Answer: pi/3
Step-by-step explanation:
All of the other answers are asymptotes of the function, which by definition means they are not included in the domain, because they are undefined in the domain at that point. If you graph the function and graph all of those x values, you will see that (pi/3) is the only line that crosses the function.
Also, I took the test and got it right.
Only the value of x , [tex]\frac{\pi }{3}[/tex] is in the domain of the function.
What is domain of a function?The domain of a function is the set of values that we are allowed to plug into our function which makes the function defined.
What are the trigonometric functions?The trigonometric functions are also called the angle functions, which relates the angles and the ratios of the sides of a right angle triangle.
According to the given question.
We have a trigonomtery function.
[tex]f(x) = 4cot(2x)+3[/tex]
The above trigonometry function can be written as
[tex]f(x) = 4\frac{cos(2x)}{sin(2x)} + 3[/tex]
For the function to be defined the denominator can't be zero.
[tex]sin(2x) \neq 2n\pi ( n \in0, 1, 2, 3, ..)[/tex]
Therefore, from the given values for the x we can only put [tex]\frac{\pi }{3}[/tex] in the given function because [tex]\frac{\pi }{2}[/tex] makes the denominator o which makes the function undefined. Similarly for the π also.
Hence, only the value of x , [tex]\frac{\pi }{3}[/tex] is in the domain of the function.
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Find the GCF of 12a and 18a²
Answer:
6
Step-by-step explanation:
the blue factors are all the factors 12 and 18 have in common.
A boardwalk game of chance costs $1 to play. You have a 25% chance of winning $1 back, a 20% chance of winning $2
(your $1 back, plus an additional $1), and a 10% chance to win $5 (a gain of $4). What is the expected value of playing
the game if you lose your bet 45% of the time?
A. -$1.00
B. -$0.25
C.-$0.15
D. $0.15
Answer:
the answer is c
Step-by-step explanation:
Evaluate.
-|a+bl
2-c
when a = 1, b = -2, and c = -7
Enter your answer as a simplified fraction in the box.
Answer:
-9
Step-by-step explanation:
-|1-2|2+7
-|-1|9
-9×1
-9
I need help with question 12
The value of the integral over limit is 20, the average is 1.73
The signed area is shown in the graph attached.
What is a Function ?A function is a mathematical statement used to find a relation between two variable.
To Evaluate the definite integral between
f(x) = 5 if 4≤x ≤9
f(x) = -1 if 9≤x≤14
[tex]\rm \int_{4}^{14}f(x) dx = \int_{4}^{9} 5 dx +\int_{9}^{14} (-1)dx\\\\\int_{4}^{14}f(x) dx = (5x)^{9}_{4} -(x)^{14}_{9}\\\\\int_{4}^{14}f(x) dx = 5*(9-4) - (14-9)\\\\\int_{4}^{14}f(x) dx = 20[/tex]
The average value of the interval is
= (5+5+5+5+5-1-1-1-1-1-1)/ 11 = 1.73
Therefore the average is 1.73.
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A school is arranging a field trip to the zoo. The school spends 737.38 dollars on passes for 44
students and 2 teachers. The school also spends 393.36 dollars on lunch for just the students.
How much money was spent on a pass and lunch for each student?
Step-by-step explanation:
since there is no other information, we have to assume that the prices for student passes and teacher passes are the same.
therefore, the pass price per person is
$737.38 / (44 + 2) = $737.38 / 46 = $16.03
and the lunch costs per student are
$393.36 / 44 = $8.94
altogether,
$16.03 + $8.94 = $24.97
was spent for each student.
What grade is middle school geography?
Answer:
5th or 6th grade
Step-by-step explanation:
The reason why we learn geography in 5th grade is to prepare us for 6th grade geography. The reason why we learn geography in 6th grade is because Geography helps us understand basic physical systems that affect everyday life. In other words, geography is a nice skill to have when you're learning about the water cycle or rock formations, or the moving of the tectonic plates (and other natural disasters). It's also a very important skill to have when you want to start traveling.
parallelogram
b=12 cm, h=10 cm, a=
You are choosing between two different cell phone plans. The first plan charges a rate of
21 cents per minute. The second plan charges a monthly fee of $44.95 plus 11 cents per
minute. How many minutes would you have to use in a month in order for the second
plan to be preferable?
Answer:
at least 450 minutes
Step-by-step explanation:
Find an expression for the cost of each plan as a function of the number of minutes. Set the expressions equal to each other, and solve for the number of minutes.
Let x = number of minutes.
First plan:
cost (in dollars) = 0.21x
Second plan:
cost (in dollars) = 0.11x + 44.95
Set the expressions equal:
0.21x = 0.11x + 44.95
Subtract 0.11x from both sides.
0.1x = 44.95
Divide both sides by 0.1
x = 44.95/0.1
x = 449.5
Since you cannot have a fraction of a minute, the answer is 450 minutes.
When we're solving minimum or maximum problems, are we h or the constant k? looking for the constant
In solving minimum and maximum problems, result we are looking for would be the constant, k.
What is being solved for in minimum and maximum problems?When looking for the minimum functional value, we are looking for the constant, k because it can be thought of as the absolute minimum value.
An open parabola would then have k as the maximum functional value which means that the constant k is the value being sought.
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The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm. Their present sum after cutting 2cm from each is 30cm. What is the length of the shorter pole? The product of the length of 2 unequal poles before cutting 2 cm from each was 285 cm . Their present sum after cutting 2cm from each is 30cm . What is the length of the shorter pole ?
Answer:
15 cm
Step-by-step explanation:
The length of the shorter pole can be found by forming and subsequently solving 2 equations.
Start by defining the variables that are going to be used in the working.
Let the original length of the shorter pole be a cm and that of the longer pole be b cm.
'Product' refers to the multiplication operation.
ab= 285 -----(1)
On the other hand, 'sum' refers to the addition operation.
Length of shorter pole after cutting= a -2
Length of longer pole after cutting= b -2
(a -2) +(b-2)= 30
a +b -4= 30
Adding 4 to both sides:
a +b= 30 +4
a +b= 34 -----(2)
From (2):
a= 34 -b -----(3)
Let's solve by substitution:
Substitute (3) into (1):
b(34 -b)= 285
Expand:
34b -b²= 285
b² -34b +285= 0
Factorise:
(b -15)(b -19)= 0
b -15= 0 or b -19= 0
b= 15 or b= 19
Substitute into (1):
a(15)= 285 or a(19)= 285
a= 285 ÷15 or a= 285 ÷19
a= 19 or a= 15
Since a <b, a= 15 and b= 19.
Thus, the length of the shorter pole is 15 cm.
In 2009, there were 12,078 Burger King restaurants; in 2017, there were 16,717 Burger King restaurants. Calculate the average rate of change (slope) for the number of Burger King restaurants over this time period.
PLS HELP ME
Slope of the given data is 579.88
What is Slope?The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line.
Here, given data;
x₁ = 2009 y₁ = 12078 burger
x₂ = 2017 y₂ = 16717 burger
Now, Slope = (y₂ - y₁)/(x₂ - x₁)
Slope = (16717 - 12078) / (2017 - 2009)
Slope = 4639 / 8
Slope = 579.88
Thus, Slope of the given data is 579.88
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Use the Distributive Property to find $(n-6)(n-4)$ .
Answer:
n^2 -10n + 24
Step-by-step explanation:
Given expression:
(n-6)(n-4)
Solution:
Apply distributive property,then simplifying using PEMDAS,we obtain
n^2 - 4n - 6n + 24n^2 -10n +24Hence,n^2 -10n -24 is the answer.
Question 4(Multiple Choice Worth 4 points)
Which of the following is a rational number?
√1. √2. √3, √5
O√1
O √2
O√3
√√5
Answer:
1
Step-by-step explanation:
The square root of 1 is 1 so it is a rational number while others are irrational
HELP PLS 100 POINTS PLS BRAINLY IF CAN
find the domain y=[tex]\frac{2-3x}{12-|x-12|}[/tex]
Step-by-step explanation:
hope you can understand
Write the domain and range using interval notation
The domain of the graph is [-3, 2) and the range is (-4, 5]
How to determine the domain and the range?From the given graph, we have the following highlights:
Minimum x value = -3 (closed circle)Maximum x value = 2 (open circle)Minimum y value = -4 (open circle)Maximum y value = 5 (closed circle)Open circles are represented with () while closed circles are represented with []
Hence, the domain of the graph is [-3, 2) and the range is (-4, 5]
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THE
^
Solve: x=4+(4x-4)
O
O
O
x = 2
x = 10
x = 2 or x = 10
Ono real solution
DONE
Answer: x=0
Step-by-step explanation:
[tex]x=4+(4x-4)\\\\x=4+4x-4\\\\x=4x\\\\3x=0\\\\\boxed{x=0}[/tex]
The solution to the equation x = 4 + (x + 4) is 0.
The correct option is "one real solution".
What is an equation?Two algebraic expressions having the same value and symbol '=' in between are called an equation.
Expanding the expression on the right-hand side, we have:
x = 4 + (4x - 4)
x = 4x
Subtracting 4x from both sides, we get:
x - 4x = 0
-3x = 0
Dividing both sides by -3, we get:
x = 0
Therefore, there is one solution to the equation x = 4 + (4x - 4) as the equation simplifies to 0.
So the correct answer is 0, "one real solution".
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Amy and Laura recorded the average gas mileage (MPG) of their vehicles each week for four weeks. What can be concluded about the relationships shown in the graph and table?
Amy and Laura recorded the same gas mileage each week.
Both Amy and Laura increased their gas mileage in the first two weeks.
Amy had greater gas mileage than Laura.
Laura had a constant gas mileage in the first four weeks of data.
Who runs fastest?
When do Andy and Berta cross paths?
Who is closest to the 1.5 mile mark after 6 minutes?
Both Amy and Laura increased their gas mileage in the first two weeks.
Option B is the correct answer.
The missing graph is attached with the answer.
What is a Graph ?A graph is a statistical way of showing data , it is used to show relation between the points.
A graph is useful in understanding the nature of a function.
From the data given in the question
The statements that can be concluded is , Option B
Both Amy and Laura increased their gas mileage in the first two weeks.
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5. Find the quadratic equation with root alpha and beta,given that alpha-beta=2 and alpha^2-beta^2=3.
Answer:
[tex]x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]
Step-by-step explanation:
[tex]\begin{cases}\alpha -\beta =2\\ \alpha^{2} -\beta^{2} =3\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \left( \alpha +\beta \right) \left( \alpha -\beta \right) =3&\end{cases}[/tex]
[tex]\Longleftrightarrow \begin{cases}\alpha -\beta =2&\\ \alpha +\beta =\frac{3}{2} &\end{cases}[/tex]
Then
2α = 2 + 3/2 = 7/2
2β = (3/2) - 2 = -1/2
Then
Then
α = 7/4
β = -1/4
Then
a quadratic equation with root α and β can be :
[tex]\left( x+\frac{1}{4} \right) \left( x-\frac{7}{4} \right) =0[/tex]
[tex]\Longrightarrow x^{2}-\frac{3}{2} x-\frac{7}{16} =0[/tex]
Which of the following is the midpoint between (6, 3) and (-2, -5)
Answer:
( 2, -1)
Step-by-step explanation:
(X1 + X2)/2 , (Y1 + Y2)/2
(6-2)/2 , (3-5)/2
4/2 , -2/2
2 , -1
Answer:
(2, -1)
Step-by-step explanation:
(x1, y1)=(6, 3)
(x2, y2)=(-2, -5)
[(6+(-2))/2, (3+(-5))/2]
=(4/2, -2/2)
=(2, -1)
Write 4 1/7 as an improper fraction?
Answer:
29/7
Step-by-step explanation:
4 1/7 = 4 + 1/7
4 = 28/7
then:
4 1/7 = 28/7 + 1/7 = (28+1) / 7
= 29/7
Find the distance between the parallel lines y=x-5 and y=x+6
Answer:
11
Step-by-step explanation:
i don't know
Sid makes a graph for estimating the y-value.He wants to compare it to the table before he turns it in. Do the table and the graph represent the same function?
Answer:
No
Step-by-step explanation:
The graph and the table do not show the same function as none of the y values on the graph correspond to the y values on the table.
Help please confused
Answer:
AB : y=1/5x+12
CB : y=-3x+10
CD : y=1/2x-1
DA : y=-2x+1
if you put 25ml of concentration in a glass, how much water should be added
Answer:
50 ml
Step-by-step explanation:
50 ml
List all the factors of 66 from least to greatest.
The factors of 66 are 1, 2, 3, 6, 11, 22, 33, and 66. Out of these factors, the greatest factor of 66. The next highest factor other than 66 is 33. A number which is three more than 33 is 33 + 3 = 36.
Question is the attachment
If both pipes are opened. Then the number of hours to fill up the tank fully is 100 hours.
The complete question is attached below.
What are ratio and proportion?A ratio is a collection of ordered integers a and b represented as a/b, with b never equaling zero. A proportionate expression is one in which two items are equal.
Let t be the filling time.
Then we have
Time is inversely proportional to rate of filling tank.
1/20 – 1/25 = 1/t
0.05 - 0.04 = 1/t
0.01 = 1/t
t = 1/0.01
t = 100 hours
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Brad wants to buy flowers for his friend
with $33. The daisies are $1 each and
the roses are $2 each. He buys 3 more daisies than roses.
how much did the roses cost?
Answer:
20
Step-by-step explanation:
Answer:
20$ For the Roses
Step-by-step explanation:
Think about it like this. For each daisy (1$), the price is double for roses (2$).
Brad has a limit of 33$. And he bought 3 more daisies than roses.
If each daisy is 1$, and he bought 3+ over roses, take away 3$ to get 30$. If he bought 10 (excluding 3+) Daisies, He must have bought 10 roses.
(10 Daisies = 10$) + (10 Roses = 20$) = 30$
30$ + (3 Daisies = 3$) = 33$
46. Machine A produces 500 springs a day. The number of defective springs produced by this machine each day is recorded for 60 days. Based on the distribution given below, what is the expected value of the number of defective springs produced by Machine A in any single day?
F. 0.00
G. 0.45
H. 0.70
J. 1.00
K. 1.50
Answer:
G. 0.45
Step-by-step explanation:
To find expected value, you simply multiply the value of each outcome (the numbers in the left column) by its probability
(the numbers in the right column) and then add them all together.
0(0.7) + 1(0.2) + 2(0.05) + 3(0.05)
0 + 0.2 + 0.1 + 0.15 = 0.3 + 0.15 = 0.45
The expected value is 0.45. Thus, the correct option is G.
What is the expected value?In parameter estimation, the expected value is an application of the weighted sum. Informally, the expected value is the simple average of a considerable number of individually determined outcomes of a randomly picked variable.
The expected value is given below.
E(x) = np
Where n is the number of samples and p is the probability.
The expected value is calculated as,
E(x) = 0 x 0.70 + 1 x 0.20 + 2 x 0.05 + 3 x 0.05
E(x) = 0 + 0.20 + 0.10 + 0.15
E(x) = 0.45
Thus, the correct option is G.
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PLS HELP ME ASAP!! TEN POINTS!!! Select each correct answer.
Answer:
It's 3
Step-by-step explanation:
if you go to desmos graphing calculator it'll help you get the solutions for these if you type it in every number and letter and for exponents type ^ its shift then type 6.
Which of the following equations would correspond to a conic section formed when a plane intersects a cone parallel to the base?
x2 + y2 = 32
x squared over 2 squared plus y squared over 3 squared equals 1
x2 = 8y
x squared over 2 squared minus y squared over 3 squared equals 1
The equation of the circle, ellipse, and hyperbola will be x² + y² = 3², x² + y² / 3² = 1, and x² / 2² - y² / 3² = 1, respectively.
What is the conic section?The curve that is derived from the section of the cone is known as conic section.
The following equations are given below.
x² + y² = 3², this is the equation of the circle.
x² + y² / 3² = 1, this is the equation of the ellipse.
x² / 2² - y² / 3² = 1, this is the equation of the hyperbola.
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