Answers
The exact values of the sine of the addition and subtraction of two angles are 576 / 1105 and 264 / 1105, respectively.
How to find the exact value of the sine of the addition and the subtraction of two angles
Since angle A is in the fourth quadrant and B is in the second quadrant, then we find the following inequalities:
cos A > 0, sin A < 0
cos B < 0, sin B > 0
If we know that cos A = 13 / 85 and sin B = 12 / 13, then the missing trigonometric functions according to the fundamental trigonometric formula are:
sin A = - √(1 - cos² A)
sin A = - √[1 - (13 / 85)²]
sin A = - 84 / 85
cos B = - √(1 - sin² B)
cos B = - √[1 - (12 / 13)²]
cos B = - 5 / 13
And the exact value of the sine of the addition and subtraction of two angles is found by the following formula:
sin (A + B) = sin A · cos B + cos A · sin B
sin (A + B) = (- 84 / 85) · (- 5 / 13) + (13 / 85) · (12 / 13)
sin (A + B) = 576 / 1105
sin (A - B) = sin A · cos B - cos A · sin B
sin (A - B) = (- 84 / 85) · (- 5 / 13) - (13 / 85) · (12 / 13)
sin (A - B) = 264 / 1105
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Related Questions
1. Tina is getting ready to take the final exam for MAT 143. Her averages before the final exam are given.
Test average-68 Hand-in-Assignment average = 75
MML average 90
The Test is 60% of the grade, Hand-in Assignment is 10% of the grade, MML is 10% of the grade
and the Final exam is 20% of the grade.
a) What should she score in the final exam to make a B (minimum 80) in the class? Note that the
maximum you can earn in the final exam is 100 points. Use PCC grading scale.
b) What should she score in the final exam to make a C (minimum 70) in the class? Note that the
maximum points you can earn in the final exam is 100 points. Use PCC grading scale.
Answers
Using the weighted mean, the minimum scores needed are given as follows:
a) To earn a B: Not possible.
b) To earn a C: 63.5.
How to obtain the weighted mean?The weighted mean is obtained by the sum of all elements in a data-set multiplied by it's weight, divided by the sum of the weights.
If these weights are proportions, then the weighted mean is given by the sum of each grade multiplied by it's proportion.
In the context of this problem, Tina grades are given as follows:
68 with a weight of 0.6.75 with a weight of 0.1.90 with a weight of 0.1.x with a weight of 0.2.Hence her final grade is given as follows:
G = 68 x 0.6 + 75 x 0.1 + 90 x 0.1 + 0.2x = 57.3 + 0.2x.
For a grade of B, the minimum score is given as follows:
57.3 + 0.2x = 80
0.2x = 22.7
x = 22.7/0.2
x = 113.
Hence it is not possible to earn a B, as the maximum possible score is of 100.
For a grade of C, the minimum score is given as follows:
57.3 + 0.2x = 70
0.2x = 12.7
x = 12.7/0.2
x = 63.5.
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Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S,S, in terms of n,n, representing Dianelys' salary after working nn years for the company.
Answers
An equation for S in terms of n representing Dianelys' salary after working n years for the company is equal to S = 40000 + 2500(n-1).
As given in the question,
Dianelys' first year salary is equal to $40000.
Raise given to Dianelys' every year is $2500
Table to represent the value for different years
First year = $40000
Second year = 40000 + 2500(1)
= $42500
Third year = 42500 + 2500
= 45000
= 40000 + 2500(2)
Fourth year = 45000 +2500
= $47500
= 40000 +2500(3) .....
An equation for S in terms of n years
S = 40000 + 2500(n -1)
Therefore, an equation for S in terms of n representing Dianelys' salary after working n years for the company is equal to
S = 40000 + 2500(n-1).
The complete question is:
Dianelys accepted a new job at a company with a contract guaranteeing annual raises. In the first year, Dianelys' salary will be $40000, and she will get a raise of $2500 every year. Make a table of values and then write an equation for S, in terms of n, representing Dianelys' salary after working n years for the company.
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May u please help me with the 2 last Questions.
Answers
omeWe are asked to find the length of the diagonal of a square with side = 7 ft
So, we can use the Pythagoras Theorem to find its length, since we are dealing with a right anhle triangle that the diagonal determines, being the 7 ft sides the "legs" of the triangle, and the diagonal of the square being the hypotenuse:
[tex]\text{hyp}=\sqrt[]{7^2+7^2}=\sqrt[]{49+49}=\sqrt[]{98}\approx9.899[/tex]which can be rounded to about 9.9 feet for this diagonal.
In the second problem, we are given the value of the diagonal, and we are asked to find the value of the square's sides, so we use Pythagoras again:
[tex]\begin{gathered} 12^2=x^2+x^2=2x^2 \\ 144=2x^2 \\ \frac{144}{2}=x^2 \\ 72=x^2 \end{gathered}[/tex]where we have named "x" the length of the unknown sides of the square, and used that 12 is the length of the diagonal.
We solved for x^2, but now to find "x" (the length of the side) we use the square root property:
[tex]\begin{gathered} x^2=72 \\ x=\sqrt[\square]{72} \\ x\approx8.485 \end{gathered}[/tex]Then the sides of the square must be approximately 8.5 ft if we round the answer to one decimal.
Jill claims that for positive fractions a/b+a/c= a/b+c because the fractions have a common numerator. How do you respond?
Answers
Answer:
Jill is incorrect.
Step-by-step explanation:
To add fractions, you need a common denominator, not a common numerator, so Jill is incorrect and her sum of fractions is incorrect.
The correct addition is:
[tex] \dfrac{a}{b} + \dfrac{a}{c} = \dfrac{ac}{bc} + \dfrac{ab}{bc} = \dfrac{ac + ab}{bc} [/tex]
the difference between 9 thirty-seven and 8 thirty sevens
Answers
100 is the difference between 9 thirty-seven and 8 thirty sevens.
Define subtraction.To subtract in mathematics is to take something away from a group or a number of objects. The group's total number of items decreases or becomes lower when we subtract from it. The components of a subtraction issue are the minuend, subtrahend, and difference. An arithmetic operation called subtraction simulates the process of deleting items from a collection. The negative symbol, or, denotes subtraction. For instance, in the following image, there are 5 2 peaches, which means that 5 peaches have had 2 removed, leaving a total of 3 peaches. Wikipedia
Given Data
difference between 9 thirty-seven and 8 thirty sevens
Converting into numerical:
937 and 837
Subtraction:
937 - 837
100
100 is the difference between 9 thirty-seven and 8 thirty sevens.
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what is the first step to solving 3.7x-15.9=2.79
Answers
The first step to solving the expression:
[tex]3.7x\text{ - 15.9 = 2.79}[/tex]We need to transfer that term that doesn't have "x" from the left side to the right side. To do this we need to invert its signal as shown below:
[tex]3.7x=2.79+15.9[/tex]The second step is to sum the terms with similar letters or no letters at all.
[tex]3.7x\text{ = }18.69[/tex]The third step is to isolate the "x" variable by switching the constant that is multiplying it from the left side to the right side. To do that the constant needs to divide on the right.
[tex]\begin{gathered} x\text{ = }\frac{18.69}{3.7} \\ x\text{ = }5\text{.}05 \end{gathered}[/tex][tex]5 ( a - 5 ) 25[/tex]5 ( a - 5 ) 25
Answers
The value of the variable a in the equation is a = 10
What is a linear equation?A linear equation is any equation with a constant rate
How to evaluate the equation?The equation is given as
5(a - 5) = 25
Open the brackets in the above equation
So, we have the following equation
5a - 5 * 5 = 25
Evaluate the products in the above equation
So, we have the following equation
5a - 25 = 25
Add 25 to both sides of the equation
So, we have the following equation
5a - 25 + 25 = 25 + 25
Evaluate the sum in the above equation
So, we have the following equation
5a = 50
Divide both sides by 5
So, we have
5a/5 = 50/5
Evaluate the quotient
a = 50/5
Evaluate the quotient
a = 10
Hence, the solution to the equation is a = 10
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The length of a shadow of a building is 26 m. The distance from the top of the building to the tip of the shadow is 35 m. Find the height of the building. If necessary, round your answer to the nearest tenth.
Answers
Using the length of shadow, the height of the building to the nearest tenth is 23.4 metres.
How to find the height of the building?The length of a shadow of a building is 26 m.
The distance from the top of the building to the tip of the shadow is 35 m.
The height of the building can be found as follows:
This situation forms a right angle triangle.
Therefore, the length of the shadow is the adjacent side and the distance from the top of the building to the tip of the shadow is the hypotenuse side.
Hence, using Pythagoras theorem,
c² = a² + b²
35² - 26² = b²
1225 - 676 = b²
b² = 549
b = √549
b = 23.4307490277
Therefore, the height of the building is 23.4 m.
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If K is the midpoint of HJ, HK= x + 6, and HJ = 4x - 6, then KJ equals
Answers
Consider the figure,
We have,
[tex]\begin{gathered} HK=x+6 \\ \text{HJ}=4x-6 \end{gathered}[/tex]As we can understand from the figure that,
HJ=HK+KJ and HK=KJ
[tex]\begin{gathered} HJ=HK+KJ \\ 4x-6=x+6+KJ \\ 4x-6-x-6=KJ \\ 3x-12=KJ \\ 3x-12=x+6 \\ x=9 \\ \therefore KJ=3\times9-12=15 \end{gathered}[/tex],
Suposse you ran 2 km in 10 min. With what speed did you run?
Answers
Answer:
12km/h
Step-by-step explanation:
10*6=60min=1hr
2*6=12km
10, 11, 12, 14, 12, 11, 13, 12, 14, 11 find the mean
Answers
Answer:
12
Step-by-step explanation:
Add all the numbers up. Then, you divided the answer by the number of values. So, its 120 divided by 10. which equals 12.
Which measure of spread is least affected by the long tail in the graph vehicle A
Answers
The measure of the spread that is least affected by the long tail in the box plot is IQR.
What is the Interquartile Range (IQR)?The range of the rectangular box in a box plot represents the interquartile range (IQR), which is the difference between the highest quartile (Q3) and the lower quartile (Q1).
An evaluation of dispersion is the interquartile range (IQR). According to the box plot shown in the graph, the value of IQR is mostly unaffected by the length of the tail.
As a result, in the box plot, IQR is the measure of the spread that is least impacted by the long tail.
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Lisa has 1/3 of a chocolate bar. Minah on the other hand, has 2/3 more. They both calorie wise equal 3020. How much calories do Lisa have? How much calories do Minah have?
Does this question make sense? If so, what's the answer?
HELP.
Answers
Answer: lisa should have about 1006 cal minah should have 2014 cals thequestion has some spelling errors like "How much calories do Lisa have?" and "How much calories do Minah have?"
se debe de pintar de azuluna barda en forma de romboide la cual mide 4.5metros de base por 2.3 metros de altura si se han pintado 4.50 metros cuadrados cuantos metros cuadrados faltan por terminar
Answers
Sabemos que
El área del romboide se obtiene multiplicando la base por altura .
A = b · h
en este problema tenemos que
b=4.5 m
h=2.3 m
A=4.5*2.3=10.35 m^2
Sustrae 4.50 de 10.35
10.35-4.50=5.85 m^2
La respuesta es
Faltan por terminar 5 .85 metros cuadrados
Solve the system.
x - 5y = 4
3x - 4y = 12
Answers
x=4+5y is the third equation. Note I will solve this by substitution.
⇒In the place of x in the equation 3x-4y=12 plug in 4+5y
[tex]3(4+5y)-4y=12\\12+15y-4y=12\\12-11y=12\\-11y=12-12\\-11y=0\\\frac{-11y}{-11}=\frac{0}{-11} \\ y=0[/tex]
x=4+5y
x=4+5(0)
x=4
Attached is the solution.
Goodluck
the number of seeds found in a sample of 7 different oranges were: 3 3 4 5 7 8 and 12 what range of the number of seeds in the sample of oranges?
Answers
SOLUTION
The range = Largest number - smallest number
The largest number is 12 and the smallest is 3.
Therefore, the range = 12 - 3 = 9.
The correct answer is option D. 9
Which statement is true of this function?
f(x) = (1) ² - 2
Answers
..........................................
a ceiling fan makes 1/8 of a full rotation in 2/5 seconds how many rotations per seconds does the fan make?
Answers
The Solution:
The question says a ceiling fan makes 1/8 of a full rotation in 2/5 of a second. That is,
[tex]\begin{gathered} \frac{1}{8}r=\frac{2}{5}s \\ where\text{ r=a full rotation} \\ s=\text{ a second} \end{gathered}[/tex]We are asked to find how many rotations per second the fan makes. By making s the subject of the formula in the above equation, we get
[tex]\begin{gathered} \frac{1}{8}r=\frac{2}{5}s \\ \text{Cross multiplying, we get} \\ 16s=5r \end{gathered}[/tex]Dividing both sides by 16, we get
[tex]\begin{gathered} \frac{16s}{16}=\frac{5r}{16} \\ \\ s=\frac{5r}{16} \end{gathered}[/tex]So, the fan makes 5/16 of a full rotation in every second.
part b)what is the slope of the line the rest of the question is provided in the picture
Answers
We want to find the slope of the graph. The formula for calculating slope is expressed as
slope = (y2 - y1)/(x2 - x1)
where
y1 and y2 are the y coordinates of initial and final points on the line.
x1 and x2 are the x coordinates of initial and final points on the line.
Locating initial and final points on the line, we have
when x1 = 1, y1 = 2000
when x2 = 2, y2 = 3500
By substituting these values into the formula, we have
slope = (3500 - 2000)/(2 - 1) = 1500/1
Slope = 1500
The cost increases by $1500 for each ton of sugar being transported
There is a rectangular lot in the garden, with 10 ft in length and 4 ft in width. You plan to expand the lot by an equal length around its
four sides, and make the area of the expanded rectangle 72 ft². How long should you expand the original lot in four directions?
You should expand the original lot by blank in four directions. Please type ft to represent feet.
Answers
Answer:
You should expand the four sides of the original lot by 2 ft.
Step-by-step explanation:
10 x 4 = 40
72 - 40 = 32
32/4 = 8
10 - 8 = 2
10 + 2 = 12
4 + 2 =6
12 x 6 = 72
Write out the Harmonic Sequence
Answers
Answer:
Step-by-step explanation:
maybe try to add pollyonxies
the circumference of a circle is 22cm. what is the area of 1/10 of the circular region? use π= 22/7
Answers
Answer
(1/10) of Area = 3.85 cm²
Explanation
Circumference of a circle = 2πr
where
π = pi = (22/7)
r = radius of the circle = ?
Circumference = 22 cm
Circumference = 2πr
22 = 2 × (22/7) × r
22 = (44r/7)
(44r/7) = 22
44r = (22)(7)
r = [(22)(7)/44]
r = 3.5 cm
Area of a circle = πr²
We are then asked to find (1/10) of the area of this circle
(1/10) of Area = (1/10) × (22/7) × 3.5²
(1/10) of Area = 3.85 cm²
Hope this Helps!!!
Someone please help me answer this and i need the correct answer
Answers
Answer: D
Step-by-step explanation:
Victoria is purchasing a futonmattress for $223.80,including tax. She gives thesales clerk 2 fifty-dollar bills, 3twenty-dollar bills, and 13five-dollar bills. How muchshould she receive in change?T
Answers
According to the given data we have the following:
Victoria is purchasing a futon mattress.
futon mattress price=$223.80
Victoria would pay the futon mattress with 2 fifty-dollar bills, 3 twenty-dollar bills, and 13 five-dollar bills.
So, 2 fifty-dollar bills would be=2*50=$100
please help me do this i think i’mdoing it right but i’m not sure The graph shows a parabola and its focus. Write the equation of the parabola in vertex form.
Answers
Step 1
Write the parabola in vertex form eqaution
[tex](x-h)^2=-4a(y-k)[/tex]where
[tex]\begin{gathered} h=0=x-\text{coordinate of the vertex} \\ k=1=y-\text{coordinate of the vertex} \end{gathered}[/tex]Step 2
Find the required equation
The distance between the vertex and the focus = a
Therefore,
[tex]\begin{gathered} \text{The vertex=(0,1)} \\ \text{The focus= (0,-2)} \end{gathered}[/tex]Hence with the formula for the distance between two points we have
[tex]\begin{gathered} D=\sqrt[]{(0-0)^2+(-2-1)^2}^{}_{} \\ D=\sqrt[]{0^2+(-3)^2} \\ D=\sqrt[]{0+9} \\ D=\sqrt[]{9} \\ D=3 \\ a=D=3 \end{gathered}[/tex]Step 3
Get the required equation by substitution
[tex]\begin{gathered} (x-h)^2=-4(a)(y-k) \\ (x-0)^2=-4(3)(y-1) \\ x^2=-12(y-1) \end{gathered}[/tex]Hence in vertex form, the equation of the parabola will be
[tex]y=-\frac{1}{12}x^2+1[/tex]The answer is written as;
[tex]y=-\frac{1}{12}x^2+1[/tex](5x +
6)(-10x² + 9x - 4)
Answers
-110x^3 + 99x^2 - 44x
The firm Bosox and Yankee has a monopoly on the production of baseball memorabilia. The firm faces the following demand curve for its product:The firm has a fixed cost of $1,000.00 and a constant marginal cost of $14 for producing units of baseball memorabilia.1. Assume the firm cannot price discriminate. How may units will the firm produce in order to maximize theprofits? a. 25 b. 50 c. 100 d. 290
Answers
Answer:
Step by step
the current in a stream flows at a rate of 4 mph. A boat travels 9 miles upstream and 9 miles downstream in a total time of 3 hours. What is the speed of the boat in still water?
Answers
The boat is moving at a speed of 8 miles per hours in still water.
How to find the speed of the boat in still water?
In this problem we find that the absolute speed of a boat (v''), in miles per hour, is the combination of the speed of the boat in still water (v) and the stream speed (v'), in miles per hour. If we assume that the boat travels at constant speed, then we have the following two equations:
Upstream
v - v' = x / t
v - 4 = 9 / t (1)
Downstream
v + v' = x / (3 - t)
v + 4 = 9 / (3 - t) (2)
By (1) and (2):
4 + 9 / t = 9 / (3 - t) - 4
9 / t - 9 / (3 - t) = - 8
9 / (3 - t) - 9 / t = 8
9 · t - 9 · (3 - t) = 8 · t · (3 - t)
9 · t - 27 + 9 · t = 24 · t - 8 · t²
18 · t - 27 = 24 · t - 8 · t²
8 · t² - 6 · t - 27 = 0
By quadratic formula we find that t₁ = 9 / 4 h and t₂ = - 3 / 2 h. Only the first root is physically reasonable. Finally, we find the speed of the boat in still water:
v - 4 = 9 / t
v = 4 + 9 / t
v = 4 + 9 / (9 / 4)
v = 8 mi / h
The speed of the boat in still water is equal to 8 miles per hour.
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Directions: Solve each system of equations algebraically. Verify the solution using the graph of the system. 1. y=-x-4 y = 3x у I o X
Answers
Directions: Solve each system of equations algebraically. Verify the solution using the graph of the system.
y=-x-4 (I)
y = 3x (II)
________________________
Using the substitution method
y = 3x
Substituting (II) in (I)
y=-x-4
3x =-x-4
3x +x = -4
4x= -4
x= -1
_____________________
Replacing in one of the equations
y = 3x
y= 3*-2
y= -3
___________
Verify the solution using the graph of the system
_____________________
Answer x= -1, y = -3
The equation y = 8z + 50 models the cost y for 2 members of the art club to go to a museum,including the shared cost of hiring a tour guide for $50. Which statement must be true?АIt will cost $240 altogether it 30 members go.BIt will cost $130 altogether it 10 members go.8 members of the art club will go to the museum.D50members of the art club will go to the museum.
Answers
According to the information given, the equation allow us to know the cost for x members to go to the museum not how many will go. For that reason option C and D cannot be true unless a fix cost was given too.
Then using the equation we can find the cost for 30 and 10 members and select the statement that is true.
[tex]\begin{gathered} y=8\cdot(30)+50 \\ y=240+50 \\ y=290 \end{gathered}[/tex][tex]\begin{gathered} y=8\cdot(10)+50 \\ y=80+50 \\ y=130 \end{gathered}[/tex]The statement that is true is b, the costr for 10 members is $130.
