Algebra was made to solve mathematical problems that involve unknown quantities.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Algebra was developed to solve mathematical problems that involve unknown quantities.
It provides a way to represent and manipulate mathematical equations using symbols and rules, making it easier to solve complex problems and answer questions about relationships between variables.
The earliest known algebraic text is the "Al-jabr wa'l muqabalah" by the Persian mathematician Al-Khwarizmi, which was written in the 9th century.
Hence, Algebra was made to solve mathematical problems that involve unknown quantities.
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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.
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35:60 in its simple form
Answer:7/12
Step-by-step explanation:
Answer:
7/12
Step-by-step explanation:
what is function transformation rules?
Function transformation rules are a set of rules that can be applied to a basic function in order to transform or modify its graph. These rules include:
1. Vertical translation: adding or subtracting a constant to the function. This shifts the graph up or down without changing its shape.
2. Horizontal translation: replacing x with x + c. This shifts the graph left or right without changing its shape.
3. Vertical scaling: multiplying the function by a constant. This stretches or compresses the graph vertically.
4. Horizontal scaling: replacing x with kx. This stretches or compresses the graph horizontally.
5. Reflection: reflecting the graph across the x-axis or y-axis. This changes the orientation of the graph.
6. Composition: combining two or more functions to create a new function.
These rules allow mathematicians to manipulate and analyze functions in order to better understand their properties and behavior. By applying these rules to a basic function, mathematicians can create a variety of related functions with different features and behaviors.
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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]
PLEASE HELP 20 POINTS 1. Jack, Art, Fran, and Megan work as volunteers at the local kennel. Jack gives the dogs baths every 4 days; Art cleans out cages every 6 days; Fran feeds the animals in Section Bevery 2 days; and Megan helps the receptionist every 3 days. How many times in 12 weeks will all 4 helpers be at the clinic on the same day? Show all work and explain how you got your power Due date
All 4 helpers will be at the clinic on the same day 7 times in 12 weeks.
What is Prime Factorization?
"Prime Factorization" is the process of determining which prime numbers multiply together to get the original number.
To find the number of times in 12 weeks that all 4 helpers will be at the clinic on the same day, we need to find the least common multiple (LCM) of the numbers 4, 6, 2, and 3.
First, we can find the prime factorization of each number:
4 = 2 x 2
6 = 2 x 3
2 = 2
3 = 3
Next, we can find the LCM by taking the highest power of each prime factor that appears in the factorizations:
LCM = 2 x 2 x 3 = 12
Therefore, all 4 helpers will be at the clinic on the same day every 12 days. Since 12 weeks is equivalent to 84 days, we can divide 84 by 12 to get the number of times:
84 ÷ 12 = 7
So, all 4 helpers will be at the clinic on the same day 7 times in 12 weeks.
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Given: (x+y)^2 evaluate the expression if x=6 and if y=9
Answer:
225
Step-by-step explanation:
(x+y)^2, if x=6 and y=9
Put 6 in place of x and 9 in place of y.
(6+9)^2 According to order of operations, add the 6+9 first.
(6+9)^2
= 15^2
= 225
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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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
You randomly choose one marble from the jar. What is the theoretical probability of choosing a green marble.
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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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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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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What is Simpson's 1 3rd rule?
Simpson's 1/3rd rule is a method of numerical integration that is used to approximate the value of a definite integral.
It is based on the idea of approximating the area under a curve by dividing it into a series of trapezoids and calculating the area of each trapezoid. The formula for Simpson's 1/3rd rule is:
∫abf(x)dx ≈ (b-a)/6 [f(a) + 4f((a+b)/2) + f(b)]
In this formula, a and b are the limits of integration, and f(x) is the function being integrated. The rule is called the "1/3rd rule" because the coefficient of the middle term is 4/3, which is equal to 1/3 when multiplied by the 3 in the denominator.
To use Simpson's 1/3rd rule, you first need to divide the interval [a,b] into an even number of subintervals. Then, you can apply the formula to each subinterval to get an approximation of the integral over that subinterval. Finally, you can add up the approximations for each subinterval to get an approximation of the integral over the entire interval.
Simpson's 1/3rd rule is a more accurate method of numerical integration than the trapezoidal rule, but it is still an approximation. The accuracy of the approximation depends on the number of subintervals used and the smoothness of the function being integrated.
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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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Solve the first word problem .Will mark brainliest.
Answer: Area of path = 1492 m^2 Area of "no path" = 123508 m^2
Step-by-step explanation:
Probably wrong
Which equation does the graph below represent? (5 points)
O
A
-5-4-3 -2 -10 1 2 3 4 5
Ob
Oc
Od
20
16
12
22
280
4
ܬܬ ܣ ܘ ܗ 8
-8
-12
-20
1
y-¼+x
y= +X
1
y = 4x
y=4+x
y = 4x
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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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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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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How do you find the horizontal and vertical asymptote of a curve?
Answer: search it up
Step-by-step explanation:
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 ASAP‼️‼️ I’ve been wasting my points and I don’t know the answer
The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
In given two triangles,
RST and NLM
In the triangle RST ,
The sum of angles is 180
so,
44 + 15 + S = 180
S = 180 - 59
S = 121
And similarly in the triangle NLM,
N + 121 + 44 = 180
N = 180 - 165
N = 15
Therefore, The values of given angles S and N are 121 , 15 respectively
SR / ML = 3.61 / 5.415 = 0.667
ST / MN = 9.71 / 14.565 = 0.667
Hence, The ratio of SR and ML and ratio of ST , MN are equal ,so they are similar triangles .
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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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Question 5 of 10
The area of the triangle below is_____
Sq.units.
A. 34
B. 42
C. 21
D. 68
The area of the triangle below is 34 Square per units. The Option A is correct.
How do we find area of the triangle?The area of a triangle is total region that is enclosed by the three sides of any particular triangle. It is equal to half of the base multiplied by the height.
The area of a triangle is given as: Area of triangle= 1/2 * Base of triangle * Height of Triangle where the height is 4 and base is 17
The calculation of our area:
= 1/2 * 17 * 4.
= 34²
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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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Adam and Shane are competing to see who can save the most money
in one month. Which statement gives a correct comparison of their
rate of savings?
The slope in both equations shows the rate of their savings per week, is Adma saves 3$ per week while Shane saves $4 per week.
What is the slope of the line?The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees. And also it is defined as the rate of change of a function.
Here,
Adam and Shane are competing to see who can save the most money in one month. From the graph, Adam's linear function of saving is given as by slope-intercept form of equation as,
y = 3x + 3
While the linear function for Shane is not given, so we assume the function as y = 4x.
The slope in both equations shows the rate of their savings per week, is Adma saves 3$ per week while Shane saves $4 per week.
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Jim rented a truck for one day. There was a base fee of 15.99 and there was an additional charge of 86 cents for each mile driven. Jim had to pay 206.91 when he returned the truck. For how many miles did he drive the truck?
The required, Jim can drive the truck for approximately 221.51 miles.
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.
We can use algebra to solve this problem. Let x be the number of miles Jim drove the truck. Then the total cost can be represented as:
15.99 + 0.86x = 206.91
To find the number of miles driven, we can subtract the base fee from both sides of the equation:
15.99 + 0.86x - 15.99 = 206.91 - 15.99
0.86x = 190.92
Finally, we can divide both sides of the equation by 0.86 to find x:
x = 221.51 miles
So, Jim drove the truck for approximately 221.51 miles.
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Solve the equation AB=BC for A, assuming that A,B and C are square matrices and B is invertible.
The solution of AB = BC for A, assuming that A,B and C are square matrices and B is invertible is [tex]A = BCB^{-1}[/tex]
We have to solve the equation
AB = BC , given that these all are square matrices and B is invertible.
Write the required Equation:
AB = BC
Multiply both sides by inverse of B
The multiplicative inverse of a matrix is the matrix that gives you the identity matrix when multiplied by the original matrix.
Matrix multiplied by an identity matrix, the result is always the same original non-identity (non-unit) matrix, and thus, as explained before, the identity matrix gets the nickname of "unit matrix"
[tex]ABB^{-1} = BCB^{-1}\\AI = BCB^{-1}\\A = BCB^{-1}[/tex]
so the solution of AB = BC is [tex]A = BCB^{-1}[/tex]
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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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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