Answers
The determinant of the given matrix is [tex]2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]
Determinant of the matrix:
Determinant of the matrix is defined as a scalar value which is associated with the square matrix.
Given,
Here we have the matrix show in the question.
Now, we need to find the determinant of the matrix.
To find the determinant of the matrix we have to do the following steps:
1) First we have to pick any row or column in the matrix. It does not matter which row or which column you use, the answer will be the same for any row or column.
2) After the selection you have to multiply every element in that row or column by its cofactor and add. The result is the determinant.
This process can be elaborated in the following steps:
[tex]=(b+c)^2 \times ((a+c)^2 \times (a+b)^2 - b^2 \times c^2) -a^2 \times (b^2 \times (a+b)^2 - b^2 \times c^2) +a^2 \times (b^2 \times c^2 - (a+c)^2 \times c^2)[/tex]
When we expand the equation then we get,
[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+c^2b^2+2acb^2 -b^2c^2) -a^2 \times(b^4+2b^3a+b^2a^2 -b^2c^2) +a^2 \times(b^2c^2 -c^4-2c^3a-c^2a^2)[/tex]
Group the similar terms and arrange them in order,
[tex]=(b+c)^2 \times (a^4+2a^3b+2a^3c+a^2b^2+4a^2cb+c^2a^2+2c^2ab+2acb^2) -a^2 \times (b^4+2b^3a+b^2a^2-b^2c^2) +a^2 \times (-c^4-2c^3a+b^2c^2-c^2a^2)[/tex]
Again we have to expand it and then we get,
[tex]= a^4b^2+2a^4bc+a^4c^2+c^4a^2+2c^4ab+2a^3b^3+6a^3b^2c+6a^3bc^2+2a^3c^3+6c^3ab^2+a^2b^4+6a^2b^3c+10a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4 -b^4a^2-2b^3a^3-b^2a^4+b^2c^2a^2 -c^4a^2-2c^3a^3+b^2c^2a^2-c^2a^4[/tex]
After the simplification, the resulting determinant is
[tex]=2a^4bc+2c^4ab+6a^3b^2c+6a^3bc^2+6c^3ab^2+6a^2b^3c+12a^2b^2c^2+6a^2c^3b+6c^2ab^3+2acb^4[/tex]
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Related Questions
a train increased its prices from £663 to £895.05 how much has this increased in a percentage
Answers
Answer:
The price has increased 35%
Step-by-step explanation:
GivenInitial price = £663,New price = £895.05.Find the percent increaseFind the amount of increase:
£895.05 - £663 = £232.05Find the percent value of the increase over the initial price:
232.05/663 × 100% = 35%ASAP NEED HELP WILL GIVE BRAINLIEST
Answers
The value of the unknown angle x is 22 degrees.
How to find the angle x?SV is a parallel to RU.
RV is a transversal line that cut across the parallel lines SV and RU.
Therefore,
x = ∠V(alternate angles)
Alternate angles are congruent.
Hence,
∠V + 44 + 5x + 4 = 180 (sum of angles in a triangle)
x + 44 + 5x + 4 = 180
x + 5x + 48 = 180
6x + 48 = 180
6x = 180 - 48
6x = 132
divide both sides by 6
x = 132 /6
x = 22 degrees
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Write an explicit formula for an, the nth term of the sequence
64, -16, 4,....
Answers
The formula for the given arithmetic series for the term aₙ will be aₙ=a₁+(n-1)d.
What is arithmetic series?An arithmetic series is the sum of a sequence like 2,..., where each term is calculated by adding (or subtracting) a constant from the previous one. An ordered group of numbers with a shared difference between each succeeding term is known as an arithmetic sequence. For instance, the common difference in the arithmetic series 3, 9, 15, 21, and 27 is 6.So, the possible sequence of -64, -16, 4:
We can notice the sequence as -(4³), -(4²), 4, 4², 4³.So, the formula for the aₙ term will be:
aₙ = a₁ + (n - 1)dTherefore, the formula for the given arithmetic series for the term aₙ will be aₙ = a₁ + (n - 1)d.
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The correct question is given below:
Write an explicit formula for an, the nth term of the sequence
-64, -16, 4,....
Triangle TAB has a perimeter of 40 cmeters. Could the measures of the sides as shown actually represent the measures of the sides of the triangle? Justify your answer.
Answers
EXPLANATION
We can apply the Obtuse Triangle Theorem to check if the the measures of the sides appropiately represents the measures of the triangle:
Perimeter = 40 cm = 4x + 2x + 2 + x + 3
Adding like terms:
40 = 7x + 5
Subtracting 5 to both sides:
40 - 5 = 7x
Adding like terms:
35 = 7x
Dividing both sides by 7:
35/7 = x
Simplifying:
[tex]5=x[/tex]Then, by the obtuse triangle theorem, the following relationship should be fulfilled.
Given h(t) = –16t2 + 32t + 5, what is the value of h(2)? *Type in your answer. h(2) =
Answers
The value of the function h(2) for h(t) = -16t2 + 32t + 5 is h(2) = 5
How to determine the function value?From the question, the function definition is given as
h(t) = -16t2 + 32t + 5
First, we express the exponent in the function properly
This is represented as
h(t) = -16t² + 32t + 5
The function value to calculate is given as
h(2)
This means that we calculate h(t) when t = 2
So, we have
h(2) = -16(2)² + 32(2) + 5
Evaluate the exponents
h(2) = -16(4) + 32(2) + 5
So, we have
h(2) = 5
Hence, the function value is 5
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The average price of a certain model of pickup truck in 1992 was $12,500. In 2013, the average price of the pickup truck was $22,000. What is the percentage increase in the average price of the pickup truck?
Answers
The average price in 1992 and 2013 was given. It is required to find the percentage increase in the average price over these years.
Recall that the formula for Percentage Increase is:
[tex]\text{percent increase}=\frac{\text{final price-initial price}}{\text{initial price}}\times100\%[/tex]Substitute initial price=12500 and final price= 22000 into the formula:
[tex]\begin{gathered} \text{percent increase}=\frac{22000-12500}{12500}\times100\%=\frac{9500}{12500}\times100\%=0.76\times100\% \\ \Rightarrow\text{percent increase}=76\% \end{gathered}[/tex]Hence, the percent increase in the average price is 76%.
Answer:
depends on whether or not the dealerships are scammers
Step-by-step explanation:
Which number line and equation show how to find the distance from -2 to 5? O O A. 1-2-(-5) 2 3 12-1-5) sing O c. 1-2-5 D. 2-5
Answers
To find the distance between two numbers on the number line, you have tu use absolute value
So, if I want to know the distance from -2 to 5, all I have to do is to substract 5 from -2 and then apply absolute value, like this:
[tex]\mleft|-2-5\mright|\text{ = }\mleft|-7\mright|\text{ = 7}[/tex]And the number line should look like this:
Which is greater 12.5 or |-13|?
Answers
From the question, we are asked to find which is great between 12.5 or |-13|
recall:
|-13|
The absolute value is the distance between a number and zero. The distance between -13 and 0 is 13.
The absolute symbol makes any number positive.
So, |-13| is the greater because |-13| = 13.
So, between 12.5 and |-13|, |-13| is greater since it is same as 13.
Ten bags of oranges were sold to a family of eight.each family member ate six oranges, what fraction of the oranges were eaten?
Answers
The fraction of oranges eaten by the family is 3/5
Given,
Number of oranges in a bag = 8 oranges
Number of bags sold to a family = 10 bags
Number of members in the family = 6 members
Number oranges ate by each member of the family = 6 oranges
We have to find the fraction of the oranges eaten by the family members;
Here,
8 oranges in 1 bag and 10 bags sold.
So, total number of oranges sold = 8 x 10 = 80 oranges
Each member ate 6 oranges and there are 8 members.
So, total number of oranges eaten by them = 6 x 8 = 48 oranges
Now,
The fraction of oranges eaten by the family = 48/80 = 6/10 = 3/5
That is,
3/5th of oranges were eaten by the family.
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Hakeem is the oldest of three siblings who ages are consecutive integers. If the sum of their ages are 69, find Hakeem age
Answers
Answer:
24
Step-by-step explanation:
Hakeem is the oldest of three siblings who ages are consecutive integers. If the sum of their ages are 69, find Hakeem age.
It should be noted that:
= 22 + 23 + 24
= 69
Hakeem's age is 24
What is 1 1/4 Divided by 10
Answers
Answer: 0.125
Step-by-step explanation:
1 1/4 is equal to 5/4
5/4 is equal to 1.25
then you would do 1.25 divided by 10
once you do that you would get your answer of 0.125!
Answer:
11/4÷10 =
11/4 ×1/10=
11/40=
0.275
Step-by-step explanation:
you can ask questions for clarification
Which is the better buy? 2-gallon container of laundry detergent for $23.36. or 17-cup container of laundry detergent for $20.06
Answers
we gotta know the conversion between cups and gallons
We know
1 cup (US) = 0.0625 gallons
So, 2 gallon would be 2/0.0625 = 32 cups
So, the problem in cups is:
32 cups = $23.36
17 cups = $20.06
Definitely 32 cups for 23.36 is better buy
2 gallons for $23.36 is the better buy
Note:
23.36/32 = $0.73 per cup
20.06/17 = $1.18 per cup
The image of the point (1, 1) under a translation is (0, 3). Find the coordinates of the image of the point (-4, "-1) under the same translation.
Answers
The image of the point (-4, -1) after the translation is:
(-3, 1)
How to identify the translation?
A translation:
Tᵃ'ᵇ applied to a point (x, y) gives:
Tᵃ'ᵇ(x, y) = (x + a, y + b).
In this case, we know that:
Tᵃᵇ(1, 1) = (1 + a, 1 + b) = (0, 3)
Then:
1 + a = 0
1 + b = 3
Solving these we get:
a = 1
b = 3 - 1 = 2
The translation is:
T¹'²
Applying this to the point (-4, -1) gives:
T¹'²(-4, -1) = (-4 + 1, -1 + 2) = (-3, 1)
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Write the sentence as an equation.
y decreased by 283 is equal to 48
Answers
Answer:
y - 283 = 48
Step-by-step explanation:
y decreased by 283 means that 283 is subtracted from y. All set equal to 48.
283 is being subtracted from y therefore y-283 is equal to 48
How to solve? Please help i will give good rating.
Answers
Answer:
6. Draw a vertical line that goes though points (4,7) and (4,9). For a relation to be a function, each input has to have only one output. The input 4 cannot have the output of 7 and 9. This proves that this is not a function
7. The range is 91, 3, 6, 10 and 15)
Step-by-step explanation:
The range is the answer if you put in the x for range that they give you.
For example:
x ( x+ 1)/2 If I put in 1 for x, I will get
1(1+1)/2
2/2
1
When the input is 1, the output is one. You that for each of the domains given and you will find the ranges (outputs) that I have written above.
Factorise 4x^2+13x-15
Answers
The factors of the given quadratic equations are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]
What is factorization?
When we try to write the given equation in terms of linear values from which we calculate the roots of the given equation then we say that we have factorized them. Root of a equation means a value which satisfies a equation.
We are given a quadratic equation
[tex]4x^2+13x-15[/tex]
We use quadratic formula to compute the factor of the equation
[tex]x=\frac{-b}{2a}[/tex]±[tex]\frac{\sqrt{b^2-4ac} }{2a}[/tex]
[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{169+240} }{8}[/tex]
[tex]x=\frac{-13}{8}[/tex]±[tex]\frac{\sqrt{409} }{8}[/tex]
Therefore the factors are [tex]\frac{-13+\sqrt{409} }{8}[/tex] and [tex]\frac{-13-\sqrt{409} }{8}[/tex]
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it usually takes davin 1 3/4 hours to get to his aunt's house . due to labor day traffic this year it took 3 1/5 hours .how much longer did it take this year
Answers
It took David 1 [tex]\frac{3}{4}[/tex] hours more to reach her aunt's home due to labor day traffic.
What is unitary method?The unitary method is a method in which you find the value of a single unit and then the value of a required number of units.
Given is Davin who needs 1 3/4 hours to get to his aunt's house. However, due to the labor day traffic this year it took him 3 1/5 years.
We have to find the difference between the time span Davin took to reach his aunt's house.
Time taken by Davin without the labor day traffic = T[N] = 1 3/4 = 7/4 hours
Time taken by Davin with the labor day traffic = T[L] = 3 1/5 = 16/5 hours
Difference in time spans = T[D] = T[L] - T[N]
T[D] = 16/5 - 7/4
T[D] = 3.2 - 1.75
T[D] = 1.45 = 1 + 0.45
T[D] = 1 [tex]\frac{3}{4}[/tex] hours
Davin took 1 [tex]\frac{3}{4}[/tex] hours more.
Therefore, it took David 1 [tex]\frac{3}{4}[/tex] hours more to reach her aunt's home due to labor day traffic.
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Evaluate cos 150° without using a calculator.Ο Α.√32B. 2O C. -1/2OD. -32
Answers
Note that:
[tex]\begin{gathered} cos(A+B)=cosAcosB-sinAsinB \\ cos(150^0)=cos(90+60) \end{gathered}[/tex]Applying the addition formula given above to cos 150:
[tex]\begin{gathered} cos(150)=cos(90)cos(60)-sin(90)sin(60) \\ \\ cos(150)=0(\frac{1}{2})-1(\frac{\sqrt{3}}{2}) \\ \\ cos(150)=0-\frac{\sqrt{3}}{2} \\ \\ cos \end{gathered}[/tex]5. Identify whether each unit measures length, volume, or weight (or mass).
1.
Mile
Cup.
Pound
Centimeter
2.
3.
4.
5.
Liter
6.
Gram
7.
Pint
8.
Yard
9. Kilogram
10. Teaspoon,
11. Milliliter
Answers
Answer:
See below
Step-by-step explanation:
Length (L), volume (V), weight(W), or mass(M)
Mile L
Cup V
Pound W
Centimeter L
Liter V
Gram M
Pint V
Yard L
Kilogram M
Teaspoon V
Milliliter V
1. Mile
2. Cup
3. Pound
4. Centimeter
5. Liter
6. Gram
7. Pint
8. Yard
9. Kilogram
10. Teaspoon,
11. Milliliter
ABCD is a quadrilateral
Work out the length of BC
Give your answer correct to 1 decimal place.
Answers
Using the law of cosines, the length of BC in the given quadrilateral is: 8.1 cm.
What is the Law of Cosines?The law of cosines that can be used to find the length of a side of a triangle with a known included angle and two sides is:
c² = a² + b² - 2 × a × b × Cos C.
Considering right triangle ABD,
BD = a
DC = b
BC = c
Use the Pythagorean theorem to find the length of BD in the quadrilateral as shown in the diagram:
BD = √(7.5² + 5²)
BD = √(7.5² + 5²)
BD = 9.0 cm
Use the law of cosines to find the length of BC:
BC² = BD² + DC² - 2 × BD × DC × Cos <BDC.
Substitute
BC² = 9.0² + 13² - 2 × 9.0 × 13 × Cos 38
BC² = 250 - 184.4
BC² = 65.6
BC = √65.6
BC = 8.1 cm
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Kala earns 45 dollars each week working part-time at a bookstore. She earns one additional dollar for each book that she sells.
Let A be the amount (in dollars) that Kala earns in a week if she sells
B books.
Write an equation relating to A to B Then use this equation to find the amount of money Kala earns if she sells 21 books.
Answers
The equation relating to A to B is A = 45 + b and the amount is $66.
What is an equation?An equation is used to show the relationship between the variables that are illustrated.
In this case, Kala earns 45 dollars each week working part-time at a bookstore and she earns one additional dollar for each book that she sells.
Let the books be represented as b. The equation will be:.
A = 45 + 1b
A = 45 + b
where A = amount earned.
The amount earned when 21 books are sold will be:
A = 45 + b
A = 45 + 21
A = 66
The amount is $66.
This illustrates the concept of equations.
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Which inequality statements are true? Select all that apply.-0.7<-0.40.5 -0.6-0.8<-0.70.6 > 0.4
Answers
Answer:
-0.7 < -0.4
0.5 > -0.6
-0.8 < -0.7
0.6 > 0.4
Explanation:
The symbol < means less than and the symbol > means greater than.
On the other hand, if we identify each number on a number line, we get:
Therefore, the true statements are:
-0.7 < -0.4
0.5 > -0.6
-0.8 < -0.7
0.6 > 0.4
Because, for example, -0.7 is on the left of -0.4 which means that -0.7 is less than -0.4.
0.5 in on the right of -0.6 which means that 0.5 is greater than -0.6.
m(x) = | x + 1 |
Graph
Answers
The value of x = 1/M-1 , x = -1/M+1
What is Graph?
The graph of a function f is the set of ordered pairs where "displaystyle f(x)=y" exists. In the common scenario when x and f(x) are real integers, these pairings represent Cartesian coordinates of points in two-dimensional space and hence constitute a subset of this plane.
M(x) = |x + 1|
|x + 1| = M(x)
x + 1 = M(x)
x + 1 = -M(x)
Adding (-x) both side
x + 1 + (- x) = M(x) + (- x)
x + 1 + (- x) = -M(x) + (- x)
x + 1 - x = M(x) - x
x + 1 - x = -M(x) - x
1 = M(x) - x
1 = -M(x) - x
M(x) - x = 1
-M(x) - x = 1
x(M-1) = 1
x(-M-1) = 1
Dividing both side with (M - 1) and (-M - 1)
x(M-1)/(M - 1) = 1/(M - 1)
x(-M-1)/(-M - 1) = 1 /(-M - 1)
x = 1/(M - 1)
x = 1/(-M - 1)
Hence, x = 1/M-1 , x = -1/M+1
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Question 2 of 10
Multiply the following complex numbers:
(4-6) (6-8)
OA. -24-68i
OB. 72 +68i
O C. -24 +68/
OD. 72-68i
Answers
-24-68i is solution of complex number.
What is the best definition of a complex number?
Complex numbers are those that are expressed as a+ib, where a, b are actual numbers, and I is a fictitious number termed a "iota."Real and imaginary components are split into two separate numbers, which are referred to as complex numbers. The foundation of more complex mathematics, like algebra, are complex numbers. They have numerous practical applications, particularly in the fields of electronics and electromagnetism.(4-6i)(6-8i)
= 24-32i-36i+48i²
= 24 + -68i - 48
= -24-68i
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The complete question is -
Multiply the following complex numbers (4-6i)(6-8i)
Select the correct answer.
Function g is a transformation of the parent cosine function such that g(x) = 3 cos (x + 2) + 1. Which graph represents function g?
Answers
Option C gives the graph of Function g is a transformation of the parent cosine function such that g(x) = 3 cos(x + 2) + 1 as it the graph of cosine function.
What is cosine function?The ratio between the adjacent side and the hypotenuse is known as the cosine function (or cos function) in triangles. One of the three primary trigonometric functions, cosine is the complement of sine (co+sine) and one of the three main trigonometric functions.
What is Graph?A graph is a structure that resembles a set of objects in mathematics, more specifically in graph theory, in which some pairs of the objects are conceptually "related." The objects are represented by mathematical abstractions known as vertices, and each pair of connected vertices is referred to as an edge.
Choice C provides a graph of the parent cosine function is transformed into function g such that g(x) = 3 cos(x + 2) + 1 on the cosine function graph.
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Answer:
see photo
be sure to look closely, the top curves go to 4 and the bottom goes to -2, there are 2 with this same shape but the other one does not go high enough.
Step-by-step explanation:
Plato/Edmentum
can you show how to solve this proplem
Answers
In the given figure : lines l and m are parallel and a, b are transversal
Since, the lines a and b are parallel and l act as a transversal.
Then,
[tex]\begin{gathered} \angle BAC=\angle ACb\text{ (alternate interior angles)} \\ \text{ Substitute the values} \\ 2x=46 \\ x=\frac{46}{2} \\ x=23 \end{gathered}[/tex]x = 23
Answer : x = 23
Paul biked 7 miles on Saturday and 15 miles on Sunday. What was the total distance, in miles, Paul biked during those 2 days?
Answers
We have that:
Paul biked 7 miles on Saturday.
Paul bike 15 miles on Sunday.
The total distance, in miles, the Paul biked during Saturday and Sunday is:
[tex]T=7+15=22[/tex]determine the measure of angle j.
Answers
The measure of the value of ∠j is 10°.
What are a few properties of a triangle considering its angles?
A triangle's outer angle is the sum of its internal angles' two opposite sides.
The sum of two linear angles is supplementary.
Given, the three angles of the triangle are measured as (5x - 3)°,
(4x - 2)° and j°.
Also, the exterior angle of the triangle is (10x - 20)°.
Following the literature established above, considering that a triangle's outer angle is the product of its internal angles' two opposite sides, we have: (5x - 3) + (4x - 2) = 10x - 20 ⇒ 9x - 5 = 10x - 20 ⇒ 10x - 9x = 20 - 5
⇒ x = 15 --(i)
Again, since the sum of two linear angles is supplementary, we have using (i):
j + (10x - 20) = 180 ⇒ j + 150 - 20 = 180 ⇒ j = 10°
Therefore, the measure of the value of ∠j is 10°.
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Suppose a golf ball bounces off a wall at a point P, and that
line mis perpendicular to the wall at point P.
What is the measure of the angle of reflection?
A. 50°
B. 40°
C. 140°
D. 90°
Answers
3. 40 ounces of granola costs $6.52
a. How much does granola cost per ounce? (Give your answer to the nearest cent.) pleasee help
Answers
Answer: $0.2
Step-by-step explanation:
To find the answer you divide 6.52 by 40 which will get 0.163. To check the answer and make sure its correct you can multiply 0.163 by 40 to get 6.52 making the answer correct so 0.2 is the answer to the nearest cent. Hope this helps :)
Here is the answer again