Verifying trig identities can be difficult because they involve manipulating complex equations with multiple trigonometric functions that have various associated angles and coefficients.
For example, the Pythagorean Identity states that sin2θ + cos2θ = 1, which must be verified by using the identity sin2θ = 2sinθcosθ and substituting it into the equation. This results in a complex equation: 2sinθcosθ + cos2θ = 1, which must then be simplified and rearranged in order to show that it is true for all values of θ. Furthermore, trig identities can involve multiple steps that involve multiple functions and angles, which can make verifying them even more difficult.
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Here is an equation: x + 3y = 6.
Use the whole numbers 0-6 without repeating to create two (x, y) coordinate pairs that are solutions and one that is not.
The two solutions of the linear equation are:
(0, 2)
(3, 1)
And a coordinate pair that is not a solution is:
(0, 5)
How to find the coordinate pairs?Here we have the linear equation:
x + 3y = 6
And we want to find two ordered pairs that are solutions.
To find them,wecan evaluate in two values of x and then find the correspondent values of y.
if x = 0
0 + 3y = 6
y = 6/3 = 2
if x = 3
3 + 3y = 6
3y = 6 - 3
3y = 3
y = 3/3 = 1
So the two solutions are (0, 2) and (3, 1)
And a point that is not a solution can be one with the same x-value than one of the above ones but a different y-value, like (0, 5)
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According to the midpoint method, the price elasticity of demand for apples between point X and point Y is approximately （0.02/0.1/0.2/5） , which suggests that the demand for apples is (elastic/inelastic) between points X and Y.
If the price elasticity of demand is equal to 0.02/0.1, then the demand for apples is inelastic and if the price elasticity of demand is equal to 0.2/5, then the demand for apples is elastic.
The price elasticity of demand is calculated using the midpoint method with formula:
Price Elasticity of Demand = (Percent Change in Quantity Demanded) / (Percent Change in Price)
The value of the price elasticity of demand tells us whether the demand for a product is elastic (sensitive to price changes), inelastic (insensitive to price changes), or unitary elastic (neither elastic nor inelastic). A value of price elasticity of demand greater than 1 indicates that the demand for the product is elastic, meaning that a small change in price leads to a large change in the quantity demanded. A value of price elasticity of demand less than 1 indicates that the demand for the product is inelastic, meaning that a small change in price leads to a small change in the quantity demanded.
If the price elasticity of demand is equal to 0.02/0.1, then the demand for apples is inelastic between points X and Y, meaning that a small change in price leads to a small change in the quantity demanded. If the price elasticity of demand is equal to 0.2/5, then the demand for apples is elastic between points X and Y, meaning that a small change in price leads to a large change in the quantity demanded.
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Please help!!!!!Triangle ABC is similar to triangle FGH. Given the following angle measures, find the
missing angle measures.
The measures of angles in similar triangles are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
What are similar triangles?Similar triangles have the same corresponding angle measures and proportional side lengths.
Given that, Triangle ABC is similar to triangle FGH, we need to find the measures of the angles,
The sum of interior angles of a triangle = 180°
Considering Δ ABC,
∠ A + ∠ B + ∠ C = 180°
∠ C = 180°-(22°+75°)
∠ C = 83°
Since, we know that the similar triangles have congruent corresponding angles,
Therefore,
∠ A = ∠ F, ∠ B = ∠ G and ∠ C = ∠ H
Therefore, the measures of angles in Δ FGH are ∠ F = 22°, ∠ G = 75° and ∠ H = 83°
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Which values of x make the following statement true? Choose all correct
answers.
x-9.5 = a negative number
X = 9
X = -9.5
x = -9
x = 10
X = -10
x = 10.5
The values of x make the statement true are x = 9 X = -9.5 x = -9 and x = -10
Which values of x make the statement true?From the question, we have the following parameters that can be used in our computation:
x-9.5 = a negative number
Using the above as a guide, we have the following:
x - 9.5 < 0
Make x the subject
x < 9.5
This means that the values of x are less than 9.5
From the options, we have:
x = 9 X = -9.5 x = -9 and x = -10
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URGENT ANSWER PLS
The explicit formula below describes a linear function, where n
is a positive integer.
f(n)=3n−8
Which recursive formula describes the same function?
A
a1=3an=an−1−8
B
a1=−5an=an−1+3
C
a1=3an=an−1−5
D
a1=−8an=an−1+3
Answer:
[tex]Option\ B[/tex]
Step-by-step explanation:
[tex]The\ explicit\ formula\ given:\\f(n)=3n-8\\Since\ n\ can\ be\ any\ positive\ real\ number\,\\The\ formula\ describes\ an\ AP\ whose\ d=3.\\Also,\ Substituting\ n=1:\\f(n)=3*1-8\\f(n)=-5\\Hence, a_1=-5[/tex]
[tex]However,\\We\ also\ know\ that,\\d=a_n-a_{n-1}\\Hence,\\a_n-a_{n-1}=3\\Or,\\a_n=a_{n-1}+3\\These\ conditions\ are\ appropriately\ specified\ on\ Option\ B.[/tex]
In excerise 13-16 find the measures of the numbered angles in rhombus DEFG image it’s only one question image below
The measures of the numbered angles in rhombus DEFG are m ∠ 1 = m ∠ 2 = m ∠ 4 = 27°, m ∠ 3 = 90° and m ∠ 5 = m ∠ 6 = 63°
What is a rhombus?A flat shape with 4 straight sides that are all equal length. Also opposite sides are parallel and opposite angles are equal. It is a type of parallelogram.
Given is a rhombus DEFG, we need to find the measures of the numbered angles,
We know that, diagonals of a rhombus bisect each other at right angle, and also bisects the vertex angles,
Also, the opposite angles are equal,
Therefore,
m ∠ 1 = m ∠ 2 = m ∠ 4 = 27°
m ∠ 3 = 90°
m ∠ 5 = m ∠ 6 = 90° - m ∠ 1
m ∠ 5 = m ∠ 6 = 90° - 27° = 63°
m ∠ 5 = m ∠ 6 = 63°
Hence, the measures of the numbered angles in rhombus DEFG are m ∠ 1 = m ∠ 2 = m ∠ 4 = 27°, m ∠ 3 = 90° and m ∠ 5 = m ∠ 6 = 63°
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please answer the question below!
The values of x in f(x)=2x g(x)=2^x is x=2 and x=0.77.
What is the solution for an equation?
The solution of an equation refers usually to the values of the variables involved in that equation which if substituted in place of those variable would give a true mathematical statement.
We are given that;
f(x) 2x and g(x)=2^x
Now,
To graph the functions on the same coordinate plane, we can plot some points and connect them with a line:
f(x) = 2x
(0, 0), (1, 2), (2, 4), (3, 6), ...
g(x) = 2^x
(0, 1), (1, 2), (2, 4), (3, 8), ...
To find the solutions to the equation f(x) = g(x), we need to set the two expressions equal to each other and solve for x:
2x = 2^x
x=2, 0.77
Therefore, the answer of the given equation will be x=2, 0.77
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PLEASE HELP I REALLY NEED IT! Write an equation for the nth term of the geometric sequence 5,15,45,135,405,…
Then find a8
Answer:
An equation to represent the given geometric sequence would be [tex]a(x)=5*3^{x-1}[/tex], and a(8) of the geometric sequence will be 10,935.
Step-by-step explanation:
In order to write an equation for a geometric sequence, first we must analyze the sequence to find its starting value and its constant ratio. The starting value is simply the first term in the sequence, which is 5. As for the constant ratio, it is the rate of change that the equation uses. In this sequence, the constant ratio is 3. Now, we can write out an equation for this geometric sequence.
We know the first term of the sequence is 5, and the common ratio is 3, so we can write out a function for the geometric sequence, which will be [tex]a(n)=5*3^{n-1}[/tex]. NOTE that the exponential power is n - 1, and not n. This is because the first term of the sequence is 5, and not the "0th" term, therefore we must subtract 1 from n (the term number) to have the right sequence.
Lastly, we can use the equation [tex]a(n)=5*3^{n-1}[/tex] to find the 8th term of the sequence by replacing n with 8. So [tex]a(x)=5*3^{n-1}[/tex] would become [tex]a(8)=5*3^{8-1}[/tex], and you will get [tex]a(8)=5*3^{8-1}[/tex] ⇒ [tex]a(8)=5*3^{7}[/tex] ⇒ [tex]a(8)=5*2187[/tex] ⇒ [tex]a(8)=10,935[/tex]. Therefore, the equation for the nth term of the geometric sequence would be [tex]a(n)=5*3^{n-1}[/tex], and the 8th term of the sequence is 10,935.
Have a great day! Feel free to let me know if you have any more questions :)
a process in which a number is changed, such as by adding, subtracting, dividing or multiplying is called___
The process in which a number is changed, such as by adding, subtracting, dividing or multiplying is called mathematical operation.
A mathematical operation is a process that changes a number in some way. The most common mathematical operations are:
Addition is adding two or more numbers together to find their sum.
Subtraction is finding the difference between two numbers by subtracting one from the other.
Multiplication is finding the product of two or more numbers by multiplying them together.
Division is finding the quotient of two numbers by dividing one by the other.
In addition to these basic operations, there are also other mathematical operations such as modulo, exponentiation, and square roots.
These operations are used to perform various mathematical calculations and are fundamental to many areas of mathematics, including algebra, calculus, and geometry. They are also used in many real-world applications, such as in finance, engineering, and science.
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give example discrete variable
Discrete variables are a subset of variables that have a limited range of values. A variable that counts how many kids a family has, for instance, can only be a whole number, such as 0, 1, 2, etc.
Discrete variables, like integers or categories, are a form of variable that can only take specified, distinct values. For instance, a discrete variable is the number of siblings a person has because it can only be 0, 1, 2, 3, etc.Discrete variables are a subset of variables that have a limited range of values. A continuous variable, on the other hand, can accept any value within a range.Whole numbers like 0, 1, 2, 3, and so forth are frequently used as discrete variables. The number of kids in a household, the number of products in a shopping cart, or the number of individuals in a room are all examples of discrete variables.
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what does (0 -1)(1 -3) equal in y=a(b)^x form
The exponential equation that coordinate points formed is y = -(3)^x
Determining exponential function from coordinate pointsGiven the coordinate points (0 -1) and (1 -3), we need to determine the equivalent in the form y=a(b)^x
The equivalent simultaneous equation is:
-1 = ab^0 .......... 1
-3 = ab^1 ............ 2
From equation 1;
-1 = a(1)
a = -1
Substitute a = -1 into equation 2
-3 = (-1)b
b = 3
The required exponential equation is y = -1(3)^x
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A candle maker is ordering wax. Each small candle uses 12 ounces of wax. Each large candle uses 18 ounces of wax. The candle maker wants to make 42 small candles and 38 large candles.
Which answer is the most reasonable estimate of the total amount of wax needed?
Answer:
1188
Step-by-step explanation:
12x42 + 18x38 = 1188
35:60 in its simple form
Answer:7/12
Step-by-step explanation:
Answer:
7/12
Step-by-step explanation:
how to convert torr to mmhg
Torr and mmHg are two units of pressure that are often used interchangeably. In fact, 1 mmHg is equal to 1 torr, which means that they are equivalent units of measurement.
To convert torr to mmHg, you can simply multiply the pressure value in torr by 1, since 1 torr is equivalent to 1 mmHg. For example, if you have a pressure of 760 torr, you can convert it to mmHg as follows:
760 torr x 1 mmHg/torr = 760 mmHg
Therefore, 760 torr is equivalent to 760 mmHg. Alternatively, you can also convert mmHg to torr by dividing the pressure value in mmHg by 1. For example, if you have a pressure of 760 mmHg, you can convert it to torr as follows:
760 mmHg ÷ 1 mmHg/torr = 760 torr
Therefore, 760 mmHg is equivalent to 760 torr.
Torr and mmHg are two units of pressure that are often used interchangeably. In fact, 1 mmHg is equal to 1 torr, which means that they are equivalent units of measurement.
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Can someone help me with this please
The sides of the rectangle are
1. (x - 1)2. (x + 6)3. (x - 5)4. (x + 1)the codes are CFID
How to find the unknow part of the rectangleThe unknown part of the rectangle is solved using division of polynomial and the check is completed by multiplication of the polynomial involved
checking for the correct answers
1. 2(x + 5)(x - 1) = (2x + 10)(x - 1)
2x² - 2x + 10x - 10
2x² + 8x - 10
2. 3(x - 1)(x + 6) = (3x - 3)(x + 6)
3x² + 18x - 3x - 18
3x² + 15x - 18
3. 2(x + 1)(x - 5) = (2x + 2)(x -5)
2x² - 10x + 2x - 10
2x² - 8x - 10
4. 5(x - 1)(x + 1) = (5x -5)(x + 1)
5x² + 5x - 5x - 5
5x² - 5
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Mr. Yu applies 12 ounce of fertilizer to every 58 square meter of his lawn.
How many ounces of fertilizer does Mr. Yu use per square meter for his lawn?
Enter your answer in the box as a fraction in simplest form.
ounces per square meter
Answer: 0.20689655
Step-by-step explanation: because you take 12 divided by 58
Ernest has 16 math problems to do for homework. He has already finished p of them. Write an expression that shows how many math problems Ernest has left.
The mathematical expression that shows the number of math problem left for Ernest is 16-p
What is linear expressions?Linear expressions are expression that it's highest power in of it's variable is 1. Linear expression can have more than one variables.
Some of the examples of linear equations are 2x – 3 = 0, 2y = 8, m + 1 = 0, x/2 = 3, x + y = 2, 3x – y + z = 3.
Ernest has 16 math problem , he has solved p out of it.
To actually know the remaining math problem left, we subtract the number he has done from the number of original problem
This means the number r of problem left = 16-p
therefore the expression is 16-p
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How do you find the horizontal and vertical asymptote of a curve?
Answer: search it up
Step-by-step explanation:
Does someone mind helping me with this problem? Thank you!
Answer:3y +=7
=>3y-7-x
=>y=(7-x)/3 Step-by-step explanation:Solve for 'y' means, solve the equation to get the value of y and in terms of ,x means value of y not necessarily in pure constant form,but in the form of x.
The table shows the total amount of fuel used based
on the number miles flown by a plane.
Find the amount of used fuel per mile (m) and the Initial amount of fuel used (b).
The amount of fuel used per mile (m) = unit rate = 5.2 gallons per mile.
Initial amount (b) = 0 gallon.
How to Find the Unit Rate and Initial Amount of a Proportional Relationship?A proportional relationship can be represented as an equation of the form y = mx, where x and y are variables and m is the constant of proportionality, also known as the unit rate
Unit rate (m) = amount of fuel used per mile = 156/30 or 312/60 = 5.2 gallons per mile.
Initial amount (b) = starting value or y-intercept = 0 gallon.
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Directions: Using the withholding tax tables for federal and state taxes on Figure 2.2, Figure 2.3, and Figure 2.4 of your textbook, complete the following phrases.
For a single person, 0 allowances, who made $295 last week
State withholding tax: $
Federal withholding tax: $
The amount of State withholding tax is, $20.65 and the amount of Federal withholding tax is, $17.7.
What is the percentage?A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.
Assuming the State withholding tax to be 7% and the Federal withholding tax to be 6%.
Given, A person made $295 last week.
Therefore, The amount of Federal withholding tax is,
= $(6/100)×295.
= $17.7.
And, The amount of State withholding tax is,
= (7/100)×295.
= $20.65
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What are the measures of the angles? Please help 55 points.
Answer: 5
Step-by-step explanation:
Opposite angles of parallelograms are always equal, thus resulting in the equation, 20 + 2x = 6x simplified to 20 = 4x, so x is equal to 5. Hope this helps!
Answer:
The answer is a) 5
Step-by-step explanation:
Linda bought 6 pounds of rice for 4$ How many dollars did she pay per pound of rice
Answer: 24
Step-by-step explanation: 6*4=24
4+4+4+4+4+4=24
Answer:
she paid $1.50 / 1lb
Step-by-step explanation:
6lbs divided by $4 = 1.50 or $1.50 / 1lb
Find the solution of the system of equations
3x+7y=-17
-3x+9y=-15
Answer: The solution of the system of equations is (x, y) = (-1, -2).
Step-by-step explanation:
We can solve this system of equations by using either elimination or substitution method. Here, we'll use elimination:
Adding the two equations, we get:
(3x + 7y) + (-3x + 9y) = -17 - 15
Simplifying the left side and right side:
16y = -32
Dividing both sides by 16:
y = -2
Now we can substitute y = -2 into either of the original equations and solve for x. Let's use the first equation:
3x + 7(-2) = -17
Simplifying:
3x - 14 = -17
Adding 14 to both sides:
3x = -3
Dividing both sides by 3:
x = -1
I don’t understand the questions
The solutions to the expressions using laws of exponents are;
17) y^(19/28)
18) 1/a^(5/9)
How to use Laws of Exponents?The product rule of exponents states that "To multiply two expressions with the same base, add the exponents while keeping the base the same". Thus;
y² × y³ = y²⁺³
= y⁵
17) y^(3/7) × y^(1/4)
Applying product rule of exponents gives;
y^(³/₇ + ¹/₄)
= y^(19/28)
18) The negative exponent rule states that: To convert any negative exponent into positive exponent, the reciprocal should be taken." Thus;
x⁻³ = 1/x³
Thus;
a^(-5/9) = 1/a^(5/9)
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I need some help thank you :)
Write an algebraic expression to represent the following situation: "Greg has nickels and pennies in his pocket. The number of pennies is 7 less than twice the number of nickels. Let N represent the number the nickels. Write an expression for the number of pennies."
An expression that is used to represent the number of pennies is; 2n - 7
How to solve Algebra word problems?Algebraic word problems are defined as questions that require translating sentences to equations, then solving those equations. The equations we need to write will only involve basic arithmetic operations.
Now, we are told that;
Number of pennies is 7 less than twice the number of nickels.
Thus. if n represents the number of nickels, then we can say that;
Number of Pennies = 2n - 7
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9,372,282 rounded to 1,000
Answer: You would round down so 9,372,000
Step-by-step explanation: Since you are rounding to the nearest 1,000 it would be Answer: 9,372,000
Please give me branliest
Inga divided two identical rectangles into equal parts. She colored one part of each rectangles
Divisions of the rectangle will be equal apart from the color Inga assign.
What is a rectangle?A rectangle is a two-dimensional shape that has four sides and four right angles. The opposite sides are parallel and equal in length. The area of a rectangle can be calculated by multiplying the length of the rectangle by its width.
Here,
Since the rectangles are identical, they would have the same area and thus, the same divided parts. Therefore, the areas of the colored parts would also be equal.
Thus, divisions of the rectangle will be equal apart from the color Inga assign.
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How many quart in a cubic feet ?
The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot.
So the volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.
The quantity of cubic feet can be multiplied by 29.9220779 to get the conversion to quarts. For instance, if you have a container with a 2 cubic foot volume, the quantity of quarts in that container would be:2 cubic feet multiplied by the US liquid quart density of 29.9220779 gives 59.8441558 US quarts. The volume of a cubic foot is equal to 29.9220779 US liquid quarts. This conversion factor is based on the definitions of the cubic foot as a unit of volume equal to a cube with sides that are one foot in length and the quart as a unit of volume in the US customary system.
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Which graph has a slope of 4/5?
Answer:
B
Step-by-step explanation:
Rise over run should be 4 rise and 5 to the side run
Answer:
Step-by-step explanation:
The last one (placed below)
Just take two random points (x1,y1) and (x2,y2) from the graph and calculate the slope according to the expression:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
The graph placed below, passes through the points (5,4) and (0,0). So if we replace these coordinates within the formula:
[tex]m=\frac{5-0}{4-0}=\frac{5}{4}[/tex]