Given:
[tex]\sin x=-\dfrac{15}{17}[/tex]
x lies in the III quadrant.
To find:
The values of [tex]\sin 2x, \cos 2x, \tan 2x [/tex].
Solution:
It is given that x lies in the III quadrant. It means only tan and cot are positive and others are negative.
We know that,
[tex]\sin^2 x+\cos^2 x=1[/tex]
[tex](-\dfrac{15}{17})^2+\cos^2 x=1[/tex]
[tex]\cos^2 x=1-\dfrac{225}{289}[/tex]
[tex]\cos x=\pm\sqrt{\dfrac{289-225}{289}}[/tex]
x lies in the III quadrant. So,
[tex]\cos x=-\sqrt{\dfrac{64}{289}}[/tex]
[tex]\cos x=-\dfrac{8}{17}[/tex]
Now,
[tex]\sin 2x=2\sin x\cos x[/tex]
[tex]\sin 2x=2\times (-\dfrac{15}{17})\times (-\dfrac{8}{17})[/tex]
[tex]\sin 2x=-\dfrac{240}{289}[/tex]
And,
[tex]\cos 2x=1-2\sin^2x[/tex]
[tex]\cos 2x=1-2(-\dfrac{15}{17})^2[/tex]
[tex]\cos 2x=1-2(\dfrac{225}{289})[/tex]
[tex]\cos 2x=\dfrac{289-450}{289}[/tex]
[tex]\cos 2x=-\dfrac{161}{289}[/tex]
We know that,
[tex]\tan 2x=\dfrac{\sin 2x}{\cos 2x}[/tex]
[tex]\tan 2x=\dfrac{-\dfrac{240}{289}}{-\dfrac{161}{289}}[/tex]
[tex]\tan 2x=\dfrac{240}{161}[/tex]
Therefore, the required values are [tex]\sin 2x=-\dfrac{240}{289},\cos 2x=-\dfrac{161}{289},\tan 2x=\dfrac{240}{161}[/tex].
What is the ratio in which point P 1 and 2 divides the join of a 2 and 1 and B 7 and 4?
The ratio in which P (1,2) divides AB at (2,1) and (7,4) is 1:6.
What is ratio?Ratio is the term for the proportion between two or more things in terms of number, amount, or size.
How to calculate ratio?Ratios contrast two figures by ordinarily dividing them. A/B would be your formula if you were comparing one data point (A) to another data point (B). This indicates that you are multiplying information A by information B. For instance, your ratio will be 5/10 if A is 5 and B is 10.
Given,
Point P → (1, 2)
Point A → (2, 1)
Point B → (7, 4)
Let m1:m2 be the ration
The formula that is used is:
[tex]x=\frac{m1x2+m2x1}{m1+m2} ; y=\frac{m1y2+m2y1}{m1+m2}[/tex]
Now we have been given the Point P → (1, 2), hence x = 1 and y = 2
Also, (x₁, y₁) = (2, 1) and (x₂, y₂) = (7, 4)
[tex]1=\frac{7m1+2m2}{m1+m2} ; 2=\frac{4m1+m2}{m1+m2}[/tex]
m₁ + m₂ = 7m₁ + 2m₂
0=6m1-m2
m2=6m1
1/6=m1/m2
The ratio in which P divides AB is 1:6.
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What is the nature of roots of 2x² 3x 5 0?
The nature of the roots of 2x² 3x 5 0 are imaginary, as it is not possible to solve for real numbers.
To solve this equation, we first factor out the coefficients (2 and 5). Factoring out 2 gives us x² + 1.5x + 5 = 0. After that, we solve for x using the quadratic formula:
x
= -1.5 ± √(-1.5² - 4(1)(5)) / 2(1). This is reduced to x = -1.5 9.5 / 2, an imaginary number that cannot be solved using real values. This indicates that the equation's roots are fictitious.
x
= -1.5 ± √(-1.5² - 4(1)(5)) / 2(1)
x = -1.5 ± √9.5 / 2
x = -1.5 ± √(9.5)i / 2
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What is a horizontal asymptote example?
An example of a horizontal asymptote is when the input values of a function f(x) is significantly large or significantly small.
What is an asymptote?In Mathematics, an asymptote can be defined as a line which the graph of a given function approaches but would never touch. Additionally, the vertical asymptote of a function simply refers to the value of x which makes its denominator equal to zero (0).
What is a horizontal asymptote?In Mathematics, a horizontal asymptote can be defined as a horizontal line (y = b) where the graph of a function approaches the line as the input values approach negative infinity (-∞) to positive infinity (∞).
For instance, we can determine the horizontal asymptote of this function as follows;
y = 3/x
yx = 3
x = 3/y
x = 3/0
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Kardal used the trend line to predict that a man 72 inches tall would wear about a size 10. 5 shoe. What can be concluded about this prediction? check all that apply. The prediction is not reasonable. The prediction is an interpolation. No data is given in the scatterplot for a height of 72 inches, but a shoe size can still be predicted. A prediction cannot be made without the linear regression equation. A 72-inch tall man will wear a size 11. 5 shoe.
The prediction is not reasonable and The prediction is an interpolation is correct
How to use a regression calculator to make a reasonable prediction given a data table?
Kardal used the trend line to predict that a man 72 inches tall would wear about a size 10. 5 shoe.
Given data, first determine which is the independent variable, x, and which is the dependent variable, y. Enter the data pairs into the regression calculator. Substitute the value for one variable into the equation for the regression line produced by the calculator, and then predict the value of the other variable.
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What is the quotient 3x2 4x 15 )/( x 3?
Answer:
What is the quotient (3x2 + 4x - 15) ÷ (x + 3)? Summary: The quotient of (3x2 + 4x - 15) ÷ (x + 3) is 3x - 5.
Step-by-step explanation:
-3x - 8y = 20
-5x + y = 19
Answer:
x=4 y=-1
Simplify:
100+43y over 3 = 19
Step-by-step explanation:
-3x-8y=20
-5x+y=19
How many rows and columns are there in Excel 2006?
There is a limit in Microsoft Excel on the number of rows and columns an Excel file can contain. An Excel file may have upto 256 columns and 65536 rows.
Now, According to the question:
There is a limit in Microsoft Excel on the number of rows and columns an Excel file can contain. An Excel file may have upto 256 columns and 65536 rows.
Excel sheet:-
In Microsoft Excel, a sheet is often called a worksheet. A sheet is a single page that contains its own collection of cells to help you organize your data. There can be many sheets in your Excel document and you can see the sheets listed as tabs along the bottom of your document.
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What are the types of continuity of a function?
The types of continuity of a function are: pointwise continuity, uniform continuity, absolute continuity, and uniform convergence.
The types of continuity of a function are: pointwise continuity, uniform continuity, absolute continuity, and uniform convergence. Pointwise continuity means that the function is continuous at each point in its domain. Uniform continuity means that the function is continuous over some larger region. Absolute continuity means that the function is continuous over its entire domain. Finally, uniform convergence means that the function converges to a limit value over a range of values. Pointwise continuity is the weakest form of continuity and uniform convergence is the strongest. All of these types of continuity are important for understanding the behavior of functions and their properties.
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find the length of the arc of the curve from point p to point q. y = 1 2 x2, p −3, 9 2 , q 3, 9 2
As per the given equation, the length of the arc of the curve from point p to point q is 1.8973
Here we have given the equation y = 1/2 x².
Then the the length of the arc of the curve from point p to point q is calculated by using the formula,
=> [tex]\int\limits^q_p {\sqrt{1+(\frac{dy}{dx} )^2} } \, dx[/tex]
Here we have to extract the value of (x1, x2) from the given coordinates, then we get,
=> (x1, x2) = (-3, 3)
Now, we have to find the derivative of y, then we get he value as,
=> dy/dx = x
So, the length is calculated as,
=> [tex]\int\limits^3_{-3} {\sqrt{1+x^2} } \, dx[/tex]
As per the power rule of derivative, then reduced form of the equation is written as.
=> [x/√x²+1]₋₃³
When we apply the value of x as the given limit, then we get,
=> [3/√3²+1] - [(-3)/√(-3)²+1]
=> [3/√10] + [3/√10]
=> 6/√10
=> 1.8973
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What is the formula in getting possible zeros in rational root theorem?
The formula in getting possible zeros in rational root theorem is given as ± p / q.
According to rational root theorem if a polynomial expression which is written in descending order of the exponents and has integer coefficients, then any rational zero must be of the form ± p / q
Here, p is a factor of the constant term or the numerator and q is a factor of the leading coefficient or the denominator.
As the name implies, the rational root theorem is used to find the rational solutions to a polynomial equation . Polynomial roots or zeros are the solutions we get when we solve a polynomial equation. A polynomial does not need required rational zeros only.
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Find the value of x and y in the image below!
Applying the properties of a parallelogram, the values of x and y are:
y = 81°
What are some Properties of a Parallelogram?Opposite angles have equal angle measures.Adjacent angles are supplementary.The shape given is a parallelogram, therefore:
3x = 2x + 33 [opposite angles]
3x - 2x = 33
x = 33
3x + y = 180 [adjacent angles]
Plug in the value of x
3(33) + y = 180
99 + y = 180
y = 180 - 99
y = 81°
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What is the slope of the line 4y 3x 1?
The slope of the line 4y - 3x = 1 is 3/4.
Define slope.A line's slope is the ratio of how much y grows as x grows by a certain amount. You may determine a line's slope by looking at how steep it is or how much y grows as x grows. Anywhere along the line, the slope is uniform. In mathematics, measuring steepness is a common goal. It is obvious that slopes B and C are steeper than slope A. They both stand seven units tall, although slope A is only four. Therefore, it would seem that steepness and height are related.
Given
Equation
4y - 3x = 1
3x added to both sides,
4y = 1 + 3x
Dividing by 4,
y = 3/4x + 1/4
Using slope intercept form,
y = mx + b
m = slope
m = 3/4
The slope of the line 4y - 3x = 1 is 3/4.
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What is the side side side theorem?
The side-side-side (SSS) theorem states that if three sides of one triangle are equal to the corresponding sides of another triangle, then the two triangles are congruent.
In other words, if the lengths of the sides of two triangles are the same, then the triangles must be the same shape and size.
For example, consider two triangles ABC and DEF. If we know that
AB = DE, BC = EF, and AC = DF,we can use the SSS theorem to conclude that triangle ABC is congruent to triangle DEF.
It is important to note that the SSS theorem is only applicable if the three sides of each triangle are equal in length. If the sides are not equal, the theorem does not apply and we cannot use it to prove the congruence of the triangles.
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Help FAST PLEASE......................!!!!!!!!!!!!!!!11
The lines intersect to form a rectangular prism, therefore the plane that is parallel to EFG is BCD. option D
How to find similar objects?We should know that in plane geometry, parallel lines do not intersect and intersecting lines form angles at the points of intersection.
To determine the similarity of the lines, Let us consider the following lines
From the rectangular prism
EF//AB
BC//FG
GH//CD
AD//EH
Each of the lines lies on opposite side of the rectangular prism.
Also, quadrilateral ABCD ≡ Quadrilateral EFGH
In conclusion, the plane that is parallel to EFG is BCD.
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Population parameters are used to estimate sample statistics.
a. true
b. false
Population parameters are used to estimate sample statistics, and this is true.
Population parameters are used to describe the characteristics of a population, such as the mean, median, and standard deviation, and are used to make inferences about a population. Sample statistics, on the other hand, are used to describe the characteristics of a sample of a population. For example, a sample statistic could be the mean of a sample of people's heights.
To estimate sample statistics, population parameters must first be known. For example, the sample mean can be estimated using the population mean. If the population means are unknown, then the sample means can be estimated using the sample mean.
In conclusion, population parameters are used to estimate sample statistics, and this is true. Population parameters provide useful information about a population that can be used to make inferences about a sample. Knowing the population parameters allows researchers to make more accurate estimates of sample statistics, which in turn can be used to make more reliable inferences about a population.
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Do the one you would like please show work
Pipe will take 21.5 hours to fill tank completely.
How to solve pipes and cistern problems?A tank can be partially filled in 1 hour = 1/x if it takes x hours to fill it completely.
If the tank must be emptied in y hours, then the portion drained in an hour is equal to 1/y.
If a pipe can fill a tank and drain it in x and y hours, respectively.
When both pipes are opened simultaneously, the tank's net volume is filled in one hour using the formula (xy) / (y-x), provided y>x.
If a pipe can fill a tank and drain it in x and y hours, respectively.
When both pipes are opened simultaneously, the tank's net volume is filled in one hour using the formula (xy) / (x-y), provided x>y.
Net work completed equals the sum of all inlets' work (Sum of work done by Outlets)
Volume of tank be V
Pipe A and Pipe B together fill (1/9)V in one hour.
Pipe A fills (1/15)V in one hour.
Pipe B fills (1/9 - 1/15)V in one hour.
Solving for pipe B, we get
1/9 - 1/15
[tex]=\frac{15-9}{15*9}\\=\frac{6}{15*9}\\=\frac{2}{45}\\[/tex]
So, tank B will take total 21.5 hours to fill tank individually.
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For a fundraiser, a group plans to sell granola bars and bottles of water at the same prices as described in Part A. The group wants the income from the fundraiser to be at least $150.Choose the inequality to show the number of granola bars x and the number of bottles of water y that must be sold.A. 1.4x + 0.75 y > 150B. 1.4x + 0.75y ≥ 150C. 1.4x + 0.75 < 150D. 1.4x + 0.75 ≤ 150
Answer:
the answer is D i think
Greg earned $32 dollars for washing cars this month. He earned twice as much for washing cars than he did for mowing lawns. Write an equation to determine how much he earned for mowing lawns.
Answer: x = 32/2
Step-by-step explanation:
10. A teacher buys 12 boxes of candies. There are 8 candies in each box. The
teacher wants to distribute candies among students so that all students get the
same number of candies and most of the candies are distributed. If there are
30 students in the classroom, how many candies does the teacher have left?
Answer:
6
Step-by-step explanation:
12*8=96
96/3= 3 remainder 6
What is the median of 4 and 7?
The median of 4 and 7 is 5.5.
The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.
The data set's median is the value in the center. Put all the numbers in ascending or descending order, and then choose the middle number to determine the median. There will only be one middle integer if the number of data points is odd. If the number of data points is even, you must choose the middle two numbers, add them together, and divide by two. Your median will be that value.
The mean of these middle values is (4+7)/2 = 11/2= 5.5
Thus, the median of 4 and 7 is 5.5.
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When 122 is decreased by five times a number, the result is equal to the number increased by 20. What is the number?.
When 122 is decreased by five times a number, the result is equal to the number increased by 20 so the number is 17 .
Given :
Number :
A number is an arithmetic value used for representing the quantity and used in making calculations.
Let x be the number .
( 122- 5x ) = ( x + 20 )
122 - 5x = x + 20
122 - 6x = 20
122 - 20 = 6x
102 = 6x
divide by 6 on both sides
6x / 6 = 102 / 6
x = 102 / 6
x = 17
Hence the number is 17
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it took oliva 2 hours to drive 240 miles. at this rate how long does it take to drive 80 miles
Answer:
It takes 1 hour to drive 80mph at the rate Oliva is going
Step-by-step explanation:
How do you solve a binomial expression?
To solve a binomial expression, use the FOIL (First, Outer, Inner, Last) method to multiply the two terms together. Then use the distributive property to simplify the expression and combine like terms.
1.Identify the two terms of the binomial expression and write them in the correct order.
2. Use the FOIL method to multiply the two terms together:
the first term of each binomial is multiplied together first.
Outer: Divide the second term of the second binomial by the first term of the first binomial.
Multiplying the first term of the second binomial by the second term of the first binomial yields the inner product.
Lastly, combine the second terms of each binomial.
3. To make the expression simpler, use the distributive property.
4. Combine like terms, if applicable.
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What is the formula for solving quadrilaterals?
Therefore, the formula for solving the area of quadrilateral is given by
area of quadrilateral = 1/2(sum of perpendicular drawn from residual two vertices).
What is quadrilateral?
A closed quadrilateral is a form of polygon with four sides, four vertices, and four angles. It is made up of four linked non-collinear points. The sum of the internal angles of quadrilaterals is always 360 degrees.
According to the given question:
When the diagonal and the sum of the lengths of the perpendiculars traced from the remaining two vertices are known,
The area of the quadrilateral can be calculated as follows:
Area of quadrilateral = (1/2) diagonal length sum of the lengths of the perpendiculars drawn from the residual two vertices.
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Examine the system of equations.
6x + y = −30,
36x + 6y = 24
Which statement is true about the system of equations?
After solving this system, you get a true statement.
This system has one solution.
If this system were graphed, the lines would be parallel.
The equations in this system have the same y-intercept.
Answer:
C
Step-by-step explanation:
6x + y = - 30
36/6 x + 6/6 y = 24/6
6x + y = -30
6x + y = 4
If this system were graphed, the lines would be parallel, because they have the same slope
Need help with this equation . Asap
The measure of segments mAG, mAC, and mBC are 11.4, 16.1 and 7.1 respectively,
What is the triangle?The triangle is a geometric shape that includes 3 sides and the sum of the interior angle should not be greater than 180°
Here,
Apply Pythagoras theorem in triangle ABG,
mAG = √[7² + 9²]
mAG = √[49 + 81]
mAG = √[130] = 11.4
Apply Pythagoras theorem in triangle BGC,
mBC = √[10² - 7²]
mBC = √51
mBC = 7.1
Now
mAC = mAB + mBC
mAC = 9 + 7.1
mAC = 16.1
Thus, the segments mAG, mAC, and mBC have measures of 11.4, 11.1, and 7.1, respectively.
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There are 14 dogs in a particular class at a dog show. blue, red, yellow, and white ribbons will be awarded to the first through fourth place finishers, respectively. in how many different ways can the ribbons be awarded?
a. 1,001
b. 6,006
c. 24,024
d. 38,416
As per the combination method, the number of ways can the ribbons be awarded is 24,024
The general formula to calculate the combination is written as,
nCr = n!/r! (n - r)!
where n refers the set or population and r refers subset of n or sample set
Here we have given that there are 14 dogs in a particular class at a dog show. blue, red, yellow, and white ribbons will be awarded to the first through fourth place finishers,
Here we need to find the number of different ways can the ribbons be awarded.
While we looking into the given question, the following details are given in it,
Total number of dogs = 14
Number of ribbons = 5
Which means that the value on n = 14 and the value of r = 5.
As per the given question we know that,
There are 14 possibilities for blue one
And then there are 14 - 1 = 13 possibilities for red ribbon.
And for the next yellow one has 12 possibilities
Then the white one has 11 possibilities.
Therefore, the total number of ways is
=> 14 x 13 x 12 x 11
=> 24024
Therefore, option (c) is correct.
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following this nut 10 exam, you make yourself a giant ice cream sundae. total saturated fat for this meal is 95 grams. based on the 2020 dietary guidelines, what percent of the daily value for saturated fat does this provide? divide 855 grams by 2000 grams and multiply by 100 to find the percent daily value for saturated fat from this meal, which is 43 % (round to the nearest whole number [ > 0.5
Percent of the daily value for saturated fat provided would be 48%
What is Percent Daily Value?
Daily Values are recommendations that specify the amounts of certain nutrients that the average person should obtain each day. Daily Values are only a general guide because they are calculated for the average person who consumes a total of 2,000 calories a day.
If the total saturated fat for the meal is 95 grams, this is equal to 95,000 milligrams of saturated fat.
To find the percent daily value for saturated fat from this meal, we can use the following formula:
percent daily value = (total saturated fat / recommended daily intake) * 100
= (95,000 / 2000) * 100
= 47.5
Rounded to the nearest whole number, the percent daily value for saturated fat from this meal is approximately 48%
This means that this meal provides approximately 48% of the recommended daily intake of saturated fat.
Hence, Percent of the daily value for saturated fat provided would be 48%
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anova can be used to test whether more than two population variances are different. group of answer choices true fals
To determine whether there are differences between more than two population variances, utilise anova is True
What is Anova?
A statistical technique called analysis of variance, or ANOVA, divides observed variance data into various components for use in further testing. When there are three or more data groups, a one-way ANOVA is used to find out how the dependent and independent variables are related.
Concept:
One-way ANOVAs are typically used when there are three or more categorical independent groups, although they can also be employed when there are only two groups (but an independent-samples t-test is more commonly used for two groups)
A statistical procedure called Analysis of Variance (ANOVA) is used to examine variations between the means (or averages) of several groups. It is used in a variety of situations to discover whether there are any differences between the means of various groups.
To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilised. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.
The absence of a difference in means is always the null hypothesis in an ANOVA. The alternative or research hypothesis, which is typically expressed in words rather than mathematical symbols, asserts that the means are not all equal. The research hypothesis involves any difference in means, such as when all four means are different from one another, one mean differs from the other three, two means differ, and so on. All scenarios other than the equality of all means described in the null hypothesis are covered by the alternative hypothesis, as it was previously illustrated.
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A statistical procedure called Analysis of Variance (ANOVA) is used to examine variations between the means (or averages) of several groups. It is used in a variety of situations to discover whether there are any differences between the means of various groups.
To determine how the values of two categorical factors affect the mean of a quantitative variable, a two-way ANOVA is utilised. When you wish to determine how two independent factors interact with one another to effect a dependent variable, use a two-way ANOVA.
How do you explain greater than less than equal to?
As per the concept of numbers, the way of explaining the greater than, less than, and equal to are defined below.
The term number in math is referred to an arithmetic value used for representing the quantity and used in making calculations.
Here we have to know that the greater than sign (>) denotes that the number after the more than sign is smaller than the number before the symbol whereas less than sign (<) denotes that the number after the sign is bigger than the number before the sign.
Similarly, to this definition, the term equal defines the number as being equal to each other or it can be used to assign the value to the variable that has been placed on the left-hand side.
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