The cost of the bench is $ 375 and the Cost of the garden table is $ 446.
Calculating Unknown Quantity:We can Calculate unknown quantities mathematically using Algebra Expressions. Unknown values in an equation are represented by variables, which are often represented by a letter of the alphabet like x, y, and z or a, b, and c, etc.
Here we have
A garden table and a bench cost $ 821 combined
Let x, and y be the cost of the garden table and bench
Given that
The garden table costs $71 more than the bench.
=> x = y + $ 71 ---- (1)
It is also given that
The total cost of the garden table and a bench = $ 821
=> x + y = 821
=> y + 71 + y = 821
=> 2y = 821 - 71
=> 2y = 750
=> y = 375
=> Cost of bench, y = $ 375
=> The cost of the garden table, x = $ 375 + $ 71 = $ 446
Therefore,
The cost of the bench is $ 375 and the Cost of the garden table is $ 446.
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4
If figure ABCD is congruent to MNOP, what
is the length of PM?
6
A
F
H
D 7 C
6789
10
10
8
8
P
N
M
The length of the PM is 6 if ABCD is congruent to MNOP.
What do you mean by congruent?When it comes to geometry, two figures or objects are said to be congruent if they are the same size and shape, or if one is the mirror image of the other.
More specifically, two sets of points are said to be congruent if—and only if—they can be changed into one another by an isometry, which is a combination of rigid motions including translation, rotation, and reflection. This indicates that either object may be exactly aligned with the other object by moving and reflecting it, but not by resizing it. If we can cut out and then perfectly match up two separate plane figures on a piece of paper, they are then congruent. I'm allowed to turn the paper over.
Here both the given figures are congruent figures. So, their shape and size must be equal.
Therefore from the two figures, PM=DA
So, PM=6
Therefore, the length of the PM is 6 if ABCD is congruent to MNOP.
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What is the value of x in the equation 2/3 (1/2×+ 12) = 1/2(1/3x +14) - 32
Answer:
Step-by-step explanation:
x = 174
i have no idea how to do this can anyone help
The long term behavior of the rational function f(x) = (x² - 3) / (x³ + 2) is 0, for the rational function g(x) = (x³ - 3) / (x³ + 2) is 1 and for the rational function h(x) = (x⁴ - 3) / (x³ + 2) does not exist.
How to determine the long run behavior of a rational function
In this case we find three rational functions, that is, functions of the form:
m(x) = p(x) / q(x)
Where:
p(x) - Function numerator.q(x) - Function denominator.Please notice that both numerator and denominator are polynomic functions, the long run behavior of the function depends on the grades of numerator and denominator according to these rules:
If the grade of the numerator is greater than the grade of the denominator, then long run behavior is divergent as x → ± ∞.If the grade of the numerator and the grade of the denominator are the same, then the function tends to a / b as x → ± ∞, where a and b are the lead coefficients of the numerator and the denominator, respectively.If the grade of the numerator is less than the grade of the denominator, the function tends to be 0 as x → ± ∞.Now we proceed to analyze the long run behavior of each rational function:
Case 1: f(x) = (x² - 3) / (x³ + 2)
Grade of numerator: 2, grade of denominator: 3
Result: 0
Case 2: g(x) = (x³ - 3) / (x³ + 2)
Grade of numerator: 3, grade of denominator: 3
Result: 1
Case 3: h(x) = (x⁴ - 3) / (x³ + 2)
Grade of numerator: 4, grade of denominator: 3
Result: N / A
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This is the question in the picture
The inequality for the value of y can be given as -1/8 < -2/3y, where y < 3/16.
What is inequality?Inequality shows relation between two expression which are not equal to each others.
Let the required number is y.
To find the inequality that represents the -1/8 is less than the product of -2/3 and number y.
The product of -2/3 and y = -2/3y
The inequality for the y can be written as,
-1/8 < -2/3y
Solve for the value of y,
1/8 > 2/3 y
3/16 > y
Or y < 3 / 16
The required inequality is -1/8 < -2/3y, where y < 3/16.
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1. Without solving, explain why the two linear systems below have the same solution. 4x + 2y = 26 x+y=8 4x + 2y = 26 -2x - 2y = -16
Answer
The first equation is the same (4x+2y=26), so we only need to compare the second equation. Just by looking at the second equation, you can see that x+y=8 and -2x - 2y = -16 are the same equation because -2 is multiplied to both sides of the equation x+y=8.
The expected return on HiLo stock is 13.69 percent while the expected return on the
market is 11.5 percent. The beta of HiLo is 1.3. What is the market risk premium?
The risk-free rate of return on Hilo stock is 1.58%
What is the market risk premium?
Expected return on the stock=risk free rate beta x (expected market return-risk free rate)
14.08%=risk free rate+1.26 x (11.5%-risk free rate)
14.08%=risk free rate+14.49%-1.26 x risk free rate
0.41=0.26 x risk-free rate
risk-free rate=[tex]\frac{0.41}{0.26} %=1.58%[/tex]%=1.58%
The hazard-free price is the price of going back offered by means of funding that carries 0 risks. each investment asset incorporates a few degrees of threat, however small, So the risk-free price is something of a theoretical concept. In practice, it is taken into consideration to be the hobby price paid on short-time period government debt. the risk-free rate threat-unfastened price of going back no longer genuinely exists, as each investment carries at least a small quantity of hazard.To calculate the actual chance-unfastened charge, subtract the inflation rate from the yield of the Treasury bond matching your funding duration. Crucial banks control the threat-loose fee – nicely understood as the yield on short-term authorities’ payments.That is a risk-free rate fact of financial life but not one that we frequently think about. The capital asset pricing model and present-day portfolio idea take the danger-loose price as “given” instead of as “determined”.To learn more about risk-free rates visit here:
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In a recipe for fizzy grape juice, the ratio of cups of sparkling water to cups of grape juice concentrate is 3 to 1
Answer:
Yes it is
Step-by-step explanation:
what is (3z+1)+(1+7z)
Answer:
10z + 2
Step-by-step explanation:
combine the like terms
3z + 7z = 10z
1 + 1 = 2
10z + 2
"Question 60
Find the probabilities below using a standard 52 card deck.
By using the concept of probability, it can be calculated that-
1) P(Ace [tex]\cup[/tex] 5) = [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) P(Even [tex]\cup[/tex] Black) = [tex]\frac{36}{52}[/tex]
5) P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
What is probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
1) Number of ace card = 4
Number of '5' card = 4
P(Ace [tex]\cup[/tex] 5) = [tex]\frac{4}{52} + \frac{4}{52}[/tex]
= [tex]\frac{8}{52}[/tex]
2) P(Ace [tex]\cap[/tex] 5) = 0
3) Number of odd numbered cards = [tex]5 \times 4[/tex] = 20 (Assuming the ace is odd)
Probability of getting an odd numbered card = [tex]\frac{20}{52}[/tex]
P([tex]Even^c[/tex]) = [tex]\frac{20}{52}[/tex]
4) Number of black coloured even numbered card = 10
Number of even numbered card = 20
Number of card of black colour = 26
P(Even [tex]\cup[/tex] Black) = [tex]\frac{20}{52} + \frac{26}{52} - \frac{10}{52}[/tex]
= [tex]\frac{36}{52}[/tex]
5) Number of face cards of diamond = 3
P(Face [tex]\cap[/tex] Diamond) = [tex]\frac{3}{52}[/tex]
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50 POINTS URGENT!
Choose the expression that is equivalent to the quantity 7 raised to the negative second power times 7 raised to the third power end quantity all raised to the negative third power.
Group of answer choices
−76
1 divided by 7 raised to the third power
negative 1 divided by 7 raised to the sixth power
718
Answer:
1 divided by 7 raised to the third power
Step-by-step explanation:
To find the equivalent expression, we can start by applying the rule for multiplying powers with the same base:
(7^(-2)) * (7^3) = 7^(-2+3) = 7^1 = 7
Then, we can apply the rule for raising a power to a power:
7^1 = (7^1)^(-3) = 7^(-3)
Finally, we can apply the rule for raising a number to a negative power:
7^(-3) = 1 / (7^3) = 1 / 343 = 1/7^3
Therefore, the equivalent expression is 1 divided by 7 raised to the third power.
During a sale, a store offered a 25% discount on a bed that originally sold for $890. After the sale, the discounted price of the bed was marked up by 25%. To the nearest whole number, what percent of the original price was the price after markup?
The percent of the original price was the price after markup will be 6.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
During a deal, a store offered a 25% rebate on a bed that initially sold for $890. After the deal, the limited cost of the bed was increased by 25%.
The marked-up price is given as,
⇒ $890 x (1 - 0.25) x (1 + 1.25)
⇒ $890 x 0.75 x 1.25
⇒ $834
The percentage is given as,
P = [(890 - 834) / 890] x 100
P = (56 / 890) x 100
P = 0.0629 x 100
P = 6.29%
The percent of the original price was the price after markup will be 6.29%.
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Answer: 94%
Step-by-step explanation:
Find what percent of the original price this represents:
$834.375 / $890 = 0.9375
0.9375 × 100 = 93.75%
93.75% ≈ 94%
Round to the nearest whole number
The price after markup was 94% of the original price.
1/3 + 2/3
Please help! This is due tomorrow and I need it now
Answer: 1
Step-by-step explanation:
Answer:
1 or 3/3
Step-by-step explanation:
There is a common denominator (bottom number) so you add straight across.
1+2=3 so it is 3/3, which is a whole, making it 1.
What is the area of triangle UVW?
Answer:
30 units²
Step-by-step explanation:
Triangle Area = 1/2bxh
Base (b) = 12 units
Height (h) = 5 units
let's apply the formula1/2 × 12 × 5 =
6 × 5 =
30 units²
Fill in the blanks below in order to justify whether or not the mapping shown represents a function.
The mapping diagram above a function since
in where there
The mapping diagram above is a function since there are no two values in set B where there is only one mapping from Set A.
What is a function?
A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
In the example provided, each element in Set A is mapped to one specific element in Set B.
Set A stands for the domain, whereas Set B stands for the range. There would be exactly one value in the range for each value in the domain as a result.
Hence, the mapping diagram above is a function since there are no two values in set B where there is only one mapping from Set A.
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Select all the correct locations on the table.
Classify each situation as an exponential growth, exponential decay, or linear relationship.
A catering company purchased a delivery van
for $25,000. After 2 years, the value of the van
was $17,500. After 4 years, the value of the van
was $12,250.
At the beginning of the day, a laptop had 100%
battery life. After 3 hours, the laptop had 60%
battery life. After 6 hours, it had 20% battery life.
A tiger reserve had an initial population of
20 tigers. After 5 years, the population was
30 tigers. After 10 years, the population was
45 tigers.
exponential growth
exponential decay
linear
The required answer choices are (i)exponential decay (ii) linear and (iii) exponential growth
What are exponential growth and exponential decay?
Quantities that fluctuate quickly are subject to exponential growth and decay. The idea of geometric progression has been used to infer exponential growth and decay. Exponential growth or exponential decay are terms used to describe quantities that vary exponentially rather than continuously.
From question,
1) The first question is like, initially delivery van price is $25,000 after 2 years, the value of the van becomes $17,500
This means it is decaying. The difference between the initial price and after 2 years price is $7500.
To be linear, further after 2 years, or from start after 6 years, the price should be $10000. But it is given to be $12250.
Thus exponential decay.
2) In the second, Initially, a laptop had 100% battery life. After 3 hours, the laptop has 60% battery life. Thus the loss in 3 hours is (100 - 60) = 40%.
After 4 hours, the loss is (60 -20) = 40%
As the loss is the same in equal intervals of time, the decay is linear.
3) In the third one, A tiger reserve had an initial population of 20 tigers.
After 5 years the population was 30 tigers, thus the growth is (30-20) =10.
After 10 years, the population was 45 tigers. Thus the growth is (45-30) = 15.
Thus the increase is non-linear, and so is exponential growth.
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3.
The angles of a triangle are 120°, (x + 16)°, and x°.
What is the value of x?
Pls explain how you get the answer
The triangle has a value of x=22°.
What is a triangle?The three vertices of a triangle make it a three-sided polygon. The angles of the triangle are formed by the three sides' end-to-end connections at a point. 180 degrees is the sum of the triangle's three angles.
Having three sides, a triangle is a form. Each kind of triangle has a unique name. The size of the angles and side lengths determine what kind of triangle it is (corners). Triangles can be classified as equilateral, isosceles, or scalene depending on how long their sides are.
The sum of all the angles in a triangle must be °
120° + (x+16)° + x° = 180°
2x + 136° = 180°
2x = 180° - 136°
2x° = 44°
x = 22°
The triangle has a value of x=22°.
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Sum of -5a + 6 and 3a + 2
Answer:
:)
Step-by-step explanation:
-5a + 6 + 3a + 2
Combine like terms:
-5a + 3a + 6 + 2
2a + 8 is your answer, you can't simplify it further
----------------------------------------------------------------------------------------------------------
If you want to solve for the a value:
-5a + 6 = 3a + 2
Subtract 2 from both sides
-5a + 6 = 3a + 2
- 2 - 2
-5a + 4 = 3a
(The +2 and -2 cancel each other out, it makes 0)
Add +5a to both sides
-5a + 4 = 3a
+5a +5a
(The -5a and +5a cancel each other out, it makes 0)
4 = 8a
Divide by 8 on both sides
4/8 (OR 1/2 OR 0.5) = a
Thanks for reading my ted talk lol pls mark as brainliest and give lots of points i need them lol help a girl out!!
WILL MARK BRAINLIEST PLEASE HELP ME ‼️‼️‼️‼️‼️‼️
NEED #13 AND #14 ‼️‼️
PLEASE HELP ME I NEED THIS FINISHED ASAP IM DOING OVERDUE ASSIGNMENTS FOR MATH I NEED THIS PELASE
Answer:
Step-by-step explanation: Q13 Find the perimeter of the shape
42x *2=84x
72x*2=72x
Perimeter=84x+72x=156x
Q14 Find the perimeter of the shape just add up 3x +(4x+8)+3(x-2)
=3x+4x+8+3*x+3 *-2
=3x+4x+8+3x-6
=3x+4x+3x+8-6......add together like terms and number terms
=10x+2
Answer:
13.) 156x
14.) 10x + 2 or 2( 5x + 1)
Step-by-step explanation:
13.)perimeter of a parallelogram is
p = 2(a + b)
P = 2( 36x + 42x)
P = 2( 78x )
P = 156x
14.) perimeter of a scalene triangle
P = a + b + c
P = 3x + 3(x – 2) + 4x + 8
P = 3x + 3x –6 + 4x +8
P = 6x + 4x –6 + 8
P = 10x + 2
in factorise form
P = 2(5x + 1)
I hope this helps pls rate as brainliest
[tex]\sqrt{2x-6 =x-3\\[/tex]
The value of x in the quadratic equation using mathematical operations is 4±√19
What are Quadratic EquationsTo solve this problem, we have to use some mathematical operations to find the value of x.
In this process, we have to remove the square root and solve for x. This will eventually result to a quadratic equation
In the equation given;
√(2x - 6) = x - 3
Square both sides
(√(2x - 6)² = (x - 3)²
This will eliminate the square root
2x - 6 = (x - 3)²
Open the bracket on the right hand side
2x - 6 = x² - 6x - 9
Collect like terms
x² - 6x - 9 - 2x + 6 = 0
x² - 8x - 3 = 0
Solving for x
x = 4±√19
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✓
The principal P is borrowed and the loan's future value A at time t is given. Determine the loan's simple interest rater.
P = $6000.00, A = $6180.00, t = 1 year
% (Round to the nearest tenth of a percent as needed.)
1. What is the decay factor?
From 2000 to 2013, the value of the U.S. dollar was shrinking. The value of the U.S. dollar
over time v(t) can be modeled by the following formula:
1.36(0.9758)', where t is the number of years since 2000.
0.9758 is the decay factor of the model
How to determine the decay factor?Given that:
The value of the U.S. dollar over time v(t) can be modeled by the following formula:
v(t) = 1.36(0.9758)^t , where t is the number of years since 2000
The form of the exponential decay models is f(t) = ab^t
where,
a is the initial value, b is the decay factor and t is the time
Comparing f(t) = ab^t with v(t) = 1.36(0.9758)^t :
a = 1.36
b = 0.9758
Therefore, the decay factor is 0.9758
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Insert a monomial such that each expression can be rewritten as the square of a sum or the square of a difference.
0.01 b²+.....+100 c²
0.01 b²+____+100 c²
The monomial that completes the expression 0.01 b²+.....+100 c² is 2bc
How to determine the monomial that completes the expression?From the question, we have the following parameters that can be used in our computation:
0.01 b²+.....+100 c²
Complete the expression with a variable
So, we have
0.01 b² + x + 100 c²
The given terms of the expression are factors/multiples of 10
By trial and error, we make use the following representation
0.01 b² + x + 100 c² = (0.1b + 10c)²
Expand the expression
0.01 b² + x + 100 c² = 0.01 b² + 2bc + 100 c²
Evaluate the like terms
x = 2bc
Hence, the monomial is 2bc
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For the figure below, suppose
∠3 = 30°
and
∠7 = 97°.
Find the measures (in degrees) of the other angles.
∠1 =
°
∠2 =
°
∠4 =
°
∠5 =
°
∠6 =
°
∠8 =
°
[tex]\angle 1=150^{\circ}[/tex] (linear pair)
[tex]\angle 2=30^{\circ}[/tex] (vertical angles)
[tex]\angle 4=150^{\circ}[/tex] (linear pair)
[tex]\angle 5=83^{\circ}[/tex] (linear pair)
[tex]\angle 6=97^{\circ}[/tex] (vertical angles)
[tex]\angle 8=83^{\circ}[/tex] (linear pair)
Solve the equation -3.98=x-11.24
x = 7.26
Step-by-step explanation:How to solve your problem:1. Add 11.24 to both sides
-3.98 = x - 11.24
-3.98 + 11.24 = x - 11.24 + 11.24
2. Simplify
Add the numbers:
-3.98 + 11.24 = x - 11.24 + 11.24
7.26 = x - 11.24 + 11.24
Add the numbers:
7.26 = x - 11.24 + 11.24
7.26 = x
Move the variable to the left:
7.26 = x
x = 7.26
Solution:
x = 7.26
I hope my answer helped you! If you need more information or help, comment down below and I will be sure to respond if I am online. Have a wonderful rest of your day!
Answer:
x = 7.26
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other.
First, add 11.24 to both sides of the equation:
-3.98 = x - 11.24
-3.98 (+11.24) = x - 11.24 (+11.24)
Next, simplify.
11.24 - 3.98 = x
x = 7.26
x = 7.26 is your answer.
~
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The discount d is 50% of the list price L
The expression for the discount will be written as d = 0.5L.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the discount d is 50% of the list price L. The expression for the discount will be written as below,
Discount = 50% of the list price
d = ( 50 / 100) x L
d = 0.5L
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The expression (4k + 8)/4 simplifies to an expression of the form ak+b where a and b are integers. find a/b.
If the expression (4k + 8)/4 simplifies to an expression of the form ak + b, then the value of a/b is 1/2
The expression is (4k + 8) / 4
The expression is the mathematical statement that consist of the different variables, numbers and the mathematical operator. The mathematical operators are addition, subtraction, division and multiplication.
The given expression is (4k + 8)/ 4
Solve the expression
(4k + 8) / 4 = 4k/4 + 8/4
Divide the terms
=k + 2
The result is in the form of ak + b
The value of a = 1
The value of b = 2
The value of a/b = 1/2
Therefore, the value of the expression a/b is 1/2
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For each of the following equations, solve for the variable. If there are multiple solutions, separate them by a comma.
Answers should be integers, fractions, radicals, or in exponential form. No decimals!
1/7㏒ (x-1) + 3㏒ (2)
x=______
3㏑(ω+6) = 5㏑ (6)
ω=____
The solutions to the x and w variables are x = 2097153 and w = (6)⁻²/⁵
How to determine the solution to the variables?From the question, we have the following parameters that can be used in our computation:
1/7log(x - 1) = 3log(2)
3 ln(w + 6) = 5 ln(6)
Solving the equation (1), we have the following equation
1/7log(x - 1) = 3log(2)
Multiply both sides of the equation by 7
So, we have the following representation
log(x - 1) = 21log(2)
Apply the power rule of logarithm
log(x - 1) = log(2)²¹
By comparison, we have
x - 1 = (2)²¹
Evaluate the exponent
x - 1 = 2097152
So, we have
x = 2097153
Solving the equation (2), we have the following equation
3 ln(w + 6) = 5 ln(6)
Multiply both sides of the equation by 1/3
So, we have the following representation
ln(w + 6) = 5/3 ln(6)
Apply the power rule of logarithm
ln(w + 6) = ln(6)³/⁵
By comparison, we have
w + 6 = (6)³/⁵
So, we have
w = (6)⁻²/⁵
Hence, the solutions are x = 2097153 and w = (6)⁻²/⁵
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At a certain zoo, the average mass of one blue whale is measured to be 190000 kilograms. Use scientific notation to express the mass of 125 blue whales.
PLEASE ONLY ANSWER IF YOU KNOW THE ANSWER, PLEASE DON'T JUST USE IT TO GET THE POINTS!!!!!!!!!!!!!
The weight of the 125 blue whales in the scientific notation will be 23.75 × 10⁶ kilograms.
What is Algebra?Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.
The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.
At a specific zoo, the typical mass of one blue whale is estimated to be 190000 kilograms. Utilize logical documentation to communicate the mass of 125 blue whales.
⇒ 190,000 × 125
Simplify the expression in the scientific notation, then we have
⇒ 190,000 × 125
⇒ 23,750,000
⇒ 23.75 × 10⁶ kilograms
The weight of the 125 blue whales in the scientific notation will be 23.75 × 10⁶ kilograms.
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At the beginning of each quarter, rupees 2000 is deposited in the savings account which pays an interest of 10% p.a compounded quarterly. Find the balance in the account after 5 years.
Find the root of the polynomial by factoring
(if you can give steps that’d be great)
Step-by-step explanation:
[tex]x + \frac{75}{4} (x) = 0[/tex]
[tex] \frac{79x}{4} = 0[/tex]
[tex]x = 0[/tex]