which trig function is used to find the angle if the length of the hypotenuse and of the adjacent side are know
The cosine functions are used to find the angle if the length of the hypotenuse and the length of the adjacent side is known.
The ratio of the adjacent side of a right triangle to the hypotenuse is called the cosine and is given the symbol cos.
The cosine function in a triangle is the ratio of the adjacent side to that of the hypotenuse.
The general formula for cosine is:
cos α = Adjacent Side/Hypotenuse
Cosine has a few properties, which are periodic and even.
It is the ratio of the length of the side that is ADJACENT the angle to the length of the longest side, or HYPOTENUSE, of the triangle.
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Please help asap with correct answer I will give brainliest please!!!
Answer:
I cant really see it sorry, make it a big bigger please and I will try my best.
A pump fills a pool at a constant rate. At the end of 18 minutes it has filled 2 gallons of water. Which table represents the relationship between the number of minutes and the number of gallons of water in the pool?
The table can be written as,
Minutes Gallons
9 1
18 2
27 3
36 4
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 7 is an equation.
We have,
At the end of 18 minutes, it has filled 2.
This can be written as
y = kx
Where x is minutes and y is the number of gallons.
So,
2 = 18k
k = 2/18 = 1/9
Now,
The equation is y = (1/9)x
The table can be written as,
Minutes Gallons
9 1
18 2
27 3
36 4
Thus,
The table that represents the relationship between the number of minutes and the number of gallons of water in the pool is given above.
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at 9:30 a.m., sean started filling swimming pool. At 11:30a.m.,, he had filled 1,800 gallons. at what time will the pool be full?
At 2:30 AM,
the pool will be full.
What is division?The division in mathematics is one kind of operation. In this process, we split the expressions or numbers into the same number of parts.
At 9:30 AM,
Sean started filling a 4,500-gallonswimming pool.
At 11:30 AM,
he had filled 1,800 gallons.
The unit rate = 1800/2 = 900 gallons per hour.
The pool completely filled in 5 hours.
Therefore, the pool be full at 2:30 AM.
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The complete question:
At 9:30 AM,
Sean started filling a4,500-gallonswimming =~ pool. At 11:30 a.m., he had filled 1,800 : gallons. At what time will the pool be full? :
What would be the reason for statement three
Answer:
For # 3
Step-by-step explanation:
BOTH of the angles at K are equal , thus you have the Side-Angle-Side theorem of congruency, often abbreviated S A S
for the fractured expression use the distributive property to write an equivalent expression
3(2x + 11y)
An equivalent expression of 3(2x + 11y) is 6x + 33y.
What are the equivalent expressions?Expressions that are equivalent to the same thing, even when they have distinct appearances. When we enter the same value(s) for the variable, two algebraic expressions that are equivalent have the same value (s).
Given:
An expression,
3(2x + 11y).
The distributive property:
a(b + c) = ab + ac.
So,
3(2x + 11y) = 6x + 33y
Therefore, 6x + 33y is an equivalent expression.
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3¼% of $500 is? ........
Answer:
3¼% of $500 is $16.25.
Step-by-step explanation:
What base can you rewrite both 8 and 16 as using exponents?
2 can be used as the base for 8 and 16 to write in exponent form.
What is Number system?A number system is defined as a system of writing to express numbers.
We have to rewrite both 8 and 16 with same base as using exponents.
8 can be written 2×2×2
8 as 2³
16 can be written as 2×2×2×2
16 as 2⁴
Hence, 2 can be used as the base for 8 and 16 to write in exponent form.
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An object is launched at 24. 5 meters per second from a platform that is 68. 6 meters tall. The equation for the object's height in meters, h, at seconds after the launch is -4. 9 + 2 + 24. 5t + 68. 6
•To find the number of seconds it will take the object to hit the ground after it is thrown, h must be set equal to 0: True or False?
•If h is set equal to 0, then t = 0 is a solution to the equation: True or False?
•The object will hit the ground at t=7 seconds: True or False?
To find the time it takes for the object to hit the ground, h must be set equal to 0.
• To find the number of seconds it will take the object to hit the ground after it is thrown, h must be set equal to 0: True
• If h is set equal to 0, then t = 0 is a solution to the equation: False
• The object will hit the ground at t=7 seconds: False
To find the number of seconds it will take the object to hit the ground, we must determine when its height is 0, since this is when it hits the ground. To do this, we set h equal to 0 and solve for t. So, setting h equal to 0 is the correct step in finding the time it takes for the object to hit the ground.
However, t = 0 is not a solution to the equation when h is set equal to 0. The equation for the object's height, h, at time t is -4.9t^2 + 24.5t + 68.6, which is a parabolic function. The value of t = 0 represents the time when the object is first launched from the platform, and the height of the object at that time is 68.6 meters. So, t = 0 is not a solution to the equation when h is set equal to 0, because at that time the height of the object is not 0.
The value of t = 7 is not the time when the object hits the ground. To find the time when the object hits the ground, we must set h equal to 0 and solve for t. This is a quadratic equation, and we can use the quadratic formula to find the two solutions. One of these solutions will represent the time when the object hits the ground, while the other will represent the time when the object reaches its maximum height.
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When h is set to 0, however, t = 0 does not represent an answer to the problem. The height of the item, h, at time t is given by the equation -4.9t2 + 24.5t + 68.6, which represents a parabolic function. The moment at which the object is first launched from the platform is represented by the value of t = 0, and the object's height at that point is 68.6 meters. Therefore, when h is set to 0, t = 0 is not a solution to the equation because the object's height is not 0 at that moment.
The moment the object strikes the ground is not at time t = 7. We must put h equal to in order to determine the moment the object touches the ground.
It costs a small production company a fixed cost of $2,600 for props and costumes plus
$140 for each performance to put on plays at area schools. For each performance, the
company earns $400. Let x represent the number of performances and let y represent
the amount of dollars of expenses or income. Then the two equations graphed below
represent the expenses and income earned by the production company. How many
performances must the company put on in order to break even?
The number of performances which the company must put on in order to break even is equal to 10 performances.
What is a point of intersection?In Mathematics, a point of intersection can be defined as the location on a graph where two (2) lines intersect or cross each other, which is primarily represented as an ordered pair containing the point that corresponds to the x-coordinate (x-axis) and y-coordinate (y-axis) on a cartesian coordinate.
By critically observing the graph of the lines representing the given system of equations, we can reasonably and logically deduce that the correct solution set lies in Quadrant I and it is denoted by the point of intersection of both the x-coordinate (x-axis) and y-axis, which is given by the ordered pair (10, 4,000).
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Ruby’s model for a Fourth of July party hat is shown. The model is composed of a rectangle and 2 right triangles. What is the area of Ruby’s model for a Fourth of July party hat?
Total area of Ruby’s model for a Fourth of July party hat is 182.75 square centimeter.
What is Area of Rectangle?The area of Rectangle is length times of width.
Let us find the area of the red colour right triangle.
Area of red triangle=1/2×13.5×9
=60.75 square cm.
Area of blue triangle=1/2×8×9
=36 square cm.
Area of rectangle=Length×breadth
=(13.5+8)4
=21.5×4
=86 square cm.
The total area of Ruby’s model for a Fourth of July party hat is
60.75+36+86
182.75 square centimeter.
Hence, total area of Ruby’s model for a Fourth of July party hat is 182.75 square centimeter.
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What is 15 meters to feet?
Answer: It is approximately 49.2126 or 49, for short.
Step-by-step explanation:
For a more approximate result, multiply the length value by 3.281
49.21 feet or 15 meters are the same.
What is the length of a mile in meters?This is due to the fact that 1,609.344 meters, or one mile, are equivalent.The Hollywood Sign is comparable in height to it. Aproximately 15 meters tall is The Hollywood Sign. (Also known as Hollywoodland Sign) The Hollywood Sign has 15 m-tall white letters that are each individual.The average person can anticipate to walk a mile in 15 to 22 minutes, according to data from a 2019 study spanning five decades. The Centers for Disease Control and Prevention estimate that people typically walk between 2.5 and 4 mph.49.21 feet or 15 meters are the same.The Hollywood Sign is comparable in height to it. Aproximately 15 meters tall is The Hollywood Sign.To learn more about meters refer to:
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Original Price Percent of Discount Sale Price
$69.80 60% $
Answer:$45.60
Step-by-step explanation:
p=%w
69.8(.60)w
/.6 /.6
116. =w
-69.8
46.5
Answer:
349/5/5
Step-by-step explanation:
(69,8) % of 60x$
simplify the expression
According to vsepr theory, if there are five electron domains in the valence shell of an atom, they will be arranged in a(n) __________ geometry.
According to VSEPR (Valence Shell Electron Pair Repulsion) theory, the electron domains around an atom will arrange themselves in a trigonal bipyramidal geometry based on the number of domains in the valence shell.
If there are five electron domains in the valence shell, they will be arranged in a trigonal bipyramidal geometry. In this geometry, the five domains occupy the positions of three axial domains (120 degrees apart) and two equatorial domains (90 degrees apart). This arrangement minimizes the repulsion between the electron domains, leading to a more stable molecule.
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Alfred borrowed $10,400 at a fixed annual interest rate of 3%. The amount he owes, A, can
The required amount Alfred owes is given as $10712 for a year.
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
here,
Let the amount owes be x,
According to the question,
x = 10400 + 3% of 10400
x = 10400 + 312
x = 10712
Thus, the required amount Alfred owes is given as $10712 for a year.
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How many solutions does the system of linear equations represented in the graph have?
Coordinate plane with one line that passes through the points 0 comma 3 and 3 comma 4 and another line that passes through the points 0 comma negative 2 and 3 comma negative 1.
One solution at (−2, 0)
One solution at (0, −2)
No solution
Infinitely many solutions
Answer:
No solutions
Step-by-step explanation:
Sorry to say, there are no solutions to this system of linear equations. A quick look at the attached graph will illustrate this conclusion. The two lines that go through the given points are parallel. They both have a slope of (1/3), with y-intercepts of 4 and -2.
Calculate the slopes of both lines:
Line A:
Point 1 (0,3)
Point 2 (3,4)
Rise = 4-3 = 1
Run = 3-0 = 3
Slope = Rise/Run = (1/3)
Line B:
Point 1 (0,-2)
Point 2 (3,-1)
Rise = -1-(-2) = 1
Run = 3-0 = 3
Slope = Rise/Run = (1/3)
Since the lines have the same slope, no more work is needed. They are parallel and will not intersect. Therefore, there are no solutions.
=====
If interested:
The y-intercept for each line can be found by using one of the points for each line in the equation y = mx + b, where m is the slope of (1/3) and b is the y-intercept.
Line 1: y = (1/3)x + b
3 = (1/3)*(0) + b for (0,3)
b = 3
Both lines have a slope of (1/3). They are parallel and will never meet, even though they have a lot in common.
Line 2: y = (1/3)x + b
-2 = (1/3)*(0) + b for (0,-2)
b = -2
Answer:
No solutions
Step-by-step explanation:
I got it right on the test
the mean number of cars sold by each salesman at kovak motors is 10 cars per month, with a standard deviation of 3 cars (distribution is symmetric). ben polamalu only sold 6 cars last month. which statement is true?
The mean number of cars sold by each salesman at Kovak Motors is 10 cars per month, with a standard deviation of 3 cars (distribution is symmetric). Ben Polamalu only sold 6 cars last month. The statement which true is B) Ben's sales were not unusual last month.
ABOUT MEAN IN MATHThe mean is one of the important formulas in mathematics. Another term for the mean is the average. The mean is a calculation that is studied further in statistics.
Calculating the mean is a basic math skill. The mean is a calculation that can be calculated using a simple formula. Usually, the mean is a formula that is used in conjunction with other statistical formulas such as the mode and median.
In everyday life, the mean is a calculation that is often used. An example of using the mean is to find out the average income of employees in an office.
Your question is incomplete but most probably your full question was:
The mean number of cars sold by each salesman at Kovak Motors is 10 cars per month, with a standard deviation of 3 cars (distribution is symmetric). Ben Polamalu only sold 6 cars last month. which statement is true?
A) Ben's sales were unusual last month.
B) Ben's sales were not unusual last month.
C) Ben's sales were not unusual this month.
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Assume you have a future liability of $12000 per year for 4 years beginning 7 years from today. You will fund this liability over the next 5 years, with the first deposit to occur 1 year from today. If you earn an interest rate of 8% per year, compounded annually, on deposits, how much will you have to deposit at the end of each of the next 5 years to fund this liability?
$6273.04 have to deposit at the end of each of the next 5 years to fund this liability
PV of Annuity = P*[1-{[tex]{1+i}^{n}[/tex]}]/i
Where, P = Annuity = 12000, i = Interest Rate = 0.08, n = Number of Periods = 4
PV at 6 years from today = 12000*[1-{(1+0.08)^-4}]/0.08 = 12000*0.26497/0.08 = $39745.52
PV at 5 years from today = PV at 6 years from today/[1+Interest Rate] = 39745.52/[1+0.08] = $36801.41
FV of Annuity = P*[{[tex]1+i^{n}[/tex]}-1]/i
Where, FV = 36801.41, i = Interest Rate = 0.08, n = Number of Periods = 5
Therefore,
36801.41 = P*[{(1+0.08)^5}-1]/0.08
2944.1127 = P*0.469328
Therefore, Amount to be deposited =
P = 2944.1127/0.469328 = $6273.04
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A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6. Which statements are always true regarding the diagram? Select three options. m∠5 + m∠3 = m∠4 m∠3 + m∠4 + m∠5 = 180° m∠5 + m∠6 =180° m∠2 + m∠3 = m∠6 m∠2 + m∠3 + m∠5 = 180°
Answer: the answer is 189
Step-by-step explanation:
LN = LN because of ____
Answer:
Reflexive Property
Answer:
reflexive property
Step-by-step explanation:
We can use the reflexive property to state that LN = LN.
It states that a value is equal to itself.
PLEASE PLEASE HELP ANSWER THE QUESTIONS
Answer:
Step 1: m<KHG + m<GHJ=180 degrees
Step 2: x=13
Step-by-step explanation:
This pair of angles is called vertical angles. In a vertical angle situation, opposite angles are equal to each other. An opposite angle and an adjacent angle are ALWAYS equal to 180 degrees.
To start off...
Make both parts of the equation equal to 180 degrees
5x+38+7x-14=180
Combine like terms and add the regular numbers together
5x+7x and 38 + -14
12x+24=180
Subtract 24 from each side of the equation
12x=156
Divide 12 from each side.
x=13
PLS HELP AND SHOW WORK
the humane society receives $45 for each dog that is adopted. if they spent $920 on supplies, how much profit will they make if they have 24 dogs for adoption? Write a linear equation and solve.
Answer: 160
Step-by-step explanation:45 x 24 = 1080
1080 -920 = 160
Answer:24 x 45 = 1080
Step-by-step explanation:
Alex, Bob, Clay, Daisy and Elly are eating a big cake.
After eating, there was one slice left, and they decided to leave it for Fredy but someone ate it!
Fredy knows that these 5
people are each telling one truth and one lie:
Alex says, "It wasn't Elly. It was Bob."
Bob says, "It wasn't Clay. It wasn't Elly."
Clay says, "It was Elly. It wasn't Alex."
Daisy says, "It was Clay. It was Bob."
Elly says, "It was Daisy. It wasn't Alex."
Who ate the last slice of cake?
The person who ate the last slice of cake is Daisy.
Who ate the last slice of cake?We have to know that the question that we have been asked here borders on the ability of the individual to be able to apply his or her reasoning so as to analyze the statement that have been made.
The person that is to be suspected is the one that is blaming everyone else as in this case can see is what Daisy is saying. We would pick up from there and then suspect a foul play and that is how we can know who ate the cake.
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Laine correctly factor expreion 16. 5 a - 77. 2 b 36 and give two poible anwer Laine could have written
The two possible answer is 3(5.5a - 2.4b + 12) that Laine could have written for expression 16.5a - 77.2b + 36 .
Laine could just just used another common number to write it down as,
LCM(165, 36, 72) = 3960
Prime factorization of the numbers:
165 = 3 × 5 × 11
36 = 2 × 2 × 3 × 3
72 = 2 × 2 × 2 × 3 × 3
LCM(165, 36, 72)
= 2 × 2 × 2 × 3 × 3 × 5 × 11
= 3960
GCD(165, 36, 72) = 3
So we get three as a common multiple of them so after removing 3 common from them we can write 16.5a - 7.2b + 36 as
3(5.5a - 2.4b + 12)
Hence, The two possible answer is 3(5.5a - 2.4b + 12) that Laine could have written for expression 16.5a - 77.2b + 36.
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How many solutions does the system of equations below have? 9x 6y=-2 - 18x12y = -4
The system is dependent and has infinitely many solutions.
What is the system of equations?
A system of linear equations is a set of two or more equations that includes common variables. To solve a system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
The system of equations below can be written as:
9x + 6y = -2
-18x - 12y = -4
To find the number of solutions, we need to determine if the system has a unique solution, no solution, or infinitely many solutions.
To do this, we can use the concept of compatibility. If the system is compatible, meaning that there exists a set of values for x and y that satisfy both equations, then the system has at least one solution.
If the system is inconsistent, meaning that there is no set of values for x and y that satisfies both equations, then the system has no solution.
If the system is dependent, meaning that the two equations represent the same line in the plane, then the system has infinitely many solutions.
In this case, we can see that both equations represent the same line in the plane.
Therefore, the system is dependent and has infinitely many solutions.
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How does counting cubes compare to multiplying dimensions when finding the volume of a rectangular prism?
Select from the drop-down menus to correctly complete the statements.
Amelie correctly determined the volume of this prism by counting unit cubes. She counted
Choose...
unit cubes.
Eloise correctly determined the volume of this prism by multiplying the three dimensions. She got a product of
Choose...
cubic units.
Amelie and Eloise correctly concluded that counting unit cubes gives
Choose...
result as multiplying the dimensions.
Eloise correctly determined the volume of this prism by multiplying the three dimensions, She got a product of (3×8×4) unit³.
What is a cuboid?A cuboid is a three-dimensional closed figure which has volume along with surface area.
The volume of a cuboid is the product of its length, width, and height.
The total surface area of a cuboid is 2(lw + wh + wl) and the lateral surface area is 2(l + w)×h.
The given figure is a cuboid made up of unit cubes.
We know the volume of a cuboid is (length×width×height).
By observing the figure we have 3 unit cubes of width, 8 unit cubes of length, and 4 unit cubes of height.
Therefore, The volume of the cuboid is,
= (3×8×4) unit³.
= 96 unit³.
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What exactly is the relationship between the concepts of conjugate complex vector space and conjugations/real structures?
Conjugations and real structures are important tools used to study complex vector spaces.
A vector is a mathematical object with magnitude and direction. A complex vector space is a vector space where the vectors have complex numbers as components.
Conjugation is a mathematical operation that involves changing the sign of the imaginary part of a complex number.
Real structures refer to certain mathematical objects or operations that preserve the real part of a complex number.
The relationship between the concepts of conjugate complex vector space and conjugations/real structures is that they are both used to study complex vector spaces.
A conjugate complex vector space is a complex vector space equipped with a conjugation, which is an antilinear and involatile map.
The conjugation on a complex vector space allows us to distinguish between real and imaginary parts of a vector.
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Select an ordered pair that is a solution to the equation represented by the graph.
(-4,0)
(-2, -4)
(-2,0)
(0, -4)
An ordered pair that is a solution to the equation represented by the graph include the following: A. (-4, 0).
What is an ordered pair?In Mathematics, an ordered pair is sometimes referred to as a coordinate and it can be defined as a pair of two (2) elements or data points that are commonly written in a fixed order within parentheses as (x, y), which represents the x-coordinate (abscissa) and the y-coordinate (ordinate) on the coordinate plane of any graph.
How to find an ordered pair that is a solution to the equation?In order to determine the ordered pairs that represent points on the graph of any given function, we would read all the ordered pairs that lie on its line, with respect to the x-coordinate (abscissa) and the y-coordinate (ordinate).
By critically observing the graph of the given function, the required solutions are include following;
Ordered pair = (-4, 0).
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find the area of the trapezoid
The area of the trapezoid is 24 square units.
What is the area of the trapezoid?
A trapezoid is a quadrilateral in American and Canadian English that has at least one pair of parallel sides. In British and other dialects of English, it is referred to as a trapezium. By definition, a trapezoid in Euclidean geometry is a convex quadrilateral. Its parallel sides serve as its bases.
The area of a trapezoid can be calculated by using the formula:
Area = (a + b)h / 2,
where a and b are the lengths of the parallel sides and h is the height.
By the given figure, we can find the area of the trapezoid
Area = (a+b)h/2
Area = (4.3 + 7.7)*4/2
Area = 12*4/2
Area = 24 Square units.
Hence, the area of the trapezoid is 24 square units.
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Activity 2: Planting Trees
The best time to plant trees was 20 years ago
The second best time is NOW
Data from the lumber industry shows that the
older the tree (a), the greater the number of board feet
(n) that can be created from the tree. For a tree that is
160 years old, 18,200 board feet can be used
a) Write an equation in slope-intercept form to represent this situation
b) What does the independent variable represent?
c) What does the dependent variable represent?
d) How much board feet can be used from a tree that is 100 years old?
e) If 6,825 board feet was used from a tree, how old was the tree?
pleaseeeee answer thissss kailangan ko na toh
a) The equation in slope-intercept form is y = 112.5x - 11,875, where x is the age of the tree in years and y is the number of board feet that can be created from the tree.
b) The independent variable represents the age of the tree in years.
c) The dependent variable represents the number of board feet that can be created from the tree.
d) For a tree that is 100 years old, the number of board feet that can be used is 11,875.
e) To find how old the tree is, we need to solve the equation for x.
First, subtract 6,825 from both sides of the equation to get y = 112.5x - 11,875 - 6,825.
Next, add 11,875 to both sides of the equation to get y + 11,875 = 112.5x.
Finally, divide both sides of the equation by 112.5 to get x = (y + 11,875) / 112.5.
Thus, the age of the tree is x = (6,825 + 11,875) / 112.5 = 100 years old.
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