Answers
In this case, just take all the x values. They are:
-1, 4, 8, and 4.
Of course, there are no repeats with domain values.
So the domain set would just be -1, 4, and 8.
Or the last choice,
{-1, 4, 8}
Related Questions
Rearrange the formula A = \pi r ^ ( 2) for r
Answers
If A = pi*r^2, and we wish to solve for r, then divide both sides by pi:
A/pi = r^2
Taking the square root of both sides, sqrt(A/pi) = r (r must be positive in this situation).
Which inequality models this problem?
Esin started a T-shirt-printing business. She spent $2500 to purchase supplies to get started and she uses about $4.50 worth of supplies per T-shirt printed. Esin charges $25 for each T-shirt. Let s represent the number of T-shirts.
What is the minimum number of T-shirts Esin will need to sell to make a profit?
25s<2500+4.5s
4.5s≥2500+25s
4.5s>2500+25s
25s>2500+4.5s
Answers
Bob has a dog who weighs 12 pounds. His cat weighs 2/3 as much as the dog. How many pounds does his cat weigh?
Answers
The cat weighs 2/3 as much as the dog
- Divide 12 by 3
= 4
- Then multiply by 2
= 8
His cat weighs 8 pounds.
Select all statements below which are true for all invertible n×nn×n matrices aa and bb
a. (ab)−1=a−1b−1(ab)−1=a−1b−1
b. aba−1=baba−1=b
c. (in+a)(in+a−1)=2in+a+a−1(in+a)(in+a−1)=2in+a+a−1
d. a2b7a2b7 is invertible
e. a+ba+b is invertible f. (a+b)(a−b)=a2−b2(a+b)(a−b)=a2−b2
Answers
Answer:
The statements that are correct are:
c) [tex](in+a)(in+a^{-1})=2in+a+a^{-1}[/tex]
d) [tex]a^2b^7[/tex] is invertible.
e) [tex]a+b[/tex] is invertible.
Step-by-step explanation:
We are given that:
a and b are invertible n×n matrices.
We have to tell which of the following statements are true.
a)
[tex](ab)^{-1}=a^{-1}b^{-1}[/tex]
This statement is false.
Since:
[tex](ab)^{-1}=b^{-1}a^{-1}[/tex] and it may not be equal to the term [tex]a^{-1}b^{-1}[/tex]
b)
[tex]aba{-1}=b[/tex]
This expression could also be written as:
[tex]ab=ba[/tex]
Since on Post multiplying by a on both the sides.
But here we don't know whether the matrices are commutative or not.
Hence, the statement is false.
c)
[tex](in+a)(in+a^{-1})=2in+a+a^{-1}[/tex]
This statement is true.
since,
[tex](in+a)(in+a^{-1})=in(in+a^{-1})+a(in+a^{-1})\\\\=in^2+in.a^{-1}+a.in+aa^{-1}\\\\=in+a^{-1}+a+in\\\\=in+a^{-1}+a[/tex]
where in denote the identity matrix.
and we know that:
[tex]in^2=in[/tex]
d)
[tex]a^2b^7[/tex] is invertible.
This statement is true.
Since we know that prodct of invertible matrices is also invertible.
As [tex]a[/tex] is invertible so is [tex]a^2[/tex].
Also [tex]b[/tex] is invertible so is [tex]b^7[/tex].
Hence Product of [tex]a^2[/tex] and [tex]b^7[/tex] is also invertible.
i.e. [tex]a^2b^7[/tex] is invertible.
e)
[tex]a+b[/tex] is invertible.
This statement is true as sum of two invertible matrices is invertible.
f)
[tex](a+b).(a-b)=a^2-b^2[/tex]
This statement is false.
Since,
[tex](a+b).(a-b)=a(a-b)+b(a-b)\\\\=a.a-a.b+b.a-b.b\\\\=a^2-ab+ba-b^2[/tex]
Now as we are not given that:
[tex]ab=ba[/tex]
Hence, we could not say that:
[tex](a+b).(a-b)=a^2-b^2[/tex]
The correct statements which are true for all invertible [tex]\left({n\times n}\right)\cdot\left({n\times n}\right)[/tex] are:
(c). [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex]
(d). [tex]{a^2}{b^7}[/tex] is invertible.
(e). [tex]a+b[/tex] is invertible.
Further Explanation:
Given:
The matrix [tex]a[/tex] and [tex]b[/tex] are invertible [tex]\left({n\times n}\right)[/tex] matrices.
Calculation:
(a)
The statement is [tex]{\left({ab}\right)^{-1}}={a^{-1}}{b^{-1}}[/tex] false.
[tex]\begin{aligned}{\left({ab}\right)^{-1}}&={a^{-1}}{b^{-1}}\\\left({ab}\right){\left({ab}\right)^{-1}}&=\left({ab}\right){a^{-1}}{b^{-1}}\\I&\ne ab{a^{-1}}{b^{-1}}\\\end{aligned}[/tex]
The statement is [tex]{\left({ab}\right)^{-1}}={a^{-1}}{b^{-1}}[/tex] false.
(b)
The statement is [tex]ab{a^{-1}}=b[/tex].
Now multiply by a both the side.
[tex]\begin{aligned}ab{a^{-1}}a&=ba\\ab&\ne ba\\\end{aligned}[/tex]
The statement is [tex]ab{a^{-1}}=b[/tex] is false.
(c)
The statement is [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex].
Solve the above equation to check whether it is invertible.
[tex]\begin{aligned}\left({in+a}\right)\left({in+{a^{-1}}}\right)&=in\left({in+{a^{-1}}}\right)+a\left({in+{a^{-1}}}\right)\\&=i{n^2}+in\cdot{a^{-1}}+a\cdot in+a{a^{-1}}\\&=in+{a^{-1}}+a+in\\&=in+{a^{-1}}+a\\\end{aligned}[/tex]
The statement is true.
(d)
The statement is [tex]{a^2}{b^7}[/tex].
The product of invertible matrices is always invertible.
As [tex]a[/tex] is invertible so [tex]{a^2}[/tex] is also invertible.
As [tex]b[/tex] is invertible so [tex]{b^7}[/tex] is also invertible.
Hence, the product of [tex]{a^2}[/tex] and [tex]{b^7}[/tex] is also invertible.
The statement is true.
(e)
The statement [tex]a+b[/tex] is true as [tex]a+b[/tex] is always invertible.
(f)
The statement is [tex]\left({a+b}\right)\cdot\left({a-b}\right)={a^2}-{b^2}[/tex].
Solve the equation to check the inevitability.
[tex]\left({a+b}\right)\times\left({a-b}\right)={a^2}-ab+ba-{b^2}[/tex]
The statement is not true as [tex]ab=ba[/tex].
Hence, the correct statements which are true for all invertible [tex]\left({n\times n}\right)\cdot\left({n\times n}\right)[/tex] are:
(c). [tex]\left({in+a}\right)\left({in+{a^{-1}}}\right)=2in+a+{a^{-1}}[/tex]
(d). [tex]{a^2}{b^7}[/tex] is invertible.
(e). [tex]a+b[/tex] is invertible.
Learn more:
1. Learn more about unit conversion https://brainly.com/question/4837736
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3. Learn more about binomial and trinomial https://brainly.com/question/1394854
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Linear equation
Keywords: Invertible, matrices, matrix, statement, function, true, determinants, elements, inverse.
A game of chance involves rolling a 14-sided die once. If a number from 1 to 3 comes up, you win 2 dollars. If the number 4 or 5 comes up, you win 9 dollars. If any other number comes up, you lose. If it costs 5 dollars to play, what is your expected net winnings?
Answers
The expected net winnings are -$36. That is you lose $36 according to chance.
We have given
A game of chance involves rolling a 14-sided die once. If a number from 1 to 3 comes up, you win 2 dollars.
We have to determine expected net winnings
What is the expected net winnings?The expected value is what the player can expect to win or lose if they were to play many times with the same game.
let's say that you have a 3/13 chance of winning $3 and a 2/13 chance of winning $10 and an 8/13 chance of winning $0.
Therefore if the dice is rolled 13 times then the expected to win 3X$3 + 2X$10 = $29
But you pay $5 per roll so 13 rolls would cost me 13X$5 = $65
Therefore the expected net winnings are $29-$65 = -$36
Therefore the expected net winnings are -$36.
So you lose $36 according to chance.
To learn more about the expected winnings visit:
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A swimming pool is being filled ata rate of 15 pints per minute. How many gallons per hour is this
Answers
1 gallon = 8 pints
15/8 = 1.875 gallons per minute
60 minutes per hour
1.875 * 60 = 112.5 gallons per hour
Barbara sells iced tea for $1.49 per bottle and water for $1.25 per bottle. She wrote an equation to find the number of drinks she needs to sell to earn $100.
1.25x + 1.49 = 100
What error did Barbara make in writing the equation?
Answers
Line segment CD is shown on a coordinate grid:
A coordinate plane is shown. Line segment CD has endpoints 1 comma 2 and 1 comma negative 1.
The line segment is rotated 90 degrees counterclockwise about the origin to form C'D'. Which statement describes C'D'?
A) C'D' and CD are equal in length.
B) C'D' is parallel to CD.
C) C'D' is half the length of CD.
D) C'D' is greater than twice the length of CD.
Answers
A) C'D' and CD are equal in length. Is your answer have a nice day. ;)
The answer to this question is A.C'D' and CD are equal in length.
Hope this helps
What is the inverse of the statement? A number that has exactly two distinct factors is prime.
Answers
Answer:
The inverse statement is
"A number that does not has exactly two distinct factors is not prime"
Step-by-step explanation:
Given a statement we have to tell the inverse of that statement.
The given statement is
"A number that has exactly two distinct factors is prime".
We have to write the inverse of the above statement.
The inverse of the statement is
"A number that does not has exactly two distinct factors is not prime"
need help with this plz help me
Answers
Which expression is modeled by this arrangement of tiles?
A.-40/10
B.40/(-10)
C.40/10
D.40/40
ASAP
Answers
C.40/10
----------------
Put a check by all the factors of 15
answers : 1, 2, 3, 4, 5, 10, 15.
please answer ASAP
Answers
Plz help it’s du in like 1 hour
Answers
From the frequency table, X stands for the number and F stands for the number of time that a particular number occur.
So, if we break the table down, we are going to have the following numbers:
1, 1, 2, 2, 3, 3, 3, 3, 3, 4.
The total number of occurrence = Addition of F = 10
Mean = [Summation of all occurrence] / Number of occurrence
Mean = [1+1+2+ 2+3 +3 +3 +3 +3 + 4] / 10 = 25 /10 = 2.5
Therefore, mean = 2.5
SECOND METHOD
Mean = [ 1*2] + [2* 2] + [3 * 5] + [4*1] / [2+ 2 + 5+ 1]
Mean = 2 + 4 + 15 + 4 / 10 = 25 / 10 2.5
Therefore, Mean = 2.5
A rectangular table is 4 times as long as it is wide. If the area is 100ft^2, find the width and length of the table.
Answers
the sum of two consecutive numbers is 73. what are the numbers?
Answers
2x+1=73.
2x=72.
x=36.
So the 2 consecutive numbers are 72 and 36!
Hope this helps! :)
Let's say 1 number is x,
1st = x
2nd = x+1
x+x+1 = 73
2x + 1 =73
2x = 73 - 1
2x = 72
x = 72 / 2
= 36
1st = 36
2nd = 37
Hope this helps :))
~Top
On a recent business trip, a salesman traveled 52 miles the first hour, 64 miles the second hour and 49 miles the third hour.
How many miles did he average per hour?
Answers
☺☺☺☺
Answer: He traveled 54.28 miles per hour as an average.
Step-by-step explanation:
Since we have given that
Number of miles traveled in first hour = 52 miles
Number of miles traveled in second hour = 64 miles
Number of miles traveled in third hour = 49 miles
Average per hour is given by
[tex]=\dfrac{3}{\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}}\\\\\\=\dfrac{3}{\dfrac{1}{52}+\dfrac{1}{64}+\dfrac{1}{49}}\\\\\\=\dfrac{3}{\dfrac{784+637+832}{40768}}\\\\\\=\dfrac{3}{\dfrac{2253}{40768}}\\\\\\=\dfrac{40768\times 3}{2253}\\\\\\=\dfrac{122304}{2253}\\\\\=54.28\ miles/hr[/tex]
Hence, he traveled 54.28 miles per hour as an average.
Pascal wants to find the sum of the measures of the interior angles of a polygon that has n sides. How could he do this?
Answers
multiply by 180 (n-2)
count how many sides you have.. subtract the sides by the number 2. then multiply tht by 180
Answer with explanation:
Smallest Polygon = Triangle , which has 3 sides
Sum of angles of triangle = 180°→→, Using the angle sum property of triangle.
We can find the Sum of angles of triangle, using the formula
= (n-2)×180°
= (3-2)×180°
= 1 × 180°
= 180°
A Quadrilateral has four sides.
Sum of angles of Quadrilateral = 360°
Or , using the formula
=(4-2)×180°
=2 × 180°
=360°
For, n sided Polygon
Sum of it's Interior angles = (n-2) × 180°
To prove this, we should divide that polygon into triangles, and multiply number of triangles by angle of 180°.
For, example, Quadrilateral can be divided into two triangles , sum of interior angles of Quadrilateral =2 × 180°=360°
In 1943 the temperature in rapid city South Dakota fell about 45 degrees in 5 minutes what was the average drop in temperature per minute
Answers
Answer:-9 degrees
Step-by-step explanation:The average drop in temperature per minute is 9 degrees.
How many 1/2 cups servings of r ice are in 3/8 cups of rice? Explain your answer
Answers
1/2÷ 3/8=4/3. To divide one fraction by another, invert (turn upside-down) the second fraction, then multiply.
Jeremy Spent 1/4hours on homework after school another 1/2 after she got home and a final 1/3 hour after dinner. Did she spend more or less than one hour on homework and all? Explain.
Answers
how do you write 2.22 in expanded form
Answers
Answer:
[tex]2 + \frac{2}{10}+\frac{2}{100}[/tex]
Step-by-step explanation:
In the expanded form we write a number as the sum of all place value of its digits from left to right,
Here, the given number,
2.22
By the place value chart,
Place value of first digit = 2 ( ones )
Place value of the first digit after decimal = [tex]\frac{2}{10}[/tex] ( tenth )
Place value of the second digit after decimal = [tex]\frac{2}{100}[/tex] ( hundredth )
[tex]\implies 2.22 = 2 + \frac{2}{10}+\frac{2}{100}[/tex]
Is the symbol μμ used for the population mean or sample mean?
choices are.....
population mean
sample mean
Answers
The symbol μ is used for population mean, while x is used for sample mean in statistics.
Explanation:The symbol μ (pronounced "mew") is used to represent the population mean.
The population mean is a parameter that represents the average value of a variable in the entire population.
On the other hand, the symbol x is used to represent the sample mean, which is the average value calculated from a subset of the population called a sample.
The symbol μ (pronounced "mew") is used to represent the population mean.
It denotes the mean of all values within an entire population, which is a parameter of that population.
To illustrate why μ represents the population mean, consider a dataset: 1, 1, 1, 2, 2, 3, 4, 4, 4, 4, 4.
If this were to represent an entire population, we would calculate the mean and then denote it with μ.
Please help! (Picture included)
Answers
HELP QUICK!!! 3. There is a special sale at the pet store. You can buy a fish bowl and get 6 free goldfish. Carlos and Olivia each buy a bowl and get 6 fish. They want to keep track of their fishes’ growth, so they carefully measure each fish and record these lengths:
1 ¼ in
1 7/8in.
1 1/4in.
1 3/4in.
1 3/8 in.
1 7/8 in.
1 3/8 in.
1 1/4in.
1 4/8in.
1 6/8in.
1 7/8in.
1 3/4in.
(a) Plot the lengths of each of the 12 goldfish on the line plot.
(b) Which is greater: the amount of fish that measure less than 1 1/2 inches in length or the amount of fish with a length greater than 1 1/2 inches?
Answers
for a, make a dot on the line plot at each of the given lengths
b) there are more fishes greater than 1 1/2
Describe the graph of the basic rational function, f(x)=1/x. Talk about its domain and range and compare the function to other ones, i.e. linear or quadratic or exponential.
Answers
negative values of x with produce negative values of f(x) and positive values will produce positive function values. so this hyperbola is symmetric with respect to the origin and all negative values are in Q3 and all positive values are in Q1.
as x gets farther and farther from 0 in either direction, you can see that 1/x will be an ever-increasingly smaller distance from the x-axis. indeed, the limit of this function is zero as x approaches either positive or negative infinity.
if x is between -1 and 1, then the value of f(x) increases until x = 0, the limit of the function as x approaches 0 being positive and negative infinity depending on which direction you are coming from.
the domain is all real numbers with the exception of 0
the range also happens to be all real numbers with the exception of zero. all that really means is that zero has no multiplicative inverse.
strictly speaking, this is an exponential function, as the function is f(x) = x^(-1).
Final answer:
The graph of f(x) = 1/x is a hyperbola with vertical and horizontal asymptotes at x = 0 and y = 0, respectively. The domain is all real numbers except 0, and the range is the same. Unlike linear, quadratic, or exponential functions, the hyperbolic shape of 1/x presents its unique characteristics needing careful domain consideration.
Explanation:
The graph of the basic rational function f(x) = 1/x is characterized by two distinct branches, one in the first quadrant (where x and y are both positive) and the other in the third quadrant (where x and y are both negative). This function is a hyperbola, and as the value of x approaches zero from either the positive or negative side, the value of f(x) increases without bound, referred to as a vertical asymptote at x = 0. Additionally, as the value of x becomes very large or very small (approaching positive or negative infinity), the value of f(x) approaches zero, creating a horizontal asymptote at y = 0. Importantly, this function is undefined at x = 0, so the domain is all real numbers except 0, (domain: ℝ \ {0}). The function takes on all real number values for the output, so the range is also all real numbers except 0 (range: ℝ \ {0}).
Comparing to other types of functions, unlike linear functions like f(x) = 7x which produces a straight line or quadratic functions such as f(x) = 2x² which graphs as a parabola, the rational function f(x) = 1/x leads to a non-linear graph with two separate branches. Exponential functions like f(x) = eⁿ¹, however, grow or decline at an increasing rate, which is a different behavior compared to the hyperbolic decline or rise of a rational function. It's vital to note that as with the function |√x|, there are points along the graph of 1/x where the function is not defined, highlighting the importance of considering the domain in function analysis.
The function 1/x² also represents a rational function but with a different characteristic as it exhibits positive blowup on both sides. This means that as x approaches zero, whether from the positive or negative side, the function tends to positive infinity, a behavior different from the reciprocal function 1/x.
how many 5/16 are in 1 7/8
Answers
15
---
8
====
5
----
16
Invert the 5/16 and then multiply:
15 16 3*2
---- * ---- = ------- = 6 (answer)
8 5
To determine how many 5/16 are in 1 7/8, you convert 1 7/8 to an improper fraction, 15/8, and then divide it by 5/16, which yields 6.
Explanation:To find out how many 5/16 are in 1 7/8, you first need to convert 1 7/8 to a improper fraction. Since 1 is equal to 8/8, adding 7/8 gives us 15/8. Now, to find how many 5/16 are in 15/8, you can divide 15/8 by 5/16. To do this, you multiply 15/8 by the reciprocal of 5/16, which is 16/5.
15/8 × 16/5 = (15×16)/(8×5) = 240/40. This simplifies to 6, meaning there are 6 segments of 5/16 in 1 7/8.
Learn more about Fractions here:https://brainly.com/question/10354322
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At one basketball game there were 1207 people. At the next game they were 958 people how many people were at two games?
Answers
A bag contains 450 blue and yellow marbles. The probability of drawing a yellow marble is 46%. How many blue marbles are in the bag?
Answers
Hope this helps! :)
Which expression shows the result of applying the distributive property to 12(5y+4) ?
A. 17y + 16
B. 5y + 48
C. 60y + 48
D. 60y + 4
Answers
60y + 12 * 4
60y + 48
Answer: C)
12(5y + 4)
12*5y + 12*4
60y + 48
I hope this helps love! :)
Find the perimeter of 6 regular octagons linked together side by side,if one side is 4.5 inches.
Answers
also notice, the octagons on either edge, include 7 sides to the perimeter, whilst the octagons in between, only include 6 sides to the perimeter.
so, add all sides, excluding those borders, and that's the perimeter.
The shape has 38 equal sides, each side is 4.5 inches, so the perimeter is
4.5 × 38 = 171 inches