If a 2×2 matrix A is reverse and is multiplied by its inverse (indicate by the symbol A−1), the develop product is the Identity matrix which is indicate by I.
In fact, I can control the order or direction of multiplication between matrices A and A−1, and I would still get the Identity matrix I. That means reverse matrices are commutative.
A×A^-1= I.
In normal, the inverse of a matrix A is found using the formula (adj A)/ (det A), where "adj A" is the "adjoint of A" and "det A" is the "determinant of A".
the inverse of a 2x2 matrix, say A, is a matrix of the similar order known by A^-1 such that AA^-1 = A^-1A = I, where I is the identity matrix of order 2x2.
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For what value of k will the pair of linear equations kx 3y k 3 12x ky k have a unique solution?.
So, the given system will have a unique solution when k=,1
A system of linear equations in two variables will have a unique solution when the equations are consistent and independent.
In this case, the system of equations is kx + 3y = k and 3x + ky = k.
One way to check for consistency and independence is by using the determinant of the coefficient matrix and comparing it to the determinant of the system. The determinant of the coefficient matrix is (kk) - (3ky) = k^2 - 3ky and the determinant of the system is k^2 - k.
For the system to have a unique solution, the determinant of the coefficient matrix must be non-zero and equal to the determinant of the system.
Therefore, the system will have a unique solution when k^2 - 3ky = k^2 - k.
Which means that k=1.
This system will have a unique solution when k=1, and the pair of linear equations will be 1x + 3y = 1 and 3x + ky = 1.
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The population of a certain animal species decreases at a rate of 3.5% per year.
You have counted 80 of the animals in the habitat you are studying. When will the number of animals drop to 15? Round your answer to the nearest year.
On solving the exponential function A(t) = 80 (0.965)^t, the number of animals will drop to 15 after 47 years.
What is an exponential function?
The formula for an exponential function is f(x) = a^x, where x is a variable and a is a constant that serves as the function's base and must be bigger than 0.
The number of animals studied for the research = 80
The decrease rate of certain species = 3.5%
The rate of decay in exponential term = (1 - 0.035) = 0.965
The exponential function for the situation is -
A(t) = 80 (0.965)^t
Where, t is the number of time periods in years and A(t) = change in the population of animals.
The number of animals drop to 15.
So, substitute the value of A(t) = 15 in the equation -
A(t) = 80 (0.965)^t
15 = 80 (0.965)^t
15/80 = 0.965^t
0.1875 = 0.965^t
ln(0.1875) = t ln(0.965)
t = ln(0.1875)/ln(0.965)
t = -1.6739/-0.0356
t = 47.01
Therefore, the time period value is obtained as t=41 years.
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Shenelle has $25 to spend at the movie theater. She wants to see the regular admission showing of a 3D movie and buy
snacks. Define a variable and write an inequality to represent
the amount of money Shenelle can spend on snacks. Then solve the inequality and interpret the solution. Explain your reasoning.
Movie Ticket
Matinee 2D $5.50
Matinee 3D $7.25
Regular Admission 2D $8.50
Regular Admission 3D $10.25
The inequality that represents the amount of money Shenelle can spend on snacks is given as follows:
x + 10.25 ≤ 25.
The solution to the inequality is of:
x ≤ 14.75.
Meaning that she can spend at most $14.75 on the snacks.
How to define the inequality?The total amount that Shenelle has is given as follows:
$25.
Her spendings are given as follows:
$10.25 on the regular admission of the 3D movie.x on snacks.Hence the inequality is given as follows:
x + 10.25 ≤ 25.
The solution is obtained as follows:
x ≤ 25 - 10.25.
x ≤ 14.75.
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What is commutative property of real numbers?.
The commutative property applies only to addition and multiplication of real numbers.
What is commutative property in math?
This law simply states that with addition and multiplication of numbers, you can change the order of the numbers in the problem and it will not affect the answer. Subtraction and division are NOT commutative.
The commutative property of real numbers states that for any real numbers a and b, a + b = b + a and a * b = b * a. In other words, the order in which two real numbers are added or multiplied does not change the result. This property applies to both addition and multiplication of real numbers.
Therefore, the commutative property applies only to addition and multiplication of real numbers.
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A store sells hardcover books for $8 and paperback books for $5. You buy 7 books represented by the equation x+y=7 where xis the number of hardcover books and y is the number of paperback books. the equation 8x+5y=38 represents the total cost. How many of each type of book did you buy?
if you want to make a figure 9x larger what scale factor do you use?
Someone help me please
The dots are the shaded parts
Answer:
1 [tex]\frac{5}{9}[/tex]
Step-by-step explanation:
Both blocks contain 9 stars
left block has all 9 shaded = [tex]\frac{9}{9}[/tex] = 1
right block has 5 shaded = [tex]\frac{5}{9}[/tex]
mixed number = 1 + [tex]\frac{5}{9}[/tex] = 1 [tex]\frac{5}{9}[/tex]
Keiha i a oftware alewoman. Let y repreent her total pay (in dollar). Let x repreent the number of copie of Hitory i Fun he ell. Suppoe that x and y are related by the equation =1600110xy
Keiha sells computer software she sells 1800 if no books are sold.
Let y signify her overall salary (in dollars).
Let x be the volume of History is Fun that she sells.
Keep in mind that a change can be an improvement or a problem. Use a positive number to indicate an increase. Use a negative integer to indicate a reduction.
Consider the case when the equation =y+180070x connects x and y.
The number of books sold will affect the variable 70x in equation y=1800 + 70x.
Y=70x+1800=70(0)+1800=1800 if no books are sold.
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Full question
Keiko is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of History is Fun she sells. Suppose that x and y are related by the equation 2200 + 90x = y. Note that a change can be an increase or a decrease. For an increase, use a positive number. For a decrease, use a negative number.
What is the change in Keiko's total pay for each copy of History is Fun she sells?
Write the polynomial expression is which the GCF of is factored from the polynomial 32x^(2) - 16
Answer:
Step-by-step explanation:
7x-2y+5 xy + x 2 for x= -1and y= 2
Answer:
= - 23.
Step-by-step explanation:
7x - 2y + 5 xy + x 2
From the question
x = -1
and
y = 2
7(-1) - 2(2) + 5 (-1)(2) + (-1) 2
= -7 - 4 + 5 (-2) - 2
= -7 - 4 -10 - 2
= - 11 - 12
= - 23.
Chandler, the owner of a boutique, kept track of which sizes were worn by the store's customers. small 3 medium 32 large 22 What is the experimental probability that the next customer to come into Chandler's boutique wears a size small? Write your answer as a fraction or whole number.
The experimental probability that the next customer to come into Chandler's boutique wears a size small is; 1/19
How to find the experimental probability?Theoretical probability is defined as the term used to describe what we expect to happen based on math theory, while experimental probability refers to what actually happens when the actual situation is tried out as an experiment.
In this question, we are given;
Number of small wears = 3
Number of medium wears = 32
Number of large wears = 22
Thus;
Total number of wears = 3 + 32 + 22
= 57
Probability that next customer wears small size = 3/57 = 1/19
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the slope-intercept form is used to write a linear equation.
How do you find the equation of a function in factored form?.
Using factoring, we do the following actions to make rational expressions simpler:
As much as you can, factor the numerator and denominator. Any factors that appear in both the numerator and the denominator should be eliminated. Your expression gets simplified as a result. How is an expression factorized:
Step 1 is to identify the expression's prime factors.
Step 2: Find the GCF by enclosing the common factors.
Write each term in the expression as a combination of the GCF and the final factor in step 3.
Step 4: Simplify the equation by applying the distributive property.
Y=12(x-6)(x+2) is an illustration of a quadratic function in factored form. This shape can be examined to determine the vertex as well as the graph's x-intercepts.
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(2,n) and (0,8) Slope is -2 what is n?
Answer:
n = 4-------------------
Use slope equation:
m = (y₂ - y₁)/(x₂ - x₁), where m - slope, (x₁, y₁) and (x₂, y₂) are pointsSubstitute coordinates and solve for n:
- 2 = (8 - n)/(0 - 2)- 2 = (8 - n)/ (-2)8 - n = (-2)*(-2)8 - n = 4n = 8 - 4n = 4Solev
solve the system of inequalities
Answer:
b.
Step-by-step explanation:
5x ≥ 15 or x + 4 > 13
5x ≥ 15
x ≥ 15/5
x ≥ 3
x + 4 > 13
x > 13-4
x > 9.
So, the answer is x ≥ 3
How do you solve log base 7 1?.
The solution to log base 7 of 1 is x=0, which is the value of the power to which 7 must be raised to get the value 1.
The logarithm function is an inverse function of the exponential function, and it is defined as log_b(x) = y means b^y = x. In other words, it represents the power to which the base b must be raised to get the value x.
In this case, we are solving log_7(1), which means we are looking for the power to which 7 must be raised to get the value 1.
Since any number raised to the power of 0 is 1, we can say that 7^0 = 1, which means that log_7(1) = 0.
To solve log base 7 1, you need to find the value of x that satisfies the equation log_7(x) = 1.
Using the definition of logarithm, log_b(x) = y means b^y = x.
So to solve log7(1), we can set 1 = 7^x and get x = log7(1) = 0
So the solution to log base 7 of 1 is x=0.
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Solve for x. Round to the nearest tenth, if necessary.
The value of x is 3.67 in the given right angled triangle.
What is triangle ?
Triangle can be defined in which it consists of three sides , three angles and sum of three angles is always 180 degrees.
In the given triangle ,
Triangle STU ,
T = 90
S = 69
So, U = 180 - 90-69
U = 180 - 159
U = 21
And US = 10
sin69 = TU/US
sin69 = TU / 10
0.93 = TU/ 10
93 / 100 = TU / 10
93/10 = TU
TU = 9.3
So, in the triangle
as per pythagores theorem ,
SU^2 = ST^2 + TU^2
10*10 = x*x + 9.3*9.3
x*x = 100-86.49
x*x = 13.51
x = 3.67 (Approx)
Hence, The value of x is 3.67 in the given right angles triangle.
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Use the vertical line test to determine if the graph represents a function.
The graph that depicts a function is graph when the vertical line test is used (b).
What is meant by vertical line test?By visually counting the number of times the curve crosses vertical lines, the vertical line test is a graphical approach for verifying whether a curve in the plane accurately depicts the graph of a function. the graph of a function can only be intersected by any vertical line in the plane once as a result.
A graph must satisfy the vertical line test in order to be considered a function representation. The vertical line test requires that the line from the x-axis only once crosses an associated y-value.
Graphs (a), (c), and (e) fail the vertical line test, indicating that they do not reflect a function.
So, graph is the name of the graph that represents a function (b)
The complete question is:
Use the vertical- line Test to determine which graph represents a function? I'm thinking it's the first one...
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How to find variance in R?.
The var() function in R is used to calculate sample variance. In those uncommon situations where you want a populace change, utilize the populace mean to work out the example difference and duplicate.
The outcome by (n-1)/n; Take note of the fact that sample variance converges on population variance as sample size increases.
In R, how is variance manually calculated?Find the mean of the sample.Determine the squared difference between the sample mean and each data point.Divide the sum of squares by (i.e., the sample size minus 1) to get the sum of these squared differences.In R, how are variance and standard deviation calculated?R's sample variance and standard deviation are specified by var(y), which tells R to calculate the sample variance of Y by employing n-1 "degrees of freedom," where n is the number of observations in Y. On the other hand, sd(y) tells R to return the sample standard deviation of y by employing n-1 degrees of freedom. sqrt(var(y)) equals sd(y).
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State the equation of the graphed function.
The equation of the graphed function is given as follows:
f(x) = x³ + 2x² - 5x - 6.
How to obtain the equation of the function?
The equation of the function is obtained considering the Factor Theorem, as a product of the linear factors of the function.
From the graph, the zeros of the function are:
x = -3.x = -1.x = 2.Hence the function is:
f(x) = a(x + 3)(x + 1)(x - 2).
In which a is the leading coefficient.
Expanding the product, we have that:
f(x) = a(x² + 4x + 3)(x - 2)
f(x) = a(x³ + 2x² - 5x - 6).
When x = 0, y = -6, hence the leading coefficient a is obtained as follows:
-6a = -6
a = 1.
Hence the function is:
f(x) = x³ + 2x² - 5x - 6.
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What are the possible ways in which two consecutive odd numbers are added to sum of 2023?
Possible way in which two consecutive odd numbers are added to sum of 2023 is by evaluation using the formula (2n - 1) + (2n + 1) = 2023, so that we have 1010.5 + 1012.5 = 2023
What are consecutive odd numbersConsecutive odd numbers are a sequence of numbers that are separated by a difference of 2 and are all odd numbers. For example the first four odd numbers are: 1, 3, 5, and 7. Odd numbers can be generated using the formula 2n -1.
We shall represent the first odd number with (2n - 1) so that the two consecutive odd numbers will be expressed as:
(2n - 1) + (2n + 1) = 2023
2n + 2n = 2023
4n = 2023
n = 2023/4 {divide through by 4}
n = 505.75
Therefore the two consecutive odd numbers added to sum of 2023 are derived as:
2(505.75) - 1 = 1010.5 and 2(505.75) + 1 = 1012.5
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Answer: Well, let’s consider a number, [math]n[/math], it could be even or odd, it doesn’t ...
Step-by-step explanation:
How to solve 3 equations with 3 variables using substitution?.
Solving 3 equations with 3 variables using substitution involves using one equation to solve for one variable in terms of the other variables, and then substituting that expression into the other equations. Here is the general process:
1. Choose one of the equations and solve for one of the variables in terms of the other variables. For example, if the equation is 2x + 3y - z = 5, you can solve for x by isolating it on one side of the equation: x = (5 + z - 3y)/2
2.Substitute the expression for the solved variable into the other equations. For example, if you have the equations 2x + 3y - z = 5, x + y + z = 7, and 3x - 2y + z = 6, you would substitute x = (5 + z - 3y)/2 into the other equations.
3.For the remaining variables, solve the resulting equations. For instance, you would obtain y + z = 7 - (5 + z - 3y)/2 and 3(5 + z - 3y)/2 - 2y + z = 6 after inserting x = (5 + z - 3y)/2 into the other equations.
4.By putting the remaining variables on one side of the equation, you can solve for them. After that, you can solve for the variable's value.
5.Check to see if the solution is valid by substituting it back into the original equation.
It's crucial to remember that this approach could not always result in a singular solution; in certain circumstances, you might discover that the system has neither a solution nor an unlimited number of solutions.
therefore, using these 5 steps we can solve the equations using substitution .
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is y=8.75x linear or non-linear
Answer: liner
Step-by-step explanation:
Answer:
Step-by-step explanation:
linear, because the slope intercept fomat is y=mx+b it's just that the y intercept is zero so they just excluded it. So the equation would be y=8.75x+0 but they just removed the zero to simplify. So yes, it is linear
(Theoretical Probability LC)
When tossing a two-sided, fair coin with one side colored yellow and the other side colored green, determine P(yellow).
A: yellow/green
B: green/yellow
C: 2
D: 1/2
Total number of outcomes (n) = 2
Let E be the event of getting a yellow colored side of the coin.
Therefore, n(E) = 1
Therefore, P(E) = n(E)/n = 1/2
Answer:
1/2
Hope it helps.
If you have any query, feel free to ask.
College tudent are randomly elected and arranged in group of three. The random variable x i the number in the group who ay that they take one or more online coure. Determine whether a probability ditribution i given. If a probability ditribution i given, find it mean and tandard deviation. If a probability ditribution i not given, identify the requirement that are not atified. X P(x)
0 0. 108
1 0. 354
2 0. 390
3 0. 148
Yes, a probability distribution is given.
The mean of this probability distribution is 1.62 and the standard deviation is 0.84.
Mean = ΣxP(x) = 0*0.108 + 1*0.354 + 2*0.390 + 3*0.148 = 1.62
Standard Deviation = √Σ(x-mean)2P(x) = √(0-1.62)2*0.108 + (1-1.62)2*0.354 + (2-1.62)2*0.390 + (3-1.62)2*0.148 = 0.84
This is a probability distribution for a situation in which college students are randomly elected and arranged in groups of three. The number of people in the group who claim to take one or more online courses is the random variable, or x. The probability distribution is given by the values of x and the probabilities associated with them (P(x)). From the given values, we can calculate the mean and standard deviation of the distribution. The mean of the distribution is 1.62, and the standard deviation is 0.84. This means that, on average, 1.62 students in the groups of three will say that they take one or more online courses. The standard deviation of 0.84 implies that the actual number of students in the groups who say that they take online courses will vary from the mean value by about 0.84 students
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For a company picnic, Kenny ordered a box of fresh-baked gingerbread cookies and sugar cookies. The box included a total of 90 cookies, and 70% of them were gingerbread. How many gingerbread cookies did Kenny get
Answer: 63 gingerbread cookies
Step-by-step explanation: Okay, to find the answer to this problem, we shall use this formula:
Final amount = Whole # * Part % / 100
So, now let's plug in the numbers to find the answer:
Final amount = 90 * 70 / 100
= 6300/ 100
= 63
Therefore, Kenny ordered a total of 63 gingerbread cookies. I hope this helped!
HELP PLEASE THIS IS OVERDUE!!!!!!!!!!!!!!!
The high school tennis team is made up of boys and girls. The team has a total of 25 players. 12 of the players are girls. If a player is chosen at random, what is the probability that the player will be a boy?
A. 0.52
B.0.26
C.0.13
D.0.048 (will mark brainliest)
Answer:
0.52
Step-by-step explanation:
25-12=13
boys are equal to 13
the probability of picking a boy at random will be;
13/25=0.52
A recent college graduate is looking to begin saving for retirement. Option A is a savings account with 3.5% annual simple interest. Option B is a savings account with 3.5% annual interest compounded monthly. If the principal investment is the same for both options, which account would have a larger balance after 10 years? Option A will have the larger balance after 10 years because simple interest generates earnings from principal only. Option A will have the larger balance after 10 years because simple interest generates earnings from both principal and interest. Option B will have the larger balance after 10 years because compound interest generates earnings from both principal and interest. Option B will have the larger balance after 10 years because compound interest generates earnings from principal only.
CI will yield more amount, because simple interest generates earnings from principal only.
What is interest?Interest rate is the amount charged over and above the principal amount by the lender from the borrower.
Given that, A recent college graduate is looking to begin saving for retirement. Option A is a savings account with 3.5% annual simple interest. Option B is a savings account with 3.5% annual interest compounded monthly.
Let the principal amount be, $20000
Solving for simple interest, we get,
SI = PRT / 100
= 20000×3.5×10 / 100
= 7000
Therefore, amount = $27000
Now, CI =
A = P(1+r)ⁿ
A = 20000(1+0.035/12)¹²⁰
A = 1241286.32
Therefore, we see that CI will yield more amount.
Hence, CI will yield more amount, because simple interest generates earnings from principal only.
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How many images are formed when two plane mirrors are placed at 36?.
The images are formed when two plane mirrors are placed at 36 is 9
The term plane in math defined as a two-dimensional doubly ruled surface spanned by two linearly independent vectors.
Here we need to find the number of images are formed when two plane mirrors are placed at 36.
Here we have given that the generalization of the plane to higher dimensions is called a hyperplane.
And here we also know that the angle between two intersecting planes is known as the dihedral angle.
The by using the formula we have calculated as,
=> n = (360 / 36) - 1
=> n = 10 - 1
=> n = 9
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Beth leaves her house to drive to work. She first travels 9 miles west and 9 miles north before stopping to put
gas in her car. She then travels 6 miles west and 6 miles north before stopping to pick up a coworker. From the
coworker's home, they then travel 10 miles east and 7 miles south to their office. Overall, how far east/west and
north/south is Beth’s office from her home? What displacement is her office from her home?
Her displacement is 9.43 miles, and her office is 5 miles west and 8 miles north from her house
How to find her displacement?Let's use the notation (x, y) to denote Beth's position, we assume she starts at the point (0, 0).
The x-value defines the motion due east (+), west (-)The y-value defines the motion due north (+), south (+)First she travels 9 miles west and 9 miles north, so the new position is:
(0 - 9, 0 + 9) = (-9, 9)
Then travels 6 miles west and 6 miles nort
(-9 - 6, 9 + 6) = (-15, 15)
then travel 10 miles east and 7 miles south to their office
(-15 + 10, 15 - 7) = (-5, 8)
So the office is 5 miles west and 8 miles north from her house, and the displacement is equal as the absolute value of that point.
dispacement = √( (-5)² + 8²) = 9.43
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