The formula that represents the defined sequence is [tex]4 (-6)^{n-1}[/tex]
What is the formula for the sequence?The given recursive formula are:
[tex]a _{1} = 4[/tex]
[tex]a _{n} = -6 a _{n-1}[/tex]
Considering n = 2 ,
[tex]a _{2} = -6(a _{2-1})\\ a _{2} = -6(a _{1})\\a _{2} = 4(-6)[/tex]
Considering n = 3 ,
[tex]a _{3} = -6(a _{3-1})\\ a _{2} = -6(a _{2})\\a _{3} = -6 (4(-6))\\a _{3} = 4(-6)^2[/tex]
Considering n = 4 ,
[tex]a _{4} = -6(a _{4-1})\\ a_4}= -6(a _{3})\\a _{4} = -6 (4(-6)^{2} )\\a _{4} = 4(-6)^3[/tex]
So, the formula that represents the defined sequence is [tex]4 (-6)^{n-1}[/tex]
What is a sequence?A sequence is an ordered collection of enumerated objects in mathematics where repeats are permitted. It has members, just like a set which is also called elements, or terms. The length of the sequence refers to the total potentially unlimited number of entries. Contrary to a set, the same elements may appear more than once at various points in a sequence, and in contrast to a set, the order is important. The formal definition of a sequence is a function from natural numbers the positions of the sequence's elements to the elements at each place. A function from any index set is what is meant by an indexed family, which is a generalization of the idea of a sequence.To learn more about sequence, refer:
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What are the three identities?
Answer: (a+b)2 = a2 + b2 + 2ab., (a-b)2 = a2 + b2 – 2ab.,a2 – b2 = (a+b) (a-b)
Step-by-step explanation:
In the pair of linear equation a1x b1yc1=0 and a2xb2yc2=0,if a1/a2 i not equal to b1/b2 then the equation have no olution. (True or fale)
The statement is false. In the pair of linear equation, if a₁/a₂ ≠ b₁/b₂ then the equations have unique solution.
Given that,
The pair of linear equation
a₁x +b₁y +c₁=0 and
a₂x +b₂y +c₂=0
We have to prove if a₁/a₂ ≠ b₁/b₂ then the equations have no solution.
We know that,
In the pair of linear equation
a₁x +b₁y +c₁=0 and
a₂x +b₂y +c₂=0
If a₁/a₂ ≠ b₁/b₂ then System is called consistent and have a unique Solution
Lines intersect each other at unique point
a₁/a₂ = b₁/b₂ = c₁/c₂ then consistent (infinite solution) as both Equation represent same line
a₁/a₂ = b₁/b₂ ≠ c₁/c₂ then inconsistent (no Solution) as Lines are parallel and never intersect each other
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Is Circumcentre and centroid of a triangle same?
Answer:
no, they are different in their different ways
How do you simplify an equation?
Answer:
see explanation below
if you have any questions on equation you can send it to me
Step-by-step explanation:
We have various of ways in which we can simplify an equation
for example
simplify: 2x – 4 = 10
soln
2x – 4 = 10
since we are looking for x we need to collect like terms
2x = 10 + 4
2x = 14
Then we will divide both sides by 2 to get x
x = 14/2
x = 7
N.B:- after solving an equation if you want to check the answer just substitute for the value
2x – 4 = 10
2(7) – 4 = 10
14 – 4 = 10
10 = 10
LHS = RHS
pls rate as brainliest
4x + 6 = 2(3x - 7)
Solve
Answer:
x = 10
Step-by-step explanation:
Method 1: Algebraically
1. 4x+6 = 2(3x-7) - Multiply out the 2
2. 4x+6 = 6x-14 - make x the subject of the formula first by subtracting 4 from both sides
3. 6 = 2x-14 - add 14 to both sides
4. 20 = 2x - divide by 2 to solve for x
5. 10 = x - Answer
Method 2: Graphing
Use a graphing calculator to solve for the answer
1. set one side to y1 and the other to y2
2. set the correct window
3. press 2nd then trace
4. Select option 5 to find the intersection
A"B"C"D" is the image of ABCD after the composition of transformations
T(-2,0) R180° about the origin.
What is the sum of the x and y coordinates of D"
The sum of the x and y coordinates of D" is 6
How to determine the sum of the coordinatesFrom the question, we have the following parameters that can be used in our computation:
D = (-1, -3)
The transformation rule is given as
T(-2,0) R180° about the origin.
Mathematically, this can be represented as
(x, y) = (-x + 2, -y)
So, we have the following representation
D" = (1 + 2, 3)
Evaluate the like terms
D" = (3, 3)
When the coordinates are added, we have
Sum = 3 + 3
Evaluate
Sum = 6
Hence, the sum is 6
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Complete question
A"B"C"D" is the image of ABCD after the composition of transformations
T(-2,0) R180° about the origin.
What is the sum of the x and y coordinates of D" if the coordinate of point D is (-1, -3)?
Whats a mean example?
The mean of the given data set is 29.5.
The term "mean" refers to the arithmetic average of the data set and is derived by dividing the total number of data points in the data set by the total number of data points. It is a data point that represents the average of all the data points in the collection.
Example :
Find the mean of the following data set.
10, 20, 36, 12, 35, 40, 36, 30, 36, 40
Given,
xi = 10, 20, 36, 12, 35, 40, 36, 30, 36, 40
n = 10
Mean = ∑xi/n
= (10 + 20 + 36 + 12 + 35 + 40 + 36 + 30 + 36 + 40)/10
= 295/10
= 29.5
Therefore, the mean of the given data set is 29.5.
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Find the mean of the following data set.
10, 20, 36, 12, 35, 40, 36, 30, 36, 40
Given,
xi = 10, 20, 36, 12, 35, 40, 36, 30, 36, 40
n = 10
Mean = ∑xi/n
= (10 + 20 + 36 + 12 + 35 + 40 + 36 + 30 + 36 + 40)/10
= 295/10
= 29.5
Pleaseee help me out
If\(\triangle XYZ\sim\triangle EDFV), the measure of angle F is
Answer:
63 degrees
Step-by-step explanation:
similar triangles have the same angles.
XYZ is similar to EDF. Therefore the measure of angle Z is the same as angle F. The measure of angle Z is 63, so the measure of angle F is also 63.
How many months before you can loan at SSS?
Members who have made at least 36 months' worth of contributions overall and six months' worth within the previous 12 months are eligible to apply for a loan through SSS.
One month's worth of salary is equal to the amount of the salary loan. If you have at least 72 months of posted contributions and six months of contributions during the last 12 months, you may also be eligible to apply for a two-month wage loan.
If you have a job, your employer is responsible for keeping your loan payments and monthly contributions current. Additionally, you need to keep up with payments on all of your other loans.
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2y+(4+5y) please answer
Answer:
7y + 4
Step-by-step explanation:
2y+(4+5y)
2y + 4 + 5y
combine y terms:
7y + 4
11. Solve the Right Triangle.
The sides of the right triangle are as follows:
AC = 3.2 metres
AB = 12.4 metres
How to solve right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a right triangle is 180 degrees.
Therefore, the sides of a right triangle can be found using trigonometric ratios.
Hence, let's find AC
tan 15 = opposite / adjacent
tan 15 = AC / 12
cross multiply
AC = 12 tan 15
AC = 12 × 0.26794919243
AC = 3.21539030917
AC = 3.2 metres
Let's find AB
cos 15 = adjacent / hypotenuse
cos 15 = 12 / AB
AB = 12 / cos 15
AB = 12 / 0.96592582628
AB = 12.423314503
AB = 12.4 units
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Consider the enlargement of the rectangle. A small rectangle with length of 4 and width of 2. A larger rectangle with length of 12 and width of 6. Which proportional statements are true of the enlargement? check all that apply. Startfraction width original over length original endfraction = startfraction width enlargement over length enlargement endfraction startfraction length original over length enlargement endfraction = startfraction width original over width enlargement endfraction startfraction width original over length enlargement endfraction = startfraction length original over width enlargement endfraction startfraction width enlargement over length enlargement endfraction = startfraction width original over length original endfraction startfraction length original over width enlargement endfraction = startfraction length enlargement over width original endfraction.
The two given rectangles are proportional to each other since they have a width-to-length ratio of 2 and the area ratio between them is equal to 9.
Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:
r' = (l' · h')/(l · h) (1)
Where:
l' - Length of the enlarged rectangle.
l - Length of the original rectangle.
h' - Length of the enlarged rectangle.
h - Length of the original rectangle.
Now we determine the length-to-width ratio of each rectangle:
Original rectangle
s = 4/2
s = 2
Enlarge rectangle
s' = 12/6
s' = 2
The two rectangles have the same length-to-width ratio.
The area ratio is:
r' = (12 · 6)/(4 · 2)
r' = 72/8
r' = 9
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Two rectangles are proportional to each other when both have the same length-to-width ratio. The area ratio is defined by the following formula:
r' = (l' · h')/(l · h) (1)
Now we determine the length-to-width ratio of each rectangle:
Original rectangle
s = 4/2
s = 2
Enlarge rectangle
s' = 12/6
s' = 2
The two rectangles have the same length-to-width ratio.
The area ratio is:
r' = (12 · 6)/(4 · 2)
r' = 72/8
r' = 9
The diameter of a circle is 6 m. What is the area of the circle to the nearest square meter?
Answer:
To find the area of a circle, we can use the formula A = πr^2, where A is the area of the circle, π is a constant with a value of approximately 3.14, and r is the radius of the circle. To use this formula, we first need to find the radius of the circle. We can do this by dividing the diameter of the circle by 2:
r = Diameter / 2
r = 6 m / 2
r = 3 m
Substituting this value for r into the formula for the area of a circle, we get:
A = πr^2
A = 3.14 * 3^2
A = 3.14 * 9
A = 28.26
Therefore, the area of the circle is 28.26 square meters. Rounded to the nearest whole number, this is equal to 28 square meters.
What is the sum of 182330+23 ?
18 25/33
18 13/30
19 13/30
19 25/33
❗quick please❗
Answer:
19 and 13/30
Step-by-step explanation:
First make 2/3 have a common denominator with 23/30
You can do this by multiplying the numerator and denominator of 2/3 to get 20/30
Now add
20/30 + 23/30 = 43/ 30
Simplify this fraction
1 and 13/30
add this to 18
18 + 1 and 13/30 = 19 and 13/30
What additional information do you need to prove ∆ ABC ≅ ∆ def by the ASA postulate?
Answer:
⭐2 corresponding, congruent angles
⭐1 corresponding, congruent side length that is included between the 2 angles
Example (figures not drawn to scale);
Does the following equation has no real roots 3x² 4 √ 3x 4 0?
Yes, the equation has no real roots.
To solve this equation, we first move the constant terms to the right side and the terms with x to the left side.
3x² - 4√3x = -4
Next, we square both sides of the equation.
(3x² - 4√3x)² = (-4)²
9x⁴ - 24√3x² + 16x = 16
Next, we move the constant terms to the right side of the equation.
9x⁴ - 24√3x² = -16
Next, we factor the left side of the equation.
(3x² - 8√3)(3x² + 8√3) = 0
Finally, we set each factor equal to zero and solve for x.
3x² - 8√3 = 0
3x² + 8√3 = 0
However, these equations have no real solutions, so the original equation has no real roots.
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!Please Help.! I'm falling behind in the math and don't how to do this.
Answer:
m = 12
Step-by-step explanation:
The equation is y=mx +b
Where m is the slope
So, in this case slope is 12
12 is an integer, so my answer is correct!
Tori and Matias work as jewelers. Tori has an hourly wage of $24 and gets overtime for every hour she works over 40 hours. The overtime pay rate is 150% of the normal rate. Matias makes 5% commission on all jewelry he sells. Who earns more money in a week if Tori works 60 hours and Matias sells $21,000 worth of jewelry? Explain.
Tori earns more money.
How to find the commission rate?Add the sales income and the sales commission rate together to get the payable commission. A $10,000 product transaction would result in a $1,000 commission at a 10% commission rate.This is a pretty straightforward computation based on percentages. Simply take the selling price, multiply it by the commission rate, then divide the result by 100.Divide the base for that period by the appropriate commission rate to determine your commission for that period. For instance, if your commission rate is 5% and you generated $30,000 worth of sales between January 1 and January 15, you would multiply $30,000 by.05 to arrive at your $1,500 commission payout.Given data :
Tori : $24/h; 150% OT
Calculate Tori's overtime (OT) pay
Convert OT rate to decimals --> 150% = 1.
Tori's OT wage is 1.5*$24 = $36
Tori worked for 20h OT. (60h-40h = 20h)
(Regular pay X regular hours worked) + (OT wage X OT hours worked)
= ($24 X 40h) + ($36 X 20h)
= $1680
Matias : 5% commission
Convert 5% to decimals --> 0.05
(Jewelry sold) X (commission rate)
= $21000 X 0.05
= $1050
Since $1680 > $1080, Tori earns more.
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What is the probability distribution of getting a sum of 4?
Probability of getting the sum as 4 when a pair of dice is rolled is 1/12.
Define probability.A probability is a numerical representation of the likelihood or chance that a specific event will take place. Both proportions ranging from 0 to 1 and percentages ranging from 0% to 100% can be used to describe probabilities.
Value of probability can be greater than 1?No, probability is aways between 0 to 1.
Find total number of possible outcomes
Here it is given that a pair of dice is rolled
So the event points are
= { (1,1), (1,2), (1,3), (1,4),(1,5),(1,6),(2,1), (2,2), (2,3), (2,4),(2,5),(2,6),(3,1), (3,2), (3,3), (3,4),(3,5),(3,6),(4,1), (4,2), (4,3), (4,4),(4,5),(4,6),(5,1), (5,2), (5,3), (5,4),(5,5),(5,6),(6,1), (6,2), (6,3), (6,4),(6,5),(6,6)}
So the total number of possible outcomes = 36
Let A be the event that of getting a sum of 4
So the event points are (1,3) , (2,2) , (3,1)
So total number of possible outcomes for the event A is 3
Hence the required probability= P(A)= no. of favorable cases to event A/total no of outcomes
=3/36
=1/12
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Exponential functions have the form f(x)= b^x. What type of an exponential function would you have (increasing or decreasing) if the value of b is greater than one?.
An exponential function with a base greater than 1 will be increasing in nature.
This is because when the base of an exponential function is greater than 1, the exponent is raised to a power greater than 1, and the result will always be greater than the original number. This means that as the value of x increases, so too will the value of the function. To illustrate this, the formula for an exponential function with base b can be written as f(x) = b^x. As x increases, b^x will become larger and larger, resulting in a continually increasing function. For example, if b = 2, then f(x) = 2^x. As x increases, 2^x will increase exponentially, resulting in a function that is always increasing.
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Solve the equation. Show your work. Express your answer as both a simplified mixed number and as a decimal.
-2.25 + 0.4x = -2.8
The value of x in the equation -2.25 + 0.4x = -2.8 is -12.625
How to calculate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario. It is vital to note that an equation is a mathematical statement which is made up of two expressions that are connected by an equal sign.
The equation is given as:
-2.25 + 0.4x = -2.8
Collect like terms
0.4x = -2.8 + 2.25
0.4x = -5.05
Collect like terms
x = -5.05 / 0.4
x = -12.625
The value of x is -12.625.
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The solution to the given linear equation, -2.25 + 0.4x = -2.8, is x = -1.375 or x = -1 3/8
Solving Linear EquationsFrom the question, we are to solve the given equation
The given equation is
-2.25 + 0.4x = -2.8
To solve the equation, we will determine the value of the unknown variable.
In the given equation, the unknown variable is x
Solving for x
-2.25 + 0.4x = -2.8
Add 2.25 to both sides of the equation
-2.25 + 2.25 + 0.4x = -2.8 + 2.25
0.4x = -0.55
Divide both sides of the equation by 0.4
0.4x/0.4 = -0.55/0.4
x = -1.375
Convert to a mixed number
x = -1.375 = -1375/1000
x = -11/8
x = -1 3/8
Hence, the solution is -1.375 or -1 3/8
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What is the maximum or minimum value of the function y =- 2x 2 32x 12?
The maximum of the equation y = -2x² +32x -12 is 116 and the range of the function is y ≤ 116.
What are the Maxima and the minima of a function?The highest and smallest values of a function, respectively, can either be found inside a specific range or across the entire domain. They are sometimes referred to collectively as the function's extrema. The plural forms of a function's maximum and minimum are called maxima and minima, respectively.
Y= ax² + bx + c is the conventional form of this quadratic equation. The vertex of a quadratic function is its greatest value or smallest value. We locate the axis of symmetry to determine the x-coordinate of the vertex. This is determined by the equation x = -b/2a:
x = -32/2(-2) = -32/-4 = 8
To find the y-coordinate, plug this into the equation y = -2(8²)+32(8)-12
y=-2(64) + 256 - 12 = -128+256-12 = 128-12 = 116
The coordinates of the vertex are (8, 116).
Look at the value of a to see if this is maximum or minimal. It is -2. This indicates that the parabola widens downward and that the vertex is a maximum because it is negative.
Therefore this is a maximum at y=116, which means the range will be less than or equal to this value of 116.
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Why is i squared equal to 1?
The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.
Given that,
We have to find why i squared is equal to negative 1.
We know that,
The imaginary numbers are denoted as i.
We occasionally obtained negative integers in equations when using the radican (square root) symbol to solve them. When they realized this, some would halt and respond, "no actual solution," which is technically accurate. We can further simplify radicals by using the imaginary number I which is the square root of real numbers. We occasionally even manage to get rid of the fictitious element, which provides us with actual solutions.
The square root of -1 is the definition of i. A square root is squared to eliminate the two and leave the original number.
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What is the reason or purpose of solving system of equations?
The main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.
What is solving system?Solving system can be defined as solution set of a system of equations to the collection of all solutions. Solving the system also means finding all solutions with formulas involving some number of parameters.
There are three methods used to solve systems of equations such as:
GraphingSubstitution EliminationTherefore the main reason behind solving an equation system is to find the value of the variable that satisfies the condition of all the given equations true.
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Select all the points that segment ge¯¯¯¯¯ contains. triangle d e f with sides d e and e f congruent. segment e g is drawn from vertex e to base d f such that it bisects the base. segment e g also divides the vertex angle d e f into two angles, d e g with measure 3 y plus 4, and f e g with measure 5 y minus 10.
The segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts.
The points that segment e g contains are the points e and g.
Segment e g bisects triangle d e f, which means that it cuts the triangle into two equal parts. This means that the two sides d e and e f are congruent, and that the vertex angle d e f is divided into two equal angles, d e g with measure 3 y plus 4, and f e g with measure 5 y minus 10.
This can be expressed using the following formula:
Let d e = x
Then d e g = 3x + 4
f e g = 5x - 10
and d e + e f + f e g = 180°
Substituting the values for d e g and f e g, we get:
3x + 4 + x + 5x - 10 = 180°
9x = 196
x = 21.77
Therefore, the length of the sides d e and e f is 21.77.
Since segment e g bisects the base d f, it divides the base into two equal parts, each of length 10.88. The segment e g also divides the vertex angle d e f into two angles, d e g with measure 3 x + 4 = 67.33, and f e g with measure 5 x - 10 = 108.67.
Therefore, segment e g contains the points e and g, and it bisects the triangle d e f into two congruent parts. The segment also divides the vertex angle d e f into two angles, d e g with measure 67.33, and f e g with measure 108.67.
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What is the equation of the line that passes through the point (5,-5) and has a slope of -1/5
Considering the definition of a line, the equation of the line that passes through the point (5, -5) and has a slope of -1/5 is y= -1/5x -4.
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.Line in this caseIn this case, you know that:
The line has a slope of -1/5.The line passes through the point (5, -5).Substituting the value of the slope m and the value of the point in the expression of a line, the value of the ordinate to the origin b can be obtained as follow:
-5= -1/5×5 + b
-5= -1 + b
-5 +1= b
-4= b
Finally, the equation of the line is y= -1/5x -4.
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What is the z-score for a height of 67 inches?
Simply said, a z-score, also known as a standard score, informs you of how much a data point deviates from the mean.
It is not possible to determine the z-score for a height of 67 inches without additional information.
What is mean?The sum of all values divided by the total number of values determines the mean of a dataset.
What is z-score?A z-score, also known as a standard score, informs you of how much a data point deviates from the mean.
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factor completely? please
By Quadratic Formula factors of [tex]a^2+4b^2[/tex] are [tex](a+2bi),(a-2bi)[/tex].
What is Quadratic Formula?The quadratic formula in elementary algebra is a formula that gives the solution(s) to a quadratic equation. In addition to the quadratic formula, there are various methods for solving quadratic equations, including factoring (direct factoring, grouping, and the AC technique), completing the square, graphing, and others.
The following general quadratic equation is given:
[tex]ax^2+bx+c=0[/tex]
The quadratic formula is:
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}, \frac{-b-\sqrt{b^2-4ac} }{2a}[/tex];
where x stands for an unknown, a, b, and c are constants, and a≠0.
Each of these two answers is also referred to as a quadratic equation root (or zero). These roots, which are clearly stated as [tex]y = ax^2 + bx + c[/tex], are the x-values at which any parabola crosses the x-axis geometrically.
Calculation:Given;
[tex]y=a^2+4b^2;\\[/tex]
By comparing this with general equation [tex]x=a,a=1,b=0,[/tex][tex]c=4b^2[/tex]
By substituting in the formula;
[tex]x=\frac{-0+\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =2bi\\(or) x=\frac{-0-\sqrt{(0)^2-4(1)(4b^2)} }{2(1)} =-2bi[/tex]
That gives us;
[tex]y=(a+2bi)(a-2bi)[/tex]
By Quadratic Formula factors of [tex]a^2+4b^2[/tex] are [tex](a+2bi),(a-2bi)[/tex].
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What is the value of the current I?
The current value of "i" in the complex numbers is √(-1)
The value of I as current is expressed as Amperes
In order to know what "i" is and what its value is, we must first know what kind of number it is.
How is current expressed?The current is the flow of electric charge, it is denoted with the letter "I" and its unit of measure is Amperes, it can take any value even complex numbers.
Complex numbersComplex numbers are known as imaginary numbers and can be defined as an extension of the set of real numbers, since in its structure it has a real number followed by an imaginary number denoted with the letter "i".
In function to this type of numbers there is a particular value and it is the "i" which is the result of the square root of -1, then we have:
√(-1) = i
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How do you count 1 in an array?
To count 1 in an array, one can use a looping structure to iterate through each element in the array and increment a counter every time the element is equal to 1.
This can be accomplished using a while loop, a for loop, or a for-each loop. A while loop would use a variable to track the index of the array, and then use a conditional statement to check if the value at the current index is equal to 1. Then, the loop can increment the counter and the index variable. A for loop can be used in the same manner, but with the index variable declared within the loop.
A for-each loop can be used to iterate through the elements of the array, and a conditional statement can be used to check if the current element is equal to 1 and increment the counter if necessary. Whichever looping structure is used, the result should be the same. The counter will hold the number of 1s present in the array after the loop completes.
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