A linear function and its inverse are given.
y=4x-3
y=1/4x+3/4
Which tables could be used to verify that the functions are inverses of each other? Select two options.
x:1, 3, 5, 7, 9
y:1, 3, 5, 7, 9
x:-23, -15, -3, 1, 13
y:-5, -3, 0, 1, 4
x:-18, -12, 0, 3, 9
y:-24, -18, -6, -3, 3
x:-5, -3, 0, 1, 4
y:-23, -15, -3, 1, 13
x:-24, -18, -6, -3, 3
y:-18, -12, 0, 3, 9
Answers
Answer:
x: -5, -3, 0, 1, 4
y:-23, -15, -3, 1, 13 for the function.
x:-23, -15, -3, 1, 13
y: -5, -3, 0, 1, 4 for the inverse.
Step-by-step explanation:
we know that if we have the function f(x) = y, then the inverse of f(x) (let's call it g(x)) is such that:
g(y) = x.
now we have
y=4x-3
y=(1/4)x+3/4
The only table that works for our first function is:
x: -5, -3, 0, 1, 4
y:-23, -15, -3, 1, 13
You can see this by replacing the values of x and see if the value of y also coincides.
Then, using the fact that the other table must be for the inverse, we should se a table with the same values, but where the values of x and y are interchanged.
The second table is that one:
x:-23, -15, -3, 1, 13
y: -5, -3, 0, 1, 4
Answer: B and D
x:-23, -15, -3, 1, 13
y:-5, -3, 0, 1, 4
x:-5, -3, 0, 1, 4
y:-23, -15, -3, 1, 13
Step-by-step explanation:
Related Questions
Solve for x: (5 points)
negative 4 over 3, multiplied by x minus 6 equals negative 26
a
−27
b
−15
c
15
d
27
Answers
Answer:
the problem is like that or is showing u how are the equations ?
please help asap no trolls!
Answers
Answer:
angle wyx that is angle y is largest as it's the opposite angle to the largest side of a triangle
The sale amount is 1,250.00, 5% sales tax.
a. whats the sales Tax
b. What's the total amount paid
Answers
Answer:
1250*.05=62.5. Then just add it to the amount for the total dollars shw needs to spend with tax
Step-by-step explanation:
Simplify -8 + 6(b - 1). -2 b - 1 6 b - 14 6 b - 9 -2 b + 2
Answers
Answer:
-14-158b
Step-by-step explanation:
Answer:
6 b - 14
Step-by-step explanation:
2.
Hollyville Elementary is having a pizza party. The school secretary plans on ordering 25 pizzas. There are 10 classes in the school. If each class is given 2 1/2pizzas, is 25 pizzas enough for the entire school? If so, how much pizza, if any, will be left over? If not, how many more pizzas will they need?
Answers
Answer:
25 is enough and there will be no pizza left over.
Step-by-step explanation:
We can multiply the 2 1/2 pizza across 10 classes to see how much pizza we need and if if 25 is enough.
An easy way to do this is to turn 2 1/2 into a decimal then multiply by 10 like that.
2 1/2 = 2.5
2.5 × 10 = 25 pizzas
25 is exactly enough with no pizza left over.
Answer:
25 is enough and there will be no pizza left over.
Step-by-step explanation:
We can multiply the 2 1/2 pizza across 10 classes to see how much pizza we need and if if 25 is enough.
An easy way to do this is to turn 2 1/2 into a decimal then multiply by 10 like that.
2 1/2 = 2.5
2.5 × 10 = 25 pizzas
25 is exactly enough with no pizza left over.
Step-by-step explanation:
A cake for 6 people requires 4 eggs. How many eggs are needed to make a cake for 9 people
Answers
4 eggs / 6 people = 2/3 eggs per person
9 people x 2/3 eggs per a person = 6 eggs
answer: 6 eggs
An experiment was used to test a new migraine medicine. Each participant took either the new medicine or a placebo
then waited for one hour to see if the headache went away or remained. The results are compiled in the contingency
table below. Use the table to answer the questions.
Went Away| Medicine| Placebo
Remained|. 120. |. 68
18. | 44
Your answers should be exact numerical values.
There were
participants whose headache remained.
The probability of randomly selecting an individual whose headache remained is
There were
participants whose headache remained and took a placebo.
The probability of randomly selecting an individual whose headache remained and took a placebo is
Answers
1) Number of participants whose headache remained is: 62
2) The probability of randomly selecting an individual whose headache remained is: 0.4133
3) The probability of randomly selecting an individual whose headache remained and took a placebo is: 0.2933
How to find the probability of random selection?From the table, we have the parameters as:
Number of participants that took medicine and headache went away = 120
Number of participants that took placebo and headache went away = 68
Number of participants that took and headache remained = 18
Number of participants that took placebo and headache remained = 44
1) Number of participants whose headache remained = 18 + 44 = 62
2) The probability of randomly selecting an individual whose headache remained is:
62/(62 + 120 + 68)
= 62/150
= 0.4133
3) The probability of randomly selecting an individual whose headache remained and took a placebo is:
44/150 = 0.2933
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5.2: Bowling for Triangles (Part 2)
Here is a visual pattern of dots. The number of dots D(n) is a function of the step number n.
1. What values make sense for n in this situation? What values don't make sense for n?
Answers
Using the pattern, n can represent the the increase of dots according to step.
In the given question we have to find what values make sense for n in this situation.
n is representing the number.
As we can see that there is a pattern given.
In the step 1 have 1 dot, in step 2 have 3 dots, in step 3 have 6 dots and in step 4 have 10 dots.
So if we see the pattern then according to number of step the dots increasing accordingly.
As In step 1 have 1 dot, in step 2, 2 dots increase, in step 3, 3 dots increase and in step 4, 4 dots increase.
So, n can represent the the increase of dots according to step.
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2. Which group of numbers is in size order?
A. 3.10 - 3.20 - 3.09 - 3.55
B. 3.09 - 3.10 - 3.2 - 3.5
C. 3.10 - 3.20 - 3.09 - 3.55
D. 3.1 - 3.55 - 3.2 - 3.09
Answers
Answer:
B. 3.09-3.10-3.2-3.5 is the answer
Help
look at the picture
Answers
\(x7 - 2 \: or \: x \leqslant - 3\)
pls HELP ME ASAP DUE TODAY NOW HURRY PLEASE
Answers
Answer: so yea its the first one. im not that sure im just like saying what I know
Step-by-step explanation:
(URGENT)An engineer has a 40:1 scale drawing of a bridge. The dimensions of the scaled bridge deck are 24 inches by four and four fifths inches. What is the area of the actual bridge deck in square feet?
460 square feet
640 square feet
960 square feet
1,280 square feet
Answers
The area οf the actual bridge deck in square feet is 1,280 square feet.
What is Area?Area refers tο the measurement οf the size οf a twο-dimensiοnal surface, usually measured in square units such as square inches, square feet, οr square meters. It represents the amοunt οf space that is inside the bοundary οf a flat οbject οr shape.
The scale οf the drawing is 40:1, which means that the dimensiοns οf the scaled bridge deck are 40 times smaller than the actual bridge deck. Tο find the area οf the actual bridge deck in square feet, we need tο cοnvert the dimensiοns οf the scaled bridge deck frοm inches tο feet and then multiply by the square οf the scale factοr (40² = 1600).
The dimensiοns οf the scaled bridge deck in feet are:
24 inches = 2 feet
4 and 4/5 inches = 0.4 feet
Sο, the area οf the scaled bridge deck in square feet is:
2 feet x 0.4 feet = 0.8 square feet
Tο find the area οf the actual bridge deck in square feet, we need tο multiply the area οf the scaled bridge deck by the square οf the scale factοr:
Area οf actual bridge deck = 0.8 square feet x (40²) = 1280 square feet
Therefοre, the area οf the actual bridge deck in square feet is 1,280 square feet.
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Answer:
Step-by-step explanation:
The scale factor indicates the actual bridge is 40 times larger than the drawing.
Increase the scale dimensions by the factor of 40.
24 times 40 = 960"
4.8 times 40 = 192" (I changed 4 4/5 to 4.8)
Area = length times width
960 times 192 = 184320 sq inches actual bridge deck in square inches
Divide 183320 by 144 (sq inches in a square foot) = 1280 sq feet
The function f(x) = 1.85x2 models the cost of a square carpet, where x is the length in feet. Find the average rate of change for f, to the nearest tenth, over the interval 10 ≤ x ≤ 20.
Answers
To find the average rate of change of the function f(x) = 1.85x^2 over the interval 10 ≤ x ≤ 20, we need to find the difference in the function values at the endpoints of the interval and divide by the length of the interval.
The function value at x = 10 is:
f(10) = 1.85(10)^2 = 185
The function value at x = 20 is:
f(20) = 1.85(20)^2 = 740
The length of the interval is:
20 - 10 = 10
So the average rate of change of the function over the interval 10 ≤ x ≤ 20 is:
(f(20) - f(10)) / (20 - 10) = (740 - 185) / 10 = 55.5
Rounding to the nearest tenth, the average rate of change of the function over the interval 10 ≤ x ≤ 20 is approximately 55.5.
Pls help! College Math!
Answers
Answer:
13+5 = 18
2-(5+4) = -7
3(2-13) +2(4) = -25
a = -9/2
Step-by-step explanation:
\(\int\limits^3_0 {(a f(x) + g(x))} \, dx = 0\)
a(2) + (5+4) = 0
2a = -9
a = -9/2
sam runs a large chain of car repair shops. he pays his employees for 8 hours of work each day. the employees have to log the amount of time they spend working on each job, which results in a number of billable hours for each employee each day. sam would like to estimate the mean number of billable hours for the large number of employees at the company. to do so, he selects a random sample of 10 employees and asks them how many billable hours they tend to have each day. from their responses, he constructs a 95% confidence interval for the true mean number of billable hours for all employees in the company. which of the following may have an impact on the confidence interval, but is not accounted for by the margin of error?
Answers
Sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.
What is Sampling variation?
The term "sampling variance" describes how much a sample estimate (a statistic) is likely to fluctuate from sample to sample due to the unique nature of each sample.
Sample Sizes and Variability are the factors which lead to sampling variation. As and when the sample size is changed i.e. either increased or decreased, the variability of samples fluctuates.
Since, Sam runs a large chain of car repair shops, this means he has large number of employees.
But his sample size is only of 10 employees whom he asks about their billable hours from which he constructs a 95% confidence interval for the true mean number of billable hours for all employees in the company.
Since, sampling variation is greatly affected by the sample size and variability, therefore it will have more impact on confidence interval.
Hence, sampling variation will have more impact on confidence interval but it is not accounted for by the margin of error.
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Since the options are missing in the question, here are the options from which answer is to be chosen
response biasnonresponse biassampling variationundercoverage bias2n+3n+4n=63
Answer and Solution
Answers
Answer:
7
2n + 3n + 4n. = 63
9n = 63
n = 63/9
n = 7
hope it helps
Answer:
n=7
Step-by-step explanation:
add 2n+3n+4n, which gives 9n =63
Divide by 9 on both sides, 9n/9 =63/9
n=7
If you need to confirm that's the right answer, just plug 7 back as n
2(7)+3(7)+4(7)=63
14+21+28 =63
63=63
K= 1/2mv^2Solve for m
Answers
The given equation is expressed as
\(k\text{ = }\frac{1}{2}mv^2\)The first step is to multiply both sides of the equation by 2. It becomes
\(\begin{gathered} 2k=\frac{1}{2}\times2mv^2 \\ 2k=mv^2 \end{gathered}\)The next step is to divide both sides of the equation by v^2. It becomes
\(\begin{gathered} \frac{2k}{v^2}=\frac{mv^2}{v^2} \\ m\text{ = }\frac{2k}{v^2} \end{gathered}\)Find the missing numbers
Answers
Based on the information provided, the missing number would be number 6.
How to find the missing numbers?When it comes to finding missing numbers, the first step is to decipher or identify the pattern. This can be either a sequence of numbers or the application of a specific mathematical operation such as subtraction or addition.
In this case, we can see there is a sequence of numbers that seems to go from 1 to 9. However, if you check carefully, the number 6 is missing, which is the number you need to add.
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Bo kept track of his cookie sales. He
discovered that 3 out of 5 people who
came into his bakery for cookies bought
chocolate chip cookies.
If 400 customers bought cookies at Bo's
Bakery last month, how many of them
bought chocolate chip cookies?
Answers
Answer:240
Step-by-step explanation:
400/5 = 80
80 x 3 = 240
240/400 people bought choc chip
Let y represent the total cost of publishing a book (in dollars). Let x represent the number of copies of the book printed. Suppose that x and y are related by the equation y = 1100 + 15x.Answer the questions below.What is the change in the total cost for each book printed?What is the cost to get started (before any books are printed)?
Answers
y = 1100 + 15x.
Rewriting
y = 15x+1100
This is in slope intercept form
15 is the slope. It is the change for each x
It is the change for each book
The change in total cost for each book is 15 dollars
The y intercept is 1100. It is the cost when x =0. It is the cost when there are no books printed.
It is the cost to get started
The start up cost is 1100 dollars.
5/8 ÷ 1/4 help I will give brainalest
Answers
Answer:
your answer is 2.5 or 2 1/2
Answer:
Result in decimals: 2.5
Result in fractions 2 1/2
Step-by-step explanation:
iff(x) = (x - 3)2
for x = 3, then f-1(x) = ?
A
VX-3
B.
√x+3
O
a VX-3
IN x + 3
Answers
Answer:
Option B. √x + 3
Step-by-step explanation:
f(x) = (x - 3)²
We can obtain the inverse f¯¹(x) of the above expression as follow:
f(x) = (x - 3)²
Replace f(x) with
f(x) = (x - 3)²
y = (x - 3)²
Next, interchange x and y
y = (x - 3)²
x = (y - 3)²
Make y the subject
x = (y - 3)²
Take the square root of both side
√x = y - 3
Add 3 to both side
√x + 3 = y - 3 +3
√x + 3 = y
y = √x + 3
Finally, replace y with f¯¹(x)
y = √x + 3
f¯¹(x) = √x + 3
Which value of x makes this inequality true? x+9<4x
A.4
B.1
C.3
D.2
Answers
Answer:
A. 4
Step-by-step explanation:
Given inequality:
\(x+9 < 4x\)
Rearrange the inequality to isolate x.
Subtract x from both sides of the inequality:
\(\begin{aligned}x+9-x & < 4x-x\\9& < 3x\end{aligned}\)
Divide both sides of the inequality by 3:
\(\begin{aligned}\dfrac{9}{3}& < \dfrac{3x}{3}\\\\3& < x\\\\x& > 3\end{aligned}\)
So the values of x that make the inequality true are:
Any value of x that is greater than 3.Therefore, from the given answer options, the value of x that makes the inequality true is x = 4.
To check this, substitute x = 4 into the inequality:
\(\begin{aligned}x+9& < 4x\\x=4\implies 4+9& < 4(4)\\13& < 16\end{aligned}\)
As 13 is less than 16, the inequality is true when x = 4.
Based on the information in the two-way table, what is the probability that a person
selected at random both bikes and runs?
Round your answer to the nearest tenth of a percent.
Answers
Answer:
Step-by-step explanation:
There are 65 rows of chairs in the auditorium. I
each row as 12 chairs, how many chairs are there in all
Answers
Answer:
780
Step-by-step explanation:
12 chairs x 65 rows
Answer: 780
Step-by-step explanation: Because if each row has 12 chairs then you would already know that sounds like multipication, so just multiply 65 times 12 and that will be 780 chairs in all.
Every 20th person in line at grocery store was asked whether they had used their price plus card today. Out of 50 people, 38 said yes. Is this a valid sampling method? If so, find how many of the 800 people in the store would be expected to be using their price plus card.
Answers
Answer:
This is an example of systematic sampling, which is a valid sampling method if the ordering of the individuals in the population does not affect the results. However, it may not be a representative sample if there is any pattern or bias in the order of the individuals.
Using the given information, we can estimate the proportion of people who have used their price plus card as:
38/50 = 0.76
Therefore, we can expect that approximately 0.76 of the 800 people in the store would be using their price plus card:
0.76 x 800 = 608 people.
Answer:
Yes
608 people
Step-by-step explanation:
800 × 38 =30400
30400 ÷ 50 =608
the equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940. In this equation, a represents the average age and x represents the years since 1940. Estimate the year in which the average age of brides was the youngest
Answers
Answer:
Please help me important question in image
Step-by-step explanation:Please help me important question in image
Please help me important quePlease help me important question in image
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Please help me important question in image
Please help me important question in image
Answer:
The equation a=0.003x^2+21.3 models the average ages of women when they first married since the year 1940 in the United States. In this equation, a represents the average age and x represents the years since 1940. To estimate the year in which the average age of brides was the youngest, we need to find the minimum value of the quadratic function a=0.003x^2+21.3. This can be done by using the formula x=-b/2a, where b is the coefficient of x and a is the coefficient of x^2. In this case, b=0 and a=0.003, so x=-0/(2*0.003)=0. This means that the average age of brides was the lowest when x=0, which corresponds to the year 1940. The value of a when x=0 is a=0.003*0^2+21.3=21.3, so the average age of brides in 1940 was 21.3 years old. This is consistent with the historical data, which shows that the median age of women at their first wedding in 1940 was 21.5 years old. The average age of brides has been increasing since then, reaching 28.6 years old in 2021.
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Which of these statements is true about adaptive evolution?
Answers
Answer:
Adaptive evolution is always changing because the environment is changing continuously.
Hence,
The right answer would be :
Adaptive evolution is a fluctuating change in a trait
Step-by-step explanation:
A Van de Graaff generator is a machine that produces very high voltages by using small, safe levels of electric current. One machine has a current that can be modeled by I(t) = t+ 2, where t > 0 represents time in seconds. The power of the system can be modeled by P (t) = 0.5t3 + 6t2 + 10t. Write an equation expression that represents the voltage of the system.
The voltage V is related to current I and power P by the equation V = P
T
Answers
The equation that represents the voltage of the system is V (t) = t² + 10t.
What is the equation that represents the voltage of the system?The equation that represents the voltage of the system is calculated by applying Ohms law as follows;
P = IV
where;
P is the power of the syetemI is the current flowing in the systemV is the voltage of the systemThe voltage is calculated as;
V = P/I
P = 0.5t³ + 6t² + 10t
I = t + 2
divide P through by 0.5 and then factorize;
P = t³ + 12t² + 20t
P = t(t + 10)(t + 2)
V = P/I
V = (t(t + 10)(t + 2)) / (t+2)
V = t(t + 10)
V (t) = t² + 10t
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A tire shop counted 80 invoices at the end of the month. They charge $325 for a set of new tires and $50 for a set of used tires. The total dollar amount of the invoices was $6,750. Let x represent the number of sets of new tires and y represent the number of sets of used tires. Which system of equations represents the situation?
a. x+y=80
325z=50y + 6,750
b. z+y=80
325x=-50y+6750
c. x+y=80
325x=-50y-6750
d. x+y=80 -325z=-50y + 6,750
Answers
Answer:
\(x+y = 80\\325x+50y = 6, 750\)
Step-by-step explanation:
Le x represents the set of new tires
Let y be the set of used tires
If a tire shop counted 80 invoices at the end of the month, then the equal that represents the total amount of invoices counted at the end of the month is:
\(x+y = 80 ............ 1\)
If they charge $325 for a set of new tires, the total amount charged for new tires will be:
\(325 \times x \\325x\)
If they charge $50 for a set of used tires, the total amount charged for used tires will be:
\(50 \times y\\50y\)
If the total dollar amount of the invoices was $6,750, then the expression that models the amount generated on tickets will be:
\(325x+50y = 6,750 .............. 2\)
Hence the system of equations represents the situation is:
\(x+y = 80\\325x+50y = 6, 750\)
Answer:
x + y = 80
325x = -50y + 6,750
Step-by-step explanation: