Answer:
To factor completely using the GCMF (Greatest Common Monomial Factor), we first need to identify the common monomial factor of all three terms. In this case, the common monomial factor is 2x²:
10x^5 + 8x^4 - 4x² = 2x²(5x^3 + 4x^2 - 2)
Now, we can see that the expression can be factored further, but it cannot be factored using the GCMF. However, we can use other factoring techniques, such as grouping or factoring by grouping, to factor the remaining expression:
2x²(5x^3 + 4x^2 - 2) = 2x²(5x^3 + 10x^2 - 6x^2 - 2)
= 2x²(5x^2(x + 2) - 2(x + 2))
= 2x²(5x^2 - 2)(x + 2)
Therefore, the expression 10x^5 + 8x^4 - 4x² can be factored completely as 2x²(5x^2 - 2)(x + 2).
Step-by-step explanation:
the regular price of any souvenir at a gift shop is x dollars. During a sale today, if a customer purchases one souvenir at its regular price, the price of each additional souvenir will be 0.3x less than the regular price. if carmen purchases 10 souvenirs today, and x=$30, what does carmen pay
Answer:
If x = $30 is the regular price of a souvenir, then the sale price for each additional souvenir will be 0.3x = 0.3($30) = $9 less than the regular price. Therefore, the sale price of each additional souvenir will be:
Sale price = Regular price - $9
Sale price = $30 - $9
Sale price = $21
Since Carmen purchases 10 souvenirs, she pays the regular price for the first souvenir and the sale price for the remaining 9 souvenirs. Therefore, the total cost for all 10 souvenirs will be:
Total cost = (Regular price for first souvenir) + (Sale price for 9 additional souvenirs)
Total cost = ($30) + ($21 x 9)
Total cost = $30 + $189
Total cost = $219
Therefore, Carmen pays $219 for 10 souvenirs during the sale.
Step-by-step explanation:
Need help with short problem 3
The set of solutions in R³ of the equation x1 - 3x2 + 2x3 = 1 is classified as a plane, hence option d is the correct option in the context of the problem.
How to obtain the equation of a plane?The equation of a plane in 3-dimensional space can be written in different forms, but the most common one is the standard form:
Ax + By + Cz + D = 0
where A, B, and C are the coefficients of the variables x, y, and z, respectively, and D is a constant term.
Comparing the equation for this problem to the standard form, the coefficients are given as follows:
A = 1, B = -3, C = 2, D = -1.
Hence option d is the correct option.
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Jamie invested $1,500 in a savings account. The account earns 3.8% interest, compounded monthly. How much money will Jamie have in her account after 4 years if she does not make any deposits or withdrawals? (round to the nearest dollar)
A $2,341
B $1,746
C $1,257
D $1,557
We can say that after answering the offered question As a result, Jamie interest will have $1,746 in her account after four years. Option B is the correct answer.
what is interest ?Simple interest is calculated via dividing the investment by the interest rate, the duration of the loan, and perhaps other factors. In marketing, the formula is simple: return = principal + interest + hours. This method makes it easiest to calculate interest. The most common approach to compute interest is to use the percentages of the principle balance. If he borrows $100 from a buddy and promises to repay that with 5% interest, he will only pay his percentage of the total interest. $100 (0.05) = $5. When you borrow money, you must charge interest and extending when you lend it. The most often, interest is determined as an indicator of the overall of the loan balance. This percentage is known as the loan's interest.
To answer this problem, we can utilise the compound interest formula:
[tex]A = P(1 + r/n)^(nt) (nt)[/tex]
where A is the total amount
P = the initial principal ($1,500 in this example).
r represents the yearly interest rate (3.8%).
n denotes the number of times interest is compounded per year (12 for monthly)
t denotes the number of years (4 in this case)
When we plug in the values, we get:
[tex]A = 1500(1 + 0.038/12)^(12*4) \sA ≈ 1745.99[/tex]
As a result, Jamie will have $1,746 in her account after four years. Option B is the correct answer.
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3x+2 6x-20 solve for x
Answer: Can't solve
Step-by-step explanation: no equation sign
The age of children in kindergarten on the first day of school is uniformly distributed between 4.81 and 5.71 years old. A first time kindergarten child is selected at random. Round answers to 4 decimal places if possible.
What is the probability that the child will be older than 5 years old?
The probability that the child will be between 5.11 and 5.31 years old is:
If such a child is at the 69th percentile, how old is that child?
The child at the 69th percentile is 5.5279 years οld.
Hοw tο fin the 69th percentile?The age οf the children in kindergarten οn the first day οf schοοl is unifοrmly distributed between 4.81 and 5.71 years οld. We can find the tοtal prοbability οf the child being between 4.81 and 5.71 years οld by subtracting the prοbability οf the child being yοunger than 4.81 frοm the prοbability οf the child being yοunger than 5.71:
P(4.81 ≤ age ≤ 5.71) = P(age ≤ 5.71) - P(age < 4.81)
The prοbability οf the child being yοunger than 4.81 is 0 since the age cannοt be negative.
The prοbability οf the child being yοunger than 5.71 can be calculated as:
P(age ≤ 5.71) = (5.71 - 4.81) / (5.71 - 4.81) = 1
Therefοre,
P(4.81 ≤ age ≤ 5.71) = 1 - 0 = 1
This means that the prοbability οf the child being οlder than 5 years οld is:
P(age > 5) = P(5.00 < age ≤ 5.71) = 1 - P(age ≤ 5.00) = 1 - [(5.00 - 4.81) / (5.71 - 4.81)] = 0.7018
Sο the prοbability οf the child is οlder than 5 years οld is 0.7018.
Tο find the age οf a child at the 69th percentile, we need tο find the age x such that the prοbability οf the child being yοunger than x is 0.69.
Let's call the age at the 69th percentile x. Then we have:
P(age < x) = 0.69
We can sοlve fοr x as fοllοws:
( x - 4.81 ) / ( 5.71 - 4.81 ) = 0.69
x - 4.81 = 0.69 ( 5.71 - 4.81 )
x - 4.81 = 0.69
x = 4.81 + 0.69 ( 5.71 - 4.81 )
x = 5.5279
Therefοre, the child at the 69th percentile is 5.5279 years οld.
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*The following below can be discharged (you don't have to pay anymore) when filing a bankruptcy? (select all that apply)
a.
auto car loan
b.
credit card debt
c.
mortgage loans
d.
student loans
e. taxes
f. child support
g. fees
Please select the best answer from the choices provided
The items that can be discharged when filing fοr bankruptcy are:
b. credit card debt
d. student lοans (in rare cases, and οnly if the debtοr can prοve undue hardship)
e. sοme taxes (under certain circumstances)
g. sοme fees (depending οn the type οf fees)
What is the bankruptcy?Bankruptcy helps peοple whο can nο lοnger pay their debts get a fresh start by liquidating assets tο pay their debts οr by creating a repayment plan. Bankruptcy laws alsο prοtect financially trοubled businesses.
The items that can be discharged when filing fοr bankruptcy are:
b. credit card debt
d. student lοans (in rare cases, and οnly if the debtοr can prοve undue hardship)
e. sοme taxes (under certain circumstances)
g. sοme fees (depending οn the type οf fees)
The items that cannοt be discharged in bankruptcy are:
a. autο car lοan (if yοu want tο keep the car, yοu need tο cοntinue making payments)
c. mοrtgage lοans (if yοu want tο keep the hοuse, yοu need tο cοntinue making payments)
f. child suppοrt (this is a nοn-dischargeable debt)
Hence, the best answer frοm the chοices prοvided are:
The items that can be discharged when filing fοr bankruptcy are:
b. credit card debt
d. student lοans (in rare cases, and οnly if the debtοr can prοve undue hardship)
e. sοme taxes (under certain circumstances)
g. sοme fees (depending οn the type οf fees)
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A 3-column table with 4 rows. The first column is labeled Currency with entries Canadian dollar, Euro, Japanese yen, Indian rupee. The second column is labeled U S D /1 Unit and entries 0.97071, 1.35261, 0.01007, 0.01594. The third column is labeled Units/1 U S D and entries 1.03069, 0.73935, 99.90487, 62.72053.
Raj is visiting the United States and needs to convert 2,000 rupees to US dollars.
Raj will have $
Answer:
the answer was 31.88USD
Determine the length of x in the triangle. Give your answer to two decimal places. Most importantly show the steps, please.
Answer:35.09
Step-by-step explanation:From the question given above, the following data were:Opposite = 12Hypothenus = X Angle θ = 20 °
Find the area and perimeter
Answer:
Area = 6a^4Perimeter = 12a^2
Step-by-step explanation:
from the measurements and from the figure it is a right triangle (triple of Pythagoras 3-4-5)
Area = 1/2 b × h
Area = 1/2 3a² × 4a²
Area = 1/2 [tex]12a^{4}[/tex]
Area = [tex]6a^{4}[/tex]
----------------------------------
Perimeter
find the hypotenuse
by the rule of Pythagorean triples it is 5a²
so
3a² + 4a² + 5a² =
12a² (perimeter)
A 16 foot ladder is propped up against the roof of a house. The angle of elevation is 62 degrees. How tall is the house?
Answer is below.
Let's call the height of the house "h".
The ladder is propped up against the house, forming a right triangle with the wall of the house and the ground. The ladder is the hypotenuse of the triangle, and the height of the house is one of the legs.
We know that the length of the ladder is 16 feet, and the angle of elevation is 62 degrees. We can use trigonometry to find the height of the house.
The trigonometric function that relates the angle of elevation to the height and length of the ladder is the tangent function:
tan(62) = h/16
To solve for h, we can multiply both sides by 16:
16 tan(62) = h
Using a calculator, we can evaluate the tangent of 62 degrees to get:
16 tan(62) ≈ 28.6
So the height of the house is approximately 28.6 feet.
krista drank 3/16 of the water in her water bottle in the morning, 5/16 in the afternoon, and 3/16 in the evening. What fraction of water was left at the end of the day?
Answer:If Krista drank 3/16 of the water in her water bottle in the morning, 5/16 in the afternoon, and 3/16 in the evening, then the total amount of water she drank during the day is:
3/16 + 5/16 + 3/16 = 11/16
This means that the fraction of water that is left at the end of the day is:
1 - 11/16 = 5/16
Therefore, Krista has 5/16 of the water remaining in her water bottle at the end of the day.
Step-by-step explanation:
1/5 of a Class Study English and 3/5 Study mathematics. If the Class Consists of 80 Students, how many students study English and Mathematics in the Class?
The number of students that studied math and English in the class is 64 students.
How to find the number of student studying Math and English?1/5 of a class Study English and 3/5 study mathematics. The class consists of 80 Students.
Therefore, the number of students studying English and Maths in the class can be represented as follows:
number studying English = 1 / 5 (80)
number studying English = 16
number studying Math = 3 / 5 (80) = 240 / 5 = 48
Therefore, let's find the number of student that studied maths and English in the class
Student that studied math and English in the class = 48 + 16
Student that studied math and English in the class = 64
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Given the functions f(x)= 1/x-3 -1 and g(x)= 1/x+4-3. Which statement describes the transformation of the graph of the function f onto the graph of the function g.
For the functions f(x)= 1/x-3 -1 and g(x)= 1/x+4-3, the transformation of the graph shows that The graph shifts 7 units left and 2 units down.
What is the definition of a function?
In mathematics, a function is a rule or relationship between two sets of values, known as the domain and the range, that assigns to each element in the domain a unique element in the range.
More formally, a function f is a set of ordered pairs (x, y), where x is an element of the domain and y is an element of the range, such that each element in the domain is paired with exactly one element in the range. This can be written symbolically as:
f: X → Y
where X is the domain and Y is the range, and the arrow → indicates that each element in X is mapped to a unique element in Y.
Now,
To understand the transformation of the graph of the function f onto the graph of the function g, we need to analyze the effect of the changes in the functions.
First, let's consider the function f(x) = 1/(x-3) - 1. This function is a rational function with a vertical asymptote at x = 3 and a horizontal asymptote at y = -1. It is also reflected about the x-axis compared to the basic reciprocal function 1/x.
Next, let's consider the function g(x) = 1/(x+4) - 3. This function is also a rational function with a vertical asymptote at x = -4 and a horizontal asymptote at y = -3. It is also reflected about the x-axis compared to the basic reciprocal function 1/x.
To determine the transformation from f(x) to g(x), we need to compare the changes in the two functions. We can see that:
The term (x-3) in f(x) has been replaced with (x+4) in g(x), which indicates a horizontal shift of 7 units to the left.
The term -1 in f(x) has been replaced with -3 in g(x), which indicates a vertical shift of 2 units down.
Therefore,
the graph of the function f has been shifted 7 units to the left and 2 units down to obtain the graph of the function g. So, the correct statement is:
The graph shifts 7 units left and 2 units down.
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Right Question:-Given the functions f(x)= 1/x-3 -1 and g(x)= 1/x+4-3. Which statement describes the transformation of the graph of the function f onto the graph of the function g.
The graph shifts 2 units left and 7 units up.
The graph shifts 2 units right and 7 units down.
The graph shifts 7 units left and 2 units up.
The graph shifts 7 units right and 2 units down.
Find the component if the Vector BC if B=(2,-7) and C= (-4,-5)
The component of vector BC in the direction of the x-axis is (-6, 0).
What is the component of the vector on x-axis?
To find the component of vector BC, we need to find the projection of vector BC onto a given vector.
The component of vector BC in the direction of the x-axis can be found using the formula:
comp(x) = (BC · unit(x)) · unit(x)
where;
BC is the vector from B to C, unit(x) is the unit vector in the direction of the x-axis, and comp(x) is the component of vector BC in the direction of the x-axis.To find unit(x), we can use the following formula:
unit(x) = (1, 0)
since the x-axis is the horizontal axis and its unit vector has a horizontal component of 1 and a vertical component of 0.
Now, let's calculate the component of vector BC in the direction of the x-axis:
BC = C - B = (-4, -5) - (2, -7) = (-6, 2)
|BC| = √((-6)² + 2²)
|BC| = √(40)
unit(x) = (1, 0)
(BC · unit(x)) = (-6) · 1 + (2) · 0 = -6
comp(x) = (BC · unit(x)) · unit(x) = (-6) · (1, 0) = (-6, 0)
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The complete question is below:
Find the component of the Vector BC on x-axis, if B=(2,-7) and C= (-4,-5)
Question is on the picture
Due tomorrow!!
Answer:
The method that might have been used to result in Garcia winning is the Instant RunOff method.
In this method, voters rank the candidates in order of preference. If no candidate has a majority of first-choice votes, the candidate with the fewest votes is eliminated, and their votes are redistributed to the remaining candidates according to the second-choice preferences of the voters who supported the eliminated candidate. This process is repeated until one candidate has a majority of the votes.
In the preference ballot provided, Garcia received the most first-choice votes with a total of 26, but did not receive a majority of the votes. Therefore, the Instant RunOff method could have been used to determine the winner by redistributing the votes of the eliminated candidates (Müller and Ivanov) to the remaining candidates. Based on the preferences of the voters who chose Müller and Ivanov as their first choice, it is possible that the redistributed votes would have favored Garcia, leading to a majority win for Garcia.
The Instant RunOff method might not be fair to the other nominees because it can result in a candidate winning with a majority of second-choice or even lower preferences, rather than being the first choice of the majority of voters. This means that the candidate who is ultimately chosen may not have broad support, and may not be the candidate that the most voters actually prefer. Additionally, the method can be influenced by strategic voting, where voters rank their choices based on who they think is most likely to win, rather than their actual preferences. This can result in outcomes that do not accurately reflect the preferences of the voters.
Find an equation of the ellipse that has center (3,-1), a major axis of length 8, and endpoint of minor axis (6,-1).
The equation of the ellipse is [tex]}(x-3)^2/4^2 + (y+1)^2/2^2 = 1} or, 4x^2 + 4y^2 - 24x - 8y - 7 = 0[/tex].
What is ellipse?An ellipse is a type of closed curve which is symmetrical in shape and is the set of all points in a plane such that the sum of the distances from two fixed points (known as foci) is constant. It is a type of conic section, a curve obtained by intersecting a cone by a plane. Its shape is similar to that of an oval, but it is more elongated and slender. Ellipses are found in nature, such as in the orbits of the planets, and are used in a variety of applications, such as in engineering and architecture. They are also used in mathematics, where they can be used to represent a range of equations and to study the properties of shapes.
The equation of an ellipse with center (h,k), major axis of length 2a and minor axis of length 2b is given by:
[tex](x-h)^2/a^2 + (y-k)^2/b^2 = 1[/tex]
Given: h=3, k=-1, a=4, b=2
Therefore, the equation of the ellipse is:
[tex](x-3)^2/4^2 + (y+1)^2/2^2 = 1\\or, 4x^2 + 4y^2 - 24x - 8y - 7 = 0[/tex]
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The area of a triangle is 48 cm², If it's height is 12 cm. Find its base?
The base of the triangle is 8 cm.
The following equation determines a triangle's area A:
A = (1/2) * b * h
Where the triangle's height (h) and base (b) are the same.
In this instance, the triangle's height is 12 cm, and its size is 48 cm²
When these values are added to the formula, we obtain the following:
48 = (1/2) * b * 12
By condensing the right side, we obtain the following:
48 = 6b
When we multiply both sides by 6, we get:
b = 8
Therefore, the base of the triangle is 8 cm.
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Solce the system
y=-1/6x+5
x+6y=30
Answer: X = 1, Y = 29
Step-by-step explanation:
X + 6(-1/6X + 5) = 30
X - 1 +30 = 30
X + 29 = 30
X = 1
Y = -1/6*1 + (5/1)*6
Y = -1/6 + 30/6
Y = -1 + 30
Y = 29
Use the graph to answer the question
Determine the line of reflection
Reflection across the X-axis
Reflection across the x = 4
Reflection across the y = -5
Reflection across the y-axis
When thinking about lines of reflection, imagine that there exists a mirror and your trying to guess the location of the mirror on the xy plane. It will have to be located on horizontal line where y is -5. So your line of reflection is y = -5.
MP Model with Mathematics
the equation. Then write a related multiplication equation to solve.
The equation is true, we have confirmed that x = 3 is the correct solution.
The equation shown in the image is:
4x + 12 = 24
To write a related multiplication equation, we can simplify the left side of the equation by factoring out the common factor of 4:
4(x + 3) = 24
By multiplying both sides of the equation by 4, we can now find x:
x + 3 = 6
x = 6 - 3
x = 3
Therefore, the solution to the original equation is x = 3. We can check this solution by substituting it back into the original equation:
4x + 12 = 24
4(3) + 12 = 24
12 + 12 = 24
24 = 24
Since the equation is true, we have confirmed that x = 3 is the correct solution.
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35. Which of the following is a good reason to contribute to a retirement savings plan offered by an employer?
OA. The federal government allows your contribution to be tax deferred.
OB. Your employer will take over contributions once you have continuously contributed for 5 years.
OC. An employer will usually allow you to pay reduced taxes and premium deductions each pay cycle.
OD. You will receive stimulus funds from the federal government.
(C) "Your employer will typically allow you to pay reduced taxes and premium deductions each pay cycle" is an excellent justification for enrolling in an employer-sponsored retirement savings plan.
What is a retirement savings plan?You are permitted to contribute as much of your salary as you choose to the Retirement Savings Plan on a tax-advantaged basis, up to the yearly limit established by the Federal Revenue Agency (IRS).
A retirement savings plan (RSP), also known as an RRSP, is a form of financial account used in Canada to hold savings and investment assets.
When opposed to investing outside of tax-preferred accounts, RRSPs offer a number of tax benefits.
They were launched in 1957 to encourage both workers and independent contractors to save for retirement.
They are subject to a number of limitations outlined in the Canadian Income Tax Act.
Savings accounts, guaranteed investment certificates (GICs), bonds, mortgage loans, income trusts, mutual funds, corporate shares, exchange-traded funds, foreign currency, and funds sponsored by labor are examples of approved assets.
Therefore, (C) "your employer will typically allow you to pay reduced taxes and premium deductions each pay cycle" is an excellent justification for enrolling in an employer-sponsored retirement savings plan.
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A large statue is in the shape of a square pyramid. Each side of
the base of the square pyramid is 723 feet long, and the height
is 341 feet.
What is the volume of the statue?
4.4. A weight lifter increases his body mass by 15% after some heavy training. His new body mass is 78 kg. He claims that he has gained approximately 10 kg of weight after the training session. State whether his claim is valid or not by showing all the necessary calculations.
Answer:
Step-by-step explanation:
We can start by finding the weight lifter's original body mass before the training session:
Let x = original body mass
Then, we know that 15% of x is equal to 78 kg - x:
0.15x = 78 - x
1.15x = 78
x = 78/1.15
x ≈ 67.83 kg
Therefore, the weight lifter's original body mass was approximately 67.83 kg.
Now, let's find the difference between the weight lifter's new body mass and his original body mass:
78 kg - 67.83 kg ≈ 10.17 kg
So, the weight lifter did indeed gain approximately 10 kg of weight after the training session. Therefore, his claim is valid.
A path is 288.3 feet long. Jamie wants to walk the length of the path taking 100 equal steps. How long should each step be? A. 0.2883 foot B. 2.883 feet C. 28.83 feet D. 288.3 feet
Answer:
B) 2.883
Step-by-step explanation:
288.3/100=2.883
Check
2.883x100= 288.3
100 POINTS PLUS BRAINLIEST!!!!!
please see math problem attached SHOW YOUR WORK THIS IS A MUST
Only serious answers not serious / incorrect will be deleted.
(ATTACHED BELOW)
Answer:
Part a:
[tex]A(x)=10x^2+53x+63[/tex]
Part b:
2nd degree polynomial.
Part c:
Check step by step.
Step-by-step explanation:
since the sides of the rectangle are (2x+7) and (5x+9), the area is given by the product of the sides:
[tex]A=(2x+7)(5x+9)=10x^2+18x+35x+63=10x^2+53x+63[/tex]
So the area as a function of X is given by:
[tex]A(x)=10x^2+53x+63[/tex]
Notice is a second degree polynomial in standard form
To ensure part c, notice we can also multiply the sides in different order. This is A*B must be B*A for the sides of the rectangle. Lets check
[tex]A=(5x+9)(2x+7)=10x^2+35x+18x+63=10x^2+53x+63[/tex]
Since we obtained the same answer in part A the closure property for multiplication is check for the polynomial.
The value of 1 unit square represented as a fraction is___
A. 1/10
B. 1/100
C. 1/1000
Answer:
B.1/100 is your answer for your question
Please help me asap!
Step-by-step explanation:
the original price was $225.
that is the 100% we are basing on.
the new price is $340.
the difference is 340 - 225 = $115
to know the % increase we need to calculate how many % of the original 100% are these $115.
1% = 100%/100 = 225/100 = $2.25
$115 are as many % as 1% fits into it :
115 / 2.25 = 51.11111111...% ≈ 51%
if we need to include the additional $50 bags fee, then the price difference is not $115 but $165.
165/2.25 = 73.33333333...% ≈ 73%
the percent increase of the ticket is about 51%.
the percent increase with the baggage fee is about 73%.
A kite starts on the ground and slowly and slowly ascend into the sky.it flies at the same altitude for about 10 minutes and then quickly drops to the ground sketch a graph of the behavior of the kite over time
A possible graph that shows the movement of the kite over time is shown below.
How to graph the movement of the kite?Create a graph in which the x-axis shows the time in minutes and the y-axis shows the distance from the ground in minutes.Now plot the movement that will be divided in three sections. First, the kite ascends which means the value in both axes increases, then the kite stays at the same altitude which means there is not change in the y-axis and finally it descends, which means the line moves towards the x-axis again.Learn more about graphs in https://brainly.com/question/17267403
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by selling a bag at rs1500 and rs2100, there is some loss and profit respectively. if the loss is twice the profit , find its cost price
By selling a bag at rs1500 and rs2100, there is some loss and profit respectively. if the loss is twice the profit , its cost price is Rs 1900.
How can the cost pricebe determined?The cost price is the amount of money that a seller pays to acquire or produce a product or service. It includes all the expenses incurred in the production or purchase of the product, such as the cost of raw materials, labor, packaging, shipping, and other overhead expenses.
Based on the given inforemation , we can represent the cost price by x.
x-1500 = 2 (2100- x)
x-1500 = 4200 -2x
3x = 5700
x= 1900
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In an arithmetic sequence, the sum of the first 8 terms is 88. The product of the 1st and the 8th terms is 120. Calculate values for the 1st term.
Answer: Let's call the first term of the arithmetic sequence "a", and the common difference between the terms "d".
Then, we know that the sum of the first 8 terms is 88, so we can write:
a + (a + d) + (a + 2d) + ... + (a + 7d) = 88
Using the formula for the sum of an arithmetic sequence, we can simplify this to:
8a + 28d = 88
We also know that the product of the 1st and 8th terms is 120, so we can write:
a(a + 7d) = 120
Now we have two equations with two variables. We can solve for one of the variables in terms of the other and substitute into the other equation to solve for the remaining variable.
Solving the first equation for d:
d = (88 - 8a)/28
Substituting into the second equation:
a(a + 7[(88-8a)/28]) = 120
Multiplying both sides by 28 to eliminate the fraction:
28a^2 + 154a - 960 = 0
We can factor this quadratic equation as:
(2a - 15)(14a + 64) = 0
So either 2a - 15 = 0 or 14a + 64 = 0. Solving for "a" in each case, we get:
a = 15/2 or a = -64/14
Since we're looking for the first term of the sequence, which must be positive, we can discard the negative value and conclude that the first term is:
a = 15/2
Therefore, the first term of the arithmetic sequence is 7.5.
Step-by-step explanation: