Both Student A and Student B's representations of the expression 9/y³ⁿ are incorrect.
What is expression?In mathematics, an expression is a combination of numbers, symbols, and/or variables that are arranged in a meaningful way. An expression can represent a value, a quantity, a function, or some other mathematical object. Expressions can be made up of one or more terms. A term is a group of numbers, symbols, and/or variables that are separated by a plus or minus sign. Expressions can also include mathematical operations, such as addition, subtraction, multiplication, and division, as well as exponents and parentheses. Expressions are used in various areas of mathematics, including algebra, calculus, and statistics, to represent mathematical relationships and to solve problems.
Here,
Student A represents the expression as the product of 9 and y times the product of 3 and t, which can be written as: 9 * y * 3 * t = 27yt.
This representation is incorrect because it does not include the exponent 3 in the denominator. The correct representation of the expression is: 9 / y^3t.
Student B represents the expression as the quotient of 9 and y times the sum of 3 and t, which can be written as: 9 / y * (3 + t) = (27 + 9t) / y.
This representation is also incorrect because it incorrectly combines the sum of 3 and t in the denominator. The correct representation of the expression is: 9 / y^3t.
To represent the expression correctly, we need to include the exponent 3 in the denominator, indicating that y is being raised to the power of 3, and include t as a separate factor in the denominator. Therefore, the correct representation of the expression is: 9 / (y^3 * t).
To know more about expression,
https://brainly.com/question/30091997
#SPJ1
Answer:
Student A says prodact of Tandy, but 9 is 9 y so it's quotient.
Step-by-step explanation:
In a company, 90% of the workers are men. If 410 people work for the company who aren't men, how many workers are there in all? Use pencil and paper. Show two different ways that you can solve this problem.
The total number of workers if, In a company, 90% of the workers are women, If 440 people work for the company who aren't women is 4400.
What is percentage?
As it is clear from the term per-cent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
In a company, 90% of the workers are women,
If 440 people work for the company who aren't women,
Calculate the percentage of people who aren't women as shown below,
The percentage of people who aren't women = 100% - the percentage of women
The percentage of people who aren't women = 100% - 90%
The percentage of people who aren't women = 10%
Assume that there are a total of x workers then according to the statement,
10% of x = 440
10 / 100 × x = 440
x = 440 × 100 / 10
x = 4400
Learn more about percentages at:
brainly.com/question/20818421
#SPJ1
Question content area top
Part 1
The line models the cost of renting a kayak. Write an equation in slope-intercept form for the line, where x is the number of hours the kayak is rented and y is the total cost of renting the kayak.
The equation of the line that models the cost of renting a kayak in slope-intercept form is: y = 5x + 10
The slope and y-intercept of the line that predicts the price of renting a kayak must be identified in order to formulate the equation for the line.
We can observe from the provided graph that the line traverses points (0, 10) and (6, 40). We may determine the slope of the line using these two points:
Slope = (Y Change/X Change) = (40 - 10)/(6 - 0) = 30/6 = 5
The equation of a line can also be expressed in the slope-intercept form, which is as follows:
y = mx + b
where m denotes the line's slope and b its y-intercept.
The slope of the line is previously known to be 5. One of the points the line passes through can be used to determine the y-intercept, for instance (0, 10). When we enter these numbers into the equation, we obtain:
10 = 5(0) + b
If we simplify, we get:
b = 10
Thus, the slope-intercept form equation of the line that represents the cost of renting a kayak is as follows:
y = 5x + 10
where x represents the duration of the kayak rental and y represents the entire cost.
To know more similar question visit:
https://brainly.com/question/29099103
#SPJ1
Find the equation of the line through the points (−2,−10)
and (−2,−5).
Answer:
x = -2
Step-by-step explanation:
The line passing through the points (-2, -10) and (-2, -5) is a vertical line because both points have the same x-coordinate (-2).
Therefore, the equation of the line is simple:
x = -2
This means that for any value of y, the corresponding value of x is always -2. Visually, this line looks like a straight vertical line passing through the point (-2, -10) and (-2, -5) on the coordinate plane.
Answer:
Step-by-step explanation:
Point
�
′
(
−
4
,
−
3
)
C
′
(−4,−3)C, prime, left parenthesis, minus, 4, comma, minus, 3, right parenthesis is the image of
�
(
−
2
,
−
3
)
C(−2,−3)C, left parenthesis, minus, 2, comma, minus, 3, right parenthesis under a translation.
Answer:
Step-by-step explanation:
What are you trying to do?
It's hard ot understand the problem.
Answer:
The image of point (–2, –3)C under the translation would be point (–4, –3)C.
which of the following is equal to 9•6 divided by long division?
The solution to the expression 9•6 is 54
How to evaluate the expressionFrom the question, we have the following parameters that can be used in our computation:
9•6 divided by long division
The above expression is a product expression
This means that it cannot be evaluated using long division
When the expression is evaluated. we have
9 * 6 = 54
Hence, the solution is 54
Read more about expression at
brainly.com/question/15775046
#SPJ1
the video shows many statistics in which douglas county is higher than most communities in the united states. what is the one area in which the statistics presented suggest that douglas county is actually lower than many other communities? home ownership number of companies that employ residents diversity education which is the most likely used method to compute the average commute time to work in douglas county? researchers collected a random sample of people in douglas county and asked them for their commute time. they added up all of these commutes times and then divided this number by the number of people in the sample. researchers collected a random sample of people in douglas county and asked them for their commute time. they added up all of these commute times and then divided this number by the total population of douglas county. researchers collected a random sample of people in douglas county who are employed and asked them for their commute time. they added up all of these commute times and then divided this number by the number of people in the sample. researchers collected a random sample of people in douglas county who are employed and asked them for their commute time. they added up all of these commute times and then divided this number by the total number of employed residents in douglas county. the video lists the major employers in douglas county, but does not list any statistics with these names. which of the following statistics would help you understand why they describe these companies as major employers in douglas county? the number of employees of each of these companies. the percentages of employed douglas county residents who work for each of these companies. the percentage of employees of each of these companies who live in douglas county. the number of employees who are douglas county residents in each of these companies.
The video does not provide information to answer the question about which area suggests that Douglas County is lower than many other communities.
What is Statistics ?Statistics in mathematics is the study of data gathering, organization, interpretation, analysis, and presentation. Planning the acquired data for experimental designs and statistical surveys is the major goal of employing statistics. A mathematical science that deals with numerical data is statistics. In short, statistics is an important process that aids in decision-making based on facts.
The video does not provide information to answer the question about which area suggests that Douglas County is lower than many other communities.
The most likely used method to compute the average commute time to work in Douglas County is: researchers collected a random sample of people in Douglas County who are employed and asked them for their commute time. They added up all of these commute times and then divided this number by the number of people in the sample.
To understand why the video describes certain companies as major employers in Douglas County, the most relevant statistic would be the number of employees of each of these companies.
Learn more about statistics, visit:
https://brainly.com/question/29093686
#SPJ1
The total price of 3 mangoes and 6 apples is $42. If the price of a mango is $2 less than 2 times that of an apple, find the price of an apple.
Answer:
$4
Step-by-step explanation:
Let's denote the price of an apple by "a" and the price of a mango by "m". Then we can set up two equations based on the information given in the problem:
"The total price of 3 mangoes and 6 apples is $42"
mangoes are three times apples in this case.
3m + 6a = 42
"The price of a mango is $2 less than 2 times that of an apple"
m = 2a - 2
Now we can substitute equation 2 into equation 1 and solve for "a":
3(2a - 2) + 6a = 42
6a - 6 + 6a = 42
12a = 48
a = 4
Therefore, the price of an apple is $4.
꧁༒αηѕωєяє∂ ву gσ∂кєу༒꧂
CAN SOMEONE HELP WITH THIS QUESTION?✨
The marginal revenue is 909 dollars per unit.
What is a function?A function is a relationship between inputs where each input is related to exactly one output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
R(q) = -2q² + 1000q _____(1)
Where q is the unit sold.
Now,
Substitute q = 91 in (1).
R(q) = -2q² + 1000q
R(q) = -2 x 91² + 1000 x 91
R(q) = -8281 + 91000
R(q) = $82719
Now,
91 units = $82719
1 unit = 82719/91
1 unit = $909
Thus,
909 dollars per unit is the marginal revenue.
Learn more about functions here:
https://brainly.com/question/28533782
#SPJ1
2 A representative sample of 60 students from a high school is surveyed
which elective he or she is taking. The table shows the respons Elective Dance Music Art Photography Electronics Number of Stud 19 7 15 11 8
The Accurate Prediction of the data:
In a group of 120 students, it is expected that 16 of them are taking electronics.
About 25% of the students in the school are taking art.
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. With the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
Total students = 60
let x% of students chose Arts
So, x% of 60 = 15
x/ 100 (60) = 15
x = 1500 / 60
x = 25%
and, if there 120 students then number of students choose electronics
= 8/60 x 120
= 16
Learn more about Percentage here:
https://brainly.com/question/29306119
#SPJ9
what is the y intercept when the coordinate is -3,-3 and the slope is -1!! quick answers needed
When the coordinate is (-3, -3) and the slope is -1, the y-intercept is -4.
What is slope?Slope is a measure of the stainless of a line what is surface and it represent by the letter m. It is calculated by dividing the vertical change in the line or surface by the horizontal change in the line or surface. Slope is used in mathematics engineering and other science to measure the rate of change between two point.
The y-intercept is the point at which a line crosses the y-axis when plotting coordinates on a graph. To find the y-intercept, you need to use the equation y = mx + b, where m is the slope and b is the y-intercept. In this case, the equation would be y = -1x - 4. This equation can be used to solve for the y-intercept when the coordinate is (-3, -3). By substituting -3 for x and -3 for y, the equation can be rearranged to -3 = -1(-3) - b, which simplifies to -4 = -b. Therefore, the y-intercept is -4.
To know more about slope click-
https://brainly.com/question/3493733
#SPJ1
If the area of a rectangle with width x can be represented with the expression A(x) = x(14 – x), what is the perimeter of the rectangle?
A
28
B
56
C
56 – 4x
D
4x + 28
Answer: D
Step-by-step explanation:
To find the perimeter of the rectangle, we need to know both the length and width of the rectangle. Since we are given the expression for the area, which is A(x) = x(14 – x), we can use this expression to find the length of the rectangle that corresponds to a given width x.
The area of a rectangle is equal to its length multiplied by its width. So we have:
A(x) = x(14 – x)
We can rewrite this equation as a quadratic equation in standard form:
A(x) = -x^2 + 14x
To find the maximum value of A(x), we can use the formula for the x-coordinate of the vertex of a quadratic function:
x = -b / 2a
where a = -1 and b = 14 in this case.
x = -14 / 2(-1) = 7
So the maximum area occurs when the width of the rectangle is 7.
To find the length of the rectangle, we can substitute x = 7 into the expression for the area:
A(7) = 7(14 – 7) = 49
So the length of the rectangle is 49/7 = 7.
Now we can find the perimeter of the rectangle by using the formula:
P = 2(l + w)
where l is the length and w is the width.
Substituting l = 7 and w = x, we get:
P = 2(7 + x)
So the correct answer is (D) 4x + 28.
is this problem a one solution,no solution or all real numbers
The equation is true for all real numbers, and therefore the solution set is (C) all real numbers.
What is the solution to the equation?In arithmetic, a solution to the equation expresses can be replaced for the variable to provide a piece of real number information.
We can start simplifying the equation using the distributive property:
4(6x - 4) = 8(3x - 2)
24x - 16 = 24x - 16
We can see that both sides of the equation are identical, so the equation is an identity. This means that the equation is true for all real numbers, and therefore the solution set is all real numbers.
In other words, any value we choose for x will make the equation true.
Learn more about the solution to the equation here:
brainly.com/question/19794420
#SPJ9
The complete question would be as:
How many solutions have the below equation?
4(6x - 4) = 8(3x - 2)
A. one solution.
B. no solution.
C. all real numbers.
graph translation of (x,y) (x, y-2)
Answer:
can you explain a bit better what the problem is?
Determine the set of x-values where f(x) =
The set of x-values where f(x) is continuous is all real numbers except x=1, interval notation is (-∞, 1) U (1, ∞).
What are the set of x-values?
The function f(x) is a rational function, which is continuous for all x-values except those that make the denominator 0.
Thus, to find the set of x-values where f(x) is continuous, we need to find the values that make the denominator x-1 equal to 0:
x - 1 = 0
x = 1
Therefore, the set of x-values where f(x) is continuous is all real numbers except x=1. We can write this set in interval notation as:
(-∞, 1) U (1, ∞)
which means the set of all x-values less than 1, combined with the set of all x-values greater than 1.
Learn more about continuous function here: https://brainly.com/question/18102431
#SPJ1
how do you solve a 3 collumn table
The way to solve a 3 column table depends on the information in the table but there are general steps to follow shown below.
How to work with a three column table ?First, identify the headings for each column. Then, determine the type of data being presented in each column because the data may be numerical (such as measurements or quantities), categorical (such as types or classifications), or a combination of both.
Analyze the data in each column and use mathematical operations or formulas to calculate or analyze the data, if necessary. Finally, draw conclusions or make inferences based on the data in the table.
Find out more on three - column tables at https://brainly.com/question/28959249
#SPJ1
The sum of four times a number and seven is 27. Find the number.
Provide your answer below:
Answer:
Look at the screenshot.
Aldo and Lena are standing on a riverbank 220 meters apart at points A and B respectively (see the figure below). They want to know the distance from Aldo to a house located across the river at point C. Aldo measures angle A to be 51 and Lena measures angle B to be 65. What is the distance from Aldo to the house? Round your answer to the nearest tenth of a meter.
When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.
what is distance ?Displacement is the overall, purposeless movement of an object. Speed can be characterized as the amount of area an object has covered, disregarding of the origin or ending location. Distance has characterized by the extent or size of the distance between two places. The gap between adjacent positions and the distance moved between them are not exactly the same thing, it should be emphasized. The travelled is the entire length of a path that join different places. Distance is the average trip distance of a body. It is also known as distance. For instance, OP = 360 m would indicate the length of the path for an object traveling from 0 ° to point P.
given
BC/sin 53 = 250/sin 56
BC = 250 * sin 53 /sin 56
=240.8 m
When Aldo and Lena are standing on a riverside 220 meters apart at certain points, the distance between Lena and the home is 240.8 meters.
To know more about distance visit :-
brainly.com/question/29130992
#SPJ1
The scrap value of a machine at the end of its useful life is given by S(n)=C(1-r), where C is the original cost, n is the useful life
of the machine in years, and r is the constant annual percentage of value lost. Find the scrap value of the following machine.
Original cost, $41,000; life, 10 years; annual rate of value lost, 13%
Answer:
$ 2,484.23
Step-by-step explanation:
The formula for scrap value is
S(n) = C( 1- r)ⁿ
where
S(n) = scrap value after n years
C = original cost
r = rate of value lost in decimal
n = number of years
First convert r to a decimal by dividing by 100
r = 13/100 = 0.13
S(10) = 10,000(1 - 0.13)¹⁰
= 10,000 x (0.87)¹⁰
= 10000 x 0.248423
= $ 2,484.23
Nikki is going to use SSS to prove that PQR SQR.
Which of these is a necessary step in Nikki's proof?
A.
Prove that PQR SQR by vertical angles.
B.
Prove that PQ QR by CPCTC.
C.
Prove that QR QR by the reflexive property.
D.
Prove that QPR QSR by the transitive property.
Prove that QR QR by the reflexive property.
The triangles are congruent by reflexive property of SSS
What are Congruent Triangles?Transformations change the size or position of shapes. Congruent shapes are identical, but may be reflected, rotated or translated. Scale factors can increase or decrease the size of a shape. Congruent Triangles simply mean the triangles that possess the same size and shape
The three sides are equal (SSS: side, side, side)
Two angles are the same and a corresponding side is the same (ASA: angle, side, angle)
Two sides are equal and the angle between the two sides is equal (SAS: side, angle, side)
A right angle, the hypotenuse and a corresponding side are equal (RHS, right angle, hypotenuse, side)
Given data ,
Let the first triangle be ΔPQR
Let the second triangle be ΔQRS
And , the side QR is the common side
Now , measure of side PQ = measure of side QS
And , measure of side PR = measure of side RS
So , the three sides are equal (SSS: side, side, side) and they are congruent triangles
And , QR ≈ QR by the reflexive property.
Hence , the triangles are congruent by SSS
To learn more about congruent triangles click :
https://brainly.com/question/26131452
#SPJ5
The complete question is attached below :
Nikki is going to use SSS to prove that PQR SQR.
Which of these is a necessary step in Nikki's proof?
A.
Prove that PQR SQR by vertical angles.
B.
Prove that PQ QR by CPCTC.
C.
Prove that QR QR by the reflexive property.
D.
Prove that QPR QSR by the transitive property.
Pls answer and show me how you got that answer
The mass of the radioactive sample at the beginning of the 13th day of the experiment will be around 424.7 grams.
What does one gramme represent?A metric weight measurement unit. A gramme is one thousandth of a kilogramme, or about 30 times smaller than an ounce. Leave a space between the word "gramme" (or the symbol "g") and the number that comes before it when a specific number is provided. In technical and scientific writing, the unit name and the number are either written together in full (for example, ten grammes) or a numeral is used with the sign ( e.g. 10 g ).
When we find the mass of radioactive, we obtain:
m₀=initial mass=1500 grams, r = 13% and n =12 days
⇒m = m₀ x [tex](1 - \frac{r}{100} )^{n}[/tex]
⇒m =1500×[tex](1-\frac{13}{100}) ^{12}[/tex]
⇒m=424.7 grams.
To know more about grams visit:
https://brainly.com/question/29127168
#SPJ1
Austin runs 7 miles in 51 minutes.How many minutes does he take per mile?
Answer:
7 min 48 sec / mile
Step-by-step explanation:
51 min ÷ 7 miles = 7.2857142857142
Rounds to 7
Can somebody help..? The question is down below
The required measures of the angles are the following: ∠J = 135°, ∠F = 45°, ∠B = 135°, and ∠C = 22°.
What are supplementary angles?The supplementary angles are illustrated as when pairing of angles addendum to 180° then they are called supplementary angles.
The measure of the angles are given as follows:
∠I = 22°
∠A = 23°
∠J = 180° - ∠I - ∠A (sum of interior angles in a triangle)
∠J = 180° - 22° - 23° = 135°
∠F = 180° - ∠J (supplementary angles)
∠F = 180° - 135° = 45°
∠B = 360° - 90° - 90° - 45° (sum of interior angles in the quadrilateral)
∠B = 135°
∠C = 180° - ∠A - ∠B (sum of interior angles in a triangle)
∠C = 180° - 23° - 135° = 22°
Thus, the required measures of the angles are the following: ∠J = 135°, ∠F = 45°, ∠B = 135°, and ∠C = 22°.
Learn more about the angled here.
brainly.com/question/15767203
#SPJ9
find derivative of f(x) = 4x³ using first Principre and F(x) = 2x²-3x
Answer:
12x^2.
Step-by-step explanation:
let y = 4x^3
If y is increased by a small amount Δy then x is increased by a small amount Δx, so we write:
y + Δy = 4(x + Δx)^3
y + Δy = 4(x^3 + 3x^2 Δx + 3x(Δx)^2 + (Δx)^3)
y + Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3
Δy = 4x^3 + 12x^2 Δx + 12x(Δx)^2 + 4(Δx)^3 - y
= 4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2 - 4x^3
Δy/Δx = (4x^3 + 12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2- 4x^3 ) / Δx
= (12x^2 Δx + 12x(Δx)^3 + 4(Δx)^2) / Δx
= 12x^2 + 12x(Δx)^2 + 4Δx
Now as Δx approaches zero, the limit ( that is the derivative) of f(x)
= 12x^2
- as we can neglect the last 2 terms.
The second part can be solved by the same process.
At the Crown Interior Pizza Hat location in Faridabad, a report showed that 431 out of 778 orders were for delivery. What is the minimum sample size needed to have a 4 percentage point error for the proportion of orders that were carry-out?
*If you used a program on the graphing calculator or formula can you specify which ones please?
Answer:
Step-by-step explanation:
To determine the minimum sample size needed to have a 4 percentage point error for the proportion of orders that were carry-out, we can use the following formula:
n = (Z^2 * p * q) / E^2
where:
n is the sample size we want to determine
Z is the z-score associated with the desired level of confidence (let's assume a 95% confidence level, so Z = 1.96)
p is the estimated proportion of orders that were carry-out (we don't know this yet, so we'll use 0.5 as a conservative estimate)
q is 1 - p (i.e., the estimated proportion of orders that were delivery)
E is the desired margin of error (in this case, 0.04)
Using the given information, we can estimate that the proportion of orders that were carry-out is:
p = 1 - 431/778 = 0.446
Then, plugging in the values into the formula, we get:
n = (1.96^2 * 0.446 * 0.554) / 0.04^2 ≈ 602.25
Rounding up to the nearest whole number, the minimum sample size needed is 603.
Note that I used the formula for sample size calculation based on a finite population, since the total number of orders is known (778). If we used the formula for an infinite population, the result would be very similar (around 604). I calculated this by hand, without using any calculator program, but you could use a calculator or a spreadsheet to perform the calculations more efficiently.
Help asap please
Asap
The correct matching of the fractions
0.1 - 1/10
0.01 - 1/100
100% - 1
What is a fraction?A fraction is a way of representing a part of a whole or a quantity that is less than one. Fractions consist of two numbers separated by a horizontal or diagonal line, with the number above the line being called the numerator and the number below the line being called the denominator.
The numerator represents how many parts of the whole are being considered, while the denominator represents the total number of equal parts that the whole is divided into.
Learn more about fraction:brainly.com/question/10354322
#SPJ1
given a set of data that is skewed-right, there is at least % of the data within 3 standard deviations. use either chebyshev's theorem or the empirical rule to fill in the blank with the best answer:
The set of data that is skewed-right, there is at least 99.7% of the data within 3 standard deviations.
What Is the Empirical Rule?A statistical principle known as the empirical rule, also known as the three-sigma rule or 68-95-99.7 rule, holds that with a normal distribution, almost all observed data will lie within three standard deviations (denoted by ) of the mean or average (denoted by ).
Some points about standard deviation using Empirical Formula:
In accordance with the Empirical Rule, 99.7% of data that are found to have a normal distribution fall within 3 standard deviations of the mean.According to this formula, 68% of the data are within one standard deviation of the mean, 95% are within two standard deviations, and 99.7% are within three standard deviations.Learn more about Empirical Formula here:
https://brainly.com/question/22822888
#SPJ1
Roger will pour concrete to make a sidewalk with the dimensions, in feet, shown in the figure below. He will pour the concrete to a depth of 4 inches. One bag of concrete mix makes 0.6 cubic feet of concrete. What is the least whole number of bags of concrete mix that Roger needs in order to make the sidewalk?
F. 16
G. 44
H. 50
J. 58
K. 67
Answer:
The least whole number of bags of concrete mix that Roger needs in order to make the sidewalk is G, 44. To calculate this, we must first convert the cubic feet of the sidewalk into cubic inches, which would be 345,600 cubic inches. Then, we need to divide this by the amount of cubic inches in one bag (0.6 cubic feet = 630 cubic inches). This gives us 550 bags of concrete mix, but since Roger will be using a whole number, the closest he can get is 44 bags.
Find the perimeter of the triangle whose vertices are (−1,−14)
, (7,1)
, and (−1,7)
. Write the exact answer. Do not round.
To find the perimeter of the triangle, we need to calculate the length of each of its sides and then add them up.
Let's start by finding the length of the side between (-1, -14) and (7, 1). We can use the distance formula for this:
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((7 - (-1))^2 + (1 - (-14))^2)
= sqrt(8^2 + 15^2)
= sqrt(289)
= 17
So the length of the first side is 17.
Now let's find the length of the side between (-1, -14) and (-1, 7):
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((-1 - (-1))^2 + (7 - (-14))^2)
= sqrt(0^2 + 21^2)
= 21
So the length of the second side is 21.
Finally, let's find the length of the side between (7, 1) and (-1, 7):
distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Plugging in the coordinates, we get:
distance = sqrt((-1 - 7)^2 + (7 - 1)^2)
= sqrt((-8)^2 + 6^2)
= sqrt(100)
= 10
So the length of the third side is 10.
Now we can add up the lengths of all three sides to get the perimeter:
perimeter = 17 + 21 + 10
= 48
Therefore, the perimeter of the triangle is 48.
I wonder about polynomial and the use of polynomials in the real world?
Answer:
Step-by-step explanation:
Polynomials are a type of mathematical expression that involve variables raised to powers and added or subtracted together. They have many applications in the real world, ranging from science and engineering to finance and economics. Here are a few examples:
Physics: Polynomials are used to describe the motion of objects in space. For example, the position of a moving object over time can be represented by a polynomial function.
Engineering: Polynomials are used to design and analyze complex systems, such as electrical circuits and control systems.
Computer graphics: Polynomials are used to create curves and shapes in 3D modeling and computer graphics.
Finance: Polynomials are used in financial modeling to represent trends and make predictions. For example, a polynomial function could be used to model the growth of a company's revenue over time.
Data analysis: Polynomials are used to fit curves to data in order to make predictions or gain insights. For example, a polynomial function could be used to model the relationship between a company's advertising budget and its sales.
Overall, polynomials are a powerful tool in mathematics and have many practical applications in various fields.
If f is one-to-one and f(7)=3, then f^1(3)= ___, and (f(7))^-1= ___
Answer:
[tex]f^{-1}(3) = \boxed{7}[/tex]
[tex]f(f(7))^{-1} = \boxed{7}[/tex]
Step-by-step explanation:
These follow from two of the properties of inverse functions:
If [tex]f[/tex] is a one-to-one function then
[tex]if\; f(x) = y \;then\; f^{-1}(x) = y}[/tex][tex]f^{-1}(f(x) = x\\\\f^{-1}(f(x) \;is\;the\;same\;as; ((f(x))^{-1}[/tex]