The values of θ, i.e. the general solution of the given trigonometric equation that satisfy the given equation are: 5π/12, π/12.
What is the general solution of a trigonometric equation?The general solution of a trigonometric equation is a formula employing the integer n that provides all solutions.
Given:
EQuation: 2 cos( 4θ) - 1 = 0.Interval: 0 ≤ θ ≤ π/2TO find: Values of θ.
Finding:
In the given equation: 2 cos( 4θ) - 1 = 0,
=> cos (4θ) = 1/2
=> cos (4θ) = cos (π/3)
=> 4θ = 2nπ ± π/3
=> θ = nπ/2 ± π/12
For n = 0, θ = ± π/12
For n = 1, θ = π/2 ± π/12
Since θ ∈ [0, π/2], the possible values of θ = π/12, π/2 - π/12 = 5π/12.
Hence, The values of θ that satisfy the given equation are: 5π/12, π/12.
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Plot the points in a coordinate plane and sketch ∠ XYZ. Then classify it as right, acute, or obtuse.
X(5,-3), Y(4,-1), Z(6,-2)
The points X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below. From the obtained graph ∠XYZ is the obtuse angle.
The given coordinates are X(5,-3), Y(4,-1) and Z(6,-2).
We need to classify ∠XYZ whether it is right, acute, or obtuse.
How to plot the points in a cartesian plane?A cartesian plane or coordinate plane can be defined as a plane formed by the intersection of two coordinate axes that are perpendicular to each other. The horizontal axis is called the x-axis and the vertical one is the y-axis. These axes intersect with each other at the origin whose location is given as (0, 0). Any point on the cartesian plane is represented in the form of (x, y). Here, x is the distance of the point from the y-axis and y is the distance from the x-axis.
Now, X(5,-3), Y(4,-1) and Z(6,-2) can be plotted as given below:
The given points X(5,-3), Y(4,-1) and Z(6,-2) have positive x-coordinate and negative y-coordinate.
In the cartesian plane, the fourth quadrant positive x-coordinate and negative y-coordinate.
So, all points X(5,-3), Y(4,-1) and Z(6,-2) lie in the fourth quadrant.
From the graph, we can see that the two lines make an obtuse angle, which is more than 180° and less than 360°.
From the obtained graph ∠XYZ is the obtuse angle.
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18. Two rectangles are shown below. Rectangle P has a perimeter of 20 inches. Rectangle Q has a perimeter of [/latex]30[/latex] inches.
What are the values of j and h?
A. j = 3 and h = 3
B. j = 10 and h = 4
C. j = 2 and h = 4
D. j = 9.5 and h = 6.5
In two rectangles, the value of j and h are 2 and 4
The subject of mathematics known as mensuration is concerned with measuring geometric shapes and their various characteristics, such as length, volume, shape, surface area, lateral surface area, etc.
According to the question, we get the equations
The perimeter of rectangle = 2*[base + height]
Rectangle P
Perimeter = 20inches
Perimeter = 2*[j+4+h]
20= 2j+2h+8
2j+2h=12
J + h=6
J=6-h ……….. Equation 1
Rectangle Q
Perimeter = 30 inches
Perimeter = 2*[j+1+3h]
30=2j+6h+2
2j+6h=28
J+3h=14 ……….. Equation 2
Substitute equation (1) in equation (2)
(6-h) +3h=14
2h=8 = H=4
J=6-h
J=6-4 = J=2
Hence, the value of j and h is 2 and 4.
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a. statistics 201 is a course taught at a university. professor rauch has taught nearly 1,500 students in the course over the past 5 years. you would like to know the average grade for the course.
The information illustrated about the statistics 201 is a sample.
What is a sample?A sample is an analytical subset of a larger population in statistics. Researchers can conduct their studies more quickly and with more manageable data by using samples. If the sample size is large enough, there won't be any bias, but getting such a sample might be costly and time-consuming.
The entire group about whom you want to make conclusions is referred to as a population. The particular group from which you will gather data is known as a sample. The sample size is always smaller than the population as a whole.
Since there are many students, a sample will be used.
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For the following questions, would you collect information using a sample or population
a. statistics 201 is a course taught at a university. professor rauch has taught nearly 1500 students in the course over the past 5 years. you would like to know the average grade for the course
Help me pleaseesesese
Answer:
21
Step-by-step explanation:
35x18 is 630/30 is 21.
In the figure below, m1=103°. Find m2.
1
2
Answer:
77 degrees
Step-by-step explanation:
180 - 103
Last week a painter painted 4 houses in 6 days. what is the productivity of the painter? calculate your answer to 2 decimal places.
The productivity of the painter is 0.66 up to two decimal places. It is attained by applying the knowledge of the division of two numbers and decimals to the provided problem.
What is decimal?
A decimal is a quantity that is distributed into two components, namely a whole and a fraction. A decimal number represents the numerical value lying in between the two integers. A decimal point (.) is used to segregate the fractional part from the whole part of a number.
E.g. 1.5, 0.06, 7.05, etc.
Calculation of the productivity of the painter
Productivity of the painter is obtained by dividing the number of houses painted by the number of days taken to paint them
The number of houses painted is 4
The number of days taken to paint 4 houses is 6 days
Productivity = 4 ÷ 6
= 0.666
Thus, the productivity of the painter is 0.66 up to two decimal places.
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Can someone help(explain how)
Answer:a,8
when you do this in the graph its quite clear that in won't turn into a square so I think you should imagine it as a triangle.
what is 6.31 converted to a percentage?
Answer:
631%
Step-by-step explanation:
Answer:
631%
Step-by-step explanation:
Math homework for today
Evaluate each expression the equation is 2a+(b^2divided 3) and a=4 and b=6
Answer:
20
Step-by-step explanation:
A 48.548.5 -ounce batch of cologne will be used to fill empty bottles. Each full bottle will contain 0.350.35 ounces of cologne. This batch of cologne will fill at most how many bottles full of cologne?
This batch of cologne can fill 138 bottles at most where each bottle has 0.35 ounce of cologne.
We are given that:
The total amount of cologne that we have = 48.5 ounce
Also,
Each bottle requires = 0.35 ounces of cologne.
We need to tell that how many bottles can this batch fill with 48.5 ounce of cologne.
We will do this by dividing the total amount of cologne with the cologne required per bottle.
So, we get that:
Number of bottles that can be filled = 48.5 ounces / 0.35 ounces.
Dividing the values, we get that:
Number of bottles that can be filled = 138.57
Number of bottles that can be filled = 138 bottles.
Therefore, this batch of cologne can fill 138 bottles at most where each bottle has 0.35 ounce of cologne.
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An Air Force plane left Nairobi and flew
toward Istanbul at an average speed of 380
km/h. A cargo plane left sometime later
flying in the opposite direction with an
average speed of 220 km/h. After the Air
Force plane had flown for ten hours the
planes were 5120 km apart. How long did
the cargo plane fly?
The cargo plane flew approximately 1,760 km.
What is an equation?An equation is a mathematical statement that includes the symbol 'equal to' between two expressions with equal values. For instance, 3x + 5 = 15. There are various types of equations, such as linear, quadratic, cubic, and so on. In this article, we will learn more about equations in math.So, according to the information the equation formed will be:
380x + 220(x+1) = 5120Now, solve the equation for x:
380x + 220x + 220 = 5120600x + 220 = 5120600x = 5120 - 220600x = 4900x = 4900/600x = 8.167Rounding off: 8
Cargo plane flied: 220x = 220(8) = 1,760 kmTherefore, the cargo plane flew approximately 1,760 km.
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a car radiator contains 10 liters of a 30% antifreeze solution. how many liters will have to be replaced with pure antifreeze if the resulting solution is to be 50% antifreeze?
4 liters of pure antifreeze is needed.
What is an linear equation in math?
An algebraic equation of the form y=mx+b is referred to as a linear equation. m is the slope, and b is the y-intercept, and all that is involved is a constant and a first-order (linear) term.
The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of two variables."
Let the amount of pure antifreeze required be x + 10 liters. Thus, total solution amount will be
0.30 (10) + 1.00(x) = 0.50 ( x + 10 )
3.00 + x = 0.50x + 5.00
0.50x = 2.00
x = 4
Thus, 4 liters of pure antifreeze is needed.
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the mean of the sample group of answer choices can assume any value between the highest and the lowest value in the sample. can never be negative. can never be zero. is always smaller than the mean of the population from which the sample was taken.
The mean of the sample (D) none of these alternatives is correct.
What is a mean?In mathematics, particularly statistics, there are several types of means. Each mean is used to summarize a specific set of data, often in order to better understand the overall value (magnitude and sign) of a given data set.The arithmetic mean, also known as "arithmetic average," of a data set is a central tendency of a finite collection of numbers: specifically, the sum of the values multiplied by the number of values. In two simple steps, we can calculate the mean or average of a data set: add up all of the values to find the sum. Subtract the sum from the total number of values in the data set.Therefore, the mean of the sample (D) none of these alternatives is correct.
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The correct question is given below:
The mean of the sample
a. is always smaller than the mean of the population from which the sample was taken
b. can never be zero
c. can never be negative
d. None of these alternatives is correct.
Make a conjecture about each value or geometric relationship.the relationship between AP and PB if M is the midpoint of AB and P is the midpoint of AM
The geometric relationship between AP and PB such that M is the midpoint of AB and P is the midpoint of AM is PB = 3AP.
What is a line segment?A line section that can connect two places is referred to as a segment.
In other words, a line segment is just part of a big line that is straight and going unlimited in both directions.
Given that,
M is the midpoint of AB and P is the midpoint of AM
Let's suppose AP = x
Then,
AB = AM + MB
Since M is the midpoint so AM =
MB = AM
AB = AM + AM = 2AM
Since P is the midpoint of A and M
So,
AP = PM
AM = AP + PM
So,
AM = 2AP = 2x
So,
MB = 2x
So,
AP = x and PB = 3x
PB = 3AP
Hence "The geometric relationship between AP and PB such that M is the midpoint of AB and P is the midpoint of AM is PB = 3AP".
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how to use coordinates to compute the distance between two points on the coordinate plane
Answer:
d = √[(x2 x 2 − x1 x 1 )2 + (y2 y 2 − y1 y 1 )2]
Step-by-step explanation:
find the prime factorization of 85
The prime factors of 85 is 5 and 17
Prime factorisation:
Finding the prime factors of a given number, such as a composite number, is done through the process of prime factorization. The prime numbers are the only components in these factors. A number with just the number itself and factor 1 is said to be a prime number.
Factor:
the quantities that are multiplied to produce new quantities are called Factor.
Prime factors:
A prime factor is a factor that is a prime number and not a composite number.
85=5×17
Therefore,The prime factors of 85 is 5 and 17
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how would ninteen billion,eighty-seven thousand,three hundred fourteen be written in standard form
Answer: 190,870,314
Step-by-step explanation:
It would be 190,870,314
Swati played eight basketball games this season. her point totals for each game were 8, 14, 4, 7, 6, 14, 4, and 7. what was the mean number of points she scored per game? 7 8 9 10
The Mean number of points she scored per game is 8.
Mean is defined as the average value of the given set of data .
mean is calculated by dividing the (sum of all observations) with (total number of observations).
For Example , Smith scored 8,6,10 out of 10 in his three tests.
so the mean score of smith will be [tex]\frac{8+6+10}{3} =\frac{24}{3} =8[/tex].
In the given question
Points for each game = 8, 14, 4, 7, 6, 14, 4, and 7.
Sum of all the points = 64.
Total number of basketball games =8
[tex]Mean= \frac{Sum of all the points }{total number of games} \\ \\ Mean=\frac{64}{8} =8.[/tex]
Therefore , the mean number of points Swati scored per game is 8.
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Answer:
it is 8 the mean is 8
Step-by-step explanation:
The endpoints of segment AB are A (-7, 3) and B (1, 0). Find the coordinates of the midpoint M. SHOW WORK
Answer:
We can now solve for B(x2, y2):
-14 = -3 + x2 and 16 = 6 + y2
-11 = x2 ... and... 10 = y2
Therefore B(x2, y2) = (-11, 10)
Step-by-step explanation:
Find the indicated one-sided limits, if they exist. (if an answer does not exist, enter dne.)
The limit doesn't exist.
What is a limit?
The value that a function (or sequence) approaches when the input (or index) gets closer to a particular value is known as a limit. Calculus and mathematical analysis are impossible without limits, which are also required to determine continuity, derivatives, and integrals.
In addition to being closely related to limit and direct limit in category theory, the idea of a limit of a sequence is further generalized to include the concept of a limit of a topological net.
A function's limit is typically expressed in formulas as
[tex]\lim_{x \to c } F(x) = L[/tex]
It is typically used to assign values to specific functions at locations where none are defined while maintaining consistency with existing values.
[tex]F(x) = -x+8 ,x\leq 0[/tex]
[tex]F(x) = 4x+9 , if x > 0[/tex]
[tex]\lim_{x \to 0^{+} } F(x) = \lim_{n \to 0^{+} } (4x+9) = 9[/tex]
[tex]\lim_{x \to 0^{-} } F(x) = \lim_{x \to 0^{-} } (-x+8) =8[/tex]
[tex]\lim_{x \to 0^{+} } F(x) \neq \lim_{x \to 0^{-} } F(x)[/tex]
So limit doesn't exist
For limit to exist
[tex]\lim_{x \to 0^{+} } F(x) = \lim_{x \to 0^{-} } F(x) = \lim_{x \to 0} f(x)[/tex]
must be satisfied
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solve 9x + 7 = 12x - 3
and 4 1/2x = 3x - 1
find x please show your work!!
An initial investment of $200 is now valued at $350. The annual interest rate is 8% compounded continuously. The equation represents the situation, where t is the number of years the money has been invested. About how long has the money been invested? Use a calculator and round your answer to the nearest whole number.
5 years
7 years
19 years
22 years
ALSO IF U WANT TO AD.D ME ON SN.AP ITS
loca-kay
It would take 7 years for the initial investment of $200 to become $350
Which calculator is appropriate in this case?
The best calculator which addresses the case at hand is a financial calculator, since it is mandatory we make use of calculator to determine the number of years it takes for initial investment of $200 to grow to $350 with 8% interest compounded continuously, bearing in mind that we need to convert the interest rate to a discrete rate
Rd = (e^(Rc) - 1)
Rd=discrete annual rate=unknown
e=exponential value=2.7182818
Rc=continuous rate=8%
Rd=(2.1782818^(8%))-1
Rd=1.083287067-1
Rd=8.3287067%
I/Y=8.3287067=annual interest rate without the % sign
PMT=0(no annual additional investment)
PV=-200(initial investment)
FV=350(future value of investment)
CPT(press compute)
N=7
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Given that f ( x ) = x 2 + 9 x + 20 f(x)=x 2 +9x+20 and g ( x ) = x + 5 g(x)=x+5, find f ( x ) + g ( x ) f(x)+g(x) and express the result in standard form.
The standard form is [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125.
We have,
f ( x ) = [tex]x^{2}[/tex]+ 9 x + 20
g ( x ) = x + 5
Now we will simplify f ( x ) + g ( x ) f ( x ) + g ( x ).
On substituting the value of f ( x ) and g ( x ) in this equation, we get
( [tex]x^{2}[/tex]+ 9 x + 20 ) + ( x + 5) ( [tex]x^{2}[/tex]+ 9 x + 20 ) + ( x + 5)
Now we will simplify this equation,
( [tex]x^{2}[/tex]+ 10 x + 25 ) + ( [tex]x^{3}[/tex] + 9[tex]x^{2}[/tex] + 20x + 5[tex]x^{2}[/tex] + 45x + 100 )
⇒ [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125
The standard form is [tex]x^{3}[/tex] + 15[tex]x^{2}[/tex] + 75x + 125.
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A company that teaches self-improvement seminars is holding one of its seminars in hillsboro. the company pays a flat fee of $388 to rent a facility in which to hold each session. additionally, for every attendee who registers, the company must spend $11 to purchase books and supplies. each attendee will pay $15 for the seminar. once a certain number of attendee register, the company will be breaking even. what will be the company's total expenses and revenues? how many attendees will that take?
The total number of attendees who attended the seminar was 97. While the total cost and revenue generated are given to be $1455 each. This problem is solved using the knowledge of linear equations.
What is a linear equation?
It is the equation in which the degree of a variable is always one i.e. the greatest power of a variable is one. Linear equations consist of two major types, linear equations in one variable and linear equations in two variables. The general form of a linear equation in one variable is ax + b = 0, while for two variables is ax + by + c = 0
Calculation of the total number of attendees of seminar and total revenue generated
Let us assume x as the number of attendees and C(x) as the cost function for the company
According to the given conditions,
C(x) = 11x + 388
As the company pays $11 for every person, thus the total amount for x attendees is given by 11x, further $388 is added up to attain overall dollars.
Further, let the revenue be R(x) being equal to $15 per person i.e.
R(x) = 15x
The company will be breaking even when the cost and revenue are the same, R(x) = C(x)
15x = 11x + 388
15x - 11x = 388
4x = 388
x = 97
Thus, the total number of people attending the seminar is 97.
Now, calculate the total expense, C(x) and revenue, R(x)
C(x) = 11(97) + 388
= $1455
R(x) = 15(97)
= $1455
The cost and revenue are $1455 for each.
Hence, the total number of attendees who attended the seminar is 97. Total cost and revenue are given to be $1455 each.
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In a test run, a certain car accelerates uniformly from zero to 22.4 m/s in 2.10 s. (a) what is the magnitude of the car's acceleration?
A specific car accelerates consistently from zero to 22.4 m/s in 2.10 seconds during a test session. The car's uniform acceleration is 8.1356 meter/[tex]sec^{2}[/tex].
What is acceleration?The rate at which an object's velocity with respect to time changes is known as acceleration in mechanics. Accelerations are vector quantities (in that they have magnitude and direction). The direction of the net force acting on an object determines its acceleration.
For instance, a car accelerates in the direction of motion when it begins at rest (zero velocity in an inertial frame of reference) and moves at increasing speeds in a straight path. When a vehicle turns, its motion vector is altered and accelerates in the new direction. A linear acceleration is the acceleration of the car in the direction it is moving, and it is this acceleration that the occupants of the car feel.
Calculations:
Acceleration=([tex]\frac{change in speed}{change in time}[/tex])= (24 m/s) / (2.95 s) = 8.1356 meter/[tex]sec^{2}[/tex]
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4+2n = n+8+n
How do you solve this? Help please!!
Answer:
0=4 No solution
Step-by-step explanation:
you combine like terms like n, and n= 2n+8
then subtract 4 from both sides= 2n=2n+4
25 points plus brainliest
Answer:
y = 3x - 6
Step-by-step explanation:
to find the answer we must first find the slope
the slope must be 3x because the two lines must be parallel
so
y = 3x + b
we must plug in x and y to find b
so
9 = 3(5) + b
9 = 15 + b
b = -6
that is your b
so
y = 3x - 6
that is your equation
Answer: I'd say C (y = 3x - 6)
Step-by-step explanation:
1. I mean, it is quite obvious as a parallel line needs to go the same way
2. But a parallel line doesn't mean the line is the same one, since the coordinate says that the other line passes through (5,9).
3. Also because looking at a graphing calc, you can see it for yourself, the equation on C is the correct answer
17/3 as a mixed number
Answer:
5 2/3
Step-by-step explanation:
because 17/3= 5 so 5 then they is 2 left so the answer is 5 2/3
1. write an expression equivalent to 7(x+1)-4(x+3) in simplest form
Answer:
3x-5
Step-by-step explanation: