Answers
Answer:
-20
Step-by-step explanation:
[tex]\frac{5}{3}x +\frac{1}{3} x=13\frac{1}{3}+\frac{8}{3}x\\\\\frac{6}{3} x = 13 \frac{1}{3} +\frac{8}{3} x\\\\\frac{-40}{3} =\frac{2}{3} x\\\\\frac{3}{2} *(\frac{-40}{3} )\\\\\frac{3}{2} *\frac{2}{3} x\\\\-20 = x[/tex]
Related Questions
PLEASE Help me answer these 2 math questions!!!
Answers
1. The equation for the function is defined as follows: g(x) = (1/3)^x - 2.
2. The range of the function is given as follows: The set of real numbers less than -5.
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.For item 1, the function has an horizontal asymptote at y = -2, hence it is defined as follows:
y = a(1/3)^x - 2.
When x = 0, y = -1, hence the parameter a is obtained as follows:
-1 = a - 2
a = 1.
Thus the function is:
g(x) = (1/3)^x - 2.
For item 2, we have that the function is:
Reflected over the y-axis, due to the negative sign of a.Has an horizontal asymptote at y = -5.Hence the range of the function is given as follows:
The set of real numbers less than -5.
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100 Points! Multiple choice algebra questions. For questions 3 and 4, use f(x)=x+5 and g(x)=2x.
Find (f+g) (x).
Find (f·g) (x).
Photo attached. Thank you!
Answers
3. The value of the function (f+g)(x) is option A: 3x+5. 4. The value of: (f·g)(x) is Option C: 2x² + 10x.
What is sum and product of function?The function that results from summing the results of the two functions for a specific input value x is known as the sum of two functions (f+g)(x). To put it another way, we just add the function values at each x-axis point. The function that results from multiplying the outputs of the two functions for an input value x is known as the product of two functions (fg)(x). In other words, we multiply the values of the function at each x-axis position. Two functions can be combined or multiplied to create new functions, each of which has a unique set of attributes.
Given that, f(x)=x+5 and g(x)=2x.
3. The value of (f+g)(x) is:
f(x + g) (x)= f(x) + g(x) = (x+5) + 2x = 3x+5
4. The value of:
(f·g)(x) = f(x) · g(x) = (x+5) · 2x = 2x² + 10x
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To the nearest millimeter, a cell phone is 135 mm long and 69 mm wide. What is the ratio of the width to the length?
The ratio of the width to the length is (Type the ratio as a simplified fraction.)
Answers
The ratio of the width to the length of the cell phone is 23/65.
What is ratio?
Ratio is the quantitative relation between two amounts showing the number of times one value contains or is contained within the other.
To find the ratio of the width to the length of the cell phone, we use the formula below.
Formula:
n = W/L............................. Equation 1Where:
n = Ratio of width to length of the cell phoneW = Width of the cell phoneL = Length of the cell phoneFrom the question,
Given:
W = 69 mmL = 135 mmSubstitute these values into equation 1
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Uncle Fred gives his nephew, Jack, and niece, Jill, £60 between them every year
at Christmas. He splits it between them in the ratio of their ages.
(a) The first time he does this Jack is 1 and Jill is 3. How much does Jill
receive?
[1 mark]
(b) How much does Jack receive the following Christmas?
[1 mark]
(c) How old will Jack be when he receives £25 from Uncle Fred at Christmas?
Answers
a) Jill receives £45
b) Jack receives £20 the following Christmas
c) Jack will be 5/4 years old, which is equivalent to 1 year and 3 months when he receives £25 from Uncle Fred.
Explain the term years
Years are a unit of time measurement used to quantify the duration of one complete orbit of the Earth around the sun. A year consists of 365 days, except in a leap year when an extra day is added. The concept of a year is used in various fields, including astronomy, geology, and history.
According to the given information
(a) Let's first find the total ratio of their ages:
1 + 3 = 4
So Jack's share will be:
1/4 x £60 = £15
And Jill's share will be:
3/4 x £60 = £45
Therefore, Jill receives £45.
(b) The next Christmas, Jack will be 2 and Jill will be 4. We can use the same ratio to find Jack's share:
2/6 x £60 = £20
So Jack receives £20.
(c) Let x be the age of Jack when he receives £25 from Uncle Fred. We know that:
1/4 x £60 = £25
Multiplying both sides by 4/60, we get:x = 5/4
So Jack will be 5/4 years old, which is equivalent to 1 year and 3 months, when he receives £25 from Uncle Fred.
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Dilate figure XYZ by a scale factor of 1/4 X(-2,4) Y(-4,-4) Z(4,2)
Answers
Therefore , the solution of the given problem of expressions comes out to be points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).
What is expression?Instead of using random estimates, shifting variable numbers should be employed instead, which can be growing, diminishing, or blocking. They could only help one another by transferring items like tools, knowledge, or solutions to issues. The explanations, components, or mathematical justifications for strategies like expanded argumentation, debunking, and blending may be included in the explanation of the reality equation.
Here,
Figure XYZ will be scaled down by 1/4, with the centres being X(-2,4), Y(-4,4), and Z(4,2)
=> Old_x - Center_x - Scale_factor * New_x + Center_x
=> Scale factor * (Old y - Centre y) + Centre y = New y
Regarding X:
=> New_x = 1/4 * (-2 - (-2)) + (-2) = -2
=> New_y = 1/4 * (4 - 4) + 4 = 4
Therefore, X'(-2,4) is the image of point X after dilation.
Regarding Y:
=> New_x = 1/4 * (-4 - (-2)) + (-2) = -3
=> New_y = 1/4 * (-4 - 4) + 4 = -1
Therefore, Y'(-3,-1) is the image of point Y following dilation.
Regarding Z:
=> New_x = 1/4 * (4 - (-2)) + (-2) = 0
=> New_y = 1/4 * (2 - 4) + 4 = 3
Therefore, Z'(0,3) is the image of point Z after dilation.
As a result, the image points for the dilated figure XYZ with the centre points X(-2,4), Y(-4,4), and Z(4,2) would be X'(-2,4), Y'(-3,-1), and Z'(0,3).
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which equation can be used to find the value of x x=60 + 40
Answers
Answer:
x = 50
Step-by-step explanation:
2x = 60+40
simply 60 + 40 to 100
so 2x = 100
and then divide 2 to get it to the other side.
like this = x = 100/2
then divide 100 by 2 and get 50
so x=50
you want to hire a band for a school dance. The live band charges $75 to play for three hours and each student will pay a $2.00 admission prices, p. a, how much money will you make if 100 students attend the dance
b, how much money will you make if 100 students attend the dance
c, how many students would need to attend the dance for you to “break even” after you aging the band?
Answers
Answer:
38 stduentstudents
Step-by-step explanation:
2(100)=$200, if 100 students attend.
38(2)=$76
Breaking even means getting back the same amount you spent. The exact answer would be 37.5, but you can't have half a student.
Hi I need help finding the degree measure of Radian on a triangle with hypotenuse =7 and opposite =3
Answers
Answer:
24.6 degrees.
Step-by-step explanation:
To find the degree measure of the radians in a right triangle with hypotenuse = 7 and opposite = 3, we need to use trigonometric ratios. Since the opposite and hypotenuse are given, we can use the sine ratio.
sin(θ) = opposite/hypotenuse
sin(θ) = 3/7
Now we need to find the angle measure θ. We need to use the inverse sine or arcsine function to do this.
θ = sin^-1(3/7)
θ ≈ 0.429 radians
To find the degree measure, we must convert radians to degrees by multiplying by 180/π.
θ ≈ 0.429 x 180/π
θ ≈ 24.6 degrees
Therefore, the degree measure of the radians in the given triangle is approximately 24.6 degrees.
Chau paid 13.88 for a -pound bag of shrimp at one store. The following week, he paid 38.99 for a 5.46 -pound bag at another store.
Answers
The first bag has a better unit price, at $7.01 per pound compared to $7.13 per pound for the second bag. Based on the unit price, the first bag is a better buy.
Describe Algebra?Algebra is a branch of mathematics that deals with mathematical symbols and the rules for manipulating these symbols. It involves the use of variables, which are represented by letters or other symbols, to represent unknown quantities and to formulate and solve equations and inequalities.
The fundamental operations of algebra include addition, subtraction, multiplication, and division, which are used to manipulate the variables and simplify expressions. Algebra also involves the use of exponents, which are used to represent repeated multiplication, and logarithms, which are used to represent the inverse of exponents.
Algebra is used in a wide range of applications, including science, engineering, economics, and statistics, to model and analyze various phenomena. It is also used as a tool for problem-solving and decision-making, and it provides a powerful framework for reasoning and abstraction in many areas of mathematics and beyond.
To find the unit price, we divide the total price of each bag by its weight:
For the first bag:
Unit price = Total price / Weight = 13.88 / 1.98 = 7.01 dollars per pound
For the second bag:
Unit price = Total price / Weight = 38.99 / 5.46 = 7.13 dollars per pound
Therefore, the first bag has a better unit price, at $7.01 per pound compared to $7.13 per pound for the second bag.
Thus, based on the unit price, the first bag is a better buy.
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The complete question is:
Chau paid 13.88 for a 1.98- pound bag of shrimp at one store. The following week, he paid 38.99 for a 5.46 -pound bag at another store.
Find the unit price for each bag. Then state which bag is better buy based on the unit price.
Find the area of the regular polygon.
Answers
Answer:
This is a right angle
Step-by-step explanation:
There is a square inside of the triangle.
Anumeha knows the following information about a set of
20
2020 numbers:
9
99 numbers are a multiple of
3
33 but not a multiple of
4
44.
10
1010 numbers in total are a multiple of
3
33.
10
1010 numbers in total are a multiple of
4
44.
Can you help Anumeha organize the results into a two-way frequency table?
Answers
A
Step-by-step explanation:
There is 1 number that is a multiple of both 3 and 4.
9 numbers are a multiple of 4 and not 3.
9 numbers are a multiple of 3 and not 4.
1 number is not a multiple of 3 or 4.
Hope this helps!
A digital thermometer in Olivia's car says the temperature outside is –5°C. Which statement BEST describes the meaning of the value –5 in this context?
Answers
The value -5°C represents the temperature outside as measured by the digital thermometer in Olivia's car.
Which statement describes the meaning of the valueIn this context, the value -5 represents the temperature outside in Celsius degrees.
The minus sign indicates that the temperature is below freezing point. The Celsius scale is a temperature scale that uses the freezing point of water (0°C) and the boiling point of water (100°C) at standard atmospheric pressure as its reference points.
Thus, a temperature of -5°C means that it is five degrees Celsius below the freezing point of water.
The negative sign indicates that the temperature is below zero degrees Celsius, which is the freezing point of water.
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What is the lateral surface area
Answers
Answer:
A- 304.8 cm²
Step-by-step explanation:
Find the area for the 4 sides (excluding both the top and base).
(2(12×7.5))+(2(12×5.2)) = 302.8
Answer:
A. 304.8 cm²
Step-by-step explanation:
The rectangular prism has a total of 6 rectangular sides
~ two at the bottom and top both of equal dimensions 5.2 x 7.5
~ two at the front and back both of equal dimensions 12 x 7.5
~ two one on the left side and the other on the right side both of equal dimensions 12 x 5.2
The question is asking only for the lateral surface area. This means we ignore the top and bottom surfaces
For each of the other two pairs of rectangles, the surface area is nothing but the product of the dimensions for each rectangle
Therefore area of all the 4 rectangles is
2(5.2 x 7.5 + 12 x 5.2)
We multiply by 2 since there are 2 of each rectangular surface
2(5.2 x 7.5 + 12 x 5.2) = 304.8 cm² ANSWER
Find the indicated functional value for the ceiling function: f(−0.75)?
A. -1
B. 1
C. 2
D. 0
Answers
The ceiling function, denoted by ⌈x⌉, gives the smallest integer that is greater than or equal to x. Therefore, ⌈-0.75⌉ is the smallest integer that is greater than or equal to -0.75.
Since -1 is the smallest integer that is greater than or equal to -0.75, we have:
⌈-0.75⌉ = -1
Therefore, the functional value for the ceiling function at -0.75 is -1.
The answer is option A.
Altina Restaurant Flexible Budget for November 2010
A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?
b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?
d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?
e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?
f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?
g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?
Answers
Walton's actual check average is $9.52
The actual food cost is lower than the flexible budget by $5020
What is Net Income?Net income, considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.
The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.
Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.
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Use the table, which shows the number of sofas sold at a furniture store over 5 months. The number of sofas sold in June is 597.
Furniture Store Sofa Sales
January 255
February 234
March 263
April 229
May 248
How does the median change with the new piece of data?
Answers
We know that with the new piece of data for the month of June the median is increased by 3.5 which is now 251.5.
What is the median?The median is the value that divides a data sample, a population, or a probability distribution's upper and lower halves in statistics and probability theory.
It could be referred to as "the middle" value for a data set.
A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it.
Arrange in ascending order:
229 234 248 255 263
When, odd terms are there then the middle term is the median:
Median: 248
New Median:
229 234 248 255 263 597
When there are even terms we will add the middle two terms and divide it by 2 as follows:
248+255/2
Median: 251.5
Median change: 251.5 - 248 = 3.5
Therefore, we know that with the new piece of data for the month of June the median is increased by 3.5 which is now 251.5.
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Jason is planning to surprise his wife with a trip to Turkey this summer. He had difficulty making hotel reservations during
tourist season, but managed to reserve a room for two weeks in a nice hotel in Cappadocia in central Turkey. From there, he
plans to rent a car to take him and his wife to see the sights. After making all of his hotel and rental car reservations, Jason
is surprised to see that the trip will cost much more than he anticipated. What change(s) should Jason make to his vacation
to lower the overall cost?
Answers
The changes that Jason should make are:
1. Plan a trip not during the tourist season.
2. In place of renting car, use transportation services of the country.
3. He should go to other places to find a nice hotel.
The solution has been obtained by using cost planning.
What is cost planning?
Estimating expenses, establishing an agreed-upon budget, and managing actual and projected expenditures in relation to that budget are all parts of cost planning and control.
The changes that Jason should make are:
1. Plan a trip not during the tourist season. This is because during the tourist season prices are high.
2. In place of renting car, use transportation services of the country. This is because the local transport will cost him less that the rental.
3. He should go to other places to find a nice hotel. This is because central Turkey is costly and he might find a nice hotel in other areas in less price.
Hence, the required solution has been obtained.
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A movie theater has a seating capacity of 257. The theater charges $5.00 for children, $7.00 for
students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket
sales was $ 1870, How many children, students, and adults attended?
Answers
The attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
What is arithmetic?
Arithmetic is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots.
Here, we have
Given:
Seating capacity = 257
Charges: Children = $5.00; Students = $7.00; Adults = $12.00
Total sales of ticket = $1870
A number of children, students, and adults were present in the theatre.
Let A, C, and S represent adults, children, and students respectively.
There are half as many adults as there are children; this means that
A = ½C
If the total seat capacity is 257, then
A + C + S = 257
Also, if the total sales of tickets are $1870, then
12A + 7S + 5C = 1870
So, we have two equations to be solved simultaneously.
A + C + S = 257 --- (1)
12A + 7S + 5C = 1860 --- (2)
Substitute ½C for A in (1) and (2)
½C + C + S = 257
Multiply both sides by 2
2(½C + C + S) = 2 * 257
C + 2C + 2S = 514
3C + 2S = 514 ----- (3)
12(½C) + 7S + 5C = 1870
6C + 7S + 5C ,= 1870
6C + 5C + 7S = 1870
11C + 7S = 1870 --- (4)
Make S the subject of the formula in (3)
2S = 514 - 3C
S = ½(514 - 3C)
S = 257 - 1.5C
Substituton 257 - 1.5C for S in (4)
11C + 7(257- 1.5C) = 1870
11C + 1799 - 10.5C = 1870
Collect like terms
11C - 10.5C = 1870 - 1799
0.5C = 71
Multiply both sides by 2
2 * 0.5C = 2 * 71
C = 142
Recall that
S = 257 - 1.5C
S = 257 - 1.5(142)
S = 257 - 213
S = 44
Also, recall that
A = ½C
A = ½ * 142
A = 71
Hence, the attendance at the movie theatre is;
Children = 142
Students = 44
Adults = 71
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Classify the solid.
Explain your reasoning.
Image below.
Answers
The solid displayed in the image is a trapezoidal prism.
What is a trapezoidal prism?A trapezoidal prism is a three-dimensional solid with two parallel trapezoids as its bases, and rectangular or parallelogram sides connecting them. The top and bottom faces are identical, and the side faces are parallelograms.
To classify the solid, look at its properties. The solid has two parallel trapezoids as its bases, and the side faces are parallelograms. Therefore, it is a prism.
Since the bases are not identical rectangles or squares, it is not a rectangular or square prism. However, since the bases are trapezoids, it is a trapezoidal prism.
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5
A line passes through the point (-4, -7) and has a slope of.
4
Write an equation in slope-intercept form for this line.
ロ=ロ
X
8
5
Answers
The equation of the line in slope-intercept form is:
y = 4x + 9
Write an equation in slope-intercept formThe slope-intercept form of the equation of a line is:
y = mx + b
where m is the slope of the line and b is the y-intercept (the point where the line crosses the y-axis).
In this case, we know that the line passes through the point (-4, -7) and has a slope of 4. So, we can plug in the values of x, y, and m into the slope-intercept form and solve for b:
-7 = 4(-4) + b
Simplifying the right side:
-7 = -16 + b
Adding 16 to both sides:
9 = b
So the y-intercept is 9. Therefore, the equation of the line in slope-intercept form is:
y = 4x + 9
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Is a triangle with sides of 5 meters, 12 meters, and 13 meters a right triangle? Explain/Show your work.
Answers
Answer:
[tex]\huge\boxed{\sf Yes.}[/tex]
Step-by-step explanation:
In a right angled triangle, the longest side is called hypotenuse.
So,
Hypotenuse = 13 m
The rest are:
Base = 5 m
Perpendicular = 12 m
Using Pythagoras Theorem to verify:
[tex](Hypotenuse)^2=(Base)^2+(Perpendicular)^2[/tex]
Put the given data
(13)² = (12)² + (5)²
169 = 144 + 25
169 = 169Since, both left hand side and right hand side are equal, this means the triangle is a right-angled triangle.
[tex]\rule[225]{225}{2}[/tex]
NO LINKS!! URGENT HELP PLEASE!!!
Express the statement as an inequality Part 4a^2
Answers
The correct answer is B) |x| > 6 for the given statement
What is meant by the statement?
A statement is a declarative sentence that can be either true or false. It is a proposition that can be proven using logical reasoning or evidence. Statements are the building blocks of mathematical proofs and are used to establish the truth of mathematical theories and concepts.
According to the given information
The statement “the absolute value of x is greater than 6” can be expressed as an inequality in the following way:
|x| > 6
This means that the distance between x and 0 on the number line is greater than 6 units. In other words, x can be any number that is either less than -6 or greater than 6.
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2) (8.7A) The volume of the prism shown is 241.92 in. What is the height of the prism?
Enter your answer in the box.
5.6 in.
5.4 in.
Answers
The height of the rectangular prism is 8 inches.
What is the height of the rectangular prism?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
Given that:
Volume V = 241.92 in³
Length l = 5.6 in
Width w = 5.4 in
Height h = ?
Plug the given values into the above formula and solve for h
V = w × h × l
h = V / ( w × l )
h = 241.92 in³ / ( 5.4 in × 5.6 in )
h = 8 in
Therefore, the height is 8 inches.
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Use the power-reducing formulas to rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1. 18sin^2(x)cos^2(x)
Answers
An equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
How did we get the value?The power-reducing formulas state that:
sin^2(x) = (1 - cos(2x))/2
cos^2(x) = (1 + cos(2x))/2
Using these formulas, we can rewrite the expression 18sin^2(x)cos^2(x) as:
18sin^2(x)cos^2(x) = 18[(1 - cos(2x))/2][(1 + cos(2x))/2]
Expanding the right-hand side of the equation, we get:
18[(1 - cos^2(2x))/4]
Using the identity cos^2(2x) = (1 + cos(4x))/2, we can simplify further:
18[(1 - (1 + cos(4x))/2)/4] = 9 - 9cos(4x)/8
Therefore, an equivalent expression to 18sin^2(x)cos^2(x) that does not contain powers of trigonometric functions greater than 1 is 9 - 9cos(4x)/8.
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Please help! Show all your work. 25 pts!
Answers
Answer:
[tex] \frac{468}{14.4} = \frac{d}{16.8} [/tex]
[tex]32.5 = \frac{d}{16.8} [/tex]
[tex]d = 546[/tex]
Wyatt can drive 546 miles on a full tank (16.8 gallons) of gas.
Trigonometry help me please!
Answers
As per the question of trigonometry the another equation that describes the given graph is
y = -cos5x. And after verifying the equation given in the question as well as the new equation we conclude that both equations are equal.
In trigonometry what are the domain and range of the standard functions?The sine, cosine, tangent, cotangent, secant, and cosecant functions are the fundamental geometrical operations in trigonometry. These functions' domain and range are as follows:Sine Function (sin x): All real numbers are its domainRange: [-1, 1]The domain of the cosine function (cos x): all real numbersRange: [-1, 1]Domain: All real numbers, excluding x = (n + 1/2), where n is an integer. Tangent Function (tan x):the entire real number rangeDomain: All real numbers except for x = n, where n is an integer. Cotangent Function (cot x)the entire real number rangeDomain: All real numbers, excluding x = (n + 1/2), where n is an integer. Secant Function (sec x)Range: (-∞, -1] U [1, ∞)Domain: All real numbers except x = n, where n is an integer. What distinguishing characteristics can be found in the sine and cosine function graphs?The sine and cosine function graphs' main characteristics are:
The sine and cosine functions are both periodic, which means that their graphs repeat at regular intervals. The maximum distance between the function value and the horizontal axis is determined by the sine and cosine functions' amplitudes. Zeros: The positions where the sine and cosine functions intersect the horizontal axis are known as the zeros.The functions' maximum and minimum values occur at the period's endpoints. For charting and analyzing the behavior of the sine and cosine functions, it is crucial to comprehend these fundamental characteristics.a. We can use trigonometric identities to simplify the given equation in order to describe the graph using a different equation.
[tex]cos((a+b)/2) = 2 cos(sin(a-b)) sin((a-b)/2)[/tex][tex]Sin((a+b)/2) = cos(a) - cos(b) sin((a-b)/2)[/tex]Using this identity, the given equation can be made simpler:[tex][(2 cos(5x) sin(-4x))/(-2 sin(5x) sin(-4x)] gives y.\\y = -cos(5x)[/tex]So, the equation [tex]y = -cos(5x)[/tex] can be used to describe the graph.b. We can simplify the following equation and compare it with [tex]y = -cos(5x)[/tex]to see if the two equations are equivalent.
We obtain this by applying the same trigonometric identity as before.
Y is equal to [tex][((sinx - sin9x)/(cosx - cos9x)][/tex]Y is equal to [tex][(2 cos5x sin(-4x))/(-2 sin5x sin(-4x)][/tex] (using the identities [tex]cos(a) - cos(b) and sin(a) - sin(b))[/tex][tex]y = -cos5x[/tex]As we can see, the following equation's shortened form is equal.To know more about trigonometric functions visit:
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[tex]\left\{\frac{1}{2^n}\:+\:\frac{\left(-1\right)^n}{n+1}\::\:n\:\:N\right\}[/tex]
Find max, min, sup and inf
Answers
The maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is 1/6.
The given sequence is: [tex]{1/(2 ^ n) + ((- 1) ^ n)/(n + 1) / n * N}[/tex]
To find the maximum and minimum values of the sequence, we can start by taking the first few terms and looking for patterns:When [tex]n = 1,[/tex] the sequence evaluates to: [tex]1/2 + (-1)^1 / 2 * 2 = 0[/tex]
When [tex]n = 2,[/tex] the sequence evaluates to: [tex]1/4 + (-1)^2 / 3 * 2 = 1/6[/tex]
When [tex]n = 3,[/tex] the sequence evaluates to: [tex]1/8 + (-1)^3 / 4 * 2 = 7/96[/tex]
When [tex]n = 4,[/tex] the sequence evaluates to: [tex]1/16 + (-1)^4 / 5 * 2 = 17/240[/tex]
It appears that the sequence oscillates between positive and negative values, with the negative values getting smaller as n increases.
Therefore, the minimum value of the sequence is at n = 1, where it evaluates to 0.
The maximum value occurs at n = 2, where it evaluates to 1/6.
To find the supremum and infimum of the sequence, we can start by considering the upper and lower bounds of each term separately.The term [tex]1/(2 ^ n)[/tex] has a lower bound of 0 and an upper bound of 1.
The term [tex]((- 1) ^ n)/(n + 1) / n * N[/tex] has a lower bound of [tex]-1/4[/tex] and an upper bound of [tex]1/4[/tex].
Therefore, the supremum of the sequence occurs when [tex]n = 1[/tex], where the sequence evaluates to [tex]1/2[/tex].
The infimum of the sequence occurs when [tex]n = 2[/tex], where the sequence evaluates to [tex]1/6.[/tex]
In summary, the maximum value of the sequence is [tex]1/6[/tex], the minimum value is 0, the supremum is [tex]1/2[/tex], and the infimum is [tex]1/6.[/tex]
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square root of 54 (simplified not 7.5)
Answers
Answer:
Step-by-step explanation:
7.3 is the anwser
eading Tools
Two students began a proof of the law of sines.
C
A
Student I
sin(A)=
Sin(B) =
bsin(A) =h
asin(B) = h
bsin(A)= asin(B)
sin(A)=sin(B)
b
Student 2
sin(A)=
sin(B) ==
asin(A) = h
bsin(B) = h
B
asin(A)=bsin(B)
sin(A)=sin(B)
a
Which student correctly started the proof, and what should that student do next to complete the proof?
Answers
Answer: no answer
Step-by-step explanation:
population of a certain inner-city area is estimated to be declining according to the model P(1) = 108,000€-0.011, where t is the number of years from the present What does this model predict the population will be in 7 years? Round to the nearest person.
Answers
The model predicts that the population of the inner-city area will be 107,079 people in 7 years
How is the population of an area or country determined?The number of inhabitants in a given region is characterized as the quantity of individuals normally living around there, estimated on 1 January in a given year.
The given model for the number of inhabitants in the rough part of town region is:
P(t) = 108,000 - 0.011t
where t is the number of years from the present and P(t) is the estimated population at time t.
To find the predicted population in 7 years, we can substitute t=7 into the given model and evaluate:
P(7) = 108,000 - 0.011(7)
P(7) = 108,000 - 0.077
P(7) = 107,923
As a result, the model projects that the inner-city area will have a population of 107,079 people in seven years, rounded to the nearest person.
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