Find the exact value of sin(2x) if sin(x)=-1/2.
Answer: The value of sin(2x) can be found using the identity:
sin(2x) = 2sin(x)cos(x)
Since sin(x) = -1/2, we can use the Pythagorean identity to find the value of cos(x):
cos^2(x) + sin^2(x) = 1
So
cos^2(x) = 1 - sin^2(x) = 1 - (-1/2)^2 = 1 - 1/4 = 3/4
Taking the square root of both sides:
cos(x) = ± sqrt(3)/2
Since sin(x) is negative and cos(x) must be positive, we get:
cos(x) = sqrt(3)/2
Finally, substituting the values of sin(x) and cos(x) into the formula for sin(2x), we get:
sin(2x) = 2sin(x)cos(x) = 2 * (-1/2) * sqrt(3)/2 = -sqrt(3)
So the exact value of sin(2x) is -√(3).
Step-by-step explanation:
When purchasing a sale item, if you take the 20% discount first, then add the 10% tax, the cost of the item will be the same as when you add the 10% tax first, then take the 20% discount.
Answer:
80+90
add them together
=170
10% of 170
=17
20-17=3
Two trains leave towns 855 miles apart at the same time and travel toward each other. One train travels 13 mi/h slower than the other. If they meet in 5 hours, what is the rate of each train?
The velocity of the two trains are 79m/s and 66m/s
What is velocity?Velocity is the rate of change of displacement with time. It is a vector quantity and it is measured in meter per second.
Using addition of vectors:
The total displacement = d2-d1
displacement = velocity × time
Represent the velocity of faster train by v
therefore the velocity of the slower train = v -13
855 = 5v +5(v-13)
855 = 5v+5v+65
855 = 10v +65
10v = 855-65
10v = 790
v = 790/10
v = 79 m/s
the rate of the second train = 79-13 = 66m/s
therefore the rate of the two trains are 79m/s and 66m/s
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help please asap! ill mark brainlist
First triangle x = 30
Second triangle N = 55
Determine whether the stochastic matrix P is regular. p= | 0.5 0.1 || 0.5 0.9 |Find the steady state matrix x of the Markov chain with matrix of transition probabilities P. (If the system has an infinite number of solutions, express X1, and x2 in terms of the parameter t.)
The consistent state lattice x is equivalent to (0.6, 0.9), and the stochastic matrix P is normal.
To decide if a stochastic grid P is standard, we should initially compute the consistent state matrix x of the Markov chain with a matrix of change probabilities P. To do this, we set up the situation Px = x and address for x.
We can communicate the components of x as far as a boundary t as follows:
x1= 0.5t + 0.1
x2= 0.5t + 0.9
We can then settle for t in view of the amount of x1 and x2. The amount of x1 and x2 ought to be equivalent to 1, so:
0.5t + 0.1 + 0.5t + 0.9 = 1
t = 1
Therefore, The consistent state lattice x is equivalent to (0.6, 0.9).
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Jack lives in a house worth $172000 and pays $13760 in taxes. Write an equation to represent the relationship
Answer:
House value x Tax rate = Taxes paid
172000 x 0.08 = 13760
Uma writes 56 words in her journal. The words are shared equally on 7 lines. On the last line, Uma adds 3 words. How many words are on the last line of Uma's journal?
Answer:
11 words
Step-by-step explanation:
Thera are 56 words shared equally among 7 lines
Therefore there are 56/7 = 8 words per line
On the last line by adding 3 words, there will be 8 + 3 = 11 words
show whether or not the set of remainders z18 forms a group with the modulo addition operator. then show whether or not z18 forms a group with the modulo multiplication operator
Z18 with modulo addition satisfies all four group axioms and is a group.
Z18 with modulo multiplication does not satisfy the inverse axiom and is not a group.
what is the binary operation?
In mathematics, a binary operation is a function that takes two elements from a set and returns another element from the same set.
For a set to form a group with a binary operation, the set must satisfy the four group axioms: closure, associativity, identity, and inverse.
1. Z18 with modulo addition:
The set of remainders Z18 = {0, 1, 2, ..., 17} forms a group with the modulo addition operator.Closure: For any two elements a, b in Z18, their sum (a + b) is also in Z18. This is because modulo addition is performed by taking the sum of two numbers, dividing by 18, and taking the remainder, which will always be in the set Z18.Associativity: For any elements a, b, c in Z18, (a + b) + c = a + (b + c).Identity: There exists an element 0 in Z18 such that a + 0 = a for all elements a in Z18.Inverse: For every element a in Z18, there exists an element b in Z18 such that a + b = 0.Hence, Z18 with modulo addition satisfies all four group axioms and is a group.
2. Z18 with modulo multiplication:
The set of remainders Z18 = {0, 1, 2, ..., 17} does not form a group with the modulo multiplication operator.Closure: For any two elements a, b in Z18, their product (a * b) is also in Z18.Associativity: For any elements a, b, c in Z18, (a * b) * c = a * (b * c).Identity: There exists an element 1 in Z18 such that a * 1 = a for all elements a in Z18.Inverse: For every non-zero element a in Z18, there does not exist an element b in Z18 such that a * b = 1. This is because the modulo multiplication operator only returns values that are between 0 and 17, and not all elements in Z18 have a multiplicative inverse modulo 18.Hence, Z18 with modulo multiplication does not satisfy the inverse axiom and is not a group.
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100 POINTS BRAINLIEST HELP A trial balance indicates $10,000 in debits and $16,000 in credits. What is the amount of the misplaced entry?
A. $3,000
B. $2,000
C. $6,000
D. $4,000
Find the slope of a line to y = 3x + 7
Answer: 3
Step-by-step explanation:
The line y = 3x + 7 has a slope of 3. Slope-intercept form equations have a slope of m when written as y = mx + b. See the attached picture for more information.
y = mx + b ➜ y = 3x + 7 ➜ y = 3x + 7 ➜ 3
Answer:
3.Step-by-step explanation:
The ratio at which the y-value varies when the x-value changes is shown by a line's slope. The coefficient of x in the equation y = 3x + 7 is 3, therefore y rises by 3 units for every unit increase in x. The slope is thus 3. This indicates that the line will climb 3 units along the y-axis for every unit you move to the right along the x-axis.
Hope it helps! : )What type of number is 0/2
Answer:this is a rational number
Step-by-step explanation:
The number zero can be written as 0 ÷ any non-zero integer. For example, the rational numbers 0/1 and 0/(-2) are equal to 0. This is in the form of p/q, where p and q are integers and q ≠ 0.
Find the area and perimeter of this figure.
The area and perimeter of the shape is 4.65cm² and 9.5cm
What is area and perimeter of a triangle?Perimeter of a triangle = a + b +c , where a, b and c are the three different sides of the triangle. Area of a triangle = 1/2 b × h; where b is the base and h is the height of the triangle.
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC.
Perimeter of the triangle = 3.2+ 2.0+4.3
= 9.5cm
The area of the triangle = ½bh
= 1/2 ×3.1 × 3
= 4.65 cm²
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Sean rented an SUV for 2 days and drove it 430 miles. The daily rate was $46.9 $0.35 per mile with the first 50 miles being free. How much was the total cost?
The total cost for the rental is calculated by subtracting the first 50 miles from the total miles driven (430 miles) and then multiplying it by the per mile rate ($0.35/mile).
What is miles ?Miles is a unit of distance measurement. It is used for measuring the distance between two places. It is equivalent to 1.609 kilometers. Miles are used for measuring the length of roads, flight distances, distances between cities, and other large distances. Miles can also be used to measure the length of running, swimming, and cycling events. Miles are also used in the United States to measure the speed of vehicles, such as cars and airplanes.
This gives us a total cost of $118.50 for the miles driven. To calculate the total cost for the rental, we add the cost for the miles driven ($118.50) to the daily rate for the 2 days ($46.90 x 2 days = $93.80). This gives us a total cost of $212.30 for the rental.
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Calculate the volume of the prism.
The volume of the given prism in question is 276.7 cubic yd
Volume of a square based prismThe formula for calculating the volume of a square based prism is expressed as:
V = BH/3
where
B is the base area
H is the height of the prism
Determine the height using Pythagoras theorem
b^2 = 13^2 - 10^2
b^2 = 169 - 100
b^2 = 69
b = √69
b = 8.3yd
Determine the required volume
V = (10*10)(8.3)/3
V = 830/3
V = 276.7 cubic yd
Hence the volume of the prism is given as 276.7 cubic yd
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2/3 +2/9
2/3
4/9
1/2
8/9
Two hikers started at the same location. One
traveled 2 miles east and then 1 mile north. The
other traveled 2 mile west and then 3 miles
south.. At the end of their hikes, how many
miles apart are the two hikers? State the exact
length.
The first hiker is 2 miles east and 1 mile north of the starting point, so the position can be represented by the coordinate pair (2, 1).
What is the Pythagorean theorem in plain English?
In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The Perpendicular, Base, and Hypotenuse are the names of the three sides of this triangle.
The second hiker is 2 miles west and 3 miles south of the starting point, so the position can be represented by the coordinate pair (-2, -3).
The Pythagorean theorem can be used to calculate the separation between the two points:
d = √((2 - (-2))² + (1 - (-3))² ) = √((2 + 2)² + (1 + 3)²) = √(4² + 4²) = √(16 + 16) = √32
So, the two hikers are approximately 5.66 miles apart.
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Question: The pages of a book are numbered consecutively, beginning with 1. The digit 7 is
printed 25 times in numbering the pages. What is the largest number of pages the
book can have?
Answer:
975
Step-by-step explanation:
The largest number of pages the book can have is 975 because the maximum number of times the digit 7 can appear in the page numbers is 25. The maximum number of pages is obtained when the page numbers range from 100 to 999, inclusive, which would result in the digit 7 appearing 25 times.
Four friends A, B, C and D live in a same locality. The house of B is in the east of A's house but in the north of C's house. The house of C is in the west of D's house. D's house is in which direction of A's house?a. South-Eastb. North-Eastc. Eastd. Data is Inadequate
d. Data is inadequate as it is not possible to determine the direction of D's house relative to A's house.
What is the directions?Directions refer to the relative positions of objects or locations in space. It describes the orientation and location of an object in relation to another object or a reference point.
Based on the information given, . Further information is needed to determine the direction.
Hence, d. Data is inadequate
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A line passes through the points (4, 8) and (12, 2). What is the slope of the line?
[tex](\stackrel{x_1}{4}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{2}-\stackrel{y1}{8}}}{\underset{\textit{\large run}} {\underset{x_2}{12}-\underset{x_1}{4}}} \implies \cfrac{ -6 }{ 8 } \implies - \cfrac{3 }{ 4 }[/tex]
Can someone help me find the intervals to where it’s decreasing?
The intervals at which the parabolic equation from the graph is decreasing is (4, ∞).
Decreasing intervals of a parabolic equation.A parabolic equation is an equation of a curve usually in form of a U-shape when displayed on the graph. In the given diagram, we can use the standard form of a quadratic equation y = ax² + bx + c as the starting point for finding the equation through the three points of the curve.
Using the following points on the curve; (0,-2) (4,6), and (6,4), because these points pass along the x and y-axis of the curve.
Create a system of equations by substituting the x and y values of each point into the standard formula of a quadratic equation to create the three-equation system.
−2 = a(0)² + b(0) + c,
6 = a(4)² + b(4) + c,
4 = a(6)² + b(6) + c
Solve the system of equations to find the values of a, b, and c.
[tex]$$a= - \dfrac{1}{2}$$, b = 4, c = -2[/tex]
Substitute the actual values of a, b, and c into the formula for a quadratic equation to find the resulting equation.
[tex]y = - \dfrac{x^2}{2} + 4x - 2[/tex]
Since we know the resulting equation of the parabola, we can now deduce the intervals at which the parabola is decreasing. As such, the interval at which the parabolic equation is decreasing is (4, ∞)
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The diagonals of rectangle abcd intersect at point e. If ae = 2x + 5, and bd = 5x + 2, what is ac?.
As per the intersecting point, the length of AC is 4x + 10.
The diagonals of a rectangle are two lines that intersect at the midpoint of the rectangle. In this case, the diagonals of rectangle ABCD intersect at point E.
If AE = 2x + 5 and BD = 5x + 2, then we can calculate the length of AC. We know that AC is the sum of AE and ED, so AC = AE + ED.
Since the diagonals of a rectangle intersect at the midpoint of the rectangle, AE and ED are equal. Therefore, AC = 2x + 5 + (2x + 5) = 4x + 10.
Therefore, the length of AC is 4x + 10. Knowing the lengths of the diagonals can help us find the length of the sides of the rectangle, and can also be useful in finding the area of the rectangle
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For a project in his Geometry class, Amadou uses a mirror on the ground to measure the height of his school building. He walks a distance of 11.15 meters from the building, then places a mirror flat on the ground, marked with an X at the center. He then walks 1.05 more meters past the mirror, so that when he turns around and looks down at the mirror, he can see the top of the school clearly marked in the X. His partner measures the distance from his eyes to the ground to be 1.25 meters. How tall is the school? Round your answer to the nearest hundredth of a meter
The height of the school is 13.27 m.
What is a triangle?It is a two-dimensional figure which has three sides and the sum of the three angles is equal to 180 degrees.
We have.
From the information given, we can draw the figure given below,
Now,
Triangle ABC and Triangle DCE are similar.
So,
x / 1.25 = 11.15 / 1.05
x = (11.15 x 1.25) / 1.05
x = 13.27 m
Thus,
The height of the school is 13.27 m.
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What is the classification of -p+2p^2
-p + 2p^2 is a quadratic function, which is a polynomial function of degree 2.
What is quadratic function?Quadratic function is a polynomial function of degree 2, written in the standard form as ax^2 + bx + c, where a, b, and c are constants, and x is a variable.
The graph of a quadratic function is a parabola which opens up or down depending on the value of a. The most common application of quadratic functions is in solving problems related to parabolic motion, such as finding the maximum height, time of flight, or range of a projectile.
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Research has found that people are happiest when they have _____ hours a day of face-to-face contact with others. 3. 6. 1. 9.
Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.
What is an experiment ?
A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law
In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.
Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.
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Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.
What is an experiment ?
A method used in a controlled environment to find an unknown effect or law, test or establish a hypothesis, or provide an example of an established law
In the scenario described, individuals are chosen at random to participate in a new intervention, which appears to be an example of an experiment.
Research has found that people are happiest when they have 6 hours a day of face-to-face contact with others.
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Match the expressions on the right with the results on the right.
Some options on the right will be used more than once.
416 ÷ 100 = 4.16
4.16 ÷ 10 = 0.416
41600 ÷ 1000 = 4.1600 = 4.16
4.16 ÷ 100 = 0.0416
41.6 ÷ 100 = 0.416
When you divide by a power of 10, you move the decimal to the left the number of 0's in the number.
÷ 10 and you move the decimal point 1 place to the left
÷ 100 and you move the decimal point 2 places to the left
÷ 1000 and you move the decimal point 3 places to the left
Answer:
416 / 100 = 4.16
4.16 / 10 = 0.416
41600 / 1000 = 41.6
4.16 / 100 = 0.0416
41.6 / 100 = 0.416
Step-by-step explanation:
When you divide a number by another number, you find out how many times the second number fits into the first one. For example, in the expression 416 / 100, you are finding out how many times 100 fits into 416. The answer is 4.16, meaning 100 fits into 416 4 times with a remainder of 16.
Similarly, in the expression 4.16 / 10, you are finding out how many times 10 fits into 4.16. The answer is 0.416, meaning 10 fits into 4.16 0 times with a remainder of 4.16.
In the expression 41600 / 1000, you are finding out how many times 1000 fits into 41600. The answer is 41.6, meaning 1000 fits into 41600 41 times with a remainder of 600.
In the expression 4.16 / 100, you are finding out how many times 100 fits into 4.16. The answer is 0.0416, meaning 100 fits into 4.16 0 times with a remainder of 4.16.
In the expression 41.6 / 100, you are finding out how many times 100 fits into 41.6. The answer is 0.416, meaning 100 fits into 41.6 0 times with a remainder of 41.6.
Indicate whether the following sets are equal.
A = {x, j, a, m} and D = {x, a, b, y}
The two sets A = {x, j, a, m} and D = {x, a, b, y} are not equal.
What does the example set?
A set is a logically arranged group of items that can be represented in either set-builder form or roster form in mathematics.
Sets are typically shown using curly brackets; for instance, A = 1, 2, 3, 4 is a set.
The given two sets are
A = {x, j, a, m} and D = {x, a, b, y}
By definition,
The two sets A and B are equal sets if they contain the same elements.
Here, j, m and b, y are different in two sets.
Thus, The set A and D does not contain the same elements.
Therefore, The two sets A = {x, j, a, m} and D = {x, a, b, y} are not equal.
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Enlarge shape A by scale factor 2 with centre of enlargement (1, 4).
What are the coordinates of the vertices of the image?
Answer:
hacunamatata
Step-by-step explanation:
it means no worrys
Carlos deposited 140 dollars into his savings account.
Write a signed number to represent this change in his account.
Answer:
Carlos deposited $140 into his savings account, which can be represented by the signed number +140.
Step-by-step explanation:
This indicates an increase in his account balance of $140.
Functions K and H are both linear functions.
Function K y= 1/2x+2
Function H
x -2 1 5 8
y 0 4.5 10.5 15
Which of the statements comparing the two functions is true?
A)The slope of function K is greater than the slope of function H.
B)The y-intercept of function K is greater than the y-intercept of function H.
C) The slope of function K is equal to the slope of function H.
D) The y-intercept of function K is less than the y-intercept of function H.
On solving the provided question, we can say that the statement that is true is D) The y-intercept of function K is less than the y-intercept of function H.
what is function?Mathematicians study numbers and their variations, equations and related structures, shapes and their places, and potential placements for these things. The term "function" refers to the relationship between a set of inputs, of which each has an associated output. An relationship of inputs and outputs known as a function is one in which each input leads to a single, distinct output. Each function is given a domain or a codomain, or scope. The letter f is frequently used to indicate functions (x). Entry is an x. The four major kinds of accessible functions are on functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions.
Function K is given as y = 1/2x + 2, so the slope of K is 1/2 and the y-intercept of K is 2.
To find the slope and y-intercept of function H, we can use the given points (x,y):
When x = -2, y = 0, so we have the point (-2,0)
When x = 1, y = 4.5, so we have the point (1,4.5)
When x = 5, y = 10.5, so we have the point (5,10.5)
When x = 8, y = 15, so we have the point (8,15)
We can use two of these points to find the slope of H:
slope = (change in y) / (change in x) = (10.5 - 4.5) / (5 - 1) = 6/4 = 3/2
To find the y-intercept of H, we can use the point (0,b) where x = 0:
b = y - mx = 4.5 - (3/2)(1) = 3
So the equation for function H is y = (3/2)x + 3, which has a slope of 3/2 and a y-intercept of 3.
Now we can compare the two functions:
A) The slope of function K is greater than the slope of function H. False, since 1/2 < 3/2.
B) The y-intercept of function K is greater than the y-intercept of function H. False, since 2 < 3.
C) The slope of function K is equal to the slope of function H. False, since 1/2 ≠ 3/2.
D) The y-intercept of function K is less than the y-intercept of function H. True, since 2 < 3.
Therefore, the statement that is true is D) The y-intercept of function K is less than the y-intercept of function H.
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PLEASEEE HELPPP asappp
Answer:
y = - x - 2
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (2, - 4) ← 2 points on the line
m = [tex]\frac{-4=1}{2-(-3)}[/tex] = [tex]\frac{-5}{2+3}[/tex] = [tex]\frac{-5}{5}[/tex] = - 1
the line crosses the y- axis at (0, - 2 ) ⇒ c = - 2
y = - x - 2 ← equation of line