An expression that correctly sets up the quadratic formula include the following: C. [tex]x = \frac{-(-2)\; \pm \;\sqrt{(-2)^2 - 4(1)(4)}}{2(1)}[/tex]
What is a quadratic equation?In Mathematics and Geometry, a quadratic equation can be defined as a mathematical expression that can be used to define and represent the relationship that exists between two or more variable on a graph.
In Mathematics, the standard form of a quadratic equation is represented by the following equation;
ax² + bx + c = 0
Mathematically, the quadratic formula is represented by this mathematical equation:
[tex]x = \frac{-b\; \pm \;\sqrt{b^2 - 4ac}}{2a}[/tex]
For the given quadratic equation x² + 1 =2x-3, we have:
x² - 2x + 1 + 3 =0
x² - 2x + 4 =0
[tex]x = \frac{-(-2)\; \pm \;\sqrt{(-2)^2 - 4(1)(4)}}{2(1)}[/tex]
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URGENT!! ILL GIVE BRAINLIEST! AND 100 POINTS
Answer choices
Y=50 + 0.30x
Y=30+ 0.50x
1000
30
800
200
Blank blank blank blank blank
The y-intercept represents the base price of $200 for airfare from NYC.
The slope represent a cost of $0.30 cents per mile traveled.
According to the equation given, someone who traveled 2000 miles from NYC would pay $800 for their fare.
According to the equation given, someone who paid $500 for airfare from NYC would have traveled 1000 miles.
If the base cost for airfare changed to $50 and the cost per mile is unchanged, the new equation would be y = 50 + 0.30x.
What is the slope-intercept form?In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical equation;
y = mx + c
Where:
m represents the slope or rate of change.x and y are the points.c represents the y-intercept or initial value.Based on the information provided about this trip, a linear equation that models the situation is given by;
y = mx + c
y = 0.30x + 200
When x = 2000, the price of airfare (y) is given by;
y = 0.30(2000) + 200 = $800.
When y = 500, the distance traveled (x) is given by;
500 = 0.30x + 200
300 = 0.30x
x = 1000 miles.
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Elephant and Piggy have 56 books to give away to different
schools across America. Each school will get 7 books. Which of the
following equations will help them figure out how many schools, s,
they can give books to?
A. s ÷ 7 = 56
B. 56 + 7 = s
C. 56 x 7 = s
D.
7 xs = 56
The number of schools that can get the book is obtained using the formula
s = 56 ÷ 7
How to find the number of schoolsInformation form the problem
Elephant and Piggy have 56 books to give away to differentschools across
Each school will get 7 booksTo find the number of schools, s; that will get the book we use the formula
s = number of books / how many books each school will get
substituting into the formula
s = 56 / 7
s = 56 ÷ 7
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What is the surface area?
5 ft
6 ft
5 ft
10 ft
4 ft
square feet
The total surface area of the prism is 152 ft².
What is the total surface area of the prism?
The total surface area of the prism is calculated by applying the formula for total surface area of prism.
S.A = bh + (s₁ + s₂ + s₃)L
where;
b is the base of the triangleh is the height of the triangles₁ is the first triangular faces₂ is the second triangular faces₃ is the third triangular faceL is the length of the prismThe surface area of the prism is calculated as;
S.A = 6 ft (4 ft) + (6 ft + 5 ft+ 5 ft) x 8 ft
S.A = 24 ft² + 128 ft²
S.A = 152 ft²
Thus, the surface area of the prism is calculated using the formula for surface of right prism.
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if lauras account balance has gone from -30 to -45, what has hapened to her debt
Answer:
Laura's debt has increased by $15, as her account balance has gone from -$30 to -$45. This means that she owes $15 more than what she owed before. A negative account balance indicates that Laura owes money to someone or a company, and the increase in the negative balance implies that her debt has become more significant. It is essential for Laura to keep track of her account and try to improve her financial situation to avoid accumulating debt further.
A composite figure is represented in the image.
A six-sided composite figure. A vertical line on the left is labeled 4 meters. The base is labeled 9 meters. There is a small portion from the vertical line that is parallel to the base that is labeled 3 meters. This portion leads to two segments that come to a point, and from that point, there is a height of 3 meters labeled.
What is the total area of the figure?
a: 75 m2
b: 63 m2
c: 61.5 m2
d: 45 m2
Question 13 (1 point)
Consider the functions f(x) = 3(x + 7)(x - 5) and
g(x)= x + 2x + 35. What are the coordinates of
the vertex for the function with the greatest positive
x-intercept?
Enter the correct answer in the boxes.
Blank 1:
Blank 2:
The vertex of f(x) is ( 1, - 108) and vertex of g(x) is (1, 36).
For the given functions are;
f(x) = 3(x + 7)(x - 5)
g(x)= x² + 2x + 35
Now proceed,
f(x) = 3(x + 7)(x - 5)
= 3x² - 15x + 21x - 105
= 3x² - 6x - 105
= 3(x² - 2x ) - 105
= 3(x² - 2x + 1 - 1 ) - 105
= 3(x² - 2x + 1 ) - 108
= 3(x- 1)² - 108
Since for a function p(x) = a(x-h)²+k the vertex be (h, k)
Therefore vertex of f(x) be ( 1, - 108)
Now proceed
g(x) = x² + 2x + 35
= x² + 2x - 1 + 1 + 35
= (x-1)² + 36
Similarly vertex of g(x) is (1, 36)
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3.2x-1.8y+7.7=0
Need help solving
Answer:
y = 1.78x + 4.28
Step-by-step explanation:
first isolate y
1.8y = 3.2x + 7.7
now that y is isolated, we can divide out the 1.8
y = 1.78x + 4.28
Answer:
[tex]y=\dfrac{16}{9}x + \dfrac{77}{18}[/tex]
Step-by-step explanation:
To solve for y in this equation, we need to isolate the y term on one side, then multiply by the reciprocal of its coefficient. Remember that any number multiplied by its reciprocal is 1.
3.2x - 1.8y + 7.7 = 0
↓ add 1.8y to both sides
3.2x + 7.7 = 1.8y
↓ represent the decimals as fractions
[tex]\dfrac{16}{5}x + \dfrac{77}{10} = \dfrac{9}{5}y[/tex]
↓ multiply by the reciprocal of y's coefficient: [tex]\frac{5}{9}[/tex]
[tex]\dfrac{5}{9} \cdot \left(\dfrac{16}{5}x + \dfrac{77}{10}\right) = \left(\dfrac{9}{5}y\right) \cdot \dfrac{5}{9}[/tex]
↓ simplify
[tex]\boxed{\dfrac{16}{9}x + \dfrac{77}{18} = y}[/tex]
Suppose the following data set represents the running times for the 15 top-grossing movies rated PG or PG-13. Find the five-number summary. Report the five-number summary in the following order: Min, Q1, Median (Q2), Q3, Max.
110,121,90,108,108,106,91,128,162,90,113,120,120,102,129
The five-number summary for the given data set is Min = 90, Q1 = 102, Median (Q2) = 108, Q3 = 128, and Max = 162. These values were found by arranging the data set in order and finding the minimum, maximum, median, and quartiles.
To find the five-number summary for the given data set, we need to find the minimum, maximum, median (Q2), and the first and third quartiles (Q1 and Q3). We can do this by first arranging the data set in order
90, 90, 91, 102, 106, 108, 108, 110, 113, 120, 120, 121, 128, 129, 162
Min = 90 (the smallest value in the data set)
Q1 = 102 (the median of the lower half of the data set)
Median (Q2) = 108 (the middle value of the data set)
Q3 = 128 (the median of the upper half of the data set)
Max = 162 (the largest value in the data set)
Therefore, the five-number summary for the given data set in order is 90, 102, 108, 128, 162.
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Find the domain of the function represented by the list of ordered pairs below. {(6,7),(−5,−11),(−7,−10),(−2,8)}.
Evaluate the expression. (7 − 3)!
Answer: The expression (7 − 3) can be simplified as follows:
(7 − 3) = 4
Therefore, the value of the expression (7 − 3) is 4.
Answer:
Step-by-step explanation:
3x+y=1/3
2x-3y=8/3
Solve the system of linear equation using any method. EXPLAIN your choice of method. PLEASEE
Answer:
x = 1/3; y = -2/3
Step-by-step explanation:
We can solve using substitution by isolating y in the first equation and plug in this y for y in the second equation. I chose this method because it's very simply to isolate the y and only requires a simple subtraction:
[tex]3x+y=1/3\\y=-3x+1/3\\\\2x-3(-3x+1/3)=8/3\\2x+9x-1=8/3\\11x-1=8/3\\11x=11/3\\x=1/3[/tex]
Now, we can plug in 1/3 for x in any of the two equations. Let's try the first original equation:
[tex]3(1/3)+y=1/3\\1+y=1/3\\y=-2/3[/tex]
Finally, we can check our answers by plugging in 1/3 for x and -2/3 for y into to both equations and see that we get 1/3 and 8/3 respectively:;
First equation:
[tex]3(1/3)-2/3=1/3\\1-2/3=1/3\\1/3=1/3[/tex]
Second equation:
[tex]2(1/3)-3(-2/3)=8/3\\2/3+2=8/3\\8/3=8/3[/tex]
A couple plans to retire in 35 years. At that time, they would like to have enough money in an account so that they can receive a $6,000 every month end for the next 25 years. The account earns 8% APR compounded monthly and will continue to do so until there is a zero balance in the account. To achieve this goal, how much money does the couple need to have in this account by the time they retire?
The amount (present value) that the couple needs to have in this retirement account by the time they retire in 35 years to enable them withdraw $6,000 monthly for 25 years is $777,387.14.
How is the present value determined?The amount in 35 years' time when the couple retire that they should have can be described as the present value (in 35 years).
Based on the above conclusion, the present value can be determined using an online finance calculator as follows:
With the monthly withdrawal of $6,000 and compounded interest of 8% APR monthly, the future value of the account in 60 years' time will be $0.
N (# of periods) = 300 months (25 years x 12)
I/Y (Interest per year) = 8%
PMT (Periodic Payment) = $-6,000
FV (Future Value) = $0
Results:
Present Value in 35 years (PV) = $777,387.14
Sum of all periodic payments = $-1,800,000 ($-6,000 x 300 months)
Total Interest = $1,022,612.86
Thus, the couple should save up to $777,387.14 in 35 years' time when they retire to achieve their goal.
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exponential function passes through (1,10) and (4,80)
Answer: f(x)=2^x+5
Step-by-step explanation:
math
At a factory that produces pistons for cars, Machine 1 produced 306 satisfactory pistons and 204 unsatisfactory pistons today. Machine 2 produced 385 satisfactory pistons and 115 unsatisfactory pistons today. Suppose that one piston from Machine 1 and one piston from Machine 2 are chosen at random from today's batch. What is the probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory ?
Answer:
The probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory is 308/1700.
Step-by-step explanation:
The probability of selecting an unsatisfactory piston from Machine 1 is 204/510, because there are a total of 204 + 306 = 510 pistons produced by Machine 1, and 204 of them are unsatisfactory.
The probability of selecting a satisfactory piston from Machine 2 is 385/500, because there are a total of 385 + 115 = 500 pistons produced by Machine 2, and 385 of them are satisfactory.
To find the probability that both events occur, we multiply the probabilities:
P(unsatisfactory from Machine 1 and satisfactory from Machine 2) = (204/510) * (385/500)
Simplifying the expression, we get:
P(unsatisfactory from Machine 1 and satisfactory from Machine 2) = (4/17) * (77/100)
P(unsatisfactory from Machine 1 and satisfactory from Machine 2) = 308/1700
Therefore, the probability that the piston chosen from Machine 1 is unsatisfactory and the piston chosen from Machine 2 is satisfactory is 308/1700.
help answer this pls
Answer:
it is 17.5
Step-by-step explanation:
you add 6.2 and 11.3 equal 17.5
Answer:
≈ 681.38 ft^2 when pi≈ 3.14
Step-by-step explanation:
2(3.14)(6.2^2)+(3.14)(12.4)(11.3)
241.4032+439.9768≈ 681.38
Two identical trains, each with 31 cars, are traveling in opposite directions. When car Number 19 of one train is opposite car Number 19 of the other, which car is opposite car Number 12?
Car 12 of Train B is also 12 cars away from Car 19 on Train B.
How to explain the informationSince each train boasts 31 cars, we can ascertain the total amount of vehicles between Car 19 and Car 12 on Train A:
31 - 19 = 12
Thus, Car 12 on Train A is a dozen units distant from Car 19 on Train A.
Nevertheless, Train B is furthermore moving in an inverring direction and has its exclusive set of automobiles between Car 19 and Car 12. We comprehend that the matching figure of cars must be amongst Car 19 and Car 12 on Train B as with Train A.
In essence, Car 12 of Train B is also 12 cars away from Car 19 on Train B.
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A worker is connecting a cable from the roof top of a school to a fence pole 7 ft away. The pole is 10 ft high. He uses 25 ft of cable to reach from the rooftop to the fence pole. How tall is the school? Show your steps taken to arrive at your answer.
The height of the school is given as follows:
34 ft.
What is the Pythagorean Theorem?The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
The theorem is expressed as follows:
c² = a² + b².
In which:
c is the length of the hypotenuse.a and b are the lengths of the other two sides (the legs) of the right-angled triangle.The height of the school for this problem is given as follows:
h = x + 10 ft.
In which segment x is one of the sides of a right triangle, in which the other side is of 7 ft and the hypotenuse is of 25 ft, hence:
x² + 7² = 25²
x = sqrt(25² - 7²)
x = 24 ft.
Hence the height of the school is of:
24 ft + 10 ft = 34 ft.
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the correct answer.
Which inequality represents the values of that ensure triangle ABC exists?
A
2x+4
B
O D.
18
OA.
<< 1
OB. -< < ¹
O c. 1 < x < 5
6x
2 < < 6
Using the triangular inequalities we can get:
7/4 < x < 11/2
The image of the triangle is in the image at the end.
Which inequality represents the values of that ensure triangle ABC exists?A triangle with sides A, B, and C must meet the triangular inequality, it says that the sum of any two sides is larger than the other side.
Now, see the triangle attached at the end, the triangular inequalities say that:
18 + 6x > 2x + 4
18 + 2x + 4 > 6x
6x + 2x + 4 > 18
Now simplify these, for each one we will get:
4x > -14 -----> x > -7/2
22 > 4x -----> 11/2 > x
8x > 14 -----> x > 7/4
Using the second two we can get:
7/4 < x < 11/2
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Emmitt party supply is known for their long lasting helium balloons Emmitt kept track of the number of balloons in each order he received yesterday
Answer: It's kind of hard to answer a question you don't have all the parts too. :(
Step-by-step explanation:
For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or
Assignment Scoring
Your last submission is used for your score.
8. [0/1 Points) DETAILS PREVIOUS ANSWERS
TANFIN12 5.3.033.
Andrea, a self-employed individual, wishes to accumulate a retirement fund of $500,000. How much should she deposit each month into her retirement account, which pays interest at a rate of
2.5%/year compounded monthly, to reach her goal upon retirement 45 years from now? (Round your answer to the nearest cent.)
The density of the metal is determined as 6.1 g / cm³.
We have,
The density of the metal is defined as the ratio of the mass per unit volume of the metal.
Mathematically, the formula for density is given as;
ρ = m / V
where;
m is the mass of the metal
V is the volume of the metal
The density of the metal is calculated as follows;
ρ = ( 0.47 kg x 1000 g/kg ) / ( 77 cm³ )
ρ = 6.1 g / cm³
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complete question:
Or this assignment, you submit answers by question parts. The number of submissions remaining for each
ssignment Scoring
our last submission is used for your score.
DETAILS
………….
Compute the density in g/cm³ of a piece of metal that has a mass of 0.470 kg and a volume of 77 cm³.
X g/cm³
Enter a number.
Need Help?
Submit Answer
PREVIOUS ANSWERS
45°F
Mostly cloud
SHIPPS15 1.6.E.019.
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HELP EASY ALGEBRA 1- The equation y = 2x2 – 4x – 3 models the cross-section of a sculpture that sits in the water, where x is horizontal distance, and y is height above sea level. At what two x-values is the sculpture at sea-level?
A. 1 ± 10−−√
B. 2 ± 10√4
C. 1 ± 10√2
D. 4 ± 210−−√
The two values of x of the quadratic equation at which the sculpture is at sea level is x = 1 ± ( 1/2 )√10
Given data ,
Let the quadratic equation be represented as A
Now , the value of A is
y = 2x² - 4x - 3 = 0
At sea level , y = 0
And , roots of the quadratic equations are
x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )
On simplifying , we get
x = [ 4 ± √ ( -4 )² - 4 ( 2 ) ( -3 ) ] / 2 ( 2 )
x = [ 4 ± √ ( 16 + 24 ) ] / 4
x = ( 4 ± √40 ) / 4
On simplifying the equation , we get
x = ( 4 ± 2√10 ) / 4
x = 1 ± ( 1/2 )√10
Hence , the values of x at which the sculpture is at sea level is
x = 1 ± ( 1/2 )√10
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Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several models and compare the values of R2.
The table image below shows the population of a city (in millions) in each year during the period 1990 - 1995. Using the number of years since 1990 as the independent variable, find the regression equation of the best model.
y = 1.08 e0.228 x
y = 1.27 x0.550
y = 0.05 x2 + 0.27 x + 1.06
y = 0.930 + 0.454 x
Answer:
Step-by-step explanation:, in this function, the scatter points follow this function. Then the correct option is C.
What is a function?
The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.
Construct a scatterplot and identify the mathematical model that best fits the data.
Assume that the model is to be used only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models.
Use a calculator or computer to obtain the regression equation of the model that best fits the data.
You may need to fit several models and compare the values of R2.
A. , in this function, the scatter points do not follow this function.
B. , in this function, the scatter points do not follow this function.
C. , in this function, the scatter points follow this function. Because the best fits.
D. , in this function, the scatter points do not follow this function.
7.6.AP-6
Find the surface area of the prism.
The surface area is
(Type an integer or a decimal.)
4 m
3.7 m-
3m
4 m
3.2 m
The Total surface area of the given prism is: 46.3 sq.m
What is the surface area of the prism?The surface area of the prism is gotten by finding the areas of all surfaces and adding up to get the total surface area. Thus:
We know that formula to find the area of a triangle is:
Area of triangle = ¹/₂*base*height
Area of rectangle = length * width
Thus:
Total surface area = 2(¹/₂* 3 * 3.7) + 2(4 * 3.2) + (3 * 3.2)
Total surface area = 11.1 + 25.6 + 9.6
Total surface area = 46.3 sq.m
Thus, that is the total surface area of the given prism with dimensions
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4
Based on the March expense statement, what proportion of Maria's total expenses are for her car?
A. Less than one quarter.
B. More than a quarter but less than half.
O C. More than three-quarters.
D. More than half but less than three-quarters.
Auto
Check Number 87
Credit Card March)
Clothing
Marla's Expense 1
Get Card Mash
Food
Credit Card Mesh &
Sends Card March 11
Petal food
Cash Paya
Para Coch
Total
Based on the March expense statement, the proportion of Maria's total expenses that are for her car is D. More than half but less than three-quarters.
What is the proportion?The proportion refers to a portion or part of a whole number, value, or expression.
Proportions, which are ratios between two values, are depicted in decimals, fractions, or percentages.
The total expenses for March = $507.59
Auto expenses for March = $290.02
Proportion of auto expenses to the total expenses =0.57 ($290.02 ÷ $507.59)
One-half of $507.59 = 0.50 or $253.795)
Three-quarters of $507.59 = 0.75 or $380.69
Since $290.02 is more than $253.795 but less than $380.69, Option D is correct.
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If an object lies below the horizontal plane and behind the vertical plane, what is its location?
A.
2nd Quadrant
B.
1st Quadrant
C.
4th Quadrant
D.
3rd Quadrant
E.
on the reference line
Answer:
third quadrant
its position with respect to reference planes will be behind Vertical Plane and below the Horizontal Plane.
The given figure shows different positions and their respective views
SQUARES The area of a square y can be modeled by the function y = x², where x is
the side length of the square. The perimeter of a square can be modeled by the
function y = 4x.
a. Solve the system of equations algebraically.
b. If the area of a square in square units is equal to the perimeter of the square in
units, what is the side length of the square? What are the area and perimeter of
the square?
What is the equation, in point-slope form, of the line
that is perpendicular to the given line and passes
through the point (-4,-3)?
Oy+3=-4(x+4)
Oy+3= (x+4)
Oy+ 3 = (x+4)
Oy+3=4(x+4)
The equation of the line in point-slope form is y + 3 = 1/4(x + 4).
What is an equation of a line?The equation of a line is given by:
y = mx + c
where m is the slope of the line and c is the y-intercept.
Example:
The slope of the line y = 2x + 3 is 2.
The slope of a line that passes through (1, 2) and (2, 3) is 1.
We have,
The given line passes through the points (-1,1) and (0,-3).
The slope of the line passing through these points can be calculated as:
slope = (y2 - y1) / (x2 - x1)
= (-3 - 1) / (0 - (-1))
= -4 / 1
= -4
Since we are looking for a line that is perpendicular to this line, the slope of the new line will be the negative reciprocal of -4, which is 1/4.
Using the point-slope form of a linear equation, we can write the equation of the new line as:
y - y1 = m(x - x1)
where (x1, y1) is the point (-4,-3) and m is the slope 1/4.
Plugging in the values.
y - (-3) = 1/4(x - (-4))
Simplifying and rearranging.
y + 3 = 1/4(x + 4)
Therefore,
The equation of the line in point-slope form is y + 3 = 1/4(x + 4).
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Use the compound interest formula to determine the final value of the given amount
The final value of the given amount compounded is $1518.69
Compound interest is the interest earned on the principal and the interest previously accumulated. It is given by
[tex]A=P(1+r/n)^n^t[/tex]
where P = Principal, r = annual rate of interest, n = number of times interest is compounded per year & t = time in years.
The given principal is $800 for 11 years & annual interest rate is 6%.
To find the amount compounded annually at 6% for 11 years substituting the given values in the above formula i.e.
Amount = [tex]800(1+0.06)^1^1[/tex]
Amount = $1518.69
Hence, the Amount is equal to $1518.69.
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What is the rate of return when 35 shares of Stock A, purchased for $20/share, are sold for $815?
Answer:
Step-by-step explanation:
To calculate the rate of return when 35 shares of Stock A, purchased for $20/share, are sold for $815, you can use the following formula1:
Rate of Return = (Proceeds - Cost - Commission) / Cost
where Proceeds is the amount received from selling the shares, Cost is the amount paid for the shares, and Commission is the commission paid on the sale1. Plugging in the values, we get:
Rate of Return = (815 - (35 * 20) - 6) / (35 * 20) = 0.2875
Multiplying by 100 to convert to a percentage, we get a rate of return of 28.75%1.
i need help with the last two i cant get it
a) There are no values of x for which h'(x) is undefined.
b) The critical numbers of h(x) = sin²(x) + cos(x) in the domain 0 < x < 2π are x = kπ, x = π/3 + 2πn, and x = 5π/3 + 2πn, where k and n are integers.
a) To find the values of c for which h'(c) = 0 or is undefined, we first need to find the derivative of h(x):
h'(x) = 2sin(x)cos(x) - sin(x)
Now we can set h'(x) equal to 0 and solve for x:
2sin(x)cos(x) - sin(x) = 0
sin(x)(2cos(x) - 1) = 0
This equation is satisfied when sin(x) = 0 or 2cos(x) - 1 = 0. The first equation has solutions x = kπ, where k is an integer. The second equation has solutions x = π/3 + 2πn or x = 5π/3 + 2πn, where n is an integer.
Next, we need to check if there are any values of x for which h'(x) is undefined. Since h'(x) is a combination of sin(x) and cos(x), it is defined for all values of x in the given domain.
b) The critical numbers of h(x) are the values of x at which h'(x) = 0 or h'(x) is undefined. From part (a), we have the solutions x = kπ, x = π/3 + 2πn, and x = 5π/3 + 2πn, where k and n are integers. These are the critical numbers of h(x) in the given domain.
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