If sin A 0.3, cos A = 0.7, sin B = (1/√5)
and cos B: (-1/√5) find the exact value of cos(A - B).
(i know the answer but i want to know how to solve it as well)
Answers
The exact value of cos(A - B) is -2√5 /25.
What are Sine and Cosine?In math, the trigonometric functions of an angle are sine and cosine. In the context of a right triangle, the sine and cosine of an acute angle are defined as the ratio of the lengths of the adjacent leg to the hypotenuse, and the sine of the specified angle is the ratio of the opposite leg's length to the hypotenuse's length.The concepts of sine and cosine can be expanded to include any real value in terms of the lengths of particular line segments in a unit circle.The sine and cosine can be extended to any positive or negative value, even complex numbers, according to more recent definitions of the terms, which also represent them as infinite series or as the solutions to specific differential equations.Therefore,
sin A = 0.3
sin B = (1/√5)
cos A = 0.7
cos B = (-1/√5)
cos(A-B) = cos a cos b + sin a sin b
⇒ cos(A-B) = 0.7(-1/√5) + 0.3((1/√5))
⇒ cos(A-B) = -0.7/√5 + 0.3/√5
⇒ cos(A-B) = -0.4/√5
On multiplying, √5 on the numerator and denominator,
⇒ cos(A-B) = -0.4 x √5 / 5
⇒ cos(A-B) = -2√5 /25
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Related Questions
Can somebody help me with number 11?
Answers
The unknown angles are as follows:
m∠EFH = 80°m∠EFG = 160°The value of ST in the line segment is 22 units.
How to find angles and mid points?An angle bisector is a bisector that bisect an angles into two equal parts.
Therefore, EF is the angle bisector of ∠EFG.
The bisector divides the ∠EFG equally into ∠EFH and ∠HFG.
Hence,
∠EFH = ∠HFG
m∠HFG = 80°
m∠EFH = 80°
m∠EFG = 80 + 80
m∠EFG = 160°
12.
Let's find ST in the line segment.
PT = 40
QS = 12
PQ = QR = RS = x
QR + RS = QS
2x = 12
x = 12 / 2
x = 6
Therefore,
PQ = QR = RS = 6 units
PS = PQ + QR + RS
PS = 6 + 6 + 6
PS = 18 units
Hence,
ST = PT - PS
ST = 40 - 18
ST = 22 units
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Select the correct answer from each drop-down menu.
Triangle XYZ, with vertices X(-2, 0), Y(-2, -1), and Z(-5, -2), undergoes a transformation to form triangle X′Y′Z′, with vertices X′(4, -2), Y′(4, -3), and Z′(1, -4). The type of transformation that triangle XYZ undergoes is a
.
Triangle X′Y′Z′ then undergoes a transformation to form triangle X′′Y′′Z′′, with vertices X″(4, 2), Y″(4, 3), and Z″(1, 4). The type of transformation that triangle X′Y′Z′ undergoes is a
.
Answers
Answer:
1. (x+6, y-2)
2. reflection across the x-axis
Step-by-step explanation:
What is the area of trapezoid ABCE?A20 mB16 mEDC25 msq m
Answers
Given data:
The given figure of the trapezium.
The expression for the area of the trapezium is,
[tex]\begin{gathered} A=\frac{1}{2}(20\text{ m+25 m)(16 m)} \\ =360m^2 \end{gathered}[/tex]Thus, the area of the given trapezium is 360 sq-m.
Under his cell phone plan, Rahul pays a flat cost of $36 per month and $4 per
gigabyte. He wants to keep his bill under $95 per month. Which inequality
can be used to determine g, the maximum number of gigabytes Rahul can use
while staying within his budget?
Answers
The inequality of the function is 36 + 4x < 95 and Rahul can use 14 gigabyte while staying within his budget
How to determine the inequality of the function?The given parameters are:
Flat cost = $36 per monthRate per gigabyte = $4 per gigabyteRahul's bill = Under $95The above means that;
The total charges per month is
C(x) = Flat cost + Rate per gigabyte x Number of gigabyte
So, we have
C(x) = 36 + 4x
For the bill to be under $95, we have
36 + 4x < 95
Solving further, we have
4x > 59
Divide by 4
x < 14.75
Hence, the inequality is 36 + 4x < 95
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When an integer is subtracted from 2 times the next consecutive odd integer, the
difference is 9. Find the value of the greater integer.
Answers
Answer:
7
Step-by-step explanation:
Let x be the "integer." We'll assume it is odd.
The next consecutive odd integer would be x+2.
(2(x+2) - x) =9 [When an integer is subtracted from 2 times the next consecutive odd integer the difference is 9]
(2(x+2) - x) =9
(2x+4) - x) =9
x+4 =9
x = 5
The greater integer is x+2 or 7
Check:
If 5 is subtracted from 2 times the next consecutive odd integer, 7, is the difference 9?
2*7 - 5 = 9?
14 - 5 = 9?
14 - 5 = 9? YES
What is 3 2/5 plus 2 1/5?
Answers
Answer: 5 3/5
Step-by-step explanation:
3 + 2 = 5
2/5 + 1/5 = 3/5
5 + 3/5 = 5 3/5
Hope this helps!
The bar graph shows the percentage of college freshmen in a certain country with an average grade of Ain high school.The data displayed by the bar graph can be described by the mathematical model p =4x- + 25 where xis the number of years after 1980 and p is the percentage of college freshmen who had an average
Answers
Okay, here we have this:
Considering the provided formula and information, we are going to calculate the requested percent of college freshmen in 2010, so we obtain the following:
So since x corresponds to the number of years after 1980, in this case we will replace x with 30, since it is 30 years after 1980, we have:
p=4x/5+25
Replacing:
p=4(30)/5+25
p=120/5+25
p=24+25
p=49
So, as we can see, the model assumes that in 2010 the percentage was 49%, and the real one is 47%. It means that the model overestimates the real value by 2%.
Reflect the figure over the line y = 1. Plot all of the points of the reflected figure. You may click a plotted point to delete it.
Answers
Answer:
Step-by-step explanation:
How do you solve -m=9
Answers
Hello!
So, we are given the following to solve:
[tex]-m=9[/tex]
To solve this, simply divide both sides by -1.
[tex]\frac{-m}{-1}= \frac{9}{-1}[/tex]
Then, simplify the expression and you have your solution.
[tex]m=-9[/tex]
Hope this helps! If so, please lmk! Thanks and good luck!
Answer:
m= -9
Step-by-step explanation:
Divide both sides by -1
[tex]\frac{-m}{-1} =\frac{9}{-1}[/tex]
Simplify m = - 9
What is the answer to this question
Answers
The angles are which alternate exterior angles include the following: A. ∠XWY and ∠STR.
What are parallel lines?Parallel lines can be defined as two (2) lines that are cut through by a transversal and they always have the same (equal) distance apart and never meet.
What is the alternate exterior angle theorem?The alternate exterior angle theorem states that when two (2) parallel lines are cut through by a transversal, the alternate exterior angles that are formed lie outside the two (2) parallel lines, are located on opposite sides of the transversal, and are congruent angles.
In conclusion, we can logically deduce that both ∠XWY and ∠STR are alternate exterior angles because they lie outside the two (2) parallel lines and are located on opposite sides of the transversal.
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Evelyn is 2.5 years younger than James. Two times the sum of their age is 57. Write and solve an equation to find Evelyn age.
Answers
The age of Evelyn is 10.5 years finding by the properties of linear equation.
What is linear equation?
A linear equation in algebra is one that only contains a constant and a first-order (linear) component, like y=mx+b, where m is the slope and b is the y-intercept.
Let the age of James is x years.
The age of Evelyn is x - 2.5 years
Sum of age of Evelyn and James are x + x - 2.5 = 2x - 2.5
According to question,
2 x (2x - 2.5) = 57
=> 4x - 5 = 57
=> 4x = 57 - 5
=> 4x = 52
=> x = 52/4
=> x = 13
Age of James is 13 years and the age of Evelyn is 13 - 2.5 = 10.5 years.
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25.6 = 8x solve for x
Answers
Answer:
x = [tex]\frac{16}{5} = 3\frac{1}{5} = 3.2[/tex]
Step-by-step explanation:
25.6 = 8x
Divide both sides by 8.
[tex]\frac{25.6}{8} = x\\[/tex]
Expand [tex]\frac{25.6}{8}[/tex] by multiplying both numerator and the denominator by 10.
[tex]\frac{256}{80} = x[/tex]
Reduce the fraction [tex]\frac{256}{80\\}[/tex] to lowest terms by extracting and canceling out 16.
[tex]\frac{16}{5} = x[/tex]
Swap sides so that all variable terms are on the left-hand side.
[tex]x = \frac{16}{5}[/tex]
If you answer is meant to be a fraction, then your correct answer is [tex]3\frac{1}{5}[/tex] and if you answer is meant to be a decimal then you correct answer is 3.2.
Hope I helped and have a good day. ~sunshine~ =D
9. The density of an
object can be found by taking its mass and dividing by its volume.
equation to represent the relationship between
the three quantities
Write an (density, mass, and volume) in each situation. Let the density, D, be measured in
grams/cubic centimeters (or g/cm'3).
a. The mass is 500 grams
and the volume is 40 cubic centimeters.
b.
The mass is 125 grams and the volume is u cubic centimeters.
C.
The volume is 1.4 cubic centimeters and the density is 80 grams per cubic
centimeter.
d bnt
d. The mass is m grams and the volume is v cubic centimeters.
(From Unit 2, Lesson 2
Answers
When the mass is 500 grams and the volume is 40 cubic centimeters then density is 12.5 gm per cc.
When the mass is 125 grams and the volume is 1.4 cubic centimeters then density is 89.28 gm per cc.
What is a simple definition of density?The amount per unit of length, area, or volume as. a: a substance's mass per unit volume. b: the distribution of an amount (such as mass, electricity, or energy) per unit, typically of space.
D = M/V
a) M = 500 gms
V = 40 cubic cm
D = 500/40
D = 12.5 gm per cc
b) M = 125 gms
V = 1.4 cubic cm
D = 125/1.4
D =89.28 gm per cc
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In a company 80/ of workers are men if 1120 people workfor the company who aren’t men how many workers are there in all
Answers
Answer:
if you meant %, the answer is 2016
Step-by-step explanation:
1120 + 80% is 2016
The table shows deshawna's science grade during four grading periods. How much greater was the percentage change in her grade from grading period 1 to 2 than from grading period 2 to 3. round to nearest tenth
Answers
Since the percent grade in period 1 was 92% and in period 2 was 96%, then the percent change from period 1 to 2 was 4%.
Since the percent grade in period 2 was 96% and in period 3 was 99%, then the percent change from period 2 to 3 was 3%.
Since 4% is 1% greater than 3%, then the percent change from grading period 1 to 2 was 1% greater than the percent change from grading period 2 to 3.
Therefore, the answer is: 1.0%.
A kite is gliding 74 feet above sea level. There is a stingray coasting 7 feet below sea level. What is the vertical distance between the kite and stingray.
Answers
The vertical distance between the kite and stingray is 81 feet.
Given that, a kite is gliding 74 feet above sea level. There is a stingray coasting 7 feet below sea level.
What is the vertical distance?Vertical distance or vertical separation is the distance between two vertical positions. Many vertical coordinates exist for expressing vertical position: depth, height, altitude, elevation, etc.
The vertical distance between the kite and stingray is
74-(-7)
= 74+7
= 81 feet
Therefore, the vertical distance between the kite and stingray is 81 feet.
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Please help! Consider the following diagram where the regular polygon ABCDE has center at M, polygon DEHGF is irregular, and point D is on CF.Which of the following statements are correct? Select all that apply.
Answers
Solution:
From the given diagram;
The statements that are correct about the given diagram are
b)
[tex]m\angle EDC=108\degree\text{ \lparen Interior angle of a regular pentagon\rparen}[/tex]d) The sum of exterior angles of a polygon is 360°,
Hence, the sum of the exterior angles of polygon ABCDE and the sum of exterior angles of polygon DEHGF is 720°
e)
[tex]m\angle ABM=m\angle DCM[/tex]Students make 93.5 ounces of liquid soap for a craft fair they put the soap in a 8.5 ounce bottles and sell each bottle for 5.50 how much do the students earn if they sell all the bottles of liquid soap
Answers
For a craft show, students make 93.5 ounces of liquid soap. They package the soap in 8.5 ounce bottles and charge $5.50 per bottle. The students will earn $60.5.
Given that,
For a craft show, students make 93.5 ounces of liquid soap. They package the soap in 8.5 ounce bottles and charge $5.50 per bottle.
We have to find how much money will the students make if they sell all the liquid soap bottles.
Total amount of liquid soap prepared by the students for a craft fair = 93.5 ounces
Weight of each bottle in which students poured the soap = 8.5 ounces
Let us first calculate the number of bottles, each contains 8.5 ounces of soap from 93.5 ounces of soap.
So, Number of bottles = 93.5/8.5
= 11
So, 11 bottles are prepared which contains 8.5 ounces of soap from 93.5 ounces of soap.
The amount at which each bottle is sold = $5.50
The total amount earned by selling all the bottles of liquid soap = 11×5.50
= $60.5
Therefore, the students will earn $60.5 if they sell all the bottles of liquid soap.
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Algebra homework pls help
Answers
The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. The equation 9 x 5 = 45 consists of the two equations are separated by the 'equal' sign.
Detailed explanation:Assume that a team has N players.
Each squad may have anywhere from 3 to 5 players, so
3 ≤ 5 ...(i)
Let P represent a player's total points in a single game round.
Each round of the game allows for a maximum of 10 points for each player, so
0 ≤ p ≤ 10 ....( i)
(1) Elena assembled a team of five people.
As a result, 5 players' points in 1 round equal 5P.
Equation (ii) yields the range of
0 ≤ 5p ≤ 50.
As a result, Elena's team's points total ranges from 0 to 50.
(2) If each shot is off by one point, then
One player's points in one round are equal to 10-1=9.
So, 9 x 5 = 45 points were collected by 5 players in 1 round.
(3) Assume that R represents the number of teams as an integer.
the game involves at least three teams, therefore
R ≥ 3 ...( iii)
Given that N players make up one team,
R team has NR players, where R is 3, 4, or more.
Next, using equation (i)
3R ≤ 5R
Therefore, the number of players ranges from 3R to 5R if there are at least 3 teams.
The game can have anywhere from 3x3=9 to 5x3=15 players when R=3.
Answer:
(I) Between 0 and 50.
(ii) Between 3 and 5.
(iii) Between 3R and 5R, where R = 3,4,5,...
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Ciara how’s it going with the total area of (3x^2+4x) Square feet.What is the length and the width of the garden? explain
Answers
Ok, since we know that the area of a rectangle is given by the product of the width times the length, and the area is given to us by the function 3x^2+4x, we then factor the function of area:
[tex]3x^2+4x=x(3x+4)[/tex]By the previous definition, we will have that the lenght of the garden will be 3x+4 and the widht of the garden will be x.
1/2 x - 2 = x - 4
answersss??
Answers
boxes of nails are stacked on top of each other on a work bench. The table below shows how the height above the floor of the topmost box depends on the number of boxes. What is a rule for the height? Give the rule in words and as an algebraic expression.
Answers
The height is the sum of 39 and 9 times the number of boxes, n. The rule is 9n + 39.
What is algebraic expression?An algebraic expression is defined as the type of expression that is made up of a variable, a coefficient and a constant.
From the given box of nails,
The height of 2 boxes of nails = (9× 2) + 39 = 57 In
The height of 3 boxes of nails = ( 9 × 3) + 39 = 66 In
The height of 4 boxes of nails = ( 9× 4) + 39 = 75 ln
That is to say that the height of the box above the floor can be calculated by the sum of 39 and 9 times the number of boxes, n.
Therefore, the rule of heights is 9n + 39 where n is the number of boxes present.
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Given the 2 statements: "If you study for your test, then you will pass
your test," and "If you passed your test, then you studied for your
test." the biconditional is:
Answers
The biconditional statement is "You study for your test if and only if you passed".
What is biconditional statement?
A biconditional statement combines a conditional statement with its opposite expressed in the form of "if and only if."
The given statements are,
"If you study for your test, then you will pass your test" and "you passed your test then you studied for your test".
The biconditional statement is: "You study for your test if and only if you passed".
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thanks in advance for the help
Answers
a. The decrease road line verified by given function while increase in the highway The function representing the railroad miles has a negative slope, indicating a decrease. The function representing the highway miles has a positive slope, indicating an increase.
b. It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
Given
The function y =-1518x + 144.068 represents the railroad miles.
While the function y =-360.5x + 155.18models the number of highway miles.
For each function, x is the number of years after 1995.
The year in which it is estimated that the number of the country's railroad miles and the number of the country's highway miles were the same.
Therefore,
-1518x + 144.068= -360.5x + 155.18
-1518x+360.5x = 155.18-144.068
1157.5x = 11.112
x = 9
Then,
1995 - 9 = 1986
It is estimated that the number of railroad miles and the number of highway miles were the same during the year 1986.
What are miles?A mile, sometimes an international mile or base mile to distinguish it from other miles, is an imperial unit in the United Kingdom and a standard unit of distance in the United States. both are based on the older English unit of length, which is 5280 English feet or 1760 yards. The legal mile was standardized by an international agreement between the Commonwealth of Great Britain and the United States in 1959, when it was officially redefined in SI units to exactly 1609.3 meters.
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PLEASE HELP!! Will mark brainliest!!
Answers
Answer:
-1, 0, 1, 2
Step-by-step explanation:
[tex]\sqrt{5-5} -1\\\sqrt{0} -1\\0-1\\-1[/tex]
[tex]\sqrt{6-5} -1\\\sqrt{1} -1\\1-1\\0[/tex]
[tex]\sqrt{9-5} -1\\\sqrt{4} -1\\2-1\\1[/tex]
[tex]\sqrt{14-5} -1\\\sqrt{9} -1\\3-1\\2[/tex]
the registrar of a college examined the grade point averages of different categories of students. the results showed that the probability of a meaningful difference between men and women was .27. using the most common standard, is this a statistically significant difference?
Answers
The difference of 0.27 is not statistically significant.
A statistically significant difference indicates if the responses of one group differ significantly from those of another when using statistical testing.
The statistically significant differences between the numbers really aid in your data analysis. It is up to you how to interpret or act on your results, therefore you should also think about if they are significant.Let's imagine, for instance, that you get more consumer complaints from women than from men. How do you know that this is a genuine issue that has to be addressed? To find out if your male consumers are significantly more satisfied with your goods, doing a poll is a terrific technique. Our statistical significance tool can assist you in determining whether males are considerably more satisfied with your goods than women using a statistical formula. This enables you to base decisions on facts rather than anecdotes.Now we know that any data of t-statistic that is greater than 1.96 is statistically significant.
Now the difference is 0.27. Hence it is not statistically significant.
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1.
Rule/Equation: y = slope (x) +/- y-intercept
OR y = m(x) +/- b
X
2
6
10
14
18
y
12
8
4
0
TABLES TO EQUATIONS #2
-4
Slope (growth rate):
y-intercept (starting value):
2
Equation:
Answers
Answer:
Step-by-step explanation:
x y
2 12
6 8
10 4
14 0
18 -4
The slope is the Rise/Run, or change in y over the change in x. Pick any two points. I'll choose (2,12) and (18,-4),
Rise = (-4 - 12) = -16
Run = (18 - 2) = 16
Slope = Rise/Run = -16/15, or -1
The equation becomes y = -1x + b
To find b, use any of the points in the equation and solve for b. I'll use (14,0):
y = -1x + b
0 = -1(14) + b
b = 14
The equation is y = -x + 14
See the attached graph.
Math
Classify each algebraic expression below as polynomial or non-polynomial
Answers
In an equation such as the quadratic equation, cubic equation, etc., a polynomial function is a function that only uses non-negative integer powers or only positive integer exponents of a variable.
How are polynomials and non-polynomials categorized?
There are two ways to categorize polynomials: by degree and by number of terms. According to degree, polynomials can be classified as zero, linear, quadratic, or cubic. Monomials, binomials, trinomials, etc. are the different types of polynomials based on the quantity of terms.
A polynomial is, in general, an expression containing more than one term and non-negative integral exponents of a variable. A polynomial expression might look like this: ax + by + ca, x3 + 2x + 3, etc.
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2 Four friends go to the ice cream shop to purchase frozen
yogurt. Each friend gets a part strawberry and part
vanilla.
• Lucas gets 0.25 strawberry.
Adrianna gets % strawberry.
Ricardo gets 0.8 strawberry.
Jasmine gets % strawberry.
•
•
Arrange the friends in order from least to greatest amount of
strawberry in their yogurt.
Least
Greatest
Answers
Answer:
12
Step-by-step explanation:
Nicholas is saving money to buy a new video game. He started with $25 and after 3 weeks of doing chores he had $70.
Answers
70-25=$45
$45/3 = $15
