A.company manufactures and cells x pocket calculatoes per week. If the weekly cent and demand equations are given by: C(x) = 8,000 + 5x
P = 14 – x/4000 0≤ x ≤25,000
Find the production level that maximizes profit
Answers
To find the production level that maximizes profit for the company manufacturing x pocket calculators per week
Given cost and demand equations: C(x) = 8,000 + 5x and P = 14 - x/4000, where 0≤ x ≤25,000.
Step 1: Determine the revenue function (R(x)). Revenue is the product of the price (P) and the quantity (x) sold.
R(x) = P * x = (14 - x/4000) * x
Step 2: Simplify the revenue function.
R(x) = 14x - (x^2)/4000
Step 3: Determine the profit function (π(x)). Profit is the difference between revenue and cost.
π(x) = R(x) - C(x) = (14x - (x^2)/4000) - (8,000 + 5x)
Step 4: Simplify the profit function.
π(x) = 9x - (x^2)/4000 - 8,000
Step 5: Find the critical points of the profit function by taking the derivative with respect to x and setting it to 0.
dπ(x)/dx = 9 - (x/2000) = 0
Step 6: Solve for x.
x = 18,000
Step 7: Check if the critical point is a maximum by taking the second derivative of the profit function.
d²π(x)/dx² = -1/2000 < 0, so the critical point is a maximum.
Thus, the production level that maximizes profit is x = 18,000 pocket calculators per week.
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Related Questions
Find the value of z that corresponds to the following: a) Area = 0.1210 b) Area = 0.9898 c) 45th percentile
Answers
a) The value of z corresponding to an area of 0.1210 can be found using statistical tables or a statistical calculator.
b) Similarly, the value of z corresponding to an area of 0.9898 can be obtained using statistical tables or a statistical calculator.
c) To find the value of z at the 45th percentile, we can use the standard normal distribution table or a statistical calculator.
a) To find the value of z corresponding to an area of 0.1210, you can use a standard normal distribution table or a statistical calculator. By looking up the area of 0.1210 in the table, you can determine the corresponding z-value. For example, if you find that the z-value for an area of 0.1210 is -1.15, then -1.15 is the value of z corresponding to the given area.
b) Similarly, to find the value of z corresponding to an area of 0.9898, you can refer to a standard normal distribution table or use a statistical calculator. Find the z-value that corresponds to the area of 0.9898. For instance, if the z-value for an area of 0.9898 is 2.32, then 2.32 is the value of z corresponding to the given area.
c) To find the value of z at the 45th percentile, you can use a standard normal distribution table or a statistical calculator. The 45th percentile corresponds to an area of 0.4500. By finding the z-value for an area of 0.4500, you can determine the value of z at the 45th percentile. For example, if the z-value for an area of 0.4500 is 0.125, then 0.125 is the value of z at the 45th percentile.
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Which cylinders have the same volume as the cylinder below? Check all that apply.
A cylinder with height of 32 meters and diameter of 20 meters.
Group of answer choices
A cylinder with height of 16 meters and diameter of 40 meters.
A cylinder with height of 64 centimeters and diameter of 5 meters.
A cylinder with height of 8 meters and diameter of 40 meters.
A cylinder with height of 64 centimeters and diameter of 10 meters.
A cylinder with height of 20 meters and diameter of 32 meters.
A cylinder with height of 128 meters and diameter of 10 meters.
Answers
The cylinders that have the same volume as the one given are: option C and option F.
What is the Volume of a Cylinder?The volume of a cylinder = V = πr²h
Note: r is the radius and h is the height of the cylinder.
The cylinder given has:
h = 32 m
r = 20/2 = 10 m
V = π* 10² * 32 ≈ 10053.1 m³
Option A:
h = 16 m
r = 40/2 = 20 m
V = π*20²*16 ≈ 20106.2 m³
Option B:
h = 64 m
r = 5/2 = 2.5 m
V = π * 2.5² * 64 ≈ 1256.6 m³
Option C:
h = 8 m
r = 40/2 = 20 m
V = π * 20² * 84 ≈ 10053.1 m³
Option D:
h = 64 m
r = 10/2 = 5 m
V = π * 5² * 64 ≈ 5026.55
Option E:
h = 20 m
r = 32/2 = 16 m
Volume = π * 16² * 20 ≈ 16084.95 m³
Option F:
h = 128 m
r = 10/2 = 5 m
Volume = π * 5² * 128 ≈ 10053.1 m³
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Given v= 3i + 7j and w= – 4i - j, find the angle between v and w.
Answers
Given:
\(\begin{gathered} v=3i+7j \\ w=-4i-j \end{gathered}\)To find the angle between v and w:
Using the formula,
\(\begin{gathered} \cos \theta=\frac{v\cdot w}{|v\mleft\Vert w\mright|} \\ \cos \theta=\frac{(3i+7j)\cdot(-4i-j)}{|3i+7j||-4i-j|} \\ \cos \theta=\frac{3(-4)+7(-1)}{\sqrt[]{3^2+7^2}\sqrt[]{(-4)^2+(-1)^2}} \\ =\frac{-12-7}{\sqrt[]{9+49}\sqrt[]{16+1}} \\ =\frac{-19}{\sqrt[]{58\times17}} \\ =\frac{-19}{\sqrt[]{986}} \end{gathered}\)Rationalising the denomiantor, we get
\(\begin{gathered} \cos \theta=\frac{-19}{\sqrt[]{989}}\times\frac{\sqrt[]{986}}{\sqrt[]{986}} \\ cos\theta=\frac{-19\sqrt[]{986}}{986} \\ \theta=\cos ^{-1}(\frac{-19\sqrt[]{986}}{986}) \\ \theta=127.2348 \end{gathered}\)Hence, the angle is,
\(127.2348^{\circ}\)f(x) = 2x-9
(a) Find f
Would realllyy appreciate if you guys help me with this one :)
Answers
Answer:
x=9/2 or 4.5
Step-by-step explanation:
Imagine some cosmic catastrophe that jolts earth so that it is no longer tilted. instead, its axis is perpendicular to the line between the sun and earth. the most predictable effect of this change would be
Answers
The most predictable effect of Earth's axis being perpendicular to the line between the Sun and Earth would be the absence of seasonal variations.
The tilt of Earth's axis is what causes the change in seasons as different parts of the planet receive varying amounts of sunlight throughout the year. If Earth's axis were to become perpendicular to the line between the Sun and Earth, the planet would no longer experience these seasonal variations. This means that the climate would become more consistent throughout the year, with less temperature variation between different regions. Without the tilt, the equator would receive the same amount of sunlight year-round, leading to a relatively stable climate with minimal temperature fluctuations. The regions closer to the poles, which currently experience more pronounced seasons, would see a reduction in temperature extremes.
Additionally, the absence of a tilted axis would also affect the length of daylight hours. Currently, as Earth orbits the Sun, different parts of the planet experience longer or shorter days. However, with a perpendicular axis, there would be equal amounts of daylight and darkness across all latitudes throughout the year. This would have significant implications for ecosystems, as organisms rely on daylight and darkness cues for various biological processes such as migration, reproduction, and growth.
Overall, the most predictable effect of Earth's axis being perpendicular to the line between the Sun and Earth would be the loss of seasonal variations and the establishment of a more consistent climate throughout the year, with equal daylight hours across all latitudes.
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help me please , I appreciate it :))
Answers
The following represent the average test scores of 7 students whose completion of homework is less than 60\%: 19 47 51 62 66.5 66.5 82 a) Calculate the mean of the data. Show all work. Round to 1 decimal as needed. b) Find the median. Show all work (with numbering and circles to receive full credit). Round to 1 decimal as needed. (2 pt.) c) State the mode(s). If there is no mode, state "no mode."
Answers
The answer is "no mode. a) The mean of the data is approximately 56.3 (rounded to one decimal place).b) The median of the data is 62.c) There is no mode.
a) To find the mean, we must add up all the scores and divide by the number of scores. We can do this in one step by using the following formula: mean = (sum of all scores) / (number of scores)We are given 7 test scores: 19, 47, 51, 62, 66.5, 66.5, and 82. We are told that these scores belong to students who have less than 60% completion of homework.So, the mean can be calculated as follows: mean = (19 + 47 + 51 + 62 + 66.5 + 66.5 + 82) / 7= 394 / 7 ≈ 56.29Therefore, the mean of the data is approximately 56.3 (rounded to one decimal place).
b) The median is the middle score when the scores are arranged in order of increasing or decreasing magnitude. If there is an even number of scores, then the median is the average of the two middle scores. We must first arrange the scores in increasing order:19, 47, 51, 62, 66.5, 66.5, 82There are 7 scores, which is odd. So, the median is simply the middle score: the fourth score, which is 62.Therefore, the median of the data is 62.
c) The mode is the score that occurs most frequently in the data set. If there is no score that occurs more than once, then there is no mode.In this case, none of the scores occur more than once, so there is no mode. Therefore, the answer is "no mode. a) The mean of the data is approximately 56.3 (rounded to one decimal place).b) The median of the data is 62.c) There is no mode.
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Match each diagram with a description and an equation.
Answers
Graphs such as line and tape diagrams can be used to represent equations.
The equation of the first diagram is y = 0.6x,and it represents a decrease by 0.4 or 2/5The equation of the second diagram is y = 1.83x,and it represents an increase of 5/11 or 0.83Diagram (a)
In this diagram, all the x boxes (5 boxes) are shaded, while all the y boxes (3) are shaded.
So, the equation is:
\(y = \frac{3}{5}x\)
Express as decimal
\(y = 0.6x\)
The ratio (0.6) is less than 1.
So, it represents a decrement.
And the decrement (d) is:
\(d = 1 - 0.6\)
\(d =0.4\)
Diagram (b)
In this diagram, all the x boxes (6 boxes) are shaded, while part of the y boxes (6 of the 11) are shaded.
So, the equation is:
\(y = \frac{11}{6}x\)
Express as decimal
\(y = 1.83x\)
The ratio (1.83) is greater than 1.
So, it represents an increment.
And the increment (d) is:
\(d = 1.83 - 1\)
\(d = 0.83\)
See attachment for the diagrams at:
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Answer:576
Step-by-step explanation:
The old man looked out, then beckoned frantically for Greg to follow him. For a moment Greg couldn’t move. Then he found himself following Lemon Brown into the hallway and up the darkened stairs. Greg followed as closely as he could. They reached the top of the stairs, and Greg felt Lemon Brown’s hand first lying on his shoulder, then probing down his arm until he finally took Greg’s hand into his own as they crouched in the darkness. “They’s bad men,” Lemon Brown whispered. His breath was warm against Greg’s skin. Which relationship change occurs in this part of the story?
Answers
Answer:
i think its A?
Step-by-step explanation:
because he is warning greg?
Answer: A. Lemon Brown becomes protective of Greg.
Step-by-step explanation: I took the test and got it correct
Fill in the missing numbers in the pattern,The first number is 280. The rule is to subtract 20.280,
Answers
We have the following:
\(\begin{gathered} 280-20=260 \\ 260-20=240 \\ 240-20=220 \end{gathered}\)therefore, the answer is 260, 240, 240
XXX
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3
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Worm Length (inches)
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inch
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DONE
AZ
539 Complete
Answers
Answer:
I can't able to understand this question plz check this question if it is right or not
Fatimah is x years old and nadia is 3 years older than fatmah. find expression, in it's simplest form in terms of x, for the sum of the girls ages in two years time and in y years time
Answers
The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.
How to derive an algebraic expression from a word problem
Herein we have a situation where two people have different ages, Fatimah has an age such that she is 3 years younger than Nadia. Let be x and y variables that respesent the ages of Fatimah and Nadia, respectively. In summary, the word problem can be reduced into the following algebraic expression:
y - x = 3 (Expression that represents age difference between Fatimah and Nadia)
x + 3 = y, where x, y > 0 and y > x. (1)
The algebraic formula that represents the situation of the age difference between Fatimah and Nadia is x + 3 = y, where x, y > 0 and y > x.
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Find the mean and standard deviation for the set of data. {16,22,8,5,20,18,14,17,24}
Answers
The mean of the set is : 16
The Slandered deviation of set : 5.8689389538863
What is mean?Moderation is the quality of falling at or close to a medium point, whether it is in terms of location, period of time, quantity, or rate. 2 is the arithmetic mean. 3 denotes a plural noun: a tool for achieving one's goals. Attempt to locate it using all available techniques.
The average (mean) is equal to the sum of all the data values divided by the count of values in the data set.
What is Standard Deviation?An indicator of how much a group of numbers vary or are dispersed is the standard deviation. When the standard deviation is low, the values tend to fall within a narrow range of the set's mean, but when it is large, the values tend to deviate from that mean more.
Calculating average:Average x = 16
Count n = 9
Sum Sum =144
Average = Sum / Count
= 144 / 9
= 16
Standard Deviation, σ: 5.8689389538863
Count, N = 9
Sum, Σx: = 144
Mean, μ: = 16
Variance, σ²: = 34.444444444444
Calculating slandered devotion:
\(\sigma=\sqrt{\frac{1}{N} \sum_{i=1}^{N}\left(x_{i}-\mu\right)^{2}}\)
\(\sigma^{2}=\frac{\sum\left(x_{i}-\mu\right)^{2}}{N}\)
\(=\frac{(16-16)^{2}+\ldots+(24-16)^{2}}{9}\)
= 310/9
= 34.444444444444
σ = √34.444444444444
σ = 5.8689389538863
The mean of the set is : 16
The Standard deviation of set : 5.8689389538863
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the sales tax on a 30,000 purchese was $2.40. What was the sales tax rate for this purchese?
Answers
The sales tax on a $30,000 purchase was $2.40, so we can set up an equation:
$30,000 * r = $2.40
To find the sales tax rate, we can divide both sides of the equation by $30,000:
r = $2.40 / $30,000 = 0.008
So, the sales tax rate for this purchase was 0.008, or 0.8%.
Which system of inequalities with a solution point is represented by the graph?
y > 2x – 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x – 2 and y < Negative one-halfx + 1; (–3, 1)
y > 2x + 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x + 2 and y < Negative one-halfx + 1; (–3, 1)
Answers
Answer:
D
Step-by-step explanation:
just took the test
Answer:
d
Step-by-step explanation:
To make balloon animals at birthday parties, Ani charges $3 for each balloon animal plus $8 to cover travel costs. If she made $53 at a party, how many balloon animals did she make?
Answers
Without the travelling cost being $8, Ani made a total of $45 and she made 15 animal balloons.
We know that the total cost Ani charges for travelling is $53
and the total amount Ani made at the party = $53
therefore, first to find the number of balloons she made we need to subtract the travelling cost from the total amount she made:
= 53 - 8 = 45
therefore, now we know that Ani made a total amount $45 from balloons alone:
also, we know that each balloon costs $3 each therefore we need to divide $45 by 3, we get 15,
hence, we can say that Ani made a total of 15 animal balloons for the party.
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Solve for x please help !!!!!!!
Answers
Answer:
x ≈ 20.31
Step-by-step explanation:
By applying tangent rule in the given right triangle,
tan(55°) = \(\frac{\text{Opposite side}}{\text{Adjacent side}}\)
Measure of the opposite side = 29 units
Measure of the adjacent side = x
Substitute these values in the expression,
tan(55) = \(\frac{29}{x}\)
x = \(\frac{29}{tan(55)}\)
x = 20.306
x ≈ 20.31
Let x be the number of years since 1998, let g(x) be the average monthly bill (in dollars) for mobile phone users in the United States, and let h(x) be the average number of minutes used by U.S. mobile phone users. Then g(x) and h(x) are as given g(x) = -0.27x³ + 1.40x² + 1.05x + 39.4, h(x) = -8.25x³ + 53.1x² - 7.82x + 138 Write a rational function ƒ(x) that gives the average price per minute x years after 1998.
Answers
The rational function ƒ(x) that represents the average price per minute x years after 1998 is given by ƒ(x) = g(x) / h(x), where g(x) = -0.27x³ + 1.40x² + 1.05x + 39.4 and h(x) = -8.25x³ + 53.1x² - 7.82x + 138.
To calculate the average price per minute x years after 1998, we need to find the ratio between the average monthly bill (g(x)) and the average number of minutes used (h(x)). Therefore, the rational function ƒ(x) is defined as ƒ(x) = g(x) / h(x).
Given that g(x) = -0.27x³ + 1.40x² + 1.05x + 39.4 and h(x) = -8.25x³ + 53.1x² - 7.82x + 138, we can substitute these expressions into the rational function to obtain the final formula: ƒ(x) = (-0.27x³ + 1.40x² + 1.05x + 39.4) / (-8.25x³ + 53.1x² - 7.82x + 138).
This rational function represents the average price per minute x years after 1998 based on the given average monthly bill and average number of minutes used by U.S. mobile phone users. By plugging in different values for x, you can evaluate the function and obtain the corresponding average price per minute for each year.
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If triangle vwx is congruent to triangle day, find the length of yx
Answers
Triangle ABC's side BC measures roughly 4.17 inches when side AB's length is 10 inches, according to our analysis of the similarities between triangles XYZ and ABC.
In the described situation, the angle X of the right triangle XYZ is 90 degrees.
XY = 5 inches and XZ = 12 inches are the lengths of the other two sides.
We are also informed that triangle XYZ and triangle ABC are comparable, with angle A being 90 degrees and side AB being 10 inches in length.
The length of side BC needs to be determined.
The corresponding sides of the two triangles are proportionate because they are comparable.
Let's use the ratio of corresponding sides to find the length of BC.
In triangle XYZ, the ratio of XY to XZ is equal to the ratio of BC to AB. Therefore:
XY / XZ = BC / AB
Plugging in the given values:
5 / 12 = BC / 10
To solve for BC, we can cross-multiply:
\(5 \times 10 = 12 \times BC\)
\(50 = 12 \times BC\)
Dividing both sides by 12:
50 / 12 = BC
Simplifying the expression:
BC ≈ 4.17 inches
Therefore, the length of side BC in triangle ABC is approximately 4.17 inches.
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Question may be like:
In a right triangle XYZ, angle X is 90 degrees. The lengths of the other two sides, XY and XZ, are 5 inches and 12 inches, respectively. If triangle XYZ is similar to triangle ABC, where angle A is 90 degrees, and the length of side AB is 10 inches, find the length of side BC.
Find a three-digit number, which is 5 times greater than the product of it's digits.
Answers
Answer:
1,500 and 300
Step-by-step explanation:
300 x 5 = 1,500
Q13. In each case give your answer as a
Q In a school of 1000 pupils, 550 are girls and 450 are boys.
a) What fraction of the school are boys?
A what fraction of the school are boys?
Answers
450 / 1000 will give the fraction
450 / 1000 in its simplest form is taken by dividing both with a common factor that is 50
then the ans is
9/20
a rectangular prism has a height of 6 units anf a volume of 40 units cubed shannon states that a recctangular prism
Answers
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct. The correct option is A.
To compare the volumes of the rectangular pyramid and the rectangular prism, we need to find the base area (BA) of the pyramid. The volume (V) of a pyramid is given by the formula:
\(V = \dfrac{1}{3} \times BA \times h\)
where BA is the base area and h is the height.
Given that the volume of the pyramid is 40 units³ and the height is 6 units, we can find the base area:
40 = (1/3) x BA x 6
Now, solve for BA:
\(BA = \dfrac{(40 \times 3)} { 6}\\BA = 20\ units^2\)
Now, let's check the options:
A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units³; therefore, Shannon is incorrect.
The volume of the rectangular prism with BA = 20 and h = 6 is (20 x 6) = 120 units³, not 40 units³. So, this statement is incorrect.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units³; therefore, Shannon is incorrect.
We have already determined that the base area of the pyramid is 20 units², not 6.67 units². So, this statement is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.
This statement matches our calculations. The volume of the rectangular prism with BA = 20 and h = 6 is (20 x 6) = 120 units³, which is three times the volume of the pyramid. So, this statement is correct.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.
The base area of the pyramid is 20 units², not 6.67 units². So, this statement is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units³; therefore, Shannon is correct.
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The complete question is attached below:
A rectangular pyramid has a height of 6 units and a volume of 40 units3. Shannon states that a rectangular prism with the same base area and height has a volume that is three times the size of the given rectangular pyramid. Which statement explains whether Shannon is correct?
A rectangular prism in which BA = 20 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 40 units3; therefore, Shannon is incorrect.
A rectangular prism in which BA = 20 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
A rectangular prism in which BA = 6.67 and h = 6 has a volume of 120 units3; therefore, Shannon is correct.
There are 28 students in a class. 18 are girls. Write a ratio comparing the number of boys in the class to the total number of students in the class.
Group of answer choices
A. 18 to 28
B. 10 to 28
C. 18 to 10
Answers
Answer:
B. 10 to 28
Step-by-step explanation:
28 (students) - 18 (girls) = 10 (boys)
It says compared numbers of boys (10) to total number of students, which is 28.
10 to 28 is the ratio.
Jessica watered 12 plants. Every plant got 2/9 gallons of water.
How much water did she use in all?
Write your answer in simplest form.
Answers
Answer:
2 2/3 gallons
Step-by-step explanation:
Multiply the number of plants by the amount of water used for each plant:
12 * 2/9
24/9
Simplify by dividing the top and bottom by 3.
8/3
Change the improper fraction to a mixed number.
Three goes into 8 two times with two left over.
2 2/3 gallons
Answer:
2 2/3 gallons
Step-by-step explanation:
Rewrite without parentheses and simplify.
(x-6)?
Answers
Answer:
x-6
Step by step explanation:
1. If x equaled 3 then we would replace x with three.
2. We would then take the simplified equation and subtract.
3. 3-6 = 3
If this helped please consider marking this answer brainliest!!
The question is in the picture
Answers
Answer:
no
Step-by-step explanation:
I don't think its a function because eventually one of the x values will equal more then one y value making it not a function. I'm not sure though I hope this helps :)
A company needs to know whether the packages it is shipping meet the requirements of being
no less than 100 ounces and no greater than 125 ounces. The shipping department weighs 50
boxes and organizes the data in a table. Which data display would you use to display this
information and determine whether packaging procedures should be revised? Explain.
Answers
To display this data, I advise using a box plot or a histogram.
The distribution of package weights may be shown in a histogram, which also shows how many parcels fall within the 100-125 ounce range. The histogram can be used to find any trends or outliers in the data that can point to problems with the packing methods.
An expanded description of the data, including the median, quartiles, and any outliers, would be shown in a box plot.
Also, it would demonstrate if most of the packages fall within the acceptable weight limit. It would be very helpful to use a box plot to see any severe outliers that could be distorting the data.
By giving the data a visual representation and highlighting any trends or outliers that would point to problems with the packing operations, both of these data presentations would aid in deciding if the packaging techniques needed to be updated.
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Prove that a>b and c<0, then a/c < b/c is true
Answers
We have proven that if a>b and c < 0, then a/c < b/c as shown below
Proving expressionsFrom the question, we are to prove the given expression.
We are to prove that
If a>b and c<0, then a/c < b/c is true
Choose some numbers to satisfy the conditions
Since we have that
a > b
Let a = 8
and b = 4
Also,
We have that c < 0
Let c = -2
Now,
Evaluate a/c
a/c = 8/-2 = -4
Also, evaluate b/c
b/c = 4/-2 = -2
-4 < -2
Thus,
a/c < b/c
Hence, we have proven that if a>b and c < 0, then a/c < b/c
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Below is a formula for the volume of a pyramid
V = 1/3 Bh , where B is the base area and h is the height
Solve the formula for h.
What is the height of a pyramid with base area 15 cm² and volume 45 cm?
A:1 cm
B:3 cm
С:6 cm
D:9 cm
Answers
Answer:
D
Step-by-step explanation:
Refer to the picture that givem
the quadratic $x^2-3x 1$ can be written in the form $(x b)^2 c$, where $b$ and $c$ are constants. what is $b c$?
Answers
The value of b = -3/2 and c = -5/4
To write the quadratic x² - 3x + 1 in the form (x + b)² + c, we can expand (x + b)² and compare it to the given expression:
(x + b)² = x² + 2bx + b²
Comparing this to the given expression x² - 3x + 1, we see that we need:
2bx = -3x, so b = -3/2
b² + c = 1, so substituting b = -3/2 gives:
(9/4) + c = 1
so c = 1 - 9/4
= 4/4 - 9/4
= -5/4
The quadratic x² - 3x + 1 can be written in the form (x - 3/2)² + ( - 5/4).
Therefore, the value of b = -3/2 and c = -5/4
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the quadratic x²-3x + 1 can be written in the form (x +b)² + c, where b and c are constants. what is b, c?