The given sequence 100,10,1,0.1, ........... does not form an AP as the common difference is not same.
What is the sequence of AP arithmetic progression?In Arithmetic Progression, the difference between two mathematical orders is a fixed number (AP). Arithmetic Sequence is another name for it.
We'd come across a few key concepts in AP that had been labeled as:
The first term (a)Common difference (d)Term nth (an)The total of first n terms (Sn)As shown below, the AP can also be referred to in terms of common differences.
The following is the procedure for evaluating an AP's n-th term: an = a + (n − 1) × dThe arithmetic progression sum is as follows:Sn = n/2[2a + (n − 1) × d].Common difference 'd' of an AP: d = a2 - a1 = a3 - a2 = a4 - a3 = ...... = an - an-1.Now, the stated sequence is; 100,10,1,0.1, ...........
The series comprises of four defined terms.
Consider the initial term be 'a₁' = 100.
Consider the second term be 'a₂' = 10.
Consider the third term be 'a₃' = 1.
And, consider the fourth term is 'a₄' = 0.1.
The AP must have the equal common difference. So,
d₁ = a₃ - a₂
Substitute the values.
d₁ = 1 - 10
d₁ = -9
Thus, the computed common difference is -9.
or d₂ = a₄ - a₃ (Substitute the values)
d₂ = 0.1 - 1
d₂ = -0.9.
As, for the result it is clear that the value of both common difference is not same. That is,
d₁ ≠ d₂.
Therefore, the given sequence doesn't not form an arithmetic sequence.
To know more about the arithmetic sequence, here
https://brainly.com/question/26115620
#SPJ4
More math help please its urgent
Answer:
LMK and QPM
Step-by-step explanation:
When two lines are crossed by another line (called the transversal), the angles in matching corners are called corresponding angles.
if jimmy has 99 cups of cofe and drinks 50 how many does jimmy have
Answer:
jimmy
Step-by-step explanation:
Solve each system by elimination.
3x + 2 =10 , 6 +4y = 15
By elimination, the system of equations, 3x + 2y = 10 , 6x + 4y = 15, has no solutions.
A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.
There are three methods that can be used to solve system of equations.
1. Elimination
2. Substitution
3. Graphing
Using the elimination method, given two equations in x and y, a variable should be eliminated by adding/subtracting the two equations.
First, multiply the first equation by 2.
3x + 2y = 10 ⇒ 6x + 4y = 20 (equation 1)
6x + 4y = 15 (equation 2)
Since the new equation of equation 1 has the same coefficients with those in equation 2, but different constants, then the two lines are in parallel.
Hence, the system of equations has no solutions.
Learn more about solving systems of equations by elimination here: https://brainly.com/question/28405823
#SPJ4
You invested money in a fund and each month you receive a payment for your investment. Over the first four months, you received $ 50, $ 52, $ 55 , and $ 59 . If this pattern continues, how much will you receive in the tenth month?c. Explain the difference between an explicit formula and a recursive formula. Use your formula from part (a) as part of your explanation.
Money received in tenth month: $104
Difference between explicit formula and a recursive formula is: the use of (n-1)th term, nth term and the common difference (d) brings a great difference between the two formulae of an arithmetic progression.
What is arithmetic progression?A series of numbers called an arithmetic progression or arithmetic sequence (AP) has a constant difference between the terms.
Given:
Money received in first four months: $50, $52, $55, %59.To find: Money received in tenth month.
Finding:
As we can see, the pattern followed here is: increment in each amount received each month by $1. Thus it is an arithmetic progression.
That is: 50, 52 (0+2), 55 (2+3), 59 (2 + 3 + 4) and so on.
Thus, for the tenth month, we can use the formula of recursion, given by: [tex]a_n=a_{n-1}+n[/tex], n ≥ 1.
For a₁ = 50, a₂ = a₁ + 2
=> a₂ = 50 + 2
This way, a₅ = a₄ + 5
=> a₅ = 59 + 5 = 64
a₆ = a₅ + 6
=> a₆ = 64 + 6 = 70
a₇ = a₆ + 7
=> a₇ = 70 + 7 = 77
a₈ = a₇ + 8
=> a₈ = 77 + 8 = 85
a₉ = a₈ + 9
=> a₉ = 85 + 9 = 94
a₁₀ = a₉ + 10
=> a₁₀ = 94 + 10 = 104
Thus, the payment received in tenth month will be $104.
(b) Difference between explicit formula and recursive formula of an arithmetic progression:
The first term of a recursive formula is a₁ and the formula for the nth term uses the first term and the common difference, d. One example of a recursive formula is [tex]a_n=a_{n-1}+d[/tex]. A formula for the nth term in an explicit formula would include the initial term a₁, the common difference d, and the term number, n. The equation [tex]a_n = a_1 + (n-1)d[/tex].To learn more about arithmetic Progressions, refer to the link: https://brainly.com/question/6561461
#SPJ4
marking brainliest if a/2-3/2+22 what is A
The value of a cannot be determined because the expression is not an equation
How to determine the value of a?The expression is given as:
a/2 - 3/2 + 22
The above is an expression, and not an equation
For the value of the variable a to be solved, the expression must be an equation
Equations are mathematical expressions that are represented by the equal to or equality sign i.e =
Examples of equations are:
a + b = c
y = mx + c
Ax + By = C
y = ax^2 + bx + c
y = x
Hence, the value of a cannot be determined because the expression is not an equation
Read more about expressions at:
https://brainly.com/question/723406
#SPJ1
Point B is the center of a circle, tangent to the y -axis, and the coordinates of Point B are (3,1) . What is the area of the circle?
A π units ² D 6 π units²
B 3 π units² E 9 π units²
C 4 π units ²
The area of the circle with center located at Point B (3, 1) and tangent to the y-axis is 9π units^2. The answer is E.
The area of a circle is the area enclosed by the circle. It is the product of the square of the radius and the constant π. The Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.14159.
Area of circle = πr^2
To know the radius of a circle given its center and tangent line to it, find the distance between the the center and the point of tangency. As the radius is the distance from the center of the circle to any point in the circumference of the circle
If the circle is tangent to y-axis, then the radius is the absolute value of the x-coordinate.
r = 3 units
Using the formula for the area of a circle:
Area of circle = πr^2
Area of circle = π(3 units)^2
Area of circle = 9π units^2
To know more about area of circle: https://brainly.com/question/12269818
#SPJ4
If it takes 4 workers 21 hours to paint how many hours will it take 12 workers?
Answer:
63 hours
Step-by-step explanation:
4 workers = 21 hours
12 workers = g
[tex] \frac{21}{4} \times 12 \\ = 63hours[/tex]
16-x=x-16
I don't know what to do first for this equation
Answer:
16
Step-by-step explanation:
the first thing is to rearrange terms
A school has a total of 900 pupils .400 pupils are boys and the rest of the girls.find the ratio of boys to girls .give the ratio in the simplest form
If a school has a total of 900 pupils and 400 pupils are boys and the rest are girls, then the ratio of the boys to the girls in the simplest form is 4:5.
A ratio in mathematics can be defined as the number of times a number contains another number or is contained in another number to express the connection between two or more things in quantity or size.
To find the ratio of boys to girls, first, we calculate the number of girls in the school. The number of girls can be found by subtracting the total number of pupils which is 900 from the number of boys which is 400.
Hence,
number of pupils that are girls = total number of pupils - number of boys
number of pupils that are girls = 900 - 400
number of pupils that are girls = 500
Hence the ratio of boys to girls can be given as,
400 : 500
Simplifying,
400/100 : 500/100
4:5
Hence, the simplest ratio of boys to girls is 4:5.
To learn more about ratios, click here:
https://brainly.com/question/25927869
#SPJ4
Peter and Patty are very competitive and they both are saving money in their piggy banks. Peter has $90 and
Patty has $120. Patty's mom gives her a bonus of 20% of what she already has and Patty adds it to her piggy
bank. Peter's dad tells him that he will give him a bonus so that Peter has the same total as Patty. What percent of
Peter's money must the bonus from his dad be?
Mark decided to make Christmas presents for his classmates. he bought 10lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.
Write a function f(x) that presents the total cost of the candy, where x is the weight of the less expensive candy.
Answer:
10 times 3.50 + 10x= f(x)
Step-by-step explanation:
35+28
f(x)= 63
The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
Mark decided to make Christmas presents for his classmates. he bought 10lb of two types of candies: caramel candies for $2.80 per pound and chocolate candies for $3.50 a pound.
Let x be the number of pounds of caramel candies and (10 - x) be the number of pounds of chocolate candies. Then the equation is given as,
f(x) = 2.80x + 3.50(10 - x)
f(x) = 2.80x + 35 - 3.50x
f(x) = 35 - 0.70x
The function f(x) that presents the total cost of the candy will be f(x) = 35 - 0.70x.
More about the function link is given below.
https://brainly.com/question/5245372
#SPJ2
Find the value of y.
(14y-4)
(3x + 11)
(x+21)
The simplified value of y in the equation is x = 38 + -3.5y
Simplifying
[tex](14y + -4) + (3x + 11) + (x + 21) = 180[/tex]
Reorder the terms:
[tex](-4 + 14y) + (3x + 11) + (x + 21) = 180[/tex]
Remove parenthesis around (-4 + 14y)
[tex]-4 + 14y + (3x + 11) + (x + 21) = 180[/tex]
Reorder the terms:
[tex]-4 + 14y + (11 + 3x) + (x + 21) = 180[/tex]
Remove parenthesis around (11 + 3x)
[tex]-4 + 14y + 11 + 3x + (x + 21) = 180[/tex]
Reorder the terms:
[tex]-4 + 14y + 11 + 3x + (21 + x) = 180[/tex]
Remove parenthesis around (21 + x)
[tex]-4 + 14y + 11 + 3x + 21 + x = 180[/tex]
Reorder the terms:
[tex]-4 + 11 + 21 + 3x + x + 14y = 180[/tex]
Combine like terms: -4 + 11 = 7
[tex]7 + 21 + 3x + x + 14y = 180[/tex]
Combine like terms: 7 + 21 = 28
[tex]28 + 3x + x + 14y = 180[/tex]
Combine like terms: 3x + x = 4x
[tex]28 + 4x + 14y = 180[/tex]
Solving
[tex]28 + 4x + 14y = 180[/tex]
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-28' to each side of the equation.
[tex]28 + 4x + -28 + 14y = 180 + -28[/tex]
Reorder the terms:
[tex]28 + -28 + 4x + 14y = 180 + -28[/tex]
Combine like terms: 28 + -28 = 0
[tex]0 + 4x + 14y = 180 + -28\\4x + 14y = 180 + -28[/tex]
Combine like terms: 180 + -28 = 152
[tex]4x + 14y = 152[/tex]
Add '-14y' to each side of the equation.
[tex]4x + 14y + -14y = 152 + -14y[/tex]
Combine like terms: 14y + -14y = 0
[tex]4x + 0 = 152 + -14y\\4x = 152 + -14y[/tex]
Divide each side by '4'.
[tex]x = 38 + -3.5y[/tex]
Simplifying
[tex]x = 38 + -3.5y[/tex]
Therefore, we can simplify that the value of y can be expressed as x = 38 + -3.5y
Learn more about simplifying equation here https://brainly.com/question/17350733
#SPJ1
D Number of Sheets (x) Total Cost (y) 3 Cost of Stickers $10.25 $26.65 19
Answer: 5=10.25, 13=26.65, 19=38.95
ALGEBRA Which is a factor of x²+19 x-42 ?
F x+14
G x+2
H x-2
J x-14
The factors of x²+19x-42 are (H) (x-2).
What is factorization?Factorization is the process of reducing a quadratic equation's bracket rather than expanding the bracket and converting the equation to a product of factors that cannot be reduced further. Consider factoring (x2+5x+6) to (x+2) (x+3). In this case, (x+2) (x+3) is the factorization of a polynomial (x2+5x+6).To find the factors:
x²+19x-42x²+x(21 - 2)-42x² + 21x - 2x - 42x(x + 21) - 2(x + 21)Factors are: (x-2) and (x+21)
Therefore, factors of x²+19x-42 are (H) (x-2).
Know more about factorization here:
https://brainly.com/question/25829061
#SPJ4
Find the value of x in each case 40 points!!!
The values of x associated with each case are listed below:
1911How to find the variables behind angles in a geometric systemHerein we find two cases of geometric systems generated by two parallel lines and auxiliary line segments, wherein we must use the concept of supplementary angles and triangle properties to determine the value behind angles. Now we proceed to determine the value of the variable x for each case:
Case 1
m ∠ DCA = m ∠ CBE = 3 · x Alternate internal angles between parallel linesm ∠ CAD + m ∠ ADC + m ∠ DCA = 180° Internal angles in trianglesm ∠ ADC = 180° - 95° = 85° Supplementary angles.2 · x + 85° + 3 · x = 180° Steps 1 & 35 · x = 95° Algebrax = 19 Algebra / ResultCase 2
m ∠ BFE = 180° - 147° = 33° Supplementary anglesm ∠ FEB = 180° - 4 · x Supplementary anglesm ∠ BFE + m ∠ FEB + m ∠ EBF = 180° Internal angles in triangles33° + (180° - 4 · x) + x = 180° Steps 1 & 23 · x = 33° Algebrax = 11 Algebra / ResultTo learn more on triangles: https://brainly.com/question/2269348
#SPJ1
Sarah works as a nanny and charges different rates for working during the week and the weekend. One week, she earned 902.50 working 45 hours, of which 5 hours were during the weekend. The following week she earned 1045 working 50 hours, of which 10 hours were during the weekend. What does Sarah charge per hour, in dollars, for working during the week?
Sarah's charges per hour for working during the week will be $9.5.
What is the solution to the equation?The distribution of weights to the variables involved that establishes the equilibrium in the calculation is referred to as a result.
Sarah is a nanny who bills clients at various prices depending on whether she is working during the week or on the weekend. She worked 45 hours in a single week for a salary of $902.50, of which 5 hours were on the weekend. She worked 50 hours the next week, 10 of which were on the weekend, and made 1045 dollars.
Let x be the charge per working hour and y be the number of charges per hour during the weekend. Then the equation will be
45x + 5y = 902.5 ...1
50x + 10y = 1045
25x + 5y = 522.5 ...2
Subtract equation 2 from equation 1, then we have
45x - 25x = 902.5 - 522.5
20x = 380
x = 19
And the value of y will be
25 (19) + 5y = 522.5
475 + 5y = 522.5
5y = 47.5
y = 9.5
Sarah's charges per hour for working during the week will be $9.5.
More about the solution of the equation link is given below.
https://brainly.com/question/545403
#SPJ1
Suppose you work for a packaging company and are designing a box that has a rectangular bottom with a perimeter of 36 cm . The box must be 4cm high. What dimensions give the maximum volume?
a. How can you model the volume of the box with a quadratic function?
The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².
What is the volume of the rectangular prism?Let the prism with a length of L, a width of W, and a height of H. Then the volume of the prism is given as
V = L x W x H
Imagine you work for a packaging firm and are building a box with a 36 cm-long rectangular bottom. The box has to be 4 cm tall.
The perimeter is given as,
36 = 2 (L + W)
W = 18 - L
Then the volume is given as,
V = L x W x H
V = L x (18 - L) x 4
V = 72L - 4L²
For the maximum volume, V' = 0
V' = 0
72 - 8L = 0
8L = 72
L = 9
Then the width will be
W = 18 - 9
W = 9
The dimensions given the maximum volume will be 9 cm by 9 cm by 4 cm. The volume of the box with a quadratic function will be V = 72L - 4L².
More about the volume of the rectangular prism link is given below.
https://brainly.com/question/21334693
#SPJ1
Which linear equation has no solution? clear submit 23(9x 6)=6x 4 5x 12=5x−7 4x 7=3x 7 −3(2x−5)=15−6x
The linear equation which has no solution is 5x+12=5x-7
Given set of linear equations are:
23(9x+6)=6x+4, 5x+12=5x-7, 4x+7=3x+7, -3(2x-5)=15-6x.
We try to solve each equations one-by-one.
Consider the first equation:
23(9x+6)=6x+4
⇒207x+138 = 6x+4
⇒201x = -134
⇒ x =-134/201.
So this linear equation has a solution.
Now consider the second linear equation:
5x+12=5x-7
⇒12 = -7, which has no meaning.
Therefore, this linear equation has no solution.
Now consider 3rd linear equation:
4x+7=3x+7
⇒x = 0
It has a solution.
Consider the 4th linear equation:
-3(2x-5)=15-6x.
⇒ -6x+15=15-6x
⇒ 0=0
In this case, any value for x is a solution. So there are infinitely many solutions.
Learn more about solutions of linear equations at https://brainly.com/question/13729904
#SPJ4
Assume our initial amount is $1000, the rate is 5% and it will only compound once per year. Our equation would look something like this:
The amount of money available after x number of years is given by y = 1000(1.05)ˣ
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let y represent the amount of money after x years. Assume our initial amount is $1000, the rate is 5% (0.05) and it will only compound once per year. The equation is given by:
y = 1000(1 + 0.05)ˣ
y = 1000(1.05)ˣ
The amount of money available after x number of years is given by y = 1000(1.05)ˣ
Find out more on equation at: https://brainly.com/question/13763238
#SPJ1
i need help bad because my teacher didn't even teach this to my class and make sure its correct
Based on the information, it can be inferred that the number that is the change in height of the elevator is 12 feet.
How to complete the table?To complete the table we must take into account the height of the elevator at a given time of seconds. Additionally, we must take into account that the elevator goes down 12 ft every second. So the table would look like this:
12 × 3 = 36180 - 36 = 14412 × 6 = 72180 - 72 = 10812 × 9 = 108180 - 108 = 72What is the height of the basement with respect to the first floor?
To calculate the height of the basement with respect to the first floor, we must take into account the following information:
Every second the elevator descends 12ft.The elevator takes 4 seconds to go down from the first floor to the basement.To calculate this height we must multiply the time it takes for the elevator to go down to the basement by the distance it travels each second.
4 × 12 = 48 feet48ft is the height of the basement.Learn more about height in: https://brainly.com/question/10726356
#SPJ1
GEOMETRY HONORS
Answer Options:
Valid: Law of Detachment
Valid: Law of Syllogism
No Valid Conclusions
All questions(17-21) must be answered, thank you all so muchhh
16. Valid
Reason: congruency can be represented by the symbol ≅ hence the statement still reads <1 and <2 are congruent.
17. Invalid
Reason: A rectangle also has four right angles, It is only a square when all the sides are equal.
18. Valid
Reason: congruency can be represented by the symbol ≅ hence the statement still reads <JKM and <MKL are congruent.
19. Valid
Reason: The conclusion of the battery dying is in support of the premise giving which is leaving the light on when the car is off.
20.Valid
Reason: The conclusion, Dante obtained a part time job is in line with the premise that obtaining a pert time job, is a way to afford a car payment
21. Valid
Reason: The premise which has that selling 75% of the prom tickets will make the prom hold at country club is fulfilled, hence the prom will be held at the country club
What are valid arguments?An argument is vailed when the premises or conditions of the argument are all true. when some part of the argument is not true then it will lead to invalid conclusion.
Read more on valid arguments here:
#SPJ1
Simplify:
c3c2hhch
Write your answer with only positive exponents.
Answer:
[tex]c^6h^3[/tex]
Step-by-step explanation:
Simplify[tex]hhh=h^3\\c^3c^2h^3c\\c^3c^2c\\ccc = c^3\\=c^{3 \cdot 2}\\=c^6\\=c^6h^3[/tex]
1) A lunch service takes 3 ½ hours to complete. If the chef is getting pains $24.80, per hour, what is the total amount earned?
Answer:
The answer is $86.80. The lunch service gains $86.80 in 3 1/2 hours if they get $24.80 per hour.
Step-by-step explanation:
You have to multiply how much they earn per hour, $24.80, by the number of hours they work, 3 1/2. $24.80 times 3 1/2 equals 86.80 so the lunch service earns $86.80 in 3 1/2 hours.
Hope this helps!
Noah enlarges a photograph using the scale 1 inch : 4 inches. Explain why the area of the enlarged photograph will not be 4 times the area of the original.
The area of the enlarged photograph will be 16 times the area of original photograph.
What is defined as the scale?Scale is a ratio which defines the relation between the size of a model as well as the actual dimensions of a figure or object.Once we draw a physical image on paper, we have been using a scale to accurately describe our measurements. A scale of 1:5 signifies that the size of one unit in the picture represents five units in reality.For the given scale in the question;
Noah enlarges a photograph using the scale 1 inch : 4 inches.
Let the original length of photograph is 'L'.
Let the original width of photograph is 'B'
Old Area = LB
Thus, the length and width of the scale will get increased by 4 times.
The new length and width will be 4L and 4B.
Thus, the new area will be;
New Area = (4L)(4B)
New Area = 16 LB
New Area = 16 × (old area)
Thus, the new area of the photograph is increased by 16 times.
To know more about the scale, here
https://brainly.com/question/26467371
#SPJ9
Find the sum of -4x^{2}-3x-3−4x
2
−3x−3 and -4x^{2}-9x−4x
2
−9x.
The sum of two given expressions will be -
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex].
We have two expressions.
We have to add them.
What is Expression in mathematics?An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation in it.
According to the question -
f(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex]
g(x) = [tex]-4x^{2} -9x -4x[/tex]
Now -
h(x) = f(x) + g(x) = [tex]-4x^{2} -3x^{-3} -4x[/tex] + ( [tex]-4x^{2} -9x -4x[/tex])
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]
Hence, the sum of two given expressions will be -
h(x) = [tex]-3x^{-3} -8x^{2} -17x[/tex]
To solve more questions on Adding expressions, visit the link below-
https://brainly.com/question/28277126
#SPJ1
Simplify each complex fraction.
1/1+ x / y
The simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex] is equal to
(y)/ (y +x).
As given in the question,
Given complex fraction is equal to [tex]\frac{1}{1+\frac{x}{y} }[/tex]
Simplify the given complex fraction by taking the least common multiple of the denominator,
[tex]\frac{1}{1+\frac{x}{y} }\\\\\\= \frac{1}{\frac{y+x}{y} } \\\\\\=\frac{ (1)(y)}{y+ x} \\\\= \frac{y}{y+x}[/tex]
Therefore, the simplification form of the given complex fraction [tex]\frac{1}{1+\frac{x}{y} }[/tex] is equal to (y)/ (y +x).
Learn more about simplification here
brainly.com/question/2804192
#SPJ4
solve the equation and show the process
2 + 2 x 45/5
Answer:
20
Step-by-step explanation:
2+2x45\5
=2+90/5
=2+18
=20
The population of Smalltown was 3,187 in 2016. In 2017, 148 more people moved to Smalltown. In 2018, 219 more people moved to Smalltown. What was the population of Smalltown in 2018
The population of Smalltown in 2018, using the mathematical operation of addition, was 3,554.
What is an addition?An addition is one of the basic mathematical operations involving combining two or more numbers or values to form a single value.
Additions are used to find the sum or total of a group of numbers.
Data and Calculations:2016 population of Smalltown = 3,187
2017 addition to the population of Smalltown = 148
The total population of Smalltown in 2017 = 3,335 (3,187 + 148)
2018 addition to the population of Smalltown = 219
The total population of Smalltown in 2018 = 3,554 (3,335 + 219)
Thus, in 2018, the total population of Smalltown was 3,554, 219 more than the population in 2017.
Learn more about additions at https://brainly.com/question/654494
#SPJ1
If a manufacturer sells x units of a certain product, his revenue R and cost C (in dollars) are given by the following. R = 7x C = 1000 + 2x + 0.001x2 Use the fact that profit = revenue − cost to determine how many units the manufacturer should sell to enjoy a profit of at least $1250.
Using factorization, In order to have at least $1250 profit, manufacturer should sell the product between $4500 and $500.
Given,
Revenue (R) = 7x
Cost (C) = 1000 + 2x + 0.001x²
Profit ≥ $1250
Using factorization,
⇒ profit = revenue − cost
⇒ Profit= 7x - 1000 - 2x - 0.001x²
⇒ 7x - 1000 - 2x - 0.001x² >= 1250
⇒ 5x - 0.001x^2 >= 2250
⇒ 0.001x^2 - 5x <= - 2250
⇒ 0.001x^2 -5x + 2250 >= 0
multiplying 1000 on both sides
⇒ 1000x^2 - 5000x + 2250000 > = 0
⇒ x(x - 500) - 4500(x - 500) >=0
⇒ (x- 500) + (x - 4500) >= 0
⇒ x = 500, 4500
To learn more about factorization from given link
https://brainly.com/question/25829061
#SPJ1
Find the vertex, focus, and the directrix of each parabola. y=x² +6 x+5
For the given parabola:
We have the following data.
Vertexv = (-3,-4)
Focusf = (-3, -3.75)
Directrixd = y = -4.25
We define what a parabola is
What is a parabola?The parabola is a geometric shape that is formed from the intersection of a vertical plane in a cone.
The canonical equation of a parabola is given by
(x - h)² = 4p(y - k)
The parabola is a quadratic function, it is composed of a vertex, or inflection point, a focus and a directrix.
The parabola equation is:
y = x² + 6x + 5
y - 5 + 9 = x² + 6x + 9
y + 4 = x² + 2(3x) + 3²
y + 4 = (x + 3)²
This means that the vertex of this parabola is
v = (h, k)
v = (-3,-4)
4p = 1p = 1/4f = (-3, -4 + 1/4)
f = (-3, -3.75)
Directrixd = y = -4 - 1/4
d = y = -4.25
Learn more about parabolas in:
brainly.com/question/11780596
#SPJ4
