^2A-1)/sinA cosAsinA cosA
Now we can simplify the left side of the equation by using the identity sin^2A + cos^2A = 1:
cosAcosA -sinAsinA = (2cos^2A-1)cosAsinA
Now we can simplify the right side of the equation by using the identity cos^2A = 1 - sin^2A:
cosAcosA -sinAsinA = (2(1 - sin^2A)-1)cosAsinA
Finally, we can simplify the right side of the equation by using the identity sinAcosA = (sinAcosA)/(sinA*cosA):
cosAcosA -sinAsinA = (2(1 - sin^2A)-1)(sinAcosA)/(sinA*cosA)
Since both sides of the equation are equal, we can conclude that the statement is true.
What is the slope and y − intercept of the equation y 2x 4 *?.
The curve has a y-intercept of -4 and a slope of 2. We will need two points on the line y = 2x - 4 to plot the graph.
Y = 2x + b, where b is the y-intercept, is how the equation y = 2x - 4 can be expressed in slope-intercept form. We must perform the b-solve in order to determine the slope and y-intercept of the equation.
The line's crossing of the y-axis is known as the y-intercept. Setting x equal to 0 in the equation yields y = 2(0) - 4 and the y-intercept, which can be found. As a result, the y-intercept is determined to be y = -4.
The pace at which a line increases is referred to as its slope. Using the coefficient of x, which is 2, we can get the slope. Consequently, the slope of the equation is 2. Y = 2x – 4.
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Full Question = What are the slope and y − intercept of the equation y 2x − 4?
Todos los Factores de 28?
Answer: 1,2,4,7,14 and 28
Step-by-step explanation: Todos los Factores de 28 = Factors of 28
Theo drove 228 miles in 4 hours. Lex drove 201 miles in 3 hours. At those rates, could either man drive 112 miles in 2 hours? Complete the explanation
Ankit visited in a mall with his father. He sees that three shops are situated at P, Q, R as shown in the figure from where they have to purchase things according to their need. Distance between shop P and Q is 8 m, that of between shop Q and R is 10 m and between shop P and R is 6 m.
The measure of angle PQR is given as follows:
How to obtain the measure of angle PQR?To obtain the measure of angle PQR, first we verify if the triangle PQR is a right triangle or not.
To verify if the triangle is a right triangle we apply the Pythagorean Theorem, which states that the length of the hypotenuse squared is equals to the sum of the lengths of each side squared, in the case of a right triangle.
Hence, for this problem, considering the side lengths, we have that:
10² = 6² + 8²
100 = 36 + 64
100 = 100.
Which is true, hence this is in fact a right triangle and the measure of angle PQR is of 90º.
Missing InformationThe problem asks for the measure of angle PQR.
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What is the solution to the system of equations y equals 5x 3 and y equals 1?.
The solution of the given equations is x= 0.4 and y= 1.
The system of equations is y = -5x + 3 and y = 1. To find the solution, we can substitute the value of y from the second equation into the first equation.
To find the solution to a system of equations, we need to find the values of x and y that satisfy both equations simultaneously.
The system of equations is:
y = -5x + 3
y = 1
We can see that the second equation is already in the form y = a, which means that the y value is constant and equals to 1. Now we can substitute this value of y in the first equation:
1 = -5x +3
So the solution to the system of equations is x = 0.4, y = 1.
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What degree is 3x1?.
The degree of 3x^1 is 1.
A degree of a polynomial is the highest power of the variable in the polynomial. For example, in the polynomial 2x^3 + 4x^2 - 5x + 7, the degree is 3 (the highest power of x is x^3). A polynomial of degree 0 is a constant polynomial and a polynomial of degree 1 is a linear polynomial.
To find the degree of a polynomial, you can do the following:
→ Write the polynomial in standard form, with the terms arranged in descending order of exponents.
→ Take the exponent of the term with the highest exponent. This exponent is the degree of the polynomial.
3x^1 is a monomial with a coefficient of 3 and an exponent of 1. It is also called a linear term. The degree of a monomial is the exponent of the variable. So in this case, the degree of 3x^1 is 1.
Therefore, the degree of 3x^1 is 1.
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help me calculate the coordinates of points B, D and E
Answer:
B(-π/3, 1/2), D(7π/6, -√3/2), E(11π/12, -1/2)
Step-by-step explanation:
You want the coordinates of various points marked on the graph of the sine and cosine functions.
GraphThe horizontal divisions on the graph are multiples of π/6. That is, there are 6 divisions between 0 and π. This means the x coordinates of interest are ...
B = -π/3
D = 7π/6
E = 11π/6
Points B and D lie on the red curve, which the graph tells you is a plot of cos(x). Then the coordinates are ...
B = (-π/3, cos(-π/3)) = (-π/3, 1/2)
D = (7π/6, cos(7π/6) = (7π/6, -√3/2)
Point E lies on the blue curve, which is a plot of sin(x). Its coordinates are ...
E = (11π/6, sin(11π/6)) = (11π/6, -1/2)
__
Additional comment
The attachment shows the coordinates of points on the unit circle as (cos(θ), sin(θ)). On the given graph, θ is on the horizontal axis (x), and sine and cosine are on the vertical axis. To make use of the attachment, you find the angle, then look for the (cos, sin) coordinates at that angle.
Negative angles are clockwise from θ=0. To find the corresponding angle on the attachment, add 2π to any negative angle.
Write the relation as a set of ordered pairs. A relation. An arrow goes from 0 to 2, 2 to 6, and 4 to 10. a. ordered pairs: {(0, 2), (2, 6), (4, 10)} b. ordered pairs: {(2, 0), (6, 2), (10, 4)} c. ordered pairs: {(0, 2), (6, 2), (10, 4)} d. ordered pairs: {(2, 0), (2, 6), (4, 10)} Please select the best answer from the choices provided A B C D
The relation should be written as a set of ordered pairs as follows: A. . ordered pairs: {(0, 2), (2, 6), (4, 10)}.
What is a function?In Mathematics, a function can be defined as a mathematical expression which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.
This ultimately implies that, a function is typically used in mathematics for uniquely mapping an input variable (x-value or domain) to an output variable (y-value or range).
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph such as the following:
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In 1940, a coat cost $25.00. Thirty years later, the price increased by 310%. How much more did a coat sell for thirty years later?
Answer: 77.05
Step-by-step explanation:
Shape ‘S’ can be transformed to shape ‘T’ by the translation:
( 0
−3 )
followed by a rotation.
Describe the rotation.
Angle _____° anti-clockwise
About the point _______
Answer:
15
Step-by-step explanation:
becaue o was thinking and i was like oh search it u0 and i got snswer
