All the roots of the function will be -5, 5, and -10. Then the correct option is D.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
The function is given below.
f(x) = x³ + 10x² - 25x - 250
Factorize the equation, then we have
f(x) = x³ + 10x² - 25x - 250
f(x) = x²(x + 10) - 25(x + 10)
f(x) = (x² - 5²)(x + 10)
f(x) = (x + 5)(x - 5)(x + 10)
Then the roots of the function are given as,
f(x) = 0
(x + 5)(x - 5)(x + 10) = 0
x = -5, -10, 5
All the roots of the function will be -5, 5, and -10. Then the correct option is D.
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if x = 3 when y = 6, what is y when x = -2
Answer:
If y=6 when x=3 find y when x =-33.
Step-by-step explanation:
Worth 25 points! Pls show work on both questions inside of the picture.
The area of the composite figure is equal to 54 square inches and the perimeter is 35 inches.
How to calculate for the area and perimeter of the figureThe composite figure is made up of a trapezium and a rectangle, so we shall calculate for the areas of the two figures and then add the result to get the total area of the composite figure as follows:
area of the trapezium = [(9 + 12)/2] in × 4 in
area of the trapezium = (21/2) in × 4 in
area of the trapezium = 21 in × 2 in
area of the trapezium = 42 in²
area of the rectangle = 4 in × 3 in
area of the rectangle = 12 in²
total area of the composite figure = 42 in² + 12 in²
total area of the composite figure = 52 in²
perimeter of the composite figure = 12 + 4 + 5 + 3 + 4 + 7
perimeter of the composite figure = 35 in²
Therefore, the area of the composite figure is equal to 54 square inches and the perimeter is 35 inches.
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The area and the perimeter of the composite figure are 54 square inches and 35 inches, respectively.
How to determine the area and perimeter of the composite figure
In this problem we find the case of a composite figure, whose area and perimeter (p), in inches, should be found. Perimeter is the sum of all side lengths of the figure, while the area is the sum of areas of rectangles and triangles, whose formulas are listed below:
Rectangle
A = w · l
Triangle
A = 0.5 · w · l
Where:
A - Area, in square inches.w - Width, in inches. l - Length, in inches.First, determine the perimeter of the composite figure:
p = 12 in + 4 in + 5 in + 3 in + 4 in + 7 in
p = 35 in
Second, determine the area of the composite figure:
A = 0.5 · (4 in) · (3 in) + (9 in) · (4 in) + (4 in) · (3 in)
A = 6 in² + 36 in² + 12 in²
A = 54 in²
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Do the Math
Franklin has a total of 18 pennies and nickels worth 78 cents. How many pennies and
how many nickels does Franklin have?
Write a system of equations.
p+n=18
P+
n=78
Solve the system of equations.
Franklin has pennies and nickels.
Franklin has 3 pennies and 15 nickels.
How many pennies and nickels does he have?The number of pennies The first step is to form a system of equations that represent the question:
p + n = 18 equation 1
0.01p + 0.05n = 0.78 equation 2
Where:
p = number of pennies n = number of nickelsThe elimination method would be used to solve the system of equations.
Multiply equation 1 b y 0.01:
0.01p + 0.01n = 0.18 equation 3
Subtract equation 3 from equation 2:
0.04n = 0.60
n = 0.60 / 0.04
n = 15
Substitute for n in equation 1:
p + 15 = 18
p = 18 - 15
p = 3
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u can get brainliest just help me out asap
Which of the following results in the expression 0.86 x 22
0.22 of 86%
22% of 0.86
86% of 22
0.86 of 22%
86% of 22 is the correct answer
A pattern rule for a number pattern is represented by 55 - 8n, where n is the term number.
A) Write the first six terms in the pattern. Explain the pattern rule.
B) What is the 30th term in this pattern?
A) All the first six terms in the pattern are,
⇒ 47, 39, 31, 23, 15, 7
Every number is 8 more than the next number.
B) The 30th term in this pattern is, - 185
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
A pattern rule for a number pattern is represented by,
⇒ 55 - 8n, where n is the term number.
Now, All the first six terms in the pattern are,
Substitute n = 1;
⇒ 55 - 8n
⇒ 55 - 8 × 1
⇒ 55 - 8
⇒ 47
Substitute n = 2;
⇒ 55 - 8n
⇒ 55 - 8 × 2
⇒ 55 - 16
⇒ 39
Substitute n = 3;
⇒ 55 - 8n
⇒ 55 - 8 × 3
⇒ 55 - 24
⇒ 31
Substitute n = 4;
⇒ 55 - 8n
⇒ 55 - 8 × 4
⇒ 55 - 32
⇒ 23
Substitute n = 5;
⇒ 55 - 8n
⇒ 55 - 8 × 5
⇒ 55 - 40
⇒ 15
Substitute n = 6;
⇒ 55 - 8n
⇒ 55 - 8 × 6
⇒ 55 - 48
⇒ 7
B) The 30th term in this pattern is,
Substitute n = 30;
⇒ 55 - 8n
⇒ 55 - 8 × 30
⇒ 55 - 240
⇒ - 185
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Solve the problem below. Be sure to show all calculations. Explanations given to justify your solutions must be given in complete sentences.
Given the figure to the right and the fact that m∠ABD= 133°, find the measurements of the angles below.
m∠ABC=___ m∠BCD=___ m∠ACB=___
The angle measures for this problem are given as follows:
m∠ABC = 112º.m∠BCD = 34º.m∠ACB = 34º.How to obtain the angle measures?ADC is an isosceles triangle, with an angle of 44º, hence the base angles have the measure given as follows:
2x + 44 = 180. (sum of the internal angles of a triangle).
2x = 136
x = 136/2
x = 68º.
Hence the measure of angles ACB and BCD is of 34º, as the bisection divides the angle into two angles of equal length.
Considering the two base angles of 34º, the measure of angle ABC is given as follows:
m < ABC + 2 x 34 = 180
m < ABC = 112º.
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a certain statistic will be used as an unbiased estimator of a parameter. let j represent the sampling distribution of the estimator for samples of size 40, and let k represent the sampling distribution of the estimator for samples of size 100. which of the following must be true about j and k ?
The correct statement can identify by using a certain limit theorem.
The correct option is (c).
The sample size of J is 40.
The sample size of K is 100.
As per the central limit theorem, if the population with mean and standard deviation takes a large random sample from the population with replacement, then the distribution of the sample means will be approximately distributed.
Now from the definition of the central limit theorem, both J and K will the same means.
Write the expression for standard deviation.
[tex]s = \frac{\alpha }{\sqrt{n} }[/tex]
From the above expression, the standard deviation is inversely proportional to the sample size.
Thus, the correct statement is the expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
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The complete question is:
A certain statistic will be used as an unbiased estimator of a parameter. Let J represent the sampling distribution of the estimator for samples of size 40, and let K represent the sampling distribution of the estimator for samples of size 100.
Which of the following must be true about J and K?
a. The expected values of J and K will be equal, and the variability of J will be less than the variability of K.
b. The expected values of J and K will be equal, and the variability of J will be equal to the variability of K.
c. The expected values of J and K will be equal, and the variability of J will be greater than the variability of K.
d. The expected value of J will be greater than the expected value of K, and the variability of R will be greater than the variability of K.
e. The expected value of J will be greater than the expected value of K, and the variability of R will be less than the variability of K.
A scientist has two solutions, which she has labeled Solution A and Solution B. Each contains salt. She knows that Solution A is 45% salt and Solution B is
95% salt. She wants to obtain 90 ounces of a mixture that is 80% salt. How many ounces of each solution should she use?
She uses 27 ounces of solution A and 63 ounces of Solution B.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Solution A is 45% salt and Solution B is 95% salt.
Let x be the number of ounces of Solution A
and y be the number of ounces of Solution B
as, She wants to obtain 90 ounces of a mixture then
x + y = 90
y = 90 - x.........(1)
and, 0.45x + 0.95y = 0.80( 90)
0.45x + 0.95y = 72
Put the value of y from equation (1) we get
0.45x + 0.95( 90-x)= 72
0.45x + 85.5 - 0.95x = 72
0.5x = 13.5
x= 27 ounces
and, y= 90-27 = 63 ounces.
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pls help will mark brainliest asap
The transformed vertices of the ΔABC will be A'(- 2, 0), B'(2, 3)
and C'(0, - 1).
What are transformations?Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.
Dilation: The preimage is scaled up or down to create the image.
Reflection: The picture is a preimage that has been reversed.
Rotation: Around a given point, the preimage is rotated to create the final image.
Translation: The image is translated and moved a fixed amount from the preimage.
The given triangle has vertices A(0, 4), B(6, - 4) and C(- 2, 0).
We know a rotation of 90° counterclockwise transforms (x, y) to (- y, x)
and a dilation factor of (1/2) would make it (- y/2, x/2).
Therefore, The vertices of the triangle A'B'C' will be,
A'(- 4/2, 0/2), B'(-(-4)/2, 6/2) and C'(0/2, - 2/2).
A'(- 2, 0), B'(2, 3) and C'(0, - 1).
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HELP ASAPPPPPPPPPPP DUE IN TWO HOUR
The graph shows a function of the form f(x) = ab^x.
Use the drop-down menus to complete the statements about the function, and then write an equation that represents this function.
The function shown in the graph must be the function f(x)=2×4ˣ
What are functions?Function, in mathematics, is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given here: f(x)=abˣ and when x is equal to 0 then f(0)=2
also if x increases by the functions gets multiplied by 4
Thus if f(0)=2 then f(1)= 8 , f(2)=32
or the function can be rewritten as f(x)=2×4ˣ
Thus f(0)=2×4⁰
=2
f(1)=2×4¹
Hence, The function shown in the graph must be the function f(x)=2×4ˣ
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What is the value today of $5,100 per year, at a discount rate of 7.9%, if the first payment is received 6 years from today and the last payment is received 20 years from today?
The present value of the cash flows is $30,030.78.
What is the present value?In order to determine the value today of the series of payments, the present value has to be determined. Present value is the sum of the discounted cash flows.
Present value = 5,100 / (1.079)^6 + 5,100 / (1.079)^7 + 5,100 / (1.079)^8 + 5,100 / (1.079)^9 + 5,100 / (1.079)^10 + 5,100 / (1.079)^11 + 5,100 / (1.079)^12 + 5,100 / (1.079)^13 + 5,100 / (1.079)^14 + 5,100 / (1.079)^15 + 5,100 / (1.079)^16+ 5,100 / (1.079)^17 + 5,100 / (1.079)^18 + + 5,100 / (1.079)^19 + + 5,100 / (1.079)^20 = $30,030.78
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The letter represents the location of –1.5 on the number line. A number line going from negative 3 to positive 3 in increments of 1. Point A is halfway between negative 3 and negative 2. Point B is halfway between negative 2 and negative 1. Point C is halfway between negative 1 and 0. Point D is halfway between 1 and 2.
The location of point A on the number line is -2.5, point B is -1.5, point C is -0.5, and point D is 1.5.
What is Number Line?In math, a number line can be defined as a straight line with numbers arranged at equal segments or intervals throughout. A number line is typically shown horizontally and can be extended indefinitely in any direction.
The number line can be divided into halves to find the halfway points between consecutive integers.
Point A is the halfway point between negative 3 and negative 2,
Point A = -2.5
Point B is the halfway point between negative 2 and negative 1,
Point B = -1.5
Point C is the halfway point between negative 1 and 0,
Point C = -0.5
Point D is the halfway point between 1 and 2.
Point D = 1.5
These halfway points can be used to approximate the location of -1.5 on the number line.
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similar fraction to one and one fifth
The similar fractions to [tex]1\frac{1}{5}[/tex] are 12/10, 18/15, 24/20, 30/25, 36/30 etc
What is fraction?A fraction is a part of a whole number, and a way to split up a number into equal parts.
Given that, a fraction, [tex]1\frac{1}{5}[/tex]
Converting into improper fraction,
[tex]1\frac{1}{5}[/tex] = 6/5
So, similar fraction to 6/5 are,
12/10, 18/15, 24/20, 30/25, 36/30 etc
Hence, the similar fractions to [tex]1\frac{1}{5}[/tex] are 12/10, 18/15, 24/20, 30/25, 36/30 etc
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A line has a slope of 5 7 and passes through the point (12,9). Write its equation in slope-intercept form. Write your answer using integers, proper fractions, and improper fractions in simplest form.
The equation in slope-intercept form is y = 5/7x + 3/7
How to determine the equation of the lineIt is important to note that the equation of a line is expressed with the formula;
y = mx + c
Such that the parameters are;
y is a point on the y -axis of the graphm is the slope of the line of graphx is a point on the x-axis of the graphc is the intercept of the line on the y-axis of the graphFrom the information given, we have that;
slope, m = 5/7
Now, let's substitute the points into the formula, we have;
9 = 5/7(12) + c
expand the bracket
9 - 60/7 = c
find the lowest common multiple
c = 63-60/7
c = 3/7
The equation of the line is ; y = 5/7x + 3/7
Hence, the equation is y = 5/7x + 3/7
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Use finite differences to identify the degree of the polynomial that best describes the data.
quintic
quadratic
cubic
quartic
The degree of the polynomial that best describes the data is (c) cubic
How to determine the degree of the polynomial that best describes the data.From the question, we have the following parameters that can be used in our computation:
See attachment
Find the first dfference D1 between the consecutive y-values
D1: 10 28.4 56.4 94
Calculate the second difference
D1: 18.4 28 37.6
Calculate the third difference
D3: 9.6 9.6
The third difference are equal
Hence, the degree is (c) cubic
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the following items are found around the house. they have weight. select the items that are most likely to be measured in ounces. paper bag frying pan can of pop table
The items that are most likely to be measured in ounces are a Paper bag, a can of pop, and a table.
The weight of objects is typically measured in units of mass, such as grams or kilograms, or in units of weight, such as ounces or pounds. In general, smaller and lighter objects are measured in ounces, while heavier objects are measured in pounds or kilograms.
In this case, the paper bag, can of pop, and table are likely to be measured in ounces. These objects are relatively light and can be easily lifted and weighed on a scale, which would make it convenient to use ounces as a unit of measurement. On the other hand, a frying pan is likely to be a heavier object and would typically be measured in pounds or kilograms.
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Draw a number line to show 2/3 + 2/3
Answer:
4/3
Step-by-step explanation:
Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves. There are 555 Carlson sisters.
The quantity of jewelry that each sister will receive would be = 23+y/ 5
How to calculate the quantity of jewelry received by each sister?The total number of jewelry that was given out by Grandma Gertrude = 23 pieces
The total number of jewelry that was given out by Grandma Fien = y
The number of Carlson sisters = 5
Therefore, the quantity of jewelry that will be received by each of the sister would be represented by this expression = 23+y/ 5
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The complete question:
Grandma Gertrude gave 13 pieces of jewelry and Grandma Fien gave y pieces of jewelry to the Carlson sisters to divide evenly among themselves. There are 5 Carlson sisters, How many pieces of jewelry did each sister receive?
Please help!
Solve the equation. If there is more than one solution, separate them with a comma.│5x+3│=33
A painting contractor determined the average amount of time needed to paint a house. When 2 painters are used, it takes 15 hours to paint • When 6 painters are used, it takes 5 hours to paint. If p represents the number of painters and h represent the number of hours required to paint the house, which statement is true about this relationship?
The statement that is true about the proportional relationship is that; The time required to paint a house varies directly with the number of painters.
How to find proportional Relationship?The parameters are;
p represents the number of painters.
h represent the number of hours required to paint the house
In this case, the number of hours will be the output variable while the number of painters will be the input variable. Thus, we will have the relationship;
h = kp
where k is the constant of proportionality
When 2 painters are used, it takes 15 hours to paint and as such;
k = 15/2
k = 7.5 hours per painter
When 6 painters are used, it takes 5 hours to paint. Thus;
k = 5/6
k = 0.833 hours per painter
Thus, we can say that the time required to paint a house varies directly with the number of painters.
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Plot the following inequality on the number line. −2
The number line of x <-2 is added below
How to plot the inequality on a number lineFrom the question, we have the following parameters that can be used in our computation:
x < -2
For the inequality x < -2:
All real numbers that are less than -2 satisfy the inequality.
So, we can represent the solution set of the inequality using the interval (-∞, -2)
When represented on a number line, we have:
-∞ -3 -2 -1 0 1 2 ∞
--------------------------------------------------------------------------
. <- o . . . . .
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A rectangular prism has a base of 19 ft by 8 ft and a diagonal of 25 ft. Identify its height. Round to the nearest tenth.
Answer:
14.1
Step-by-step explanation:
To find the height of the rectangular prism, use the formula for the length of a diagonal of a right rectangular prism.
d=l2+w2+h2−−−−−−−−−−√
Substitute 8 for l, 19 for w, and 25 for d
Then solve for h
25=82+192+h2−−−−√
Simplify.
25=64+361+h2−−−−√
Square both sides.
625=425+h2
Subtract 425 from both sides.
200=h2
Take the positive square root of both sides.
200−−−√=h
Round to the nearest tenth.
14.1≈h
Therefore, the height of the rectangular prism is about 14.1ft
Simplify
6 (2x^2-5)=
x= -3
The value of the expression for x=-3 is 78.
What is an expression?An expression is a combination of terms that are combined by using mathematical operations such as subtraction, addition, multiplication, and division.
The given expression is 6(2x²-5).
Here, x=-3
Substitute x=-3 in the expression 6(2x²-5), we get
6(2(-3)²-5)
= 6(18-5)
= 78
Therefore, the value of the expression is 78.
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RECT is a square (not drawn to scale). RA = 13^2 -3x-3 inches and AC = x(x+2).
A. Find the length of ET to the nearest tenth
B. Find the length of RT to the nearest tenth
The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
RECT is a square (not drawn to scale).
RA = 13² - 3x - 3
AC = x(x + 2)
The diagonals of the square will be RC and ET. And "A" is the intersection point. Then the equation is given as,
RA = AC
13² - 3x - 3 = x(x + 2)
169 - 3x - 3 = x² + 2x
x² + 5x - 166 = 0
x = [- 5 ± √(5² - 4 × 1 × (-166))] / (2 × 1)
x = 10.62, -15.62
Then the length of AC is given as,
AC = 10.62 (10.62 + 2)
AC = 134.13 units
The diagonals of the square are congruent. Then we have
ET = RC
ET = 2 AC
ET = 2 x 134.13
ET = 268.3 units
Then the length RT is given as,
RT = ET / √2
RT = 198.7 units
The length of ET and the length of RT to the nearest tenth will be 268.3 units and 198.7 units, respectively.
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Given the rate per compounding period, find r, the annual rate.
0.425% per month
Answer:
Step-by-step explanation:
To find the annual rate given the rate per compounding period, we need to convert the rate from the compounding period to the annual period. In this case, the rate is given as 0.425% per month.
One way to convert the rate is to multiply it by the number of compounding periods in a year:
r = 0.425%/month * 12 months/year
r = 5.1%/year
Therefore, the annual rate, r, is 5.1%.
Which of the following is NOT a characteristic of both surveys and experiments?
Data collected about a population is not characteristic of both surveys and experiments. The correct answer would be an option (C).
What is a survey?The purpose of a survey is to understand populations as a whole by utilizing pertinent questions to collect data from a sample of people.
Data collected about a population is not a characteristic of both survey and experiment because, in an experiment, the researcher typically manipulates one or more variables and measures the effect on another variable, while in a survey, the researcher usually only measures variables and does not manipulate them. As a result, in a survey, the data is typically collected about a sample of the population, rather than the entire population.
Hence, the correct answer would be option (C).
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Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Debts Interest Rate Minimum Monthly Payment
Debt 1 5.5% $75
Debt 2 2.75% $250
Debt 3 13.25% $150
Alice wants to use the stack method to pay down her debts listed in the table below. If she applies an extra $150 a month to her debts, what will be the first debt she targets to pay off and what will be the monthly amount she applies to it?
Debts Interest Rate Minimum Monthly Payment
Debt 1 5.5% $75
Debt 2 2.75% $250
Debt 3 13.25% $150
The first debt that Alice would have to pay based on the Stack method would be the third debt. Option C
How to calculate the debt using the stack methodFrom the stack method, the debt that Alice would have to pay off first would be the debt that has the highest interest rate.
The amount of 150 dollars would then be added to the debt that has the second highest rate.
Hence the amount of debt that would be paid off first would be the first debt based on the stack method.
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Click on all the values that are equivalent to
-(2/3).
A.-2/-3
B.2/-3
C.-2/3
D.-3/-2
E.-3/2
F.3/-2
Answer:
-2/-3
Step-by-step explanation: Because -2/-3=2/3.
Pretest: Unit 2
Question 3 of 20
Determine the number of solutions for the equation shown below.
4x+6=4x+6
A. 2
B. 0
C. Infinitely many
D. 1
SUBMIT
Answer:
infinitely many
Step-by-step explanation:
this equation is true for each and every value.
so its solutions are infinite
Prove the following vector identities which, among other ideas, extend the chain rule to vector operations. Use index notation. a(x), b(x)-vector functions of position x; ф(x) - scalar function of position NOTE: Begin with the expression on the left and derive the expression on the right. Try not to simply expand both sides and show that they are identical (iii) V - (V xa)-0 (vii) V ab (V aba (Vb)
Vector identities can be derived using index notation. The following vector identities are to be proved: (iii) V - (V xa) = 0, (vii) V ab = (V a)b + a(V b).
Starting with the left-hand side:
V - (V x a) = V + (a x V) (by definition of cross product)
Using the vector triple product, a x (b x c) = (a . c) b - (a . b) c, we get:
V + (a x V) = V + (V . a) a - (V . a) a
= V (since the second term cancels out with the first term)
Thus, V - (V x a) = 0.
(vii) V ab = (V x (b x a))
Starting with the left-hand side:
V ab = V (ab)
Using the scalar triple product, a . (b x c) = (a x b) . c, we get:
V (ab) = (V x b) . (a x a)
= (V x (b x a)) (since a x a = 0)
Thus, V ab = (V x (b x a)).
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