) POLYNOMIAL AND RATIONAL FUNCTIONSVord problem involving the maximum or minimum of a quadrati.
Answers
SOLUTION:
Case: Minimum and Maximum functions
Given:
[tex]\begin{gathered} C(x)=0.8x^2-352x+58,583 \\ \end{gathered}[/tex]Required: To find the minimum Unit cost
Method: we apply completing square on the function
Step 1: First we find the square of half the coefficient of x
[tex]\begin{gathered} C(x)=\text{ 0.8x}^2-352x+58583 \\ C(x)=\text{ 0.8\lparen x}^2-440x+73228.75) \\ \frac{1}{2}(440)=\text{ 220}^2\Rightarrow\text{ 48400} \end{gathered}[/tex]Step 2: Add and subtract the value to the Right Hand Side
[tex]\begin{gathered} C(x)=\text{ 0.8\lparen x}^2-440x+48400-48400+73228.75) \\ Completing\text{ squares in the bracket} \\ C(x)=\text{ 0.8\lbrack\lparen x-220\rparen}^2+24828.75] \\ C(x)=0.8(x-220)^2+\text{ 19863} \end{gathered}[/tex]Step 3: From the equation
The quantity need to be produced to get the minimum unit cost is 220.
The value of the minimum cost therefore is obtained at C(220).
This would give:
C(220)= $19863
Final answer:
The minimum unit cost is $19863. Ignore the dollar sign($) when entering your answer.
Related Questions
When solving an equation for x if you get 4=10, that means what?
Answers
Given: An equation where
[tex]4=10[/tex]To Determine: the nature of the solution of the equation
Solution
Nature of solution: The example below relates to the nature of solution
[tex]\begin{gathered} Note:4=4(infinitely\text{ many solution\rparen} \\ a=4(one\text{ solution\rparen} \\ 4=10(no\text{ solution\rparen} \end{gathered}[/tex]Hence, the equation has no solution
!!!!!!!!!!!!!!!!!!!!!!!!!!!!helpppp!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
D. 4x + 3
Answer:
4x + 3
Step-by-step explanation:
Three more means you're adding three to the number. So, you have + 3 right now. Four times the number of shells Talia collects is 4x with x representing Talia's shells. We don't know how many she has so it's represented by x. Now, put everything we have together. 4x + 3.
Hope this helps! :)
2. Refer to the figure shown.a. What is JK?b. What is KM?
Answers
Point J is located at 5
Point K is located at 12
Point M is located at 27
a. The length of the segment JK is: 12 - 5 = 7
b. The length of the segment KM is: 27 - 12 = 15
For each function graphed below, state whether it is one to one !!
Answers
1 yard =3 feet1 meter= 100 cmNicholas walked 20 yards to get his mail. About how many meters did he walk?
Answers
Given:
1 yard = 3 feet
1 meter = 100 cm
Nicholas walked 20 yards to get his mail.
Here, we are required to convert 20 yards to meters.
Where,
1 yard = 0.9144 meter
20 yards = x meters
thus, we have:
[tex]20\text{ }\times0.9144\text{ = 18.29 meters}[/tex]Therefore, Nicholas walked 18.29 meters to get to his mail.
ANSWER:
18.29 meters
Laying down my n buffer is concerned after receiving her weekly paycheck she believes that her deductions for social security,Medicare,and federal income ta withholding (fit) may be incorrect Larsen is paid a salary of 4330 she is married filling jointly and prior to this payroll check has total earnings of 140,460 what are the correct deductions for social security Medicare and fit assume a rate of 6.3% on 142,809 for social security and 1.45% for Medicare
Answers
Correct deduction for social security Medicare and fit at 6.3% = 8,996.967
Correct deduction for Medicare at rate of 1.45% = 2,070.731
What is Medicare?Medicare is defined as a type of health insurance that reduces the fees incurred by an individual following the reception of health services.
After deductions the total earning = 140,460
The correct deduction for social security, Medicare and fit at the rate of 6.3% of 142,809;
= 6.3/100 × 142,809
= 899696.7/100
= 8,996.967
The correct deduction for Medicare at the rate of 1.45%;
= 1.45/100 × 142,809
= 207,073.05/100
= 2,070.731.
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Use the limit definition of the derivative to find the instantaneous rate of change of
Answers
SOLUTION:
Step 1:
In this question, we are given the following:
Use the limit definition of the derivative to find the instantaneous rate of change of
Step 2:
The details of the solution are as follows:
An alternative way to find the use the limit definition of the derivative to find the instantaneous rate of change of:
[tex]f(x)\text{ =}\sqrt[]{4x+8\text{ }}\text{ at x = 4}[/tex]Let us take the derivative of the function and we have that:
[tex]\begin{gathered} f(x)\text{ = }\sqrt[]{4x+8}=(4x+8)^{\frac{1}{2}} \\ \end{gathered}[/tex][tex]\begin{gathered} f^I(x)\text{ = }\frac{1}{2}(4x+8)^{-\frac{1}{2}}(4) \\ f^I(x)=2(4x+8)^{-\frac{1}{2}},\text{ when x = 4, we have that:} \\ f^I(4)=2(4(4)+8)^{-\frac{1}{2}} \end{gathered}[/tex][tex]\begin{gathered} f^I(4)=2(16+8)^{-\frac{1}{2}} \\ f^I(4)\text{ = 2 x }\frac{1}{\sqrt[]{24}} \end{gathered}[/tex][tex]f^I(4)\text{ =}\frac{2}{\sqrt[]{24}}[/tex][tex]f^I(4)=\frac{2}{\sqrt[]{24}}=\frac{2}{\sqrt[]{4}X\sqrt[]{6}}=\frac{2}{2X\sqrt[]{6}}=\frac{1}{\sqrt[]{6}}[/tex][tex]f^I(4)\text{ =}\frac{1}{\sqrt[]{6}}[/tex]
Which of the following is a parent function?O A. f(x) = -3x° +1ОВ.B. f(x) = 2*O c.C. f(x)=23*O D. f(x)=3* - 5
Answers
ANSWER:
B.
[tex]f(x)=2^x[/tex]STEP-BY-STEP EXPLANATION:
A parent function is the simplest formula in which no transformations have been made. Therefore, the function that would be the parent one of the answer options is:
[tex]f(x)=2^x[/tex]Choose the best estimate for the quotient.
27.2/178.6
A) 5
B) 6
C) 50
D) 60
Answers
Answer:
B
Step-by-step :
The quotient is 6.5 so the estimate is closest to 6.
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
C(x) = 75x + 1908
Step-by-step explanation:
C(x) is the cost function.
The cost of making x bicycles is the sum of the fixed costs and the cost per bicycle.
The fixed cost is $1908.
The cost per bicycle is $75, so the per bicycle cost for x bicycles is 75x.
Add the two costs, and you get:
C(x) = 75x + 1908
Im kinda lost on how to solve these could you help me and teach me!
Answers
The angles ∠IDA, ∠YDA, and ∠RDI measures 121°, 59°, and 29.5°.
The angle ∠YDF is equal to 121°. The ∠IDA is vertically opposite angle. So, ∠ADI is equal to the ∠YDF. Hence, ∠IDA = 121°.
The angle ∠YDA and the angle ∠ADI form a linear pair. It means ∠YDA and ∠ADI are complimentary angles.
∠YDA + ∠ADI = 180°
∠YDA + 121° = 180°
∠YDA = 180° - 121°
∠YDA = 59°
The ∠FDI is vertically opposite angle to ∠YDA. So, ∠FDI is equal to the ∠YDA. Hence, ∠FDI = 59°. The ray DR bisects the ∠FDI. So, the angle ∠RDI is half of the angle ∠FDI.
∠RDI = (1/2)∠FDI
∠RDI = (1/2)59
∠RDI = 29.5°
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What is the slope of y-9=3(x+12)
Answers
Step-by-step explanation:
What will be the length of the railing from point A to point B? Show or explain how you got your answer.
Answers
To know the length of the railing from point A to point B you can use Pythagoras Theorem.
You draw a right triangle:
You use the given information to know the measure of the legs in the triangle:
You can see that the value of x is the height of 5 steps: 5(7.5 in).
Then:
[tex]x=5(7.5)=37.5in[/tex][tex]x=y=37.5in[/tex][tex]Z=2y=2(37.5in)=75in[/tex]The B is equal to the lenght of 10 steps: 10(9.5in):
Then:
[tex]B=10(9.5in)=95in[/tex]You have the next triangle:
You use the Pythagoras Theorem to find the h:
[tex]h=\sqrt[]{Z^2+B^2}[/tex][tex]h=\sqrt[]{75^2+95^2}[/tex][tex]h=\sqrt[]{14650}[/tex][tex]h=5\sqrt[]{586}\approx121.03in[/tex]The length of the railing from point A to point B is 121.03inCan someone help me
Which graph represents the solution set of the system of inequalities?
{y<−3x−2y≤x−2
Responses
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1comma 1 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region below the dashed line and below the solid line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1comma 1 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region below the dashed line and below the solid line is shaded.,
A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 1 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region above the dashed line and above the solid line is shaded.
Image with alt text: A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 1 end ordered pair and begin ordered pair 0 comma negative 3 end ordered pair. A solid line passing through begin ordered pair 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. The region above the dashed line and above the solid line is shaded.,
Answers
The graph that represents the solution to the system of inequalities is given in the attachment below.
How to Determine the Graph to a System of Inequalities?To find the correct graph that represents the solution to the system of inequalities, determine which inequality represents each of the line that is plotted on the graph.
The first inequality, y < -3x - 2, has a slope of -3, a y-intercept of -2, and an inequality sign "<" which means the shaded part will be below the a dotted or dashed boundary line.
The second inequality, y ≤ x − 2, has a slope of 1, a y-intercept of -2, and an inequality sign "≤" which means the shaded region is below a solid boundary line.
The graph that represents the above stated features is the graph of the system of inequalities shown below.
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FIRST TO ANSWER ALL GETS BRAINEST
Question 1(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In triangle DEF, m∠D = (3x + 27)°, m∠E = (4x + 22)°, and m∠F = 68°. Determine the degree measure of the exterior angle to ∠D.
54°
58°
122°
126°
Question 2(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
In ΔJKL, m∠J = 78° and m∠L = 90°. Determine the measure of the exterior angle to ∠K.
168°
102°
57°
12°
Question 3(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
Triangle UVW is shown with m∠WUV = 36°. The measure of ∠UVW is (5h − 66)°, and the measure of ∠AWB is (5h − 18)°.
triangle UVW with side VW extended through point A and side UW extended through point B, with angle U labeled as 36 degrees
Determine the value of h.
h = 22.8
h = 23
h = 25.4
h = 48
Question 4(Multiple Choice Worth 2 points)
(Interior and Exterior Angles LC)
One interior angle of a triangle is 95.5°, and the other two interior angles are congruent. What is the degree measure of one of the congruent angles?
42.25°
47.75°
84.5°
90°
Question 5(Multiple Choice Worth 2 points)
(Interior and Exterior Angles LC)
For ΔABC, m∠A = 28.7° and m∠B = 123.8°. Determine m∠C.
27.5°
62.5°
76.25°
152.5°
Question 6(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
For triangle XYZ, m∠X = 38°, m∠Y = (5x − 11)°, and m∠Z = (4x − 45)°. Find m∠Y.
m∠Y = 22°
m∠Y = 43°
m∠Y = 99°
m∠Y = 158°
Question 7(Multiple Choice Worth 2 points)
(Interior and Exterior Angles MC)
Triangle ABC is shown with exterior ∠z.
triangle ABC with angle A labeled 58 degrees, angle B labeled 44 degrees, and side AC extended with angle z labeled as exterior angle to angle C
Determine m∠z.
136°
102°
78°
58°
Answers
The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126° so option (D) is correct.
What is a triangle?A triangle is a 3-sided shape that is occasionally referred to as a triangle. There are 3 sides and three angles in every triangle, some of which may be the same.
It is known that the sum of all three angles inside a triangle will be 180°.
So, m∠D + m∠E + m∠F = 180°
(3x + 27) + (4x + 22) + 68 = 180
7x + 49 + 68 = 180
7x = 63
x = 9
So, m∠D = (3(9) + 27)° = 54°.
The exterior angle of D = 180- 54 = 126°.
Hence "The sum of all interior angles of a triangle is 180° thus the measure of the exterior angle to ∠D is 126°".
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A physician borrowed $100,000 from credit union for 9 months at annual interest rate of 4%. What is the simple interest due on the loan?
Answers
Givens.
• The amount borrowed was $100,000.
,• The time elapsed is 9 months.
,• The annual interest rate of 4%.
The simple interest formula is
[tex]I=PRT[/tex]Where P = 100,000, R = 0.04, and T = 9/12.
[tex]\begin{gathered} I=100,000\cdot0.04\cdot\frac{9}{12} \\ I=3,000 \end{gathered}[/tex]Therefore, the simple interest is $3,000.the answer would be 3,000
determine which of the following relations is a function.Xyxy-1010-32-55-1100025-5110-104O3-8-2124y-4-22346XOx01225y24267
Answers
The relation between the function is X cannot repeat itself.
We have given that,
functions table
We have to determine which relation is a function.
What is the function?
A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity.
The relation between the function is
X cannot repeat itself
Therefore option C is correct.
Complete question: Determine which of the following relations is a function [see in attachment]
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I need help with a table to plot the points
Answers
In order to plot a set of coordinates on a graph page, you would need to take account of every pair of x and y values provided. The line that goes horizontally is the x-axis (from left to right). All the negative values move from point zero (the origin).
The ordered pair, or the coordinates tells you where x and y intersect. For example, the first set of coordinates are (2, 9). That means, when x is 2, then y is 9.
Observe that x equals 2 on the right side of the horizontal axis. Next, you look for the spot where y equals 9.
Next step, you carefully trace the spot where x is 2, and trace it up a straight line and at the point where y equals 9 (at the upper part of the y axis), you put a tiny "X" to mark the spot where both values intersect.
Notice that while tracing from x, you move upwards, and while tracing from y, you move towards the right. That point defines the coordinates (2, 9) which is the first line on your table.
You follow a similar step for every one of the other coordinates, which are;
[tex]\begin{gathered} (2,9) \\ (4,3) \\ (6,-6) \\ (0,15) \\ (3,6) \\ (5,0) \\ (\frac{7}{3},8) \end{gathered}[/tex]Please note that I've just attached the same graph, but this time I've labelled the points one by one.
This should help with reading the coordinates at every point.
Which equation is perpendicularl to 2x+3y=12A y=2/3X+5B y=-2/3X+5C y=3/2X+5D y= -3/2X+5
Answers
The equation of the line perpendicular to the given equation is;
[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]Option C is the correct answer
Here, we want to select which of the equations in the option is perpendicular to the given equation
Firstly, we need to understand that for two equations to be perpendicular, then the product of their slopes must be equal to -1
Before we proceed to compare, we need to write the equation in the general form
The equation of the line written in the general form will be;
[tex]y\text{ = mx + b}[/tex]where m represents the slope and the term b represents the y-intercept
Now, let us proceed to write the equation in the standard form;
We have this as;
[tex]\begin{gathered} 3y\text{ = -2x + 12} \\ \\ y\text{ = -}\frac{2}{3}x\text{ + 4} \end{gathered}[/tex]Compared with the general form, we can see that the slope of this line is -2/3
Now let us get the slope of the line that would be perpendicular to it;
[tex]\begin{gathered} \frac{-2}{3}\times\text{ m = -1} \\ \\ m\text{ = }\frac{3}{2} \end{gathered}[/tex]Now, the equation perpendicular to what was given will have a slope of 3/2
Fortunately, all the options in the question have been written in the general form
The one with a slope of 3/2 is option C
[tex]y\text{ = }\frac{3}{2}x\text{ + 5}[/tex]some one please help me! quick!
Answers
m(4) = 110° due to the Transitive Property.
The Transitive Property states a that if a = b and b = c, then a = c.
m(3) + m(4) = 180 due to the definition of Supplementary Angles. All supplementary angles add up to 180°.
m(3) = 70° because 180 - 110 = 70.
Which of the following could be the end behavior of f(x) = -x2 – 4?
Answers
Answer:
f(x) = -∞ as x → ±∞
Explanation:
The given function is
f(x) = -x² - 4
To know the end behavior, let's replace x by a greater number and by a smaller number, so
If x = 100
f(x) = -100² - 4
f(x) = -10000 - 4
f(x) = -10004
If x = -100
f(x) = -(-100)² - 4
f(x) = -10000 - 4
f(x) = -10004
So, we can see that no matter if x is negative or positive, the value of f(x) will be positive. Then, we can say that the end behavior is
f(x) = -∞ as x → ±∞
The graph of y=-2is is transformed to becomey=+5. Which of the folloA The graph is translated Sunits left and 2 units up.& The graph is translated 2 units left and Sunits ups.Oc.thegraph is mamiandumits left and sumits chosam.OD The graph is translated Sunits right and 2 units dow
Answers
Given the following function:
[tex]y=\sqrt{x-2}[/tex]notice that the transformation:
[tex]y=\sqrt{x}+5[/tex]can be written like this:
[tex]y=\sqrt{(x+2)-2}+5[/tex]first, the +2 means that the graph moves 2 units left, and the +5 makes the graph move 5 units up.
A person tosses a coin 14 times. In how many ways can he get 10 heads?
Answers
HELP NEEDED ASAP PLS
Answers
The expression in the simplest form is -9x/10 + (5).
What is termed as the simplification?Simplify simply means making something easier to understand. Simply or simplification in mathematics refers to reducing an expression / fraction / problem to a simpler form. It simplifies the problem by calculating and solving it.
We can —
Simplify fractions by removing all common factors from the numerator and denominator as well as composing the fraction in its simplest form.By grouping as well as combining similar terms, you can simplify mathematical expressions. This makes this same expression simple to understand and solve.For the given equation;
= (-3x/5 - 7) - (-12 + 3x/10)
open the parenthesis;
= -3x/5 - 7 + 12 - 3x/10
Bring the variable part together.
= -3x/5 - 3x/10 - 7 + 12
Add variables and constant separately.
= -9x/10 + 5
Thus, the simplest form of the given expression is found as -9x/10 + 5.
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hello thank you for viewing my question I seem to be stuck on this problem can you please help thank you
Answers
We have 9 boy kittens and 6 girl kittens, a total of 15 kittens.
9 cats will be selected and we have to calculate the probability that 5 boy kitttens and 4 girl kittens are chosen.
We could have modeled as a binomial experiment, but the probability of choosing a boy kitten is not constant after each selection. Then, we have to select an alternative method.
We can think of it of a combinatorial problem.
In this case, it is a combination problem, as the order of selection does not matter and each kitten is equivalent within its category.
Repetition is not allowed: a kitten selected can not be selected again.
We can start finding all the possible combinations for 9 kittens out of the total 15 kittens:
[tex]C(15,9)=\frac{15!}{9!(15-9)!}=\frac{15!}{9!6!}=5005[/tex]The probability of selecting 5 boys and 4 girls will be the relation between the outcomes where there are 5 boys and 4 girls and the total number of outcomes we have just calculated.
Then, we can now calculate how many combinations of 9 kittens have 5 boys and 4 girls as a product of two combinations: the combinations for the boys C(9;5) and the combinations for the girls C(6;4).
We can calculate this as:
[tex]\begin{gathered} C(9,5)=\frac{9!}{5!4!}=126 \\ C(6,4)=\frac{6!}{4!2!}=15 \\ =>C(9,5)*C(6,4)=126*15=1890 \end{gathered}[/tex]We can now calculate the probability as the ratio of combinations 1890/5005:
[tex]p=\frac{1890}{5005}\approx0.378[/tex]Answer: the probability is 0.378.
in one year, a town recorded a total of 79 days it did not rain, how many days did it rain
Answers
Answer:
286
Step-by-step explanation:
there are 365 in a year
365-79
286
RANGE AND DOMAIN. GRAPSWhat is the Range of this Relation:{(3,0), (-2,6), (-1,4), (-2,0), (1,5)}
Answers
Given the relation:
[tex]\mleft\{\mleft(3,0\mright),(-2,6),(-1,4),(-2,0),(1,5)\mright\}[/tex]The range of the relation can be thought of as the set of y-coordinates of a point (x, y). That is, as every second number of the ordered pairs. Additionally, the set should be ordered, and should not contain repeated values. This set is:
[tex]Range=\mleft\lbrace0,4,5,6\mright\rbrace[/tex]A total of 240 people drove to a meeting. Of those peoplewho attended the meeting, 80% drove there. How manypeople attended the meeting?
Answers
The total number of people that drove to the meeting is 240
80% drove to the meeting
Let the total number of people who attended the meeting be x
Using the percentage and whole relationship
Part = percentage x whole
whole = x
part = 240
percentage = 80%
240 = 80/100 * x
240 = 0.8x
Divide both sides by 0.8
240/0.8 = 0.8x/0.8
x = 300
The total number of people that attended the meeting is 300
If Mary fails her classes then she cannot graduate
Answers
Write the correct equation for the following statement.
You decide to rent a limo for prom. The rate is $250 plus $6 per mile
traveled. Write an equation to calculate your total cost (c) at the end of
the evening for a given number of miles (m).
250+6m
If you travel 45 miles what will be your total bill at the end
of the evening?
Answers
Answer:
Easy;
Substitute m (miles) for 45.
250+6(45)
(6 dollars per mile, times 45 miles, plus the 250 flat rate)
250+270
520
So you would be charged 520 dollars total at the end of the evening.
Hope this helped!
Answer:
520
Step-by-step explanation:
so first you would multiply 6 by 45 which is 270 then add 250 which is 520
hope this helped, have a great day