Bring the variable to the left side and bring all the remaining values to the right side.
Now, According to the question:
Let's know:
What is an algebraic value?
An algebraic number is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio, , is an algebraic number, because it is a root of the polynomial x2 − x − 1.
An algebraic formula is an equation or a rule written using mathematical and algebraic symbols and terms. It is an equation that involves algebraic expressions on both sides. The algebraic formula is a short quick formula to solve complex algebraic calculations.
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given that n is an integer greater than 1, explain why the largest prime factor of 2(7^n) - 2(7^(n-1)) + 7^(n+1) is 61.
When we put the value of 1 in place of n in the equation, the value obtained will be equal to the largest prime factor that is 61.
What is a Prime number?A prime number is any whole number that is greater than 1 and cannot be created by combining other whole numbers. Consequently, a prime number's only factors are 1 and the actual number.
As per the given expression in the question,
2(7ⁿ) - 2(7ⁿ⁻¹) + 7ⁿ⁺¹
Use exponent rule:
[tex]a^b.a^c=a^b^+^c[/tex]
Put the values accordingly,
2(7ⁿ) - 2(7ⁿ⁻¹) + 7ⁿ . 7¹
So,
[tex]\frac{a^b}{a^c}= a^b^-^c[/tex]
⇒ 2(7ⁿ) - 2(7ⁿ/7¹) + 7ⁿ . 7¹
Simplify the above equation,
2(7ⁿ) - 2/7(7ⁿ) + (7)7ⁿ
Take out 7ⁿ as common,
(2 - 2/7 + 7)7ⁿ
Therefore,
61/7(7ⁿ)
Put n = 1 to check for the largest prime number,
61/7(7¹)
= 61
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What is the nature of roots of the quadratic equation x2 2 √ 3x 3 0?
The roots of the quadratic equation x² + 2√3 x + 3 = 0 have only one root and it is -√3
What is Quadratic Equation?
A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.
The roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
where ( b² - 4ac ) is the discriminant
when ( b² - 4ac ) is positive, we get two real solutions
when discriminant is zero we get just one real solution (both answers are the same)
when discriminant is negative we get a pair of complex solutions
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
x² + 2√3 x + 3 = 0 be equation (1)
On factorizing the equation , we get
The roots of the quadratic equations are calculated by
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
Substituting the values in the equation , we get
x = [ -2√3 ± √ ( ( 2√3 )² - 4 ( 3 ) ) ] / 2
On simplifying the equation , we get
x = [ -2√3 ± √ ( 12 - 12 ) ] / 2
The discriminant is zero we get just one real solution
So ,
x = [ -2√3 ± √0 ] / 2
x = ( -2√3 ) / 2
x = -√3
Therefore , the value of x is -√3
Hence , the root of the quadratic equation is -√3
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two parallel lines are crossed by a transversal. What is the value of m? m=68 m=78 m=102 m=112 .
Answer:
m=102
Step-by-step explanation:
You forgot to attach an image of the lines, but I have it here, so no worries
We know that two parallel lines are crossed by a transversal. m are consecutive interior angles. We know that they add up to 180 degrees.
So, our equation is
78 + m = 180
m = 102
Jim invests $5,000 in an account that pays 2.5% annual interest, compounded semi-annually. What is his balance, to the nearest cent, at the end of 5 years?
The balance after 5 years would be near around 5661 dollars.
What is compound interest?
Compound interest is the addition of interest to the principal sum of a loan or deposit, or in other words, interest on principal plus interest.
According to the given question:
First, convert R as a percent to r as a decimal
r = R/100
r = 2.5/100
r = 0.025 rate per year,
Then solve the equation for A
A = P(1 + r/n)ⁿˣ
A = 5000(1 + 0.025/2)²ˣ⁵
A = 5661.35
Hence the balance after 5 years would be near around 5661 dollars.
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A toilet paper roll is 16cm tall with a radius of 6cm. The inside cylinder is a hole. It has a diameter of 3cm. What is the surface area of the toilet paper roll?
The total surface area of the cylinder is 10635 cm-square
Given, the length of the toilet paper roll = 16 cm
The radius of the toilet paper roll = 6cm
The diameter of the inside roll = 3cm
So, the radius of inside cylinder = diameter/2 = 3/2 = 1.5 cm
We know that the formula for :
The total surface area of a cylinder = 2πrh (h+r)
Here, h = 16 cm
r1 = 6cm and r2 = 1.5 cm
Since there are two cylinders one cylinder inside another so here total surface area will be equal to :
2πr1h (h+r1) - 2πr2h (h+r2)
On calculating, Total surface area = 10635 cm-square
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What is the coefficient of x³y² in the expansion of (2x+y)5?
O A 2
OB. 5
OC. 40
OD. 80
OE. It does not exist.
SUBMI
The coefficient of x³y² in the expansion of (2x+y)5 is 80.
What is the coefficient in expansion?A material's rate of expansion as a function of temperature is known as its coefficient of thermal expansion (CTE). More specifically, this coefficient is calculated under constant pressure and without a change in the material's phase, i.e., it is anticipated that the substance will continue be in either its solid or liquid state.Rather of comparing several units, it is employed to ascertain the range of values inside a single data set. The co-efficient of variation is employed when we wish to compare two or more data sets. The CV is calculated as the standard deviation to mean ratio.(x+y)n = xn + nxn-1y + n(n1)2 is the formula for the binomial expansion!Given data :
The coefficients of terms of (p+q)^n can be found by the Pascal's triangle for small values of n. Pascal's triangle will start with (1,1) = coefficients of (p,q)^n =1. For n=2, we add successive terms of the previous value of n. Thus for n-2, we have (, 1+1,11=(1,2,1), for n=3, we have (1,3,3,1), giving the following pattern:
(1,1)
(1,2,1)
(1,3,3,1)
(1,4,6,4,1)
(1,5,10,10,5,1)
meaning for n=5, the binomial expansion for (P+Q)^5 is
P^5+5P^4Q+10P^3Q^2+10P^2Q^3+5PQ^4+Q^5
Setting P=2x, Q=y in the term 10P^3Q^2, we get a term
10(2x)^3(y)^2
=10(8x^3)(y^2)
=80x^3y^2
So the required coefficient is K=80.
We can also find the coefficient 10 by binomial expansion of
n=5, x=3 in
C(n,x) = n! / (x! (n-x)!) = 5! / (2!3!) = 5*4*3/(1*2*3) = 10
Then again substituting 10(2x)^3(y)^2 = 80x^3y^2
to get the coefficient K=80.
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What does 4 more than a number mean?
'4 more than a number' implies that there exists a number which is 4 units greater than the original number, using the concept of addition.
Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication and division.The addition of two whole numbers results in the total amount or sum of those values combined. The example in the adjacent image shows a combination of three apples and two apples, making a total of five apples. This observation is equivalent to the mathematical expression "3 + 2 = 5" (that is, "3 plus 2 is equal to 5").
Besides counting items, addition can also be defined and executed without referring to concrete objects, using abstractions called numbers instead, such as integers, real numbers and complex numbers. Addition belongs to arithmetic, a branch of mathematics. In algebra, another area of mathematics, addition can also be performed on abstract objects such as vectors, matrices, subspaces and subgroups.
Now, let us understand the meaning.
Let the original number be x.
'4 more than a number' implies x + 4.
This means that the new number, x + 4, is greater than the original number, x, by 4 units. We also have to keep in mind, [tex]x + 4 > x[/tex].
Hence, the final meaning is 4 units greater than the original number.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided. What is the equation of y = 2° with the given transformations? vertical compression by a factor of 1 7, horizontal shift 8 units to the left, reflection across the x-axis
The transformation of the function is y = -1/7(2ˣ ⁺ ⁸)
How to determine the transformation of the function?From the question, we have the following parameters that can be used in our computation:
y = 2°
Rewrite properly
So, we have
y = 2ˣ
The given transformations are
vertical compression by a factor of 1/7Horizontal shift 8 units to the leftReflection across the x-axisThe riles of these transformations are
vertical compression by a factor of 1/7: 1/7f(x)Horizontal shift 8 units to the left: (x + 8, y)Reflection across the x-axis: (x, -y)When they applied, we have
y = 1/7(2ˣ)
Then, we have
y = 1/7(2ˣ ⁺ ⁸)
Lastly, we have
y = -1/7(2ˣ ⁺ ⁸)
Hence, the transformed equation is y = -1/7(2ˣ ⁺ ⁸)
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Determine the domain of the following graph:
How can I solve from problems A-F
Answer:
B. 1 & 1
C. 5 & 3
D. 2 & 2
E. 4 & 0
Something interesting about these was me having to just use simple and smaller numbers to complete the equations.
Answer:
answers is in attached picture.
Step-by-step explanation:
heart and star pls <3 brainliest will be appreciated <3(っ◔◡◔)っ -{ elyna s }-What is the equation of the line through the points (3, 2), (8, 5), (13, 8) and (18, 11)?.
Answer:
[tex]y=\frac{3}{5}x+\frac{1}{5}[/tex]
Step-by-step explanation:
Using the points [tex](3,2)[/tex] and [tex](8,5)[/tex],
[tex]m=\frac{5-2}{8-3}=\frac{3}{5} \\ \\ y-2=\frac{3}{5}(x-3) \\ \\ y-2=\frac{3}{5}x-\frac{9}{5} \\ \\ y=\frac{3}{5}x+\frac{1}{5}[/tex]
How do you find the inverse of a 3x3 matrix?
The inverse of a 3x3 matrix is found by creating an Adjugate Matrix.
How do you find the inverse of a 3x3 matrix?Step 1 : For any matrix M find the adjoint matrix.
Finding the transpose of the cofactor matrix of a matrix M yields the adjoint of that matrix. Any 3x3 matrix element's cofactor is the determinant of the 2x2 matrix that results from deleting the element's row and column. While determining the cofactors, alternate + and - signs are also written.For example :[tex]\text{Let a matrix }M= \left[\begin{array}{ccc}1&2&3\\0&1&4\\5&6&0\end{array}\right][/tex]
[tex]M^{T}= \left[\begin{array}{ccc}1&0&5\\2&1&6\\3&4&0\end{array}\right][/tex]
Adj M = [tex]\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right][/tex]
Step 2 :Find Determinant of a 3x3 Matrix
Find the sum of the product of the components of any row/column and their respective cofactors to determine the determinant of a 3x3 matrix.For example:[tex]M= \left[\begin{array}{ccc}1&2&3\\0&1&4\\5&6&0\end{array}\right][/tex]
det (M)= 1 (0- 24 ) - 2 (0 - 20 )+3 (0- 5 )
= - 24 + 40 -15
= 40 - 39
= 1
Step 3 : Find inverse matrix [tex]M^{-1}[/tex]
M determinant can be calculated in the first step to check that the inverse was possible. Now multiply each term in the matrix by that number. In each computation, replace the original term with the results. The outcome is the opposite of the initial matrix.[tex]M^{-1 } = \frac{1}{det (M)} (Adj M)[/tex]
For example :[tex]M^{-1 } = \frac{1}{det (M)} (Adj M)\\\\M^{-1 } = \frac{1}{1}\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right]\\\\M^{-1 }=\left[\begin{array}{ccc}-24&18&5\\20&-15&-4\\-5&4&1\end{array}\right][/tex]
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Answer: bro this ez 1.5 for the first one second should be 22 correct me if im wrong.
Step-by-step explanation:
the equation for line w is y=3x-4.line d contains the point (2,-1) and is parallel to line with.write an equation that describes line d?
Please answer asap.thank you
Considering the definition of parallel line, the equation of the line d is y= 3x -7.
Linear equationA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Parallel lineParallel lines are two lines that prolonged towards infinity never touch.
Two lines are parallel if they have the same slope and different y-intercepts.
Equation of parallel line in this caseIn this case, the line is y=3x-4
where:
The slope m is 3.The y-intercept is -4.Since two lines are parallel if they have the same slope, the parallel line has a slope of 3.
The line passes through the point (2, -1). Replacing in the expression for a line:
-1= 3× 2 + b
-1= 6 + b
-1 -6= b
- 7= b
Finally, the equation of parallel line is y= 3x -7.
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The procedure and the answer, Pleaseeeee
Answer:
looooookkkkkk at the picture
what is the slope of the line that passes through (4,7) and has a y-intercept of 1?
Answer:
[tex]m=\frac{3}{2}[/tex]
Step-by-step explanation:
The x value of the y-intercept must be 0, so let
[tex](x_1,y_1)=(0,1)[/tex]
and
[tex](x_2,y_2)=(4,7)[/tex]
The slope of a line can be found with the following:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
So,
[tex]m=\frac{(7)-(1)}{(4)-(0)}\\m=\frac{6}{4}\\m=\frac{3}{2}[/tex]
what is the answer of this?
Answer:
x = 43.25
Step-by-step explanation:
(x + 2 )+ (x + 2) + (2x + 3) = 180(total angles in a triangle)
x + 2 + x + 2 + 2x + 3 = 180
x + x + 2x + 2 + 2 + 3 = 180
4x + 7= 180
4x = 180 – 7
4x = 173
divide both sides by (4)
[tex] \frac{4x}{4} = \frac{173}{4} [/tex]
x = 43.25
i hope this helps
How do you find the mean of 4 numbers?
How do you find the mean of 4 numbers?
Finding the mean, refers to finding the average. To do this, add the four numbers together and then divide that number by 4.
How do I add a number to an existing cell in Excel?
On the Formula tab, click AutoSum > Sum. Excel will automatically sense the range to be summed.
Now, According to the question:
How do I add value to an existing cell in Excel?
One quick and easy way to add values in Excel is to use AutoSum. Just select an empty cell directly below a column of data. Then on the Formula tab, click AutoSum > Sum. Excel will automatically sense the range to be summed.
How do I add a digit to an existing number in Excel?
Say you have 50 in the cell in question, and want to add 30 to it. Then the clever part: Right-click on the cell with 50 in it, and select Paste Special. In the box that comes up, select 'Add'.
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Answer each of the following questions and show your reasoning. How many cubes with an edge length of 1 3 3 1 inch are needed to build a cube with an edge length of 1 inch? What is the volume, in cubic inches, of one cube with an edge length of 1 3 3 1 inch?
The number of cubes of edge length 1/3 is 27 and the volume of the cube is 1 cubic inches
How to determine the number of cubesFrom the question, we have the following parameters that can be used in our computation:
Edge length of cube 1 = 1/3 inchEdge length of cube 2 = 1 inchThe volume of a cube is the cube of its edge length
This means that the volumes are
Volume = Edge length³
So, we have
Volume of cube 1 = (1/3 inch)³ = 1/27 cubic inches
Volume of cube 2 = (1 inch)³ = 1 cubic inch
The number of cubes is then calculated as
Number of cubes = Volume of cube 2/Volume of cube 1
This gives
Number of cubes = 1/(1/27)
Number of cubes = 27
The volume of the cubesHere, we have
Edge length of cube = 1 inch
The volume of a cube is the cube of its edge length
This means that the volumes are
Volume = Edge length³
So, we have
Volume of cube = (1 inch)³ = 1 cubic inch
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What transformation can verify congruence?
It isometric to rotate, reflect, and translate. This indicates that the character size is unaffected by these modifications. If a form's size and shape have not altered, it is congruent.
What is congruence?
A "matching" figure is one that can be placed perfectly on another. The bread has the same size and form when it is stacked. Match refers to objects that are precisely the same size and form. If one of two geometric figures can be consistently overlaid on the other, they are said to be congruent or to be in a congruent relationship.
If 3 sides are equal
then By SSS, its congruent
AB = DE = 12
BC = EF = 11
AC= DF = 10
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Estimate
32.3 divided
5.6
32.3 divided 5.6 is 0.173
What is an estimation number?
Estimation of numbers is the process of estimating/approximating or rounding off the numbers in which the value is used for some other purpose in order to avoid complicated calculations.
Change the divisor 32.3 to a whole number by moving the decimal point 1 places to the right.
Then move the decimal point in the dividend the same, 1 places to the right.
Now we have the equations:
56 ÷ 323 = 0.173
and therefore:
5.6 ÷ 32.3 = 0.173
Both calculated to 3 decimal places.
32.3 divided 5.6 is 0.173
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72 minutes for 27 songs = 8 minutes for how many songs
Answer:
8 minutes = 3 songs
Step-by-step explanation:
Time taken for 1 song is,
→ 72/27
→ 2.6667
→ ≈ 2.7 minutes
Then songs played in 8 minutes,
→ Total time ÷ Time for 1 song
→ 8 ÷ 2.7
→ 2.96296
→ ≈ 3 songs
Hence, the answer is 3 songs.
HELP I NEED HELP. ASAP. PLEASE!!!!!!!!!
In the last three years, Frederico's basketball team won 50 more games than they lost. If they won 130 games, what was the ratio of wins to losses? Write the ratio in all three forms.
Please! :(
The ratios of win to lose are 13 : 8, 13/8 and 1.625%
How to determine the ratio of win to lose?From the question, we have the following parameters that can be used in our computation:
Win = 50 more than lose
Win = 130
This means that
Win = 50 + Lose
So, we have
50 + Lose = 130
Evaluate
Lose = 80
The ratio is then represented as
Ratio = win to lose
This gives
Ratio = 130 : 80
So, we have
Ratio = 13 : 8
Express as fraction
Ratio = 13/8
Lastly, we have
Ratio = 1.625%
Hence, the ratio is 1.625%
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What is the arithmetic mean of the data set 4 5 10 8 and 3?
Arithmetic mean of the data set 4,5,0,10,8and 3 is '5'
What Is the Arithmetic Mean?
The easiest and most popular way to calculate a mean or average is with simple mathematics. It simply entails adding up a collection of numbers, dividing that total by the number of numbers in the series, and adding the result together.
given data set is -
4 , 5 , 0 , 10 , 8 and 3
number of observations in given data set are '6'
arithmetic mean ( AM ) formula is
AM = (sum of all observations in given data set) / (total number of observations)
sum of all observations in given data set = 4 + 5 + 0 + 10 + 8 + 3
= 30
AM = 30 / 6 = 5
arithmetic mean of the data set 4,5,0,10,8and 3 is '5'
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[tex] \sqrt{484} [/tex]
some one tell me answer with method.
Answer:
22
Step-by-step explanation:
I factor out the radicand and get 22
Let's test if my answer is correct!
22 times 22 = 484
So, my answer is correct!
What are the 5 types of line graphs?
There are 5 types of line graphs:
1) Simple line graph 2) Compound Line Graph
3) Multiple Line Graph 4)Vertical Line Graph
5) Horizontal Line Graph 6) Straight Line Graph
1) Simple Line Graph:
A simple line chart is the most basic type of line chart. Only one dependent variable is tracked in this chart, so there is only one line connecting all the data points on the chart. All points in the chart relate to the same element and the sole purpose of the chart is to track changes in these variables over time. Only variables are graphed, so this graph cannot be used to compare one variable to another.
2) Multiple Line Graph:
In a multiple line chart, multiple dependent variables are plotted on a chart and compared against a single independent variable (often time). Different dependent variables are often marked with different colored lines to distinguish each data set. Each row relates only to points in the specified dataset. Lines do not cross between dependent variables.
3) Compound Line Graph:
If information can be subdivided into two or more types of data. This type of line graph is called a compound line graph. Composite line charts, like multiline charts, use multiple variables. However, variables are often stacked on top of each other to show the sum of all variables. This informs the user not only of the relationship between each variable, but also of how the total is changing.
4) Vertical Line Graph:
A vertical line chart is a chart in which a vertical line extends from each data point to the horizontal axis. A vertical line chart is sometimes called a column chart. A line parallel to the y-axis is called a vertical line.
5) Horizontal Line Graph:
A horizontal line chart is a chart with a horizontal line running parallel to the globe at each data point. Horizontal line charts are sometimes called line charts.
6) Straight Line Graph:
A line parallel to the X axis is called a vertical line. Line charts are often used to solve conditions that change over specific time intervals. The general linear function has the form y = mx + c, where m and c are constants.
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if there is $0.85 for 8 oz, how much would 1 oz cost?
The cost of 1 oz is $0.10625
How to determine the cost of 1 oz?From the question, we have the following parameters that can be used in our computation:
If there is $0.85 for 8 oz
This means that
The cost of 8 oz = $0.85
Assume there exist a proportional relationship between the cost and the size i.e. oz
The cost of 1 oz can be calculated using the following equation
The cost of 1 oz = $0.85/8
Evaluate the quotient
The cost of 1 oz = $0.10625
Hence, the cost of 1 oz is $0.10625
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How do you solve x squared minus 16?
All the options that result in (x + 4 ) (x 4 ) = 0 being true are the ultimate answer and x = − 4 , 4.
What is algebra?The broad field of mathematics includes algebra. Algebra is the study of mathematical symbols and the rules for using them in formulas; it is a common thread that runs through practically all of mathematics.Since many applications of mathematics include the manipulation of variables, which are frequently represented by Roman letters, elementary algebra is a prerequisite. For the most part in education, the study of algebraic structures like groups, rings, and fields is referred to as abstract algebra (the term is no more in common use outside educational context). Modern presentations of geometry are done using linear algebra, which deals with linear equations and linear translations. It also has a lot of practical uses (in weather forecasting, for example).Here, x²-16=0
rewrite 16 as 4²
then, (x+4)(x-4)
Any factor on the left side of the equation that is equal to 0 will make the entire expression equal to 0.
x+4=0 and find x
Then x=-4
x-4=0 and find x
x=4.
Hence, All the options that result in (x + 4 ) (x 4 ) = 0 being true are the ultimate answer and x = − 4 , 4.
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What is y 3x 1 in standard form?
The standard form of the linear equation can be written as -3x + y = 1
What means standard form?Standard form defines the method of expressing any mathematical concept such as expression, terms, equation or numbers in a systematic form by following a certain rule.
What is standard form of an equation?The system of writing an equation that follows particular rules is termed as standard form of equation.
The standard form of a linear equation with two variables x and y can be written as Ax + By = C
where, A and B are coefficient of x and y respectively, C is the constant.
This form of equation is required to solve linear equation.
The above equation is written in the slope intercept form, and we get
By = -Ax+C
y = -A/Bx+C/B
where, -A/B is the slope of equation, C/B is the y intercept
Now we have a linear equation written in the slope intercept form
y-3x-1 = 0
y= 3x+1
3 is the slope, 1 is the y intercept
now, we can write it in a standard form and get,
-3x+y = 1
hence, standard form of equation is -3x + y = 1
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