Determine whether f(x)= x^2-2x-3/ x^2+3x+2 has any holes. If it does, give the coordinates.
Answers
To determine whether the function f(x) = (x^2-2x-3)/(x^2+3x+2) has any holes, we can factor the numerator and denominator and simplify the expression. The numerator can be factored as:
x^2 - 2x - 3 = (x - 3)(x + 1)
And the denominator can be factored as:
x^2 + 3x + 2 = (x + 1)(x + 2)
Therefore, we can simplify the function as:
f(x) = [(x - 3)(x + 1)]/[(x + 1)(x + 2)]
The factor of (x + 1) appears in both the numerator and denominator, so we can simplify further by canceling it out:
f(x) = (x - 3)/(x + 2)
Since (x + 1) was canceled out, we have a hole in the graph of the original function at x = -1. To find the coordinates of the hole, we can evaluate the simplified function at x = -1:
f(-1) = (-1 - 3)/(-1 + 2) = -4
Therefore, the hole in the graph of the original function is located at the point (-1, -4).
Related Questions
An experiment published in The American Biology Teacher studied the efficacy of using 95% ethanol and 20% bleach as disinfectants for removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using eggplant as the plant tissue cultured. Five cuttings per plant were placed on a petri dish, disinfected using each agent, and stored at 25 Celsius for 4 weeks. The observations reported were the number of uncontaminated eggplant cuttings after the 4 weeks of storage. Relevant data is given in the following table. Are you willing to assume that the underlying population variances are equal?
Disinfectant Sample mean Sample variance Sample size
95% Ethanol 3.73 2.78095 15
20% Bleach 4.80 0.17143 15
Answers
Since t = -2.41 < -2.145, reject [tex]H_o[/tex] and conclude Ha, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.
How to solve(a) Are you willing to assume that the underlying variances are equal?
Absolutely not! The variances can NOT be assumed equal.
H_o: sigma1^2 = sigma2^2
H_a: sigma1^2 =/ sigma2^2
F = s1^2 / s2^2 = 2.78095 / 0.17143 = 16.222
alpha = .05, dfnum = 15-1 = 14 and dfdenom = 15-1 = 14
F-critical values
= .33573 = F.INV(.025,14,14) using Excel
= 2.978588 = F.INV(.025,14,14) using Excel
Since F = 16.222 > 2.978588, reject H_o and conclude H_a, i.e. that the population variances significantly differ.
Or, using the p-value from the TI-84... p-value = 5.59E-6 = .00000559 < alpha = .05, so we can reject H_o and conclude H_a, i.e. that the population variances significantly differ.
(b) Using the information from part a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested ?
Note: Since the population variances ARE significantly different, we can NOT use the pooled t-test as rapunzel shows.
H_o: mu1 = mu2
H_a: mu1 =/ mu2
t = (xbar1-xbar2) / sqrt(s1^2/n1 + s2^2/n2)
t = (3.73 - 4.80) / sqrt(2.78095/15 + .17143/15)
Note: We do NOT square the variances. They are already squared.
t = -2.41
t-critcal values
df = smaller of n1-1 and n2-1, i.e. the smaller of 15-1 = 14 and 15-1 = 14
--> df = 14
left tail critical value = -2.145 <-- alpha/2 = .025, df = 14
right tail critical value = +2.145 <-- alpha/2 = .025, df = 14
Since t = -2.41 < -2.145, reject H_o and conclude H_a, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.
Or, using the p-value from the TI-84... p-value = .028486... < alpha = .05, so we can reject H_o and conclude H_a, i.e. that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested.
Read more about p-values here:
https://brainly.com/question/4621112
#SPJ1
An experiment published in The American Biology Teacher studied the efficacy of using 95% ethanol and 20% bleach as a disinfectant in removing bacterial and fungal contamination when culturing plant tissues. The experiment was repeated 15 times with each disinfectant, using eggplant as the plant tissue being cultured. Five cuttings per plant were placed on a petri dish for each disinfectant and stored at 25 centigrades for 4 weeks. The observation reported was the number of uncontaminated eggplant cuttings after the 4-week storage.
Disinfectant 95% Ethanols 20% Bleach
Mean 3.73 4.80
Variance 2.78095 0.17143
Pooled variance: 1.47619
Are you willing to assume that the underlying variances are equal?
Using the information from part a), are you willing to conclude that there is a significant difference in the mean numbers of uncontaminated eggplants for the two disinfectants tested ?
write another ratio that is equivalent to the ratio 4:6
Answers
Answer:
2:3 , 8:12
Step-by-step explanation:
Equivalent ratio means, multiply/divide the numerator and the denominator of the fraction with the same number. So, we need to multiply the numerator and the denominator with the same number. Hence, another ratio that is equivalent to 4 : 6 is 8 : 12
Hope this helped :D
Find the total year costs for 5
years, 10
years, and 15
years for purchasing and renting a house. Then compare your answers to those in the following table.
Length of Time Purchase Home Rent Home
5
years $78,559.20
$54,900.00
10
years $127,118.40
$115,200.00
15
years $175,677.60
$180,900.00
Purchase Home
Total 5-
year cost: $30,000.00+5×12×$809.32=$78,559.20
Total 10-
year cost: $30,000.00+10×12×$809.32=$127,118.40
Total 15-
year cost: $30,000.00+15×12×$809.32=$175,677.60
Rent Home
Total 5-
year cost: (4×12×$900)+(1×12×$975)=$54,900
Total 10-
year cost: (4×12×$900)+(4×12×$975)+(2×12×$1050)=$115,200
Total 15-
year cost: (4×12×$900)+(4×12×$975)+(4×12×$1050)+(3×12×$1125)=$180,1900
Recall the pros and cons of buying a house and which conditions make it better to to purchase a home. Also, think about the pros and cons of renting a house and which conditions make it better to rent. Use this information along with the total costs you found to answer the following prompts. Make sure to write your answer in complete sentences.
Does renting or purchasing makes the most sense for the Bainters if they live in the house 1
year? 5
years? 10
years? 15
years?
For each interval, explain why you think the Bainters should rent or purchase a home. Use mathematical evidence to support your conclusions.
Answers
The table makes it abundantly evident that buying costs less than renting does. Buying a house is therefore better over the course of 15 years. By buying a home instead of renting one, you can save $5,222.4.
How are lengths determined?Every object's length can be determined using measuring tools like a ruler, measuring tape, etc. For example, a ruler may be utilized to measure the length in inches of a pencil. A foot scale can be used in a classroom to gauge the heights of the students.
Step 1
Buying a home is more advantageous if someone is looking for somewhere to live for an extended period of time. Second, if a person buys the home, it can be sold at a higher price in the future since rental prices after a specified term and after a few years, say 10 or 15, cumulative rental charges become greater than the initial purchase price.
However, according to the above table, renting a property is preferable if the need for the home is for a shorter duration, like fewer then 5 or 10 years, in order to save money.
Step 2
1 year
The cost for Purchasing a house = 30,000 + 1 × 12 × 809.32 = $39,711.84
The cost of renting a house = 1 × 12× 900 = $10,800
So, it is evident that there's a difference between buying and renting a home of $28,911.84. So, renting a home is preferable.
Step 3
5 year
The cost of purchasing the home for five years is listed as $78559.20, whereas the cost of renting the home for five years was $54,900.
Again, renting is more affordable than buying. By renting a home, one could save $23,659.2 (78559.20-54900).
10 years
The cost of purchasing the home over 10 years is shown as $127,118.40, while the cost of renting the home for 10 years was $115,200.
Renting is less expensive than buying. Yet, buying a house is advantageous if it can be bought or rented out; otherwise, leasing one is advantageous.
Step 4
15 years
The table clearly shows that purchasing is less expensive than renting. Over the period of fifteen years, purchasing a home is therefore preferable. You can save $5,222.4 by buying a house instead of renting one.
To know more about Length visit:
https://brainly.com/question/30625256
#SPJ1
The fairy fly is one of the world’s smallest insects. It may measure no more than 1.39×10−4 meter in length. What is the total length of 2 of these insects, placed end to end?
Answers
Answer: The length of one fairy fly is 1.39×10−4 meter. To find the total length of two fairy flies placed end to end, we need to add their lengths.
1 fairy fly = 1.39×10−4 meter
2 fairy flies = 2 × 1.39×10−4 meter (adding the lengths of two fairy flies)
= 2.78×10−4 meter
Therefore, the total length of two fairy flies placed end to end is 2.78×10−4 meter.
Step-by-step explanation:
The principal P is borrowed at a simple interest rate r for a period of time t. Find the loan's future value A, or the total
amount due at time t.
P = $1000, r = 6%, t = 5 years
Answers
Answer:
$1300
Step-by-step explanation:
To find the total account balance, use the simple interest account balance formula.
P(1+rt)
1000(1 + .06 · 5)
1000(1 + .3)
1000(1.3)
$1300
Give one pair of vertical angles and one pair of supplementary angles shown in the figure below.
Answers
(a) Vertical angles: [tex]$\angle 5$[/tex] and [tex]$\angle 2$[/tex]
(b) Supplementary angles: [tex]$\angle 3$[/tex] and [tex]$\angle 4$[/tex] (or [tex]$\angle 1$[/tex] and [tex]$\angle 2$[/tex], since they are also a pair of supplementary angles)
What is an angle?A figure created by two lines meeting at the same place is called an angle. The lines that make up the angle are known as its sides, and the point is known as the vertex. Angles are expressed in degrees, ranging from 0 to 360. Angles that are perpendicular to one another when two straight lines connect are known as vertical angles. Angles 1 and 3 in the image below measure 90°, while angles 2 and 4 also measure 90°. Vertical angles have the same measure.
Supplementary angles make up the second set of angles in the figure. Supplementary angles are two angles that sum up to 180°. Angles 1 and 4 and 2 and 3 form extra angle pairs in the illustration below. Angles 1 and 4 are individually 90 degrees, while angles 2 and 3 are also 90 degrees. As a result, the two angle pairs displayed in the illustration are additional angles.
(a) Vertical angles: [tex]$\angle 1$[/tex] and [tex]$\angle 3$[/tex]
(b) Supplementary angles: [tex]$\angle 3$[/tex] and [tex]$\angle 4$[/tex] (or [tex]$\angle 1$[/tex] and [tex]$\angle 2$[/tex], since they are also a pair of supplementary angles)
For more questions related to the supplementary angle
brainly.com/question/13045673
#SPJ1
The scale of the model is 1 inch = 9 feet. The fountain at the center of the city is 18 1/2 feet wide. How wide is the fountain in the model
Answers
Therefore , the solution of the given problem of unitary method comes out to be fountain's diameter in the model is roughly 2.0556 inches.
What is an unitary method?The measurements taken from this nanosecond variable section must be multiplied by two in order to complete the task using the unitary technique. In essence, the characterised by a group and the colour sections are both removed from the unit expression method when a desired object is present. For example, 40 pens with a variable price would pay Inr ($1.01).
Here,
We can use proportionality to determine the breadth of the fountain in the model if the scale is 1 inch = 9 feet. The following percentage can be configured:
Model fountain width divided by one inch equals actual fountain width multiplied by nine feet.
The diameter of the fountain is stated to be 18 1/2 feet in real life, which is the same as 18.5 feet. Adding this number to the proportion results in:
1 inch of the model fountain's diameter divided by 18.5 feet by 9 feet
If we simplify, we get:
diameter of the model's fountain / 1 = 2.0556
By dividing the two edges by one inch, we obtain:
Modeled fountain width is 2.0556 inches.
As a result, the fountain's diameter in the model is roughly 2.0556 inches.
To know more about unitary method visit:
https://brainly.com/question/28276953
#SPJ1
GUYS A NEED HELP WITH THIS ASAP, I have to turn it in tomorrow, can y’all help me pls?? :,(
Answers
The values that make the inequality m + 4 > -6 true are -4, 0, and 5.
The values that make the inequality n - 3n ≤ 8 true are -4, 0, and 5.
The values that make the inequality -5 < 5f true are 0 and 5.
The values that make the inequality 7 ≤ -y + 7 true are -10, -4, 0, and 5.
An inequality for the statement "Hank's height (h) is less than or equal to 6 feet." is h ≤ 6.
An inequality for the statement "A magazine (m) cost more than $3.50" is m > $3.50.
An inequality for the statement "The temperature (t) is at least -5 degrees" is t ≥ -5.
How to determine the true values?In this exercise, we would evaluate the given inequalities as follows;
-4 + 4 > -6
0 > - 6 (True).
0 + 4 > -6
4 > - 6 (True).
5 + 4 > -6
9 > - 6 (True).
n - 3n ≤ 8
-4 - 3(-4) ≤ 8
8 ≤ 8 (True).
0 - 3(0) ≤ 8
0 ≤ 8 (True).
5 - 3(5) ≤ 8
-10 ≤ 8 (True).
Generally speaking, the phrase "at least" simply means or represents greater than or equal to and it can be denoted by this inequality symbol (≥).
Read more on inequality here: brainly.com/question/27976143
#SPJ1
Amir got $100 for his birthday. He wants to buy a pitching machine that costs $44 and as many baseballs as he can with the money. The baseballs cost $1.25 each. Amir found a coupon for 20% off the baseballs at the sporting goods store but he isn't sure if the coupon is expired. Determine the number of baseballs he can buy if he can use the coupon, and how many he can buy if he can't use the coupon.
Answers
Answer:
Without coupon: 44 baseballs
With coupon: 56 baseballs
Step-by-step explanation:
Amount that Amir got as a birthday present = $100Cost of pitching machine = $44Amount left over for buying baseballs = 100 - 44 = $56Cost of each baseball without coupon = $1.25Number of baseballs that Amir can buy at $1.25 per baseball= 56/1.25 = 44.8.
Since you cannot buy a fraction of a baseball, round this down to 44
If the coupon works, the cost per baseball is reduced by 20%20% = 20/100 = 0.2 in decimalDiscount in $ at 20% discount = 1.25 x 0.2 = $0.25Cost after discount = $1.25 - $0.25 = $1Therefore number of baseballs that can be bought with coupon
= 56/1 = 56
32% of 120 is 38.4. pls help
Answers
Answer:
Step-by-step explanation:
pls finish question first
4) A jet travels 490 miles in 5 hours. At this rate, how far could the jet fly in
11 hours? What is the rate of speed of the jet?
Answers
The rate of speed of the jet is given by S = 98 miles per hour
What is Speed?Speed is defined as the rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude
Speed = Distance / Time
Given data ,
Let the rate of speed of the jet be represented as S
Now , the value of S is
The distance traveled by the jet D = 490 miles
The time taken by the jet to travel 490 miles T = 5 hours
So , the speed of the jet is given by
Speed = Distance / Time
On simplifying , we get
The speed of the jet S = 490 / 5
The speed of the jet S = 98 miles per hour
Now , the distance traveled by the jet in 11 hours be D₁
The time taken to travel D₁ distance is 11 hours
where D₁ = Speed x Time
On simplifying , we get
D₁ = 98 x 11
D₁ = 1,078 miles
Hence , the distance traveled at a speed of 98 mph for 11 hours is 1,078 miles
To learn more about speed click :
https://brainly.com/question/19930939
#SPJ9
Solve for the variable. I NEED HELP PLS:) THIS HW IS DUE IN A HOUR
Answers
The solution to the variable x is 60/7
How to determine the solution to the variableFrom the question, we have the following parameters that can be used in our computation:
The similar polygons
The scale factor from the big to the small polygon is represented as
Scale factor = 5/7
Using the above as a guide, we have the following:
x = 12 * 5/7
Evaluate
x = 60/7
Hence, the solution is 60/7
Read more about similar shapes at
https://brainly.com/question/14285697
#SPJ1
what is the mean absolute deviation of 42, 45, 47, 50, 53, 56, 58, 65
Answers
The mean absolute variation for the group of integers 42, 45, 47, 50, 53, 56, 58, and 65 is therefore roughly 6.5.
How does one standard deviation mean?What one standard deviation (SD) means. on a normal or bell-shaped distribution of the data. The region of a bell curve starting at position 13 on the y axis is approximately filled by 1 SD = one standard deviation = 68% of a ratings or data values.
Here's how to find the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65:
Find the mean:
mean = (42 + 45 + 47 + 50 + 53 + 56 + 58 + 65) / 8
mean = 50.375
Find the absolute difference between each number and the mean:
|42 - 50.375| = 8.375
|45 - 50.375| = 5.375
|47 - 50.375| = 3.375
|50 - 50.375| = 0.375
|53 - 50.375| = 2.625
|56 - 50.375| = 5.625
|58 - 50.375| = 7.625
|65 - 50.375| = 14.625
Find the average of these absolute differences:
mean absolute deviation = (8.375 + 5.375 + 3.375 + 0.375 + 2.625 + 5.625 + 7.625 + 14.625) / 8
mean absolute deviation ≈ 6.5
Therefore, the mean absolute deviation of the set of numbers 42, 45, 47, 50, 53, 56, 58, and 65 is approximately 6.5.
To know more about Standard deviation mean visit:
https://brainly.com/question/475676
#SPJ1
The quality control manager at a computer manufacturing company believes that the mean life of a computer is 84
months, with a variance of 100
.
If he is correct, what is the probability that the mean of a sample of 99
computers would differ from the population mean by less than 2.5
months? Round your answer to four decimal places.
Answers
SEE ATTACHED SOLUTION
Denniel chooses to never do homework. If he gets a 70 as his final grade for the class, and he knows that he did equally well on classwork and exams, what was his classwork average?
Grading System:
Tests: 40% of the grade
Classwork: 40% of the grade
Homework: 20% of the grade
Answers
Answer:
Step-by-step explanation:
Let's start by finding out what Denniel's weighted average grade is, given the grading system:
Tests: 40% of 70 = 0.4 x 70 = 28
Classwork: ? (we don't know this yet)
Homework: 0 (since he never does homework)
Weighted average grade: 0.4 x 28 + 0.4 x ? + 0.2 x 0 = 0.4 x ?
We know that his overall weighted average grade is 70, so we can set up an equation to solve for his classwork average:
0.4 x ? = 70 - 0.4 x 28 - 0.2 x 0
0.4 x ? = 42
? = 42 / 0.4
? = 105
So Denniel's classwork average is 105.
Janet hikes a trail at a local forest each day. The trail is 23.6 miles long, and she has hiked 5 days in the past week. How many miles has Janet hiked in the past week?
Answers
Answer:18
Step-by-step explanation:
If $10,000 is invested at 6% annual interest compounded annually, how long would it take for the account balance to reach $20,000? Round your answer to the nearest tenth
Answers
It would take approximately 11.6 years for the account balance to reach $20,000 if compounded annually.
What is the difference between compound interest and simple interest?The costs a borrower pays a lender for a loan are known as interest. For instance, banks charge interest on the loans that consumers take out.
Simple interest is the term used to describe interest that is based on the principle amount that a person borrows or invests. Contrarily, compound interest is computed on the principle borrowed or invested by the individual as well as the accrued interest from the prior period.
The formula for compound interest is:
A = P(1 + r/n)ⁿˣ
where, A is the amount
P is the principal amount = $10,000
r is the rate = 6% = 0.06
x is time.
n = 1
Substituting the values,
$20,000 = $10,000(1 + 0.06/1)¹ˣ
2 = (1.06)ˣ
Taking the natural logarithm of both sides:
ln(2) = t * ln(1.06)
t = ln(2) / ln(1.06) ≈ 11.6
Therefore, it would take approximately 11.6 years for the account balance to reach $20,000.
Learn more about compound interest here:
https://brainly.com/question/29335425
#SPJ1
The height (in meters) of the arch of a walkway relative to ground level can be modeled by f(x) = -0.05x", 4here * is measured in meters. The function g(x) = R represents the distance (in meters) an engineer plans to raise the walkway. Find and interpret h (x) = / (x) + 8 (x). (3 pts)
Answers
Answer:
look in the comments and have a good day
Tell whether the ordered pair is a solution of the equation 7=y-5x (4,28)
Answers
The ordered pair is not the solution of the given equation. The solution has been obtained by using the substitution method.
What is substitution method?One method for resolving equation systems is the substitution method. Use one equation to find an expression for one of the variables in terms of the other variable in order to apply the substitution procedure. Then, in the second equation, replace that variable with that expression.
We are given an equation as 7 = y - 5x.
The ordered pair is given as (4, 28).
On substituting this in the equation, we get
⇒7 = 28 - 5(4)
⇒7 = 28 - 20
⇒7 ≠ 8
Hence, the ordered pair is not the solution of the given equation.
Learn more about substitution method from the given link
https://brainly.com/question/26094713
#SPJ1
Trent works 8 hours of a 12-hour shift. Jose works of
the shift, and Lisa works of the shift. List the workers in
2 order from the least to the greatest fraction of a shift
worked.
Please show the work on why.
Answers
The workers listed in order from least to greatest fraction of a shift worked are Lisa (1/4) < Jose (1/3) < Trent (2/3).
In math, what is a fraction?A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided. In a simple fraction, both are integers. A fraction can be found in either the numerator or the denominator of a complex fraction.
Trent worked eight of the twelve hours, or roughly two-thirds of the shift.
By dividing the number of hours Jose worked by the total number of hours in the shift, we can turn the number of hours Jose worked into a fraction:
Jose worked (12 - 8)/12 = 4/12 = 1/3 of the shift.
Lisa worked of the shift:
Lisa worked (12 - 8 - 1)/12
= 3/12
= 1/4 of the shift.
To know more about fraction visit:-
https://brainly.com/question/10354322
#SPJ1
Solve for y. Explain all steps.
y/3 - 8 = -15
Answers
Answer:
y = -21
Step-by-step explanation:
Hope this helps! :))
step by step answer. differentiate/simplify
Answers
The derivative of given ƒ(x) is:
[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]
What is differentiation ?Differentiation is a mathematical process used to find the rate at which a function changes with respect to one of its variables. It is the process of finding the derivative of a function, which is a measure of how much the function changes as its input changes. The derivative is used to analyze the behavior of functions, find maximum and minimum values, and solve optimization problems. It is an important concept in calculus and is used in many areas of mathematics, science, and engineering.
According to given information :We can use the quotient rule to differentiate ƒ(x):
[tex]f(x) &= \frac{2+3\log(x)}{x^2+5} \ \\ \\ \\f'(x) &= \frac{(x^2+5)\frac{d}{dx}(2+3\log(x)) - (2+3\log(x))\frac{d}{dx}(x^2+5)}{(x^2+5)^2} \\ \\\ &\\= \frac{(x^2+5)\left(0+\frac{3}{x}\right) - (2+3\log(x))(2x)}{(x^2+5)^2} \\\ \\ \\ &= \frac{3x^2-6-6\log(x)}{x(x^2+5)^2}[/tex]
Therefore, the derivative of given ƒ(x) is:
[tex]$f'(x) = \frac{3x^2 - 6 - 6\log(x)}{x(x^2+5)^2}$[/tex]
To know more about differentiation visit :
https://brainly.com/question/954654
#SPJ1
x -3,0,5
y- 5,2,-3
Draw the straight line y=2-x
Answers
The graph of straight line y = 2 - x with the given points are shown in graph.
What is Line segment?Line segment is a part of the line which have two endpoints and bounded by two distinct end points and contain every point on the line which is between its endpoint.
Given that;
The equation of straight line is,
⇒ y = 2 - x
Now, We have to given that;
Points on the graph are,
x = -3, 0, 5
y = 5, 2, -3
Hence, We can plot the points and join all the points.
We get;
The graph of straight line with the given points as shown in figure.
Learn more aboput the line segment visit:
https://brainly.com/question/280216
#SPJ1
Exponential Functions Problems
Please help me, thank you!
Answers
The graph of both the exponential functions y = 3(11)ˣ and y = (1/12)ˣ can be plotted by assuming some arbitrary values of 'x' that correspond to
different values of 'y'.
What are exponential functions?A function is said to be n exponential function when the independent variable is the exponent.
For example -: aˣ.
The two exponential functions can be graphed by assuming some arbitrary values of 'x'.
In y = 3(11)ˣ.
At x = 1, y = 33.
At x = - 1, y = 3/11.
At x = 2, y = 363.
So, The points are (1, 33), (- 1, 3/11) and (2, 363).
Now we can plot these points and join them by free hand.
Similarly, y = (1/12)ˣ can also be graphed in a similar manner.
learn more about exponential functions here :
https://brainly.com/question/15352175
#SPJ1
Figure Y is the result of a transformation on Figure X. Which transformation would accomplish this?
Answers
The interpretation the transformation that creates the graph is 1 unit to the left and 4 units to the right.
Graph: What is it?The link between lines and points is described by a network's mathematical representation, a graph.
Given, that Figure X was transformed to produce Figure Y.
We must ascertain the transformation that is applied in this case.
The process of changing an existing graph or graphed equation to create a different version of the following graph is known as graph transformation. A vertical reflection crosses the x-axis vertically and a horizontal reflection crosses the y-axis horizontally of a graph.
A graph can be horizontally translated by moving the base graph to the left or right in the y-axis direction.
Just a little bit of a tilt to the left and upward is made to the graph.
Figure X undergoes a translation of translation 1 unit left and 4 units up.
Hence translation 1 unit left, and 4 units up is the transformation which accomplish the graph.
To know more about graphs, visit:
https://brainly.com/question/17267403
#SPJ1
The complete question is:
Figure Y is the result of a transformation on Figure X. Which transformation would accomplish this?
A tire salesperson recommends that a customer get new tires because of low tread. The customer replies, "I don’t need new tires yet. There’s enough tread for my puttering about town since I never drive very fast or far.”
Which response would best help the customer recognize the fallacy behind the faulty inference?
“What is the actual tread depth of your tires?”
“What good are low treads going to be in the rain?”
“What if I want to borrow your car and take it on the highway?”
“What if a child runs out into the street right in front of your car?”
Answers
The response that would best help the customer recognize the fallacy behind the faulty inference is: D. "What if a child runs out into the street right in front of your car?"
Which response would best help the customer recognize the fallacy behind the faulty inference?This response uses an example of a potential emergency situation to show that having low tread on tires can be dangerous even if the customer "never drives very fast or far.
" It challenges the customer's assumption that low tread is only a concern for high-speed or long-distance driving and highlights the importance of having sufficient tread depth for unexpected situations.
Therefore the correct option is C.
Learn more about customer here:https://brainly.com/question/26313265
#SPJ1
What is the meaning of "a permutation of 1, 2, ..., n is a bijection of { 1, 2, ..., n } onto { 1, 2, ..., n }"?
Answers
The permutation is a bijective function because it is both a one-one and an onto function.
What is meant by permutation?A permutation of a set in mathematics is, broadly speaking, the rearrangement of its elements if the set already has an ordered structure into a sequence or linear order. Here, the components of sets are arranged in a linear or sequential order.
The bijective function is both a one-one function and an onto function.
One-one function means that for every value of the domain, there is only one value of the range. This means that an output value never repeats.
An element x is mapped to each element y by the function f known as the onto function. In other words, there is an x for every y such that:
f(x) = y
Now we have to prove why permutation is defined as bijective.
The permutation is basically an arrangement of elements.
So for the new arrangement, at one position there is only one element.
So it is one-one.
Also, we are using the given number of elements. we are just changing its positions. So every element in the co-domain is mapped to at least one element in the domain. Also, the co-domain is the range.
So it is onto function.
Therefore the permutation is a bijective function because it is both one-one and onto function.
To learn more about permutation, follow the link.
https://brainly.com/question/12468032
#SPJ1
Sergey is solving 5x2 + 20x – 7 = 0. Which steps could he use to solve the quadratic equation by completing the square? Select three options. 5(x2 + 4x + 4) = –7 + 20 x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot 5(x2 + 4x) = 7 5(x2 + 4x + 4) = 7 + 20 5(x2 + 4x) = –7
5(x2 + 4x + 4) = –7 + 20
x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot
5(x2 + 4x) = 7
5(x2 + 4x + 4) = 7 + 20
5(x2 + 4x) = –7
Answers
Steps he could use to solve the quadratic equation by completing the square is 5(x² + 4x) = –7
What are quadratic equations?A quadratic equation is a second-degree polynomial equation of the form ax² + bx + c = 0, where x is the variable and a, b, and c are constants. It typically has two solutions, which can be found using the quadratic formula or factoring the equation.
Solution:
The three steps that Sergey could use to solve the quadratic equation by completing the square are:
1.Write the equation in the form ax² + bx + c = 0
2.Add and subtract (b/2)² to complete the square, resulting in an expression of the form a(x + p)^2 + q = 0
3.Solve for x by isolating (x + p)² and taking the square root, resulting in x = (-b ± sqrt(b² - 4ac)) / 2a
Therefore, the three options that correspond to these steps are:
5(x² + 4x + 4) = –7 + 20
x + 2 = Plus or minus StartRoot StartFraction 27 Over 5 EndFraction EndRoot
5(x² + 4x) = –7
To learn more about quadratic equations from the given link:
https://brainly.com/question/1214333
#SPJ1
How many cups of tuna does Branden need to make 3 times the rec Draw a model to show how to solve.
Answers
Hope it helps
1. A hot piece of meat is removed from an oven and its surface temperature
is given by the formula S(t) = 72 +238•0.97^t, in degrees Fahrenheit, at time t
minutes after it was removed.
(a) What was the initial surface temperature of the meat?
I am not understanding how to do this at all could someone please help me & show the work for it??
Answers
Answer:
[tex]310 ^\circ F[/tex]
Step-by-step explanation:
The formula relating surface temperature in °F and time in t minutes after removal from the oven is given as
[tex]S(t)= 72 + 238 (0.97^t)\\\\\text{The initial temperature is when t = 0}\\\\\text{At t = 0}\\\\S(0) = 72 + 238(0.97^0)\\\\0,97^0 = 1 \text{ since any number raised to 0 = 1}\\\\\text{Therefore}\\S(0) = 72 + 238 \cdot 1\\= 72 + 238\\\\= 310 ^\circ F[/tex]