Answer:
How are algebraic expressions used to represent and solve problems?
The purpose of solving an algebraic expression in an equation is to find the unknown variable. When two expressions are equated, they form an equation, and therefore, it becomes easier to solve for the unknown terms. To solve an equation, place the variables on one side and the constants on the other side.
Step-by-step explanation:
How can you use algebraic expressions to solve problems?
To solve an algebraic word problem:
1. Define a variable.
2.Write an equation using the variable.
3.Solve the equation.
4.If the variable is not the answer to the word problem, use the variable
to calculate the answer.
How are algebraic expressions applied in real life situations?
utilizing linear algebra, and this uniqueness starts to expose a lot of applications. Other real-world applications of linear algebra include ranking in search engines, decision tree induction, testing software code in software engineering, graphics, facial recognition, prediction and so on.
What is algebraic expression why it is used in mathematics?
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number). For example, 3×2 − 2xy + c is an algebraic expression.
find the first term in geometric sequence if the 11th term is -160 and the ratio is -1/3
Answer:
-9447840
Step-by-step explanation:
You want the first term of a geometric sequence whose 11th term is -160 and whose common ratio is -1/3.
N-th termThe n-th term of a geometric sequence is ...
an = a1·r^(n-1)
where a1 is the first term and r is the common ratio.
Using the given values, we have ...
-160 = a1·(-1/3)^(11 -1)
a1 = (-160)·(-3)^10 = -9447840
The first term is -9447840.
LINE GRAPH EASY PLEASE HELP!!
Rachel has 13 books and some empty boxes. She can put 4 books in each box. How many boxes can she fill completely?
How many books will be left over?
Answer:
she can fill 3 boxes completely and one book will be left over
Step-by-step explanation:
if a box can be filled with 4 book then we do 4 multiply 3 and then 12 books will can fill 3 box and there is 13 books so 1 book will be left over
hello i need help with question 5 please
5a) The total cost of buying the car, including the harmonized sales tax (HST) of 13%, is $36,160.
5b) Under the lease, the customer saves $14,760.
5c) The lessee after returning the car has the following lease options:
Lease buyoutLease extensionNew lease contractBuying out the vehicle and then reselling it.6a) The after-tax cost of the car that Jordan wants to buy is $32,199.35.
6b) The part of the Honda Civic that needs to be financed after the down payment is $26,199.35.
6c) The monthly payment will be $567.26.
6d) After four years, the total amount Jordan had paid for the vehicle is $33,228.48.
Car Financing Options:A lease is a financing option for the use of capital assets by which the lessee utilizes an asset for a stated period while making periodic payments to the lessor.
A car purchase can also be financed through loans, like home mortgages.
Value of the car = $32,000
Harmonized Sales Tax (HST) = 13%
Cost of the car with HST = $36,160 ($32,000 x 1.13)
Lease Arrangement:Down payment = $1,000
Financing part = $35,160 ($36,160 - $1,000)
Installment payments = 48
Periodic payments = $425
Total lease cost = $21,400 ($1,000 + 48 x $425)
Savings from leasing = $14,760 ($36,160 - $21,400)
Jordan's Car:The value of the Honda Civic = $28,495
Harmonized Sales Tax (HST) = 13%
After-tax cost = $32,199.35 ($28,495 x 1.13)
Annual interest rate = 1.9% compounded monthly
Down payment = $6,000
Financing part = $26,199.35 ($32,199.35 -$6,000)
Financing period = 4 years
N (# of periods) = 48 months (4 years x 12)
I/Y (Interest per year) = 1.9%
PV (Present Value) = $26,199.35
FV (Future Value) = $0
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 12
Results:
Monthly Payments (PMT) = $567.26
Sum of all periodic payments = $27,228.48
Total Interest $1,029.13
Total amount paid by Jordan after 4 years = $33,228.48 ($27,228.48 + $6,000)
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12 feet below the surface of the water. What is the pool's depth in feet?
Answer:
Step-by-step explanation:
-12
the average weight of 20 students in a certain school was found to be 165 with a standard deviation of 4.5 a) construct a 90% confidence interval for the population mean
A 90% confidence interval for the population mean is; CI = (163.355, 166.655)
How to find the confidence Interval?The formula to find the confidence level here is;
CI = x' ± z(s/√n)
Where;
CI is confidence level
z-score at confidence level
x' is sample mean
s is standard deviation
n is sample size
We are given;
Sample mean; x' = 165
Sample size; n = 20
standard deviation; s = 4.5
z at CL of 90% = 1.645
Thus;
CI = 165 ± 1.645(4.5/√20)
CI = 165 ± 1.655
CI = (163.355, 166.655)
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Determine where the graph of the given function is concave upward and concave downward. Find the coordinates of all inflection points.
g(t) = t^2 - 27/t
The coordinates of the inflection points are (3, 0) and it concave upwards
How to determine the coordinates of the inflection points.From the question, we have the following parameters that can be used in our computation:
g(t) = t^2 - 27/t
Express properly
So, we have
g(t) = t² - 27/t
Calculate the second derivative
So, we have
g''(t) = 2 - 54/t³
Set the differentiated equation to 0
2 - 54/t³ = 0
So, we have
2t³ = 54
Divide by 2
t³ = 27
Take the cube roots
t = 3
Substitute t = 3 in g(t) = t² - 27/t
g(3) = 3² - 27/3
g(3) = 0
This means that the inflection point occurs at t = 3 and the coordinates of the inflection point are (3, 0)
How to determine the point of concave upward and concave downwardRecall that
g''(t) = 2 - 54/t³
Next, we check if the second derivative exist at t = 0,
g''(0) = 2 - 54/0³
g(0) = undefined
The undefined value implies that the graph has a vertical inflection point at t = 0
And as such, the graph of the function is concave upward
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Solve each equation for both variables help please 15 points
Answer:
I hope this helps. Do let me know if you have any doubts and wish me luck I have my maths exams tomorrow!
I need help on this question it’s due tomorrow.
The transformation in the graph is 1 units vertically downwards.
The correct option is A: The graph of g(x) is the graph of f(x) shifted down 1 unit.
What is transformation on the graphs?Let the function f(x) and g(x) are two real functions.
And g (x) = f (x) + k, where k is real numbers.
Function can be sketched by shifting f (x), k units vertically.
The direction of shift can be found by the value of k:
if k > 0, the base graph shifts k units up, and
if k < 0, the base graph shifts k units down.
Given:
The function f(x) = eˣ,
and the function g(x):
g(x) = f(x)-1= eˣ-1.
The graph of both the functions are given in the attached images.
For the base function f (x) and a constant k, the function given by
The transformations in the graph is defined by:
g (x) = f (x) + k, where k is real numbers.
Function can be sketched by shifting f (x), k units vertically.
The value of k determines the direction of the shift. Specifically,
if k > 0, the base graph shifts k units upward, and
if k < 0, the base graph shifts k units downward.
Here, k = -1
And the graph of g(x) is the graph of f(x) is shifted down 1 unit.
Therefore, the f(x) is shifted to 1 unit downward.
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8. Determine whether each relation is a function. a. 2 3 -2 -1 -2 X 4 5 3 4 5 3 7 0 y b. 1 2 1 2 X 7 2 y 3 4 y 5 6 5 fur
on solving the equation, we have therefore the value of x from the given equation comes out to be 13.5
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
equation given is 3(x+2)=7x-48
value of x
[tex]3(x+2)=7x-48\\ 3x+6=7x-48\\7x-48-3x-6=0\\ 4x-54=0\\ 4x=54\\ x=54/4\\ x=13.5\\[/tex]
value of x from the given equation comes out to be 13.5
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A bag contains 9 tiles, each with a different number from 1 - 9. You chose a tile without looking, put it aside, choose a second tile without looking, put it aside, then choose a third tile without looking. What is the probability that you choose tiles with the numbers 1, 2, and 3 in that order?
Someone pls explain this. I know the answer is 1/504 but how do you get there?
The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation and is equal to 1/504.
What are permutations?Permutations refer to the arrangements of objects in certain order or way.
The number of alternative arrangements in a set can be calculated mathematically using a permutation where the order of the configurations is important.
The probability to choose tiles with the numbers 1, 2, and 3 in that order is a form of permutation.
The probability is obtained as 1 / ₉P₃
where;
₉P₃ = 9! / (9 - 3)!
₉P₃ = 9! / 6!
9! = 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 * 1
₉P₃ = 504
Hence, the probability = 1/504
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FOR BRAINIEST PLEASE ANSWER ASAP
You give tours on the Great Lakes and talk about points of interest. A lighthouse typically has 2 beacons that rotate together but not necessarily facing opposite directions. In that way, it can be a shorter time between the first and second flashes than between the second flash and the third flash
(when the first beacon comes around for the second time). One way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. If the beacons are set 120 degrees apart along the rotation, ash shown below, what is this ratio?
The required ratio is 1:2.
What is ratio?A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other.
Given that, A lighthouse typically has 2 beacons that rotate together but not necessarily facing opposite directions, it can be a shorter time between the first and second flashes than between the second flash and the third flash, One way of identifying which lighthouse you are looking at is to find the ratio of the short time between flashes to the long time between flashes. The beacons are set 120 degrees apart along the rotation
If the second beacon is 120° after the first, then the first is 360° -120° = 240° after the second.
Therefore, the ratio of the times between beacons is =
120° : 240° = 1 : 2
Hence, the ratio is 1 : 2
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If you’re currently making $10.50 per hour and you’re offered a new job that pays $11.75 per hour, what will be your percent of increase in pay?
Answer: To find the percent increase in pay, you can use the following formula:
percent increase = ((new pay - old pay)/old pay) * 100
Plugging in the values given in the question, you get:
percent increase = ((11.75 - 10.50)/10.50) * 100
= (1.25/10.50) * 100
= 0.119047619 * 100
= 11.9047619%
Therefore, the percent increase in pay is approximately 11.9%.
Step-by-step explanation:
A rectangle with an area of 5050 units^2
2
is the image of a rectangle that was dilated by a scale factor of \frac{1}{3}
3
1
. Find the area of the preimage, the original rectangle, before its dilation. Round your answer to the nearest tenth, if necessary.
Dilation is a type of transformation that enlarges or shrinks shapes (called archetypes) to create new shapes (called images). Archetype area is 5050 [tex]unit^2[/tex] * 3 = 15,150 [tex]unit^2[/tex]
How can I inflate my model?Add the square of the scaling factor s to the area of the figure before stretching Ap. In other words, the equation Ad = s2Ap gives the area of the figure after dilation Ad. a d = s2a p .
To find the archetype area, we need to undo the applied stretch. Since the stretch factor was 1/3, we can undo it by multiplying the image area by the inverse of the scale factor (1/1/3 = 3). So the area of the archetype is 5050 [tex]unit^2[/tex] * 3 = 15,150.[tex]unit^2[/tex]
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PLEASE HELP ME RIGHT NOW DUE TOADY ASAP
Answer:
A 0.9102
Step-by-step explanation:
A correlation coefficient tells us the strength of the linear relationship between two variables. It is measured on a scale from +1 to -1.
The gradient is positive as it is going up the slope, so the correlation coefficient is positive. We can rule out B.
A correlation coefficient of 0 suggests there is no correlation, however, the scatter graph shows a positive correlation, so we can rule out C.
A correlation coefficient of 1 implies that there is a perfect positive correlation, so all the scatter points lie in a straight line. In the scatter graph given, the points do not all lie on a straight line, so we can rule out D.
Hence, the correlation coefficient is A, 0.9102
Find y'' for x² + y⁴ = 20
now, this is implicit differentiation, so it comes with the assumption that "y" is a function in "x terms", as opposed to a plain vanilla variable, whilst "x" is just that, so
[tex]\cfrac{d}{dx}[x^2+y^4=20]\implies 2x+\stackrel{chain~rule}{4y^3\cdot \cfrac{dy}{dx}}=0\hspace{5em}\cfrac{d}{dx}\left[ 2x+4y^3\cdot \cfrac{dy}{dx}=0 \right] \\\\\\ 2+\stackrel{product~rule}{\left( 12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2} \right)}=0\implies 2+12y^2\cdot \cfrac{dy}{dx}+4y^3\cdot \cfrac{d^2y}{dx^2}=0 \\\\\\ 2+12y^2\cdot \cfrac{dy}{dx}=-4y^3\cdot \cfrac{d^2y}{dx^2}\implies {\Large \begin{array}{llll} \cfrac{2+12y^2\cdot \frac{dy}{dx}}{-4y^3}=\cfrac{d^2y}{dx^2} \end{array}}[/tex]
If the probability of s1 = .6 and the probability of F = .40 what is the value at node 4.
Group of answer choices
320
280
310
260
200
If the probability of s1 = .6 the value above node degree 4 will be 320, as determined by the solution.
What does a node's degree mean?The area of mathematics known as probability deals with numerical descriptions about how likely it is for an event to happen or for a claim to be true. A number between 0 and 1 is the probability of an event, where, broadly speaking, 0 denotes the event's impossibility and 1 denotes its certainty.
According to the given information:S1 probability = 0.6
F's likelihood is 0.40.
If the probability of S1 is given a value of 0.6, then
Probability of S2 then equals 0.4.
Using the table equation's payoff values as an exception.
EV=Σ
Each decision's expected value is calculated.
EV(Node 8) = 0.6 * 100 + 0.4 * 300
= 180
EV(Node 9) = 0.6 * 400 + 0.4 * 200= 320
We chose the best value for node 4 from nodes 8 and 9.
The ideal option for node 9 is the line complicated branch with EV(node 8) = 180.
The ideal anticipated value is determined to be 320.
Node 4's EV is 320.
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To find the next number in the sequence: 7, 10, 13, 16, ____ you would need to do which of the following?
Answer:
19. Add
Step-by-step explanation:
10 - 7 =
13 - 10 =
16 - 13 =
16 + 3 =
An art museum opens at 9 am and closed at 5 pm the function V gives the number of visitors in a museum h hours after it opens explain what this statement tells us about the situation: V(5)=36
Answer:
Five hours after the museum opens, there are 36 visitors.
Step-by-step explanation:
V(5)=36 means that when h is 5, V is 36. Assuming this is a function from what information this gives.
When the Bureau of Labor Statistics conducts a survey, it begins by partitioning the U.S. adult population into 2007 groups called primary sampling units. Assume that these primary sampling units all contain the same number of adults. If you randomly select one adult from each primary sampling unit, is the result a simple random sample? Why or why not? If it is not a simple random sample, what type of sample is it?
The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.
What is Probability and Non-Probability Sampling?It is not always possible to interview or survey an entire population. Therefore, in many research studies, a portion of the population that is expected to represent the population is drawn and surveyed instead. The portion that is drawn is called the sample, and the method used to draw the sample is called the sampling method. Broadly, there are two types of sampling methods. The probability sampling method is a method wherein all members of the population have an equal probability to be selected to be included in the sample. The non-probability sampling method is a method wherein not all members of the population have an equal probability to be selected to be included in the sample. Instead, members are recruited into the sample based on the researcher's subjective and personal judgment.
Simple Random Sampling Method:
Simple random sampling method, sometimes abbreviated as SRS, is the purest form of probability sampling. Figuratively, it is like putting the names of the entire population in a hat and drawing each member from the hat with a blindfold. Therefore, every member of the population has an equal chance of being included in the sample.
Two-stage Cluster Sampling Method:
In the first stage of a two-stage cluster sampling method, the population is first divided into subgroups called clusters. For instance, the population is divided into subgroups based on geographic location. Unlike strata in stratified sampling, clusters are heterogeneous and each cluster is supposed to represent the heterogeneity of the population. These clusters are also known as primary sampling units or PSUs. In the second stage, the simple random sampling method is used to draw individuals from each of the PSUs to be included in the study sample.
Hence, The method illustrated in this example is not a simple random sampling method. Instead, it is a two-stage cluster sampling method.
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determine if each liners function is a direct variation. If it is state the constant of variation.
The liners function are not direct variation
What is a direct variation?The relationship between two variables in which one is a constant multiple of the other is referred to as direct variation.
For instance, two variables are said to be in proportion when one affects the other. b = ka is the equation
If b is directly proportional to a, then k is the constant of variation and the value of k = b/a for all value of b and a
In the problem, the variables are compared as follows
feet = k * sec
k = feet / sec
For the first values, k = 33 / 3 = 11
For the second values, k = 36 / 6 = 6
since 11 ≠ 6 the function is not a direct variation
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It is industry norms and key business ratios Dunn and Bradstreet reported that Q1 Q2 and Q3 were 2037 gasoline service stations sales to inventory ratios or 24 833.4 and 53.8 respectively from this we can conclude that what percentage of these service stations have sales to inventory ratio
From the inventory ratios of 24 8, 33.4 and 53.8 of Dunn and Bradstreet report. It can be concluded that
50% of these service station had sales to inventory ratios of 53.8 or moreHow to find the correct statement about the reportsThe problem is seeking expression of ratios in percentage
Ratios represents part or share of a whole while percentage refers to a fraction of hundred
Calculation of the whole among the ratios 24 8 : 33.4 : 53.8 is done by adding up
= 24 8 + 33.4 + 53.8
= 108
Expressing as ratio 53.8 a percentage, we have
= 53.8/108 * 100
= 0.4981 * 100
= 49.81%
approximately 50%
We can therefore say that inventory of 53.8 or more is 50%
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Imagine products you might create in a given amount of time: poems, baked goods, online videos, movie reviews, video game mods, scarves, drawings, or anything else you can picture yourself making as part of a small, one-person business. Choose and describe two such products. They will be product 1 and product 2
Producing written and visual content for social media can be divided into two items that can be developed as a one-person small business in a little amount of time.
What is social Media?Social media is internet communication that enables real-time information sharing and customer interaction. Social networking can help you: better connect with your audience. building online networks sell and publicise the goods and services you offer.
Social media's effects on business
The social media presence of businesses in order to boost visibility, engagement, positioning, and value creation for their intended audience has been facilitated by the digital revolution.
In order to help businesses establish their strategy in the digital environment, marketing and advertising agencies can quickly produce digital media such posters and catalogues in addition to advertising text as their core offerings.
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O
(-∞0,00)
(-2,00)
A
{rr > -1}
{x|x < -2}
The domain of the function whose graph shown in diagram is x ≤ 1.
What is the domain of a function?The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input.
Consider the function y = f(x), which has the independent variable x and the dependent variable y. A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
The domain of the function whose graph shown in diagram is x ≤ 1 as the value of x is less than 1.
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Help
Complete the puzzle so that each row, column, and diagonal adds up to the same total.
Complete the puzzles with values -4, 0, -3 and 2
How to complete the puzzle?Since each row, column, and diagonal adds up to the same total.
For the 1st row, the total is:
3 + (-2) + (-1) = 0
That means each row, column, and diagonal will always adds up to 0.
3 + w + 1 = 0
w = -3-1
w = -4
w + y + 4 = 0
-4 + y + 4 = 0
y = 0
-1 + 4 + t = 0
3 + t = 0
t = -3
1 + h + t = 0
1 + h + (-3) = 0
h -2 = 0
h = 2
(Check the attached image for labeling)
Thus, complete the puzzle with the values accordingly
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Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa. how many dvds does marissa own?
The number of Dvds owned by Maarissa is 45
How to find the number of dvds?The given parameters that will guide us in finding the number of dvds owned by marissa are
Marissa and Kyle own a total of 66 dvds. Kyle owns 3 more than twice as many dvds as marissa.
Let the number of dvds owned by Marissa be x
Nymber of dvds owned by Kyle be y
This implies that x+y = 66 ............................1
also, 2y + 3 = x ..................................................2
Substitute x = 2y + 3 in equation 1
= 2y + 3+y =66 Collecting like terms
⇒ 3y = 63
Making y the subject of the relation we have y=21
Recall that 2y + 3 = x
That means x = 2(21) + 3
x=45
Therefore Marrissa owns 45 dvds
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1. Simplify and show your work.
3(2x^3y^5)^3
——————— or /
(2x^6y^3)^4
On solving the provided question, we can say that - here the value of exponential equation is 648/1296 = 0.5
what are exponents?Exponentiation, often known as "b raised to the nth power," is a mathematical operation denoted by the symbol bn that involves two numbers: a base number, b, and an exponent, or power, n. Exponents show how many times a number has been multiplied by itself. As an illustration, 2-3 (written as 23) denotes: 2 x 2 x 2 = 8. 23 is not equivalent to 2 + 3 = 6. Recall that an integer raised to the power of one equals itself. A approach to express huge numbers as powers is through the use of exponents. Exponent, then, is the quantity that indicates how many times a number has been multiplied by itself. As an illustration, 6 is multiplied by 4 to provide 6 x 6 x 6 x 6. It may be expressed as 64. 4 is where
So, the equation is
[tex]3(2x^3y^5)^3/ (2x^6y^3)^4[/tex]
and x=y=1
so, 648/1296 = 0.5
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Directions: Determine whether each relation is a function. Explain your answer.
X
12)
10)
#IN
13)
x
14)
15)
10
Answer:
10. Yes
11. No
12. Yes
13. Yes
14. No
15. No
Step-by-step explanation:
Use the vertical line test to determine whether or not a relation is a function. The vertical line test is when you draw a line through a relation and if that line intersects the relation more than ONCE, the relation is not a function.
10. Is a function, the vertical line only intersects the relation once.
11. Isn't a function, intersects the relation more than once.
12. Is a function, intersects the relation only once.
13. Is a function, only intersects the relation once.
14. Isn't the function, intersects the relation more than once.
15. Isn't a function, the relation intersects the function more than once.
Hope this helps.
7. Write the standard form of the
the foci.
equation of the ellipse shown in the following graph. Identify
On solving the provided question we cans ay that - equation of ellipse is given by (x2/a2) + (y2/b2) = 1.
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
distance of the focus from the centre of the ellipse is given by the equation c = √(a2 – b2).
equation of ellipse is given by (x2/a2) + (y2/b2) = 1.
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