The inverse of a number is it's reciprocal. Divide 1 by the number to obtain its reciprocal.
For example, the reciprocal of 5 is 1/5, and the reciprocal of 0.5 is 2. The reciprocal of a number x is denoted by 1/x or x^(-1).
For example, to find the reciprocal of 8, you would divide 1 by 8, like this:
1/8 = 0.125
To find the reciprocal of a fraction, you can also turn the fraction upside down to get its reciprocal. For instance, 4/3 is 3/4's inverse.
To find the inverse of a matrix, you can use the following formula:
A^(-1) = (1/det(A)) * adj(A)
where A is the matrix, det(A) is the determinant of the matrix, and adj(A) is the adjugate of the matrix. The transposition of a matrix's cofactor matrix is adjugate. The cofactor matrix is a matrix of the determinants of the minors of the original matrix, each of which is multiplied by a cofactor (-1)^(i+j). The minors of a matrix are the determinants of the square submatrices formed by deleting one row and one column from the matrix. The determinant of a matrix is a scalar value that can be computed from its elements.
For example, consider the matrix A:
[a b]
[c d]
The determinant of A is:
det(A) equals (a * d) - (b * c).
The cofactor matrix of A is:
[d -b]
[-c a]
The adjugate of A is the transpose of the cofactor matrix, so it is:
[d -c]
[-b a]
The inverse of A is then:
A^(-1) = (1/det(A)) * adj(A)
= (1/((a * d) - (b * c))) * [d -c]
[−b a]
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The union of two sets is a set that contains only the elements that appear in both sets
a. True
b. False
The union of two sets is to avoid counting the same elements twice.
What is set?
The mathematical logic subfield of set theory investigates sets, which can be loosely defined as collections of objects. Although any object can be combined into a set, set theory, as a mathematical discipline, focuses primarily on those that are relevant to mathematics as a whole.
Given union of set
(A ∪ B),
The set of all objects that are members of either A or B, or both, is the union of the sets A ∪ B.
let us take example,
A = { 1, 2, 3, 4}
B = {3, 4, 5, 6, 7}
(A ∪ B) = { 1, 2, 3, 4} ∪ {3, 4, 5, 6, 7}
we can simply write all of A and B's elements in a single set to avoid duplicates to find A U B.
(A ∪ B) = {1, 2, 3, 4, 5, 6, 7}
Hence the union of two sets is a set that contains all the elements of both set and avoid duplicates.
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-X+4=67
-4Z-9=67
-7Y-10=67
Answer:
the answer is 20
Step-by-step explanation:
20+0=20
1
Which expression is equivalent to (5³)⁹?
A 53+9
B 53x9
©5³ +5⁹
5³ x 5⁹
Answer: (D) 5³ * 5⁹.
Step-by-step explanation:
The expression (5³)⁹ is the same as 5³ * 5³ * 5³ * 5³ * 5³ * 5³ * 5³ * 5³ * 5³, which can be simplified to 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9 * 5^9. The only expression from the options above that is equivalent to this is 5³ * 5⁹, so the correct answer is (D) 5³ * 5⁹.
x and y are integers.
y>_2
x+y≤4
y≤ 2x + 2
Mark on the grid all the points
that fulfill all three inequalities.
The common region for all the inequalities y ≥ 2, y ≤ 2x + 2and x + y ≤ 4 is represented by ΔABC (the last graph).
What is an inequality?
"It is a statement which consists of an order relationship (greater than, greater than or equal to, less than, or less than or equal to) between two mathematical expressions."
For given question,
We have been given three inequalities
y ≥ 2 ,
x + y ≤ 4 ,
y ≤ 2x + 2
If we draw the graph of these three inequalities then the common region represents the all the points that fulfill all three inequalities.
An inequality y ≥ 2 represents all the points on and above the line y = 2
An inequality x + y ≤ 4 represents all the points on and below the line x + y = 4
An inequality y ≤ 2x + 2 represents all the points on and below the line y = 2x + 2
Consider the following graphs.
The first graph represents the points which fulfill the inequality y ≥ 2
The graph for an inequality x + y ≤ 4 is represented by the shaded blue region.
The graph for an inequality y ≤ 2x + 2 is represented by the shaded green region.
The common region for all the inequalities is represented by ΔABC
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Why we need to clean the measuring instrument before and after use?
Conscientiously cleaning your devices is crucial, as any residue that remains on your device may impact the accuracy of your measurements. The material your device is made of plays a significant role in the cleaning method you should use.
A tool used to measure a physical amount is called a measuring instrument. Measurement is the process of gathering and comparing physical quantities of actual things and events in the physical sciences, quality control, and engineering.
The process of measuring yields a number associating the subject under study and the referenced unit of measurement, and established standard objects and occurrences are employed as units. These numerical relations are acquired using measuring devices and rigorous test procedures that specify the instrument's use.
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can anyone help me.
Answer:
Solution:
Given,
Ratio of photo to to the photo frame=2:3
Length of photo frame=36cm
= 36÷3
=13
then,
Length of photo = 13 ×2
= 26cm
Step-by-step explanation:
Therefore,the length of the photo is 26cm
Eric rides his bike 4 1/3 hours during the week. His little brother rides his bike 1 3/4 hours during the week. How many more hours does Eric ride his bike during the week than his little brother? Enter your answer as a mixed number in simplest form by filling in the boxes.
The parent function of the function g(x)=(x-h)² + kis f(x)=2. The vertex of the function g(x) is located at (9.-
8). What are the values of h and k?
g(x)=(x-____)^2+______
Answer:
h = 9
k = -8
Step-by-step explanation:
⭐ [tex]g(x) = (x-h)^2 + k[/tex] is already written in vertex form.
⭐ Vertex form: [tex]f(x) = a(x-h)^2 +k[/tex], where the vertex is (-(-h), k)
We are already given the vertex (9,-8), so we have to substitute these numbers into g(x).
[tex]g(x) = (x-9)^2 -8[/tex]
The equation of parabola is solved and the values of h and k are 9 and -8 respectively
What is a Parabola?A Parabola, open curve, a conic section produced by the intersection of a right circular cone and a plane parallel to an element of the cone. A parabola is a plane curve generated by a point moving so that its distance from a fixed point is equal to its distance from a fixed line
The equation of the parabola is given by
( x - h )² = 4p ( y - k )
y = a ( x - h )² + k
where ( h , k ) is the vertex and ( h , k + p ) is the focus
y is the directrix and y = k – p
The equation of the parabola is also given by the equation
y = ax² + bx + c
where a , b , and c are the three coefficients and the parabola is uniquely identified
Given data ,
The vertex form of a parabola function is given by:
g(x) = a(x - h)² + k
where (h, k) is the vertex.
In this case, we are given that:
g(x) = (x - h)² + k
And the vertex is located at (9, -8)
So we have:
h = 9
k = -8
Therefore, the function g(x) can be written as:
g ( x ) = ( x - 9 )² - 8
Hence , the equation of parabola is g ( x ) = ( x - 9 )² - 8
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What is the value of 5x25 − 3x32 2x − 12 at x 1?
The value of the given expression 5x²⁵ - 3x³² + 2x - 12 at x = 1 is -8.
Explain the term power of the number?How many times you should multiply a number depends on its power. Exponents and indices are other names for powers. For instance, 8^2 may also be referred to as "8 to the power 2," "8 to the second power," or just "8 squared."The given expression is:
5x²⁵ - 3x³² + 2x - 12
To evaluate the value at x=1.
Substitute x = 1 in the given expression.
= 5(1)²⁵ - 3(1)³² + 2(1) - 12
Simplify:
= 5 - 3 + 2 - 12
= -8
Therefore, the value of the given expression at x = 1 is -8.
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The correct question is-
What is the value of 5x²⁵ - 3x³² + 2x - 12 at x=1?
The meaure of the exterior angle of a quadrilateral are x°x°, 2x°2x°, 4x°4x°, and 5x°5x°. Find the meaure of the mallet exterior angle
The meaure of the smallest exterior angle among the four exterior angles of a quadrilateral are x°,2x°, 4x°, and 5x° is x = 30° .
What is exterior angles?The angle formed between one side of a polygon and another line segment extending from the adjacent side is called the exterior angle of the polygon.
Exterior and interior angles form a straight line and form a linear pair. Therefore, if we know the interior angles of a quadrilateral, we can easily find the exterior angles.Exterior angle + interior angle = 180°A quadrilateral has 4 interior and 4 exterior angles.The sum of the exterior angle measurements of a polygon equals 360 degrees, regardless of the number of sides of the polygon..We have, quadrilateral with exterior angles x° , 2x° , 4x° and 5x° .
As we discuss, the sum of exterior angles of quadrilateral (polygon of four sides) = 360°
=> x° + 2x° + 4x° + 5x° = 360°
Adding all x values on left hand side,
=] 12x° = 360°
=> x = 360/12 = 30°
Now, the smallest exterior angle of quadrilateral is x° , so it's measure is 30°.
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Is 9 by 16 equal to 5 by 9 yes or no?
Answer:
No
Step-by-step explanation:
9/16 and 5/9 have a common factor is 144
So, we have
81/144 and 80/144
So, 9/16 > 5/9
Answer:
Step-by-step explanation:
no they are not equal, NO
What does a standard deviation of 35 mean?
As the standard deviation 35 is high so the values are far from the mean.
What is standard deviation?In the statistics, standard deviation is an estimation that implies how far each available data apart from mean value. In a word, it is a measure of variances of data in relation to the mean. A low standard deviation indicates that values are closer to mean value and high standard deviation indicates the values are distributed widely.
What does a standard deviation of 35 mean?Standard deviation of a given data set 35 means that all data set are 35 unit far from the mean value. As the value is high so all the values are dispersed widely relative to the mean value.
In the other hand, this high standard deviation implies there are enough variances in the given data in relation to the mean.
Standard deviation is one of the measures of risk assessment. Imagine an organization published a number of statistical observation data. If we find a high standard deviation, then it will be high risk of collapse of the business.
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if quadrilateral abcd is rotated 90° clockwise about point a and then reflected across the y-axis to create quadrilateral a’b’c’d’, what will be the coordinate of d’?
According to the 90° clockwise rotation, the new coordinate of the quadrilateral D' is (3, -2)
Quadrilateral
Quadrilateral refers a closed shape and a type of polygon that has four sides, four vertices and four angles.
Given,
If quadrilateral ABCD is rotated 90° clockwise about point A and then reflected across the y-axis to create quadrilateral A’B’C’D’.
Here we need to find the coordinate of D'.
In order to find the new coordinates, first we have to identify the current coordinates of the quadrilateral.
While we looking into the graph, we have identify the point of
A (0,0), B(-4, 3), C(1,5) and D(2,3)
Now, we have to use the rule of clockwise 90° rotation, states that to rotate the figure 90 degrees clockwise about a point, every point(x , y) will rotate to (y, -x).
According to this rule, the new coordinates are written as,
A(0,0) = A'(0,0)
B'(-4,3) = B'(-3,-4)
C(1,5) = C'(5, -1)
D(2,3) = D' (3, -2)
Therefore, the new coordinate of D' is (3, -2).
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A baketball player attemptd 15 baket in a game he make 9 which ratio decribe the number of baket the player made to the number of baket the playerd attempted
The ratio that describes the number of baskets the player made to the number of baskets the player attempted is 9:15. This can be simplified to 3:5.
The ratio of the number of baskets made by the player to the number of baskets attempted is 9/15. This ratio can be simplified to 3/5, which means that for every 5 baskets attempted, the player made 3 baskets. This ratio can also be expressed as a percentage by dividing the number of baskets made by the number of baskets attempted and multiplying the result by 100%. In this case, the percentage of baskets made by the player is 60% (9 baskets made / 15 baskets attempted * 100% = 60%). This means that out of every 100 baskets attempted by the player, he made 60 baskets.
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Ruth ha 12 roll at her bakery. She receive an online order for 60 roll. Ruth bake roll in batche of 24. Select the equation that repreent the given ituation and find the number of batche Ruth need to make to complete the order
the equation that represents the given situation is 12x + 24 = 60 and the number of batches Ruth needs to make to complete the order is 2 batches
The issue can be approached from the reverse. She already has 12 rolls, so take that out of the total. 48 will result from this. The "x" would then indicate how many more batches of 24 she needs to make in order to reach that 48 because she manufactures rolls in batches of 24. She would bake two additional batches to get 60 because 48 divided by 24 is equal to 2. If you put this concept into an equation, you get 24x + 12 = 60; 2 batches
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Can anyone please help me with this question?
Question: If α and β are the roots of 4x^2 + 3x + 7 = 0, find the value of 1/ α + 1/ β
The numeric value of the expression 1/α + 1/β is given as follows:
-3/7.
How to obtain the numeric value of the expression?The quadratic function in this problem is given as follows:
4x² + 3x + 7 = 0.
The coefficients of the quadratic function are given as follows:
a = 4, b = 3, c = 7.
The sum of the roots is given as follows:
α + β = -b/a.
Hence:
α + β = -3/4
The product of the roots is given as follows
αβ = c/a
Hence:
αβ =7/4.
These values are used to obtain the numeric value of the expression, as follows:
1/α + 1/β = (α + β)/αβ = (-3/4)/(7/4) = -3/7.
(the least common multiple of α and β is αβ, and then the least common factor is used to solve the expression).
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What is mode 2 2 3 3 4 4 5 5 6 6 is?
The given data (2, 2, 3, 3, 4, 4, 5, 5, 6, 6) has no mode.
A mode is defined as the value that has the highest frequency in a given set of values. It is the value that appears the most number of times.
In statistics, the value that consistently appears in a particular collection is referred to as the mode. The mode or modal value in a data collection is sometimes referred to as the value or number that occurs most frequently in the data set. In addition, to mean and median, it is one of the three measures of central tendency.
The mode is the value that occurs the most often in a given set of data.
Given data: 2, 2, 3, 3, 4, 4, 5, 5, 6, 6.
In the given observations, data is repeated an equal number of times.
So, the given data has no mode.
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How do you copy a formula in Excel?
To see the steps of copy and paste a formula.
Now, According to the question:
Here's how you copy and paste a formula:
1. Select the cell with the formula you want to copy.
2. Press. + C.
3. Click the cell where you want to paste the formula.
4. To quickly paste the formula with its formatting, press + V.
5. Clicking the arrow gives you a list of options.
Let's know to more:
How do I apply the same formula to multiple cells in Excel?
Fill formulas into adjacent cells
1. Select the cell with the formula and the adjacent cells you want to fill.
2. Click Home > Fill, and choose either Down, Right, Up, or Left. Keyboard shortcut: You can also press Ctrl+D to fill the formula down in a column, or Ctrl+R to fill the formula to the right in a row.
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what is a polynomial function in standard form with zeros 1,2,-2 and -3
The standard form of the polynomial function with zeroes 1, 2, -2, and -3 is
[tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0.
What is a polynomial?Polynomial is an equation written as the sum of terms of the form kx^n.
where k and n are positive integers.
We have,
The zeroes of a polynomial:
x = 1, 2, -2, and -3.
This can be written as,
(x - 1)(x - 2)(x + 2)(x + 3) = 0
Simplify to get the equation.
(x² - 2x - x + 2)(x² + 3x + 2x + 6) = 0
(x² - 3x + 2)(x² + 5x + 6) = 0
[tex]x^4[/tex] + 5x³ + 6x² - 3x³ - 15x² - 18x + 2x² + 10x + 12 = 0
[tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0
Thus,
The equation of the polynomial is [tex]x^4[/tex] + 2x³ - 7x² - 8x + 12 = 0.
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Which property states that the sum of any two whole number is always a whole number?
The closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number."
What is Property of Closure ?
A set has the closure property only under a particular operation which is if the result of the operation is always an element in the set. When a set has the closure property under a particular operation, then we say that the set is “closed under the operation.”
a)The set of integers is closed under the operation of addition because the sum of any two integers is always another integer and is therefore in the set of integers.
b) The set of integers is not closed under the operation of division because when you divide one integer by another, you don’t always get another integer as the answer. For example, 4 and 9 are both integers, but 4 ÷ 9 = 4/9. 4/9 is not an integer, so it is not in the set of integers!
Hence , the closure property of the whole number states that "Addition and multiplication of two whole numbers is always a whole number.
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Most graduate schools of business require applicants for admission to take the Graduate Management Admission Council’s GMAT examination. Scores on the GMAT are roughly normally distributed with a mean of 527 and a standard deviation of 112. What is the probability of an individual scoring above 500 on the GMAT?HOW HIGH MUST AN INDIVIDUAL SCORE ON THE G-MAT IN ORDER TO BE THE HIGHEST 5%
The probability of an individual scoring above 500 on the GMAT is 0.5984.
What is Normal Distribution?An example of a continuous probability distribution is the normal distribution, in which the majority of data points cluster in the middle of the range while the remaining ones taper off symmetrically toward either extreme. The distribution's mean is another name for the centre of the range.
Given:
[tex]\mu[/tex] = 527
[tex]\sigma[/tex] = 112
Now, z= (500-527)/112
z= -27/112
z= -0.2410
and, P( X>500)= P(z> -0.2401)
= 1- 0.4052
= 0.5984
Hence, the probability of an individual scoring above 500 on the GMAT is 0.5984.
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Which formula can be used to find the nth term of the geometric sequence 1/6,1,6,36?
Answer:
[tex]a_n = \frac{1}{6}(6)^{n-1}[/tex]
Step-by-step explanation:
⭐What is the formula of a geometric sequence/progression?
[tex]a_n = a_1+1(d)^{n-1}[/tex][tex]a_1[/tex] is the first term of the geometric sequence[tex]d[/tex] is the common ratio (the number each consecutive term gets multiplied by) of the geometric sequence[tex]n[/tex] is the number term you want to findWe are given the geometric sequence.
Thus, we need to find the first term and the common ratio, and substitute those values into the geometric sequence formula.
The first term is [tex]\frac{1}{6}[/tex]
⭐How do we find the common ratio?
divide one term by another termmake sure both terms are consecutive of each otherI am choosing term 1 and term 2, but you can choose any other 2 terms that are consecutive.
term 1 = [tex]\frac{1}{6}[/tex]
term 2 = [tex]1[/tex]
[tex]\frac{term2}{term1} = \frac{1}{\frac{1}{6}}[/tex]
[tex]\frac{term2}{term1} = 6[/tex]
∴ The common ratio of this sequence is 6.
Now, substitute these values (common ratio & first term) into the geometric sequence equation.
[tex]a_n = \frac{1}{6}(6)^{n-1}[/tex]
Which exponential function has a growth factor of 5?
So, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.
An exponential function of the form y = a * b^x has a growth factor of b. Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.
For example, if a = 2, then the function y = 2 * 5^x has a growth factor of 5.
Here is a table showing the values of y for some values of x:
x y
0 2
1 10
2 50
3 250
4 1250
As x increases, the values of y increase exponentially at a rate determined by the growth factor of 5.
Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.
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For example, if a = 2, then the function y = 2 * 5^x has a growth factor of 5.
Here is a table showing the values of y for some values of x:
x y
0 2
1 10
2 50
3 250
4 1250
As x increases, the values of y increase exponentially at a rate determined by the growth factor of 5.
Therefore, an exponential function with a growth factor of 5 is of the form y = a * 5^x, where a is a constant coefficient.
What is the y-intercept of 5x 4y =- 12?
The y-intercept of the equation 5x-4y = -12 is 3.
What is a slope?In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
To find the slope;
m = (y₂- y₁) / (x₂ - x₁)
We have the equation:
5x-4y = -12
To find the y-intercept:
First, we have to simplify the equation as subject to y.
5x-4y = -12
4y = 5x+ 12
y = (5/4)x+12/4
y = (5/4)x + 3
Now, we know the slope-intercept form:
y = mx+b,
where m is the slope and b is the y-intercept.
Comparing, both the equation,
b = 3
3 is the y-intercept.
Therefore, y-intercept is 3.
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Guys, can you help me with my homework?
Using two column proof, we have been able to show that ΔABE is congruent to ΔCDE via SAS Congruency Postulate.
How to handle two column proof?We are given certain statements of the given triangle and we want to get a flowchart of a proof which is a two column proof. Thus;
Statement 1; CD = AB
Reason 1; Given
Statement 2; BE = DE
Reason 2; AC is the segment bisector of BD
Statement 3; ∠ABE = ∠CDE
Reason 3; Alternate angles theorem
Statement 4; ΔABE ≅ ΔCDE
Reason 4; SAS Congruency Postulate
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What is a possible factor of x³ 6x² 11x 6?
Therefore , the solution to the given problem of the equation whose factors are (x+2)(x+1)(x+3).
Describe equation.
Two expressions joined by an equal sign form a mathematical statement known as an equation.
An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.
According to the Given question:
x³ + 6x² + 11x +6
This pattern of coefficients 1, 6, 11, 6 is actually one that you are likely to encounter frequently.
For demonstration reasons, let's see what occurs if we begin by using the typical technique for resolving a general cubic:
We can use a linear substitution, t = x + b/3a, to simplify any cubic of the form ax3 + bx2 + cx + d, resulting in a cubic in the form a + b + et + f without a quadratic term.
This is the most straightforward type of Tschirnhaus transformation.
In our example, a = 1 and b = 6, so we want t = x + 2.
Note that:
= + 6+ 12x +8
So we find:
+ 6+ 11x +6 = − (x + 2)
= - t
= t ( - 1)
= t(t − 1)(t + 1)
= (x+2)(x+1)(x+3)
Therefore , the solution to the given problem of the equation whose factors are (x+2)(x+1)(x+3).
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What are 3 examples inequality?
How many zeros can the polynomial 2x² 3x 4 have?
There are two zeros of the polynomial 2x²-3x+4.
What is Polynomial?Polynomial is an expression consisting of indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables
The given polynomial is 2x²-3x+4.
Two times of x square minus three times of x plus four.
2x²-3x+4=0
We find the roots by using quadratic equation formula.
x=-b±√b²-4ac/2a
a=2, b=-3, c=4
x=3±√9-4(8)/4
x=3±i√23/4
So the roots are x=3+i√23/4 and x=3-i√23/4.
A polynomial of degree 2 can have 2 real zeros, 1 real zero, or no real zeros
Hence, there are two zeros of the polynomial 2x²-3x+4.
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Renting a roller rink for your birthday costs $250 plus $10 per person. The total charge
for your party was $400. Translate this information into an equation using a to
represent the number of guests at your party.
Using your equation, determine how many people attended your party.
Answer:
15 people attended the party
What is value of expression example?
An example of value of expression is 5 × 2a.
In the field of mathematics, a value of an expression can be described as such an expression that includes two or more two mathematical numbers. Apart from the numbers, one or more than one mathematical operation is also a part of the value of the expression.
In the example, 5×2a, 5 and 2 are the two mathematical numbers and multiplication (×) is the mathematical operation. Hence, the expression 5×2a serves as an appropriate example of the value of expression in the field of mathematics.
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