Given: sin (A) = 5/13, pi/2 < A < pi and tan (B) = - sqr root 13, pi/2 < B <. What is tan(A - B)? A. (5 + 12sqr root 13)/(12 - 5sqr root13) B. (12 - 5sqr root)/(5 + 12sqr root13) C. (12 + 5sqr root13)/(-5 + 12 sqr root13) D. (-5 + 12 sqr root13)/(12 + 5 sqr root13)
Answers
The value of tan (A - B) is (-5 + 12√13) / (12+ 5√13)
How to determine tan(A-B)?Trigonometry is a branch of mathematics dealing with the relationship between the ratios of the sides of a right-angled triangle with its angles.
tan (B) = - √13
Since sin(A) = 5/13 (opposite/hypotenuse)
adjacent = √(13² - 5²) = 12 units
Since π/2 < A < π, adjacent = -12
Thus, tan (A) = -5/12
Applying the angle difference formula,
tan (A - B) = (tan A - tan B) / (1 + tan A tan B)
tan (A - B) = (-5/12 - (- √13)) / (1 + (-5/12)×(-√13))
tan (A - B) = (-5/12 + √13) / (1 + (5√13)/12)
tan (A - B) = (-5 + 12√13) / (12+ 5√13)
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Related Questions
Suppose you have a job teaching swimming lesson and get paid $6 an hour you also have a job as a chasier and get pay $8 and hour if you cannot work more than 15 hours a week what are the number you f hours you can work at each job and still make at least $100
Answers
Answer:
You can work no more than 10 hours teaching, and must work at least 5 hours cashiering. The remaining hours can be worked at the other job until the goal is reached.
Step-by-step explanation:
The restrictions give rise to two inequalities. If we ...
let x represent teaching hours
let y represent cashiering hours
then the restrictions are ...
x + y ≤ 15 . . . . total hours cannot exceed 15
6x +8y ≥ 100 . . . . you want to earn at least $100
The solution set for these inequalities is a triangular area on a graph with vertices at ...
(x, y) = (10, 5), (0, 12.5), (0, 15)
You must work at least 5 hours cashiering, and the remainder of necessary time at teaching.
Martin a une table ronde de 1 ,10m de diamètre il peut ajouter jusqu'à 5 rallonge de 40 cm chacune pour son repas d'anniversaire 10 personne seront présentes autour de cette table En comptant 60 cm par personne quel est le nombre minimal de rallonge qu'il doit installé
Answers
C = π x 1,10 m ≈ 3,46 m
Sachant que chaque rallonge mesure 40 cm (soit 0,4 m), le nombre minimal de rallonges que Martin doit installer est :
(nombre de personnes x largeur par personne - diamètre de la table) / longueur d'une rallonge
= (10 x 0,60 m - 1,10 m) / 0,40 m
= (6 m - 1,10 m) / 0,40 m
= 14,75
Comme il ne peut pas installer une demi-rallonge, il doit donc installer au moins 15 rallonges pour que tout le monde puisse s'asseoir confortablement autour de la table.
If <2 = <6, which must be true about <2?
Answers
Answer:
If 2 6, which must be true about 2? 2 is complementary to 5.
Step-by-step explanation:
Welcome for the answer. This answer is for good intentions only, report if necessary. Thank you and have a good rest of your day!Give a recursive definition for the following set of ordered pairs of positive integers (\(a|b\) means that a is a factor of b): \(S=\){\((a,b)|a \in Z^+, b \in Z^+, a|b\)}
Answers
A recursive definition for the set S can be given as follows:
What is recursion?
Recursion is a programming technique where a function calls itself to solve a problem.
Base case: (1, n) is in S for all positive integers n, since 1 is a factor of all positive integers.
Recursive case: If (a, b) is in S, then (a', b) is in S for all positive integers a' that are factors of a, and (a, b') is in S for all positive integers b' that are multiples of b.
In other words, the set S contains all pairs (a,b) where a is a positive integer that divides b, and b can be obtained by multiplying any such a with another positive integer. The base case includes all pairs where a=1 and b is any positive integer.
The recursive case states that if (a,b) is in S, then all pairs where a' is a factor of a and b is a positive integer such that b=a'b are also in S, as well as all pairs where b' is a multiple of b and a is a positive integer that divides b'.
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What is the meaning of "\( \varphi (x,y)\) be \( y\wedge \phi (x)\) "?
![What is the meaning of "[tex] \varphi (x,y)[/tex] be [tex] y\wedge \phi (x)[/tex] "?](https://i5t5.c14.e2-1.dev/h-images-qa/contents/attachments/IEnaK9Mnw3ftGn7VoWymvKjzqCukNTp6.png)
Answers
The given passage provides a proof that the Separation Axioms follow from the Replacement Schema.
The proof involves introducing a set F and showing that {a: e X : O(x)} is equal to F (X) for every X. Therefore, the conclusion is that the Separation Axioms can be derived from the Replacement Schema.In the given passage, the author presents a proof that demonstrates a relationship between the Separation Axioms and the Replacement Schema.
The proof involves the introduction of a set F and establishes that the set {a: e X : O(x)} is equivalent to F (X) for any given set X. This implies that the conditions of the Separation Axioms can be satisfied by applying the Replacement Schema. Essentially, the author is showing that the Replacement Schema can be used to derive or prove the Separation Axioms. By providing this proof, the passage establishes a connection between these two concepts in set theory.
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I have $100 and I want to buy tshirt that cost $10 and sweatshirts that cost $20 how many tshirts and sweatshirts can I buy
Answers
Answer:
10 tshirts or 5 sweatshirts
Step-by-step explanation:
One t-shirt + one sweatshirt = $30.
We know that $100 ÷ $30 = 3 times with $10 left over.
This leads to the conclusion that you can buy 4 t-shirts and 3 sweatshirts.
Which scenario could be modeled with an exponential function?
Please select one of this:
The amount of money in a certificate of deposit earns 4.3% interest each year.
The amount of money in Avery's wallet increases and decreases by a different amount each week.
The amount of money in Jaylon's savings account where $125 is deducted each month.
Tim adds $10 to his savings account each week.
Answers
The scenario that could be modelled with an exponential function is when Tim adds $10 to his savings account each week.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As we know that a continuous compounding function is an exponential function. Therefore, we need to find the situation where the principal amount is invested for an infinitely long time.
A.) Since the amount is invested and a certificate of deposit is taken the amount will be invested for a fixed period of time. Thus, this is not a continuous compound function.
B.) The amount put into the account and taken out of the account varies for each term. Thus, this is not a continuous function.
C.) As in Jaylon's account the money is reduced by $125 every month, therefore, at a certain point, it will become zero. Thus, this is not a continuous compound function.
D.) As Tim adds $10 to his saving account every month, and there is no time specified, also the account will be always positive. Thus, this is a continuous compound function.
Hence, the scenario that could be modelled with an exponential function is when Tim adds $10 to his savings account each week.
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Triangle XYZ is rotated 90° counterclockwise about the origin to produce X'Y'Z'. What are the coordinates of X'Y'Z'?
Answers
Answer:
59
Step-by-step explanation:
6 plus 4 equals 8 plus 9
Identify the coordinates of each vertex of triangle XYZ.
Apply the 90° counterclockwise rotation rule, which states that when rotating a point 90° counterclockwise about the origin, the new coordinates of the point will be (-y, x).
Substitute the coordinates of each vertex into the rotation rule to find the coordinates of the corresponding vertex in X'Y'Z'.
For example, let's say that the coordinates of triangle XYZ are:
X = (2, 3)
Y = (-1, 4)
Z = (0, -2)
To find the coordinates of X'Y'Z', we can apply the rotation rule to each vertex as follows:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Therefore, the coordinates of X'Y'Z' after rotating triangle XYZ 90° counterclockwise about the origin are:
X' = (-3, 2)
Y' = (-4, -1)
Z' = (2, 0)
Note that the order of the vertices may change after the rotation, but the coordinates of each vertex will correspond to the same vertex in the original triangle.
Suppose the national average dollar amount for an automobile insurance claim is $758.83. You work for an agency in Michigan and you are interested in whether or not the state average is less than the national average. The hypotheses for this scenario are as follows. Null Hypothesis: μ ≥ 758.83, Alternative Hypothesis: μ < 758.83. You take a random sample of claims and calculate a p-value of 0.0349 based on the data, what is the appropriate conclusion? Conclude at the 5% level of significance.
A. The true average claim amount is significantly higher than $758.83.
B. The true average claim amount is higher than or equal to $758.83.
C. We did not find enough evidence to say the true average claim amount is less than $758.83.
D. The true average claim amount is significantly different from $758.83.
E. The true average claim amount is significantly less than $758.83.
Answers
Answer:
The correct option is E
Step-by-step explanation:
From the question we are told that
The population mean is \(\mu = \$ 758.83\)
The null hypothesis is \(H_o : \mu \ge 758.83\)
The alternative hypothesis is \(H_a : \mu < 758.83\)
The p-value is \(p-value = 0.0349\)
The level of significance is \(\alpha = 0.05\)
Generally from the value given we see that the p-value < \(\alpha\) hence
The decision rule is
Reject the null hypothesis
The conclusion is
The true average claim amount is significantly less than $758.83.
write a real-world situation that could be modeled by the equation 8+2x=6x. Then solve the problem.
Answers
Answer:
x = 2
Step-by-step explanation:
8 = 6x + -2x
8 = 4x
8 = 4x
4 4
2 = x
As an estimation we are told £3 is €4.
Convert £15 pounds.
Answers
Answer:
£24 because 3x5=15 4 x 5=24
Jan is painting a square canvas. The length of one side of the canvas is 4 feet. Write an equation to show how to show how to find the area of the canvas
Answers
Step-by-step explanation:
It is given that, Jan is painting a square canvas. The length of one side of the canvas is 4 feet.
We need to write an equation to show how to find the area of the canvas.
For a square, all its sides are equal. Let the side is x. The area of a square is given by :
\(\text{Area}=\text{side}^2\\\\A=x^2\\\\A=4^2\\\\A=16\)
So, the equation that shows the area of the canvas is \(A=x^2\).
It took Malik 1 hour and 30 minutes to complete his English essay. He finished the essay at 5:30 pm. What time did he start working on the essay?
Answers
Answer:
4:00 pm
Step-by-step explanation:
To find the time it takes Malik to finish his English essay, let's start by subtracting one hour.
5:30 minus 1 hour is 4:30.
Now, subtract 30 minutes.
4:30 minus 30 minutes is 4:00.
Malik started working on his English essay at 4:00 pm.
Hope that helps.
Suppose that you are thinking about buying a car and have narrowed down your choices to two options.
The new-car option: The new car costs $25,000 and can be financed with a four-year loan at 6.12%.
The used-car option: A three-year old model of the same car costs $17,000 and can be financed with a three-year loan at 7.72%.
=||)
[1-(2-4) 11
What is the difference in monthly payments between financing the new car and financing the used car? Use PMT
The difference in monthly payments between financing the new car and financing the used car is $
(Round to the nearest cent as needed.)
Answers
Answer:
sjsjsuduhr r ki snsbtsuwi 3 38yv4r djvs
Write a completely simplified rational expression that represents the exchange rate Salma will receive in dollars per euro. Explain how you came up with your expression.
Answers
The exchange rate that She will receive is an algebraic expression
The exchange rate that Salma will receive in dollars per euro is \(\frac{12x - 9}{4x -6}\)
How to determine the exchange rateThe amount of dollars with Salma is given as:
\(Dollar = \frac{12x^2 + 15x - 18}{2x^2 + 14x + 20}\)
The amount of Euro she can buy is:
\(Euro = \frac{2x^2 -x-3}{x^2 + 6x +5}\)
Let the exchange rate be r.
So, we have:
\(Dollar * \frac 1r = Euro\)
The equation becomes
\(\frac{12x^2 + 15x - 18}{2x^2 + 14x + 20}* \frac 1r = \frac{2x^2 -x-3}{x^2 + 6x +5}\)
Factorize the expressions
\(\frac{3(x + 2)(4x - 3)}{2(x + 5)(x +2)}* \frac 1r = \frac{(x +1)(2x -3)}{(x + 5)*x + 1)}\)
Cancel out the common factors
\(\frac{3(4x - 3)}{2}* \frac 1r = \frac{(2x -3)}{1}\)
Make r the subject
\(\frac 1r = \frac{2(2x -3)}{3(4x - 3)}\)
Expand
\(\frac 1r = \frac{4x -6}{12x - 9}\)
Make r the subject
\(r = \frac{12x - 9}{4x -6}\)
Hence, the exchange rate is \(\frac{12x - 9}{4x -6}\)
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I have a 97 and if I make a 0/300 on a project what will my grade be?
Answers
Answer:
If it’s 10%, 90x.90 plus 0x.10 = 81.If it’s 15%, 90x.85 plus 0x.15= 76.5If it’s 20%, 90x.80 plus 0x.20= 72.If it’s 25%, 90x.75 plus 0x.25= 67.5If it’s 30%, 90x.70 plus 0x.30= 63.If it’s 40%, 90x.60 plus 0x.40= 54.If it’s 50%, 90x.50 plus 0x.50= 45.
Step-by-step explanation:
Siena draws a map of her flower garden. She wants to plant roses 6 feet away from the marigolds and 5 feet away from the lavender. Where should Siena plant the roses?
(–2, 3)? or (–2, 4)? or (–3, 2)? or (3, –2)?
Answers
Answer:
The answer would be (3,-2)
Step-by-step explanation:
At the location of (3,-2), if you went upwards 6 units, you would be at the Marigolds. If you went to the left 5 units, you would be at the Lavender. Therefore, (3,-2) is the correct answer.
The first and most important agent of socialization for young children is
Answers
Answer:
The family is the first and most important agent of socialization for young children.
Step-by-step explanation:
The family represents a child’s first emotional tie, and it is by far the most significant agent of the socialization process. Infants are extremely reliant on other people to survive, and the parents assume the role of guiding them to be able to care for themselves. Parents or guardians provide children with their initial system of beliefs, 'normals', and values, and the system is based on their ethnic community, social status, and religion among other factors. The system that parents inculcate on children normally has a profound effect throughout their lives. The family also helps the child when things get rough in society and in school, etc.
what is 3 times 106? show work
Answers
Answer:
3*3*3=27 is the rights answer
3x6=18(move 1 to the left/replace the 0)
3x1=3
Rose and Angel are caterers. Both Rose and Angel charge a flat fee plus a fee per guest. Rose charges a flat fee of $50 plus $12 per guest. The table shows how much Angel charges for different numbers of guests. Angel's Catering Charges Number of Guests Charge ($) 10 $180 15 $255 25 $405 30 $480 Part A Who charges the greater flat fee? O A. Rapse O B. Angel Part B Vhat is the difference in total charges between Angel and Rose for a party that includes 50 guests? Enter the answer in the box. Autohide sh Growth: Math 6+ GA 2015 Question ITU Shelf nositi
Answers
Answer:
a. Angel has a greater flat fee
b. Difference = $130
Step-by-step explanation:
Given
Rose:
\(Flat\ Fee = \$50\)
\(Rate = \$12\)
Angel
Guests --- Charges
10 -------- $180
15 -------- $255
25 -------- $405
30 -------- $480
Solving (a): Who charges the greater flat fee?
We have that the flat fee of Rose is:
\(Flat\ Fee = \$50\)
For Angel, we need to determine the equation of the given table
Start by calculating the slope (m) of the table
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Where x and y represent any two corresponding values of the guests and the charges.
\((x_1,y_1) = (10, 180)\)
\((x_2,y_2) = (30, 480)\)
So: \(m = \frac{y_2 - y_1}{x_2 - x_1}\) becomes
\(m = \frac{480 - 180}{30 - 10}\)
\(m = \frac{300}{20}\)
\(m = 15\)
Next, we calculate the equation using:
\(y - y_1 = m(x - x_1)\)
Where
\(m = 15\)
\((x_1,y_1) = (10, 180)\)
\(y - 180 = 15(x - 10)\)
\(y - 180 = 15x - 150\)
Add 180 to both sides
\(y - 180 + 180 = 15x - 150 + 180\)
\(y= 15x + 30\)
From the equation above:
The slope = 15 --- This represents the hourly rate
and
y intercept = 30 --- This represents the flat fee
This is better represented as:
Angel
\(Flat\ Fee = \$30\)
\(Rate = \$15\)
and
Rose:
\(Flat\ Fee = \$50\)
\(Rate = \$12\)
By comparison, Angel has a greater flat fee
Solving (b): Difference between total charges of 50 guests for both caterers.
For angel, the equation is:
\(y= 15x + 30\)
and x = 50.
So:
\(y = 15 * 50 + 30\)
\(y = 750 + 30\)
\(y = 780\)
For Rose,
First, we need to determine the equation.
\(Flat\ Fee = \$50\)
\(Rate = \$12\)
The equation is:
\(y = Flat\ Fee + Rate * x\)
\(y = 50 + 12 * x\)
So, the total charges for 50 guests is:
\(y = 50 + 12 * 50\)
\(y = 50 + 600\)
\(y = 650\)
The difference is then calculates as:
\(Difference = 780 - 650\)
\(Difference = \$130\)
If f(x) = 4x – 2 and g(x) = 5x – 3, what is g(f(2))?
Answers
Step-by-step explanation:
f(2) = 4(2) - 2
= 8 - 2
= 6
g(f(2)) = g(6)
g(6) = 5(6) - 3
= 30 - 3
= 27
g(f(2)) = 27
Which equation represents a line which is parallel to the line y=-\frac{8}{5}x-1y=−
5
8
x−1?
Answers
\(\huge\pink{Question}\)
Which equation represents a line which is parallel to the line y=-\frac{8}{5}x-1y=−
Which equation represents a line which is parallel to the line y=-\frac{8}{5}x-1y=− 5
Which equation represents a line which is parallel to the line y=-\frac{8}{5}x-1y=− 58
Which equation represents a line which is parallel to the line y=-\frac{8}{5}x-1y=− 58x−1?
\(\huge\pink{Answer}\)
The equation of a line is typically written as y = mx + b where m is the slope and b is the y-intercept. You have the equation y = 3x + 4 where the slope, m, is 3. Therefore, the parallel line will also have this slope. Hope this helps!
Determine whether each of the following functions is even, odd, or neither even nor odd.
(a) f(x) = 1 + 3x 2 − x 4
(b) ????(????) = ???? ???? ????+�
Answers
Answer:
A.) Even.
Step-by-step explanation:
If a function is an even function, then
F(-x) = f(x)
Also, if a function is an odd function, then, f(-x) = -f(x)
You are given the below function
f(x) = 1 + 3x^2 − x^4
Let x = 2
Substitute 2 for x in the function
F(x) = 1 + 3(2)^2 - (2)^4
F(x) = 1 + 3(4) - 16
F(x) = 1 + 12 - 16
F(x) = -3
Also, Substitute -2 for x in the function
F(x) = 1 + 3(-2)^2 - (-2)^4
F(x) = 1 + 3(4) - 16
F(x) = 1 + 12 - 16
F(x) = -3
Since f(-x) = f(x), we can conclude that
F(x) = 1 + 3x^2 - x^4 is even
if m1 equals (4x+2) and m2 equals 110, what is the value of x?
Answers
The value of x is 17.
Assuming that the sum of the two angles is equal to 180 degrees, then the equation to solve for angle 1 is
4x+2+110=180
4x+112=180
Then solve for x
4x=68
x=17
Then to find angle 1 just plug x into the equation for angle 1
4x+2
4(17)+2
Angle 1=70
What is a angle?
Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Angles formed by two rays lie in the plane that contains the rays. Angles are also formed by the intersection of two planes. These are called dihedral angles.
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Find the missing angle measure. Show work.
17.
7
20
24
Solve the remaining parts of the triangle.
19.
B
38
12.5 C
7
13
17.
18.
19, AC=
AB-
mzB
Need help with all these please. Asap urgent help need this done before Monday
Answers
To find the missing angle measure, we need to use the fact that the sum of angles in a triangle is 180 degrees. Let's denote the missing angle as x. We know that one angle is 38 degrees and another angle is 12.5 degrees.Therefore, the missing angle measure is 129.5 degrees.
By subtracting these two angles from 180 degrees, we get:
180 - 38 - 12.5 = 129.5
Without additional information, it is not possible to determine the remaining parts of the triangle. We would need the lengths of at least one side or the measures of other angles to solve for the missing parts.
The given information states that AC is equal to AB minus mzB. Without knowing the values of AB and mzB, we cannot determine the exact length of AC. We would need additional information to solve for the length of AC.Therefore, the missing angle measure is 129.5 degrees.
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Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s.
r= 3 inches, s = 15 inches
Answers
Answer:
45 inches
Step-by-step explanation:
Answer:
ok
Step-by-step explanation:
what is the difference between radical and rational exponents
Answers
Answer:
there the same
Step-by-step explanation:
I need the csc for this problem
Answers
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Answer:
jkhojrgephovhg rggefouhgv ouheruoegho;weurh reugeho;hgouerh;oeru ;erouhge;erhuorue greu;he; gouhgrouhrfljsshfglfsjfksjlakjfaddfslklkjfdaj;lkdf adfkd jkd jdfk dkjjdfk djkfl fdjks dfjk djkfas fdks kjdfsa jfkdsa kj;dflsa
Step-by-step explanation:
A train covers certain distance in two parts. Distance covered in first part is 200% more than the distance covered in second part while speed of train is in the ratio 2 : 1 in first and second part respectively. If average speed of train is 64 km/hr, then find the speed of train in first part? (in kmph)
Answers
Answer:
Part A speed=96*2=192km/h
Step-by-step explanation:
Two parts, parts A and part B
Part A=200% more than B
Let part B=x
Part A=200 more than B
=2x
Speed ratio=2:1
Average speed of train=64km/h
Let Part A speed=2x
Part B speed=x
A:B=2:1
Total ratio =3
Speed in the part A can be calculated thus:
Totatl speed= ratio of speed in part A / total ratio
64=2x/3
192=2x
x=96km/h
Part A speed=96*2=192km/h
Picture provided too
Answer the following questions about the given sets
a. Are the sets equivalent? Explain
b. Are the sets equal? Explain.
A=(5, 5, 5, 6, 6, 7,7,7)
B=(7,6,5)
a. Are the sets equivalent? Explain.
A. The sets are not equivalent because n(A) = n(B).
B. The sets are not equivalent because set A does not contain the exact same elements as set B
OC. The sets are equivalent because n(A) = n(B).
OD. The sets are equivalent because set A does not contain the exact same elements as set B
b. Are the sets equal? Explain
OA. The sets are not equal because n(A) = n(B).
B. The sets are equal because n(A) = n(B)
C. The sets are equal because set A contains the exact same elements as set B
D. The sets are not equal because set A contains the exact same elements as set B.
Answers
a. The sets are not equivalent because n(A) ≠ n(B).
b. The sets are equal because set A contains the exact same elements as set B
What are equivalent sets?Two sets A and B are said to be equivalent if they have the same cardinality i.e. n(A) = n(B).
In general, we can say, two sets are equivalent to each other if the number of elements in both the sets is equal.
From the information given, we have that;
A=(5, 5, 5, 6, 6, 7,7,7)
B=(7,6,5)
n(A) ≠ n(B)
Two sets A and B can be equal only if each element of set A is also the element of the set B.
n(A) = n(B)
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