A. Two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.
B. Another way to find the new average directly using:
x = 0.88v (using the second expression )
What is expression ?
In mathematics, an expression is a combination of numbers, symbols, and/or operators that represent a value or a relationship between values. Expressions can be as simple as a single number, variable, or symbol, or they can be complex combinations of terms, functions, and operations.
For example, the expression "2x + 3" is a combination of the number 2, the variable x, and the operators + and *. It represents a relationship between x and a value that is 3 more than twice x.
Expressions can be used in a wide range of mathematical contexts, including algebra, calculus, geometry, and statistics, to name a few. They are an essential tool for describing and solving mathematical problems.
A. Let x be the new acreage after the sale. Then we have:
x = v - 0.12v (12% decrease means 0.12v decrease from v)
x = 0.88v (Simplify by factoring out v)
So, two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.
B. Another way to find the new acreage is to multiply the original acreage by the decimal equivalent of the percent decrease. In this case, the percent decrease is 12%, which is equivalent to 0.12 as a decimal. So, we have:
x = v - 0.12v (using the first expression above)
x = 0.88v (simplify)
x = (1 - 0.12)v (factor out v)
x = 0.88v (simplify)
Alternatively, we can calculate the new average directly using:
x = 0.88v (using the second expression above)
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Answer:A.Two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.B.Another way to find the new average directly using:x = 0.88v (using the second expression )What is expression ?In mathematics, an expression is a combination of numbers, symbols, and/or operators that represent a value or a relationship between values. Expressions can be as simple as a single number, variable, or symbol, or they can be complex combinations of terms, functions, and operations.For example, the expression "2x + 3" is a combination of the number 2, the variable x, and the operators + and *. It represents a relationship between x and a value that is 3 more than twice x.Expressions can be used in a wide range of mathematical contexts, including algebra, calculus, geometry, and statistics, to name a few. They are an essential tool for describing and solving mathematical problems.A. Let x be the new acreage after the sale. Then we have:x = v - 0.12v (12% decrease means 0.12v decrease from v)x = 0.88v (Simplify by factoring out v)So, two equivalent expressions that represent the new average are x = v - 0.12v and x = 0.88v.B. Another way to find the new acreage is to multiply the original acreage by the decimal equivalent of the percent decrease. In this case, the percent decrease is 12%, which is equivalent to 0.12 as a decimal. So, we have:x = v - 0.12v (using the first expression above)x = 0.88v (simplify)x = (1 - 0.12)v (factor out v)x = 0.88v (simplify)Alternatively, we can calculate the new average directly using:x = 0.88v (using the second expression above)
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why does gyro never never ever bet on even numbers
Gyro never bets on even numbers because the expected value of such a bet is always negative.
To understand this concept, let's look at what an even number bet involves. When a person bets on an even number, they are essentially risking their entire stake on a 50/50 chance of winning.
This means that if they win, they will get their stake back plus the amount they would have won if the bet had been successful – in other words, their returns will be twice their original stake.
However, if they lose the bet, they will lose their entire stake. This means that the expected value of a bet on an even number is always negative. In other words, the expected outcome of the bet is always a loss.
Therefore, it is never a good idea to bet on an even number, as the expected value is always negative
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72% of the number of visitors to a zoo on a particular day were children. If 308 adults visited the zoo on that day, how many visitors did the zoo receive on that day?
The zoo received 1100 visitors that day
Jill jumped 6 7/8 feet in the long-jump event. Jill’s best friend jumped 6 15/16 feet. How much farther did Jill’s best friend jump? Describe in words the process you used to solve the problem. (Also show work so I can see how to do it on my own in the furture)
Answer:
-1/16Step-by-step explanation
6 7/8 - 6 15/16To make the problem easier, we are gonna have to change the denominator into 16
8*2=16 after we times 8 with 2 we now have to do the same 7
So this would show 7*2=14
Now it would be 6 14/16 - 6 15/16
All we have to do now is minus 14 with 15 which equals -1.
Now for the whole numbers, you can just minus the 6’s with eachother 6-6=0. Taking the denominator, we now have -1/16.
Hope this is the answer you are looking for.
Which number line model represents the expression 5 1/2 + (-3)
Answer: B
Step-by-step explanation:
the expression is the result of applying the change of base formula to a logarithmic expression. which could be the original expression?
The original expression could be log_2(1/3) / log_10(2).
The change of base formula states that:
log_a(x) = log_b(x) / log_b(a)
where a, b, and x are positive real numbers and a, b ≠ 1.
In the given expression, log1/3 / log2, the denominator is log2, which means that the base of the logarithm in the numerator must be 2 raised to some power.
So we can rewrite the logarithmic expression as:
log1/3 / log2 = log_2(1/3) / log_2(2)
Now we can apply the change of base formula, with a = 2, b = 10, and x = 1/3:
log_2(1/3) / log_2(2) = log_10(1/3) / log_10(2)
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Answer: C
Step-by-step explanation:
Which expressions can be used to find the volume of the pyramid? Select three choices
The correct answer regarding the volume of the pyramid has been explained and given below.
The volume of the pyramid shape is given by the product of its base area and its height and then the product is divided by 3.
i.e.V = (1/3)a²h
So, the options which are correct are, (a) XY and ST , (b) VU and TW and (d) TX and WX.
From the given figure we can clearly see that,
a=XY=YZ=ZU=UV=VW=WX
h=ST
Firstly, the volume of the pyramid can be easily determined by XY and ST.
and also, VU and WX can be used to calculate the area of the base and YZ and TX can be used to calculate height.
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Its asking to solve and substitue, what do i substitue and solve?
The solutions of the given equation are 3.16, 1, and - 1.
Solutions of equations:All numbers that make an equation true when the unknowns are eliminated from the equation are considered the solution of the equation.
For the given equation, we can find the solutions by factorizing as shown below.
Here finding the factors of the given polynomial is known as Factorizing. In other words, writing the given equation as a product of its factors.
Here we have
x⁴ - 11x² + 10 = 0
We can solve the above equation as follows
x⁴ - 11x² + 10 = 0
x⁴ - 10x² - x² + 10 = 0
Group out the like terms
x²(x² - 10) - (x² - 10) = 0
(x² - 10) (x² - 1) = 0
(x² - 10) (x - 1)(x + 1) = 0 [ ∵ (x² - 1²) = (x - 1)(x + 1) ]
x² - 10 = 0 => x = √10 = 3.16
x - 1 = 0 => x = 1
x + 1 = 0 => x = -1
Therefore,
The solutions of the given equation are 3.16, 1, and - 1.
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Determine whether the given value is from a discrete or continuous data set. when a truck is randomly selected, it is found to have a length of 20 feet.
The length of a truck is an example of a continuous data set, and 20 feet is just one possible value within that range.
The given value, "a truck with a length of 20 feet," is an example of a continuous data set.
Continuous data refers to values that can take on any numerical value within a range, with no gaps or interruptions. In this case, the length of a truck can take on any value between 0 and some maximum length, with no gaps or interruptions in between.
In contrast, discrete data refers to values that can only take on certain specific values, usually integers. For example, the number of tires on a truck is a discrete data set because it can only take on integer values (e.g. 4, 6, 8).
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Explain the synthetic division process for polynomials. Divide (2x4–3x³ - 5x² + 3x
+8) by (x - 2). Be as specific as possible. You may upload a picture of your work to
help explain the steps in the division process. Make sure to include the answer to
the division problem in your explanation.
Explanation:
You want synthetic division explained for division of (2x^4 -3x^3 -5x^2 +3x +8) by (x-2).
CommentIn general, synthetic division is long division without writing the variables. It takes advantage of the fact that subtracting the product of the quotient term and the divisor makes the leading term go to zero at each step. This makes it possible to write the entire division on one line, instead of several. (The long division of these polynomials is shown in the second attachment.)
Synthetic division is most easily accomplished as division of a polynomial by a monic binomial—a binomial of the form x -a. Both dividend and divisor can be divided by the leading coefficient of the divisor if it is not 1.
ProcedureThe first attachment shows the tableau that is used during the synthetic division process. At top left is the opposite of the divisor constant. (This is the value that makes the divisor zero.) By using the opposite of the constant, later steps can involve addition, rather than subtraction, which simplifies the process and reduces errors.
To the right of the divisor zero, the coefficients of the polynomial are listed in decreasing order of degree. If a polynomial term is missing, then a 0 is used for its coefficient. Typically, the tableau is drawn with a vertical line between the divisor zero and the polynomial coefficients.
A horizontal line is drawn below the coefficients, with enough space to allow for partial products to be written between the coefficients and the horizontal line. The first (left-most) dividend polynomial coefficient is copied below the line.
From here, steps for succeeding columns of the tableau are the same. Working left-to-right, the value just written below the line is multiplied by the divisor zero, and that product is written above the line in the next column to the right. The coefficient is added to that, and the sum is written below the line.
The sum in the final (rightmost) column is the remainder from the division. The quotient from the division has the set of coefficients that are the numbers below the line to the left of the remainder.
ResultAs shown in the attachment, the result of using synthetic division for the given polynomials is ...
2 1 -3 -3 2
This means the quotient is 2x³ +x² -3x -3 and the remainder is 2. That is, ...
(2x⁴-3x³-5x²+3x+8) ÷ (x-2) = 2x³ +x² -3x -3 + 2/(x-2)
__
Additional comment
Synthetic division is really designed for division by monic binomials. It can be extended (with extreme care) to division by monic polynomials of higher degree than 1. What makes it work is the fact that the leading dividend term disappears at each step, so no accounting for the coefficients of the leading terms is required.
The same trick of using sums instead of differences could be applied to long division—again, with extreme care.
. The distance from Santa Maria to Los Alamos is 16.25 mi. What is the distance in cm?
Answer: Santa Maria to Los Alamos is approximately 2,612,951.6 centimeters.
Step-by-step explanation:
To convert miles to centimeters, we need to use the following conversion factors:
1 mile = 160,934.4 centimeters
So, to find the distance from Santa Maria to Los Alamos in centimeters, we can use the following calculation:
16.25 miles x 160,934.4 centimeters/mile = 2,612,951.6 centimeters
Therefore, the distance from Santa Maria to Los Alamos is approximately 2,612,951.6 centimeters.
1 mile = 160,934 centimeters
16.25 miles = ?
16.25 * 160,934 = ?
16.25 miles = 2,615,184 centimeters
Which graph represents the function f (x) = 8 Superscript one-third x?
On a coordinate plane, an exponential function crosses the y-axis at (0, 8), increases into quadrant 1, and goes through (1, 10).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases in quadrant 1. It goes through (0, 1), (2, 4), and (3, 8).
On a coordinate plane, an exponential function decreases in quadrant 2 into quadrant 1 where it approaches y = 8. It goes through (negative 1, 10) and crosses the y-axis at (0, 8).
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases in quadrant 1. It goes through (0, 1) and (2, 8).
Answer:
On a coordinate plane, an exponential function approaches y = 0 in quadrant 2 and increases in quadrant 1. It goes through (0, 1), (2, 4), and (3, 8).
Step-by-step explanation:
Answer:
graph 2
Step-by-step explanation:
I did the assignment
A ballet school wants to buy new slippers for students in a class. They collected the sizes and displayed them in a line plot.
A horizontal number line starting at 3.5 with tick marks every 0.5 units up to 8. The following values are labeled: the value of 4 has two dots, the value of 4.5 has one dot, the value of 5 has one dot, the value of 6 has 2 dots, the value of 6.5 has one dot, the value of 7 has one dot, and the value of 7.5 has one dot. The image is titled Ballet Shoe Sizes.
What is the range, and what does it mean in terms of this data set?
The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.
What is range?The difference between the highest and lowest values for a given data collection is the range in statistics.
In statistics, we must put the given values, set of data, or set of observations in ascending order in order to determine the range. It indicates that you should start by writing the observations from lowest to highest value. The formula must now be used to determine the range of observations.
The range is the difference between the largest and smallest values in a data set.
For the given data, the largest value is 8 and the smallest value is 3.5.
Thus,
range = 8 - 3.5 = 4.5.
Hence, the range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.
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Answer:
Step-by-step explanation:The range is 4.5 and it means that the ballet shoe sizes in this class vary by 4.5, with the largest size being 8 and the smallest size being 3.5.
What is Statement 3.
Given: P is the midpoint of TQ and RS.
Prove: ATPR AQPS
X
Proof:
Statements
1. P is the midpoint of TQ and RS.
2. TP QP, RP = SP
3.
4. ATPR AQPS
O ZPTR
ZPQS
O ZPSQ ZPRT
OZSPQ LRPT
R
Reasons
1. Given
2.
3. Vertical Angles Theorem
4.
The statements required for the prove are given in the explanation.
What are vertical angle?Vertical angles are two opposite angles which have equal values because they are formed by two straight lines intersecting at a point.
And a midpoint is a point which divides a line segment into two equal parts.
The required statements to prove that ΔTPR ≅ΔQPS are given below;
STATEMENT REASON
1. P is the midpoint of TQ and RS Given
2. TP = QP, RP = SP Definition of midpoint
3. <SPQ ≅ <RPT Vertical angle theorem
4. ΔTPR ≅ΔQPS Side-Angle-Side theorem
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To mix his special energy drink, Jerome uses 8 cups of water and 3 cups of drink mix.
Twenty-two people are running in tomorrow's
Road race and Jerome thinks they will each want two cups of energy drink.
B) how much water and how much drink mix should Jerome use to make enough energy drink for all the runners?
Answer: He needs 32 cups of water and 12 cups of drink mix.
Step-by-step explanation: 8 cups + 3 cups = 11 cups
So we know that 8 cups of water + 3 cups of drink mix = 11 cups of 'special energy drink'. Now, Jerome assumes that each person wants 2 cups so we perform the following equation: 22 people x 2 cups = 44 cups. We know that 8 cups of water and 3 cups of drink mix is equal to 11 cups so we just divide: 44 cups/11 cups = 4. Now we need to multiply 8 and 3 by 4 because he needs 4 x 11 cups, that is why we need to multiply
each of the numbers that make up 11 by 4. 8 cups x 4 = 32 cups,
3 cups x 4 = 12 cups
Answer: He needs 32 cups of water and 12 cups of drink mix.
Step-by-step explanation:
An insurance company claims that in the population of homeowners, the mean annual loss from fire is u-$250 with a standard deviation of o - $ 5000. The distribution of loss is strongly right-skewed: Many policies have $0 loss, but a few have large losses. If we create a sampling distribution with a sample of 64 homeowners, what is the probability that a sample average exceeds $5100?
The probability that the sample average exceeded 5100 is given as follows:
0%.
How to obtain probabilities using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The parameters for this problem are given as follows:
[tex]\mu = 250, \sigma = 5000, n = 64, s = \frac{5000}{\sqrt{64}} = 625[/tex]
The probability that a sample average exceeds $5,100 is one subtracted by the p-value of Z when X = 5100, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem:
[tex]Z = \frac{X - \mu}{s}[/tex]
Z = (5100 - 250)/625
Z = 7.76
Z = 7.76 has a p-value of 1.
1 - 1 = 0.
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what is 1.70 m in feet?
The conversion of 1.70 meters to feet gives the value which is equal to 5.5774 feet ( approximately ) .
Meters to feet can be converted by the following relation ,
Meter and feet both represents units which is used to measure the dimension length.1 meter = 3.28084 feet
Now Substitute the given value to convert meters into feet.
Here, convert 1.70 meters into feet we get,
⇒ 1.70 meters = ( 1.70 ) × ( 3.28084 ) feet
⇒ 1.70 meters = 5.577428 feet
Rewrite upto four decimal places we get,
⇒ 1.70meters = 5.5774 feet ( approximately )
Therefore, after converting unit of 1.77 meters into feet it is equal to 5.5774 feet ( approximately ) .
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The sum of two numbers is 49. The smaller number is 21 less than the larger number. What are the numbers?
Answer:
35,14
Step-by-step explanation:
I am so sorry if this is wrong
Answer: I would have to guess 35, 14
Step-by-step explanation:
what are the coordinates of r′ for the dilation centered at p with scale factor 0.5?
The new coordinates of the triangle after dilation by a scale factor of 0.5 with the origin as the center of dilation are F'(3, 2.5), H'(1, 0.5), and G'(5, 0.5).
To find the coordinates of the triangle after dilation by a scale factor of 0.5 with the origin as the center of dilation, we can use the following formula:
(x', y') = (0.5 × x, 0.5 × y)
where (x, y) are the original coordinates of the point and (x', y') are the new coordinates after dilation.
Let's apply this formula to each point of the triangle:
For point F(6,5):
x' = 0.5 × 6 = 3
y' = 0.5 × 5 = 2.5
The new coordinates of point F are (3, 2.5)
For point H(2,1):
x' = 0.5 × 2 = 1
y' = 0.5 × 1 = 0.5
The new coordinates of point H are (1, 0.5)
For point G(10,1):
x' = 0.5 × 10 = 5
y' = 0.5 × 1 = 0.5
The new coordinates of point G are (5, 0.5)
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The given question is incomplete, the complete question is:
what are the coordinates of triangle by a scale factor of 0.5 with the origin as the center of dilation ?
Help needed please llll
Answer:
A.
Step-by-step explanation:
The key for for the drawing would only make sense if 1 inch equals 16 therefore A is the answer.
Hope it helped!
Answer:
sorry im late but its A
Step-by-step explanation:
what is the surface area of the cylinder? Use 3.14 for π and round to the nearest hundredth.
height=11 Radius=8 in.2
The surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.
What is the surface area of the cylinder?
To find the surface area of a cylinder, we need to find the sum of the areas of its curved surface (lateral area) and its two circular bases.
The formula for the lateral area of a cylinder is L = 2πrh, where r is the radius and h is the height. The formula for the area of each circular base is B = πr^2.
We are given that the height of the cylinder is 11 inches and the radius is 8 inches. Therefore, we can calculate:
L = 2πrh = 2 × 3.14 × 8 × 11 = 549.52 in²
B = πr^2 = 3.14 × 8^2 = 200.96 in²
The total surface area is the sum of the lateral area and the two base areas:
Surface area = L + 2B = 549.52 + 2(200.96) = 951.44 in²
Hence, the surface area of the cylinder is approximately 951.44 square inches, rounded to the nearest hundredth.
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What is the coefficient
Answer:
A coefficient is a number that is multiplied by a variable or term in an algebraic expression.
Examples:
[tex]3x[/tex]
[tex]60x[/tex]
what is law of cosine ?
The Law of Cosines is a formula that relates the side lengths and angles of any triangle, expressed as c^2 = a^2 + b^2 - 2abcos(C).
The Law of Cosines is a numerical formula that relates the side lengths and points of any triangle. It expresses that the square of any side of a triangle is equivalent to the number of squares of the other different sides short two times the result of those sides and the cosine of the point between them. Numerically, the Law of Cosines can be communicated as c^2 = a^2 + b^2 - 2abcos(C), where c is the length of the side inverse to the point C, and an and b are the lengths of the other different sides.
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Diego is making sandwiches for a picnic. He uses 2 slices of cheese to make each sandwich, and he has a package of cheese with 24 slices.
Write an equation that shows how the number of slices of cheese remaining, y, depends on the number of sandwiches Diego makes, x.
If Diego makes 10 sandwiches, he will have only 4 slices of cheese left over.
What is Linear equation ?
A linear equation is an algebraic equation in which the highest power of the variable(s) is 1. In other words, it is an equation that represents a straight line on a graph.
The general form of a linear equation with one variable is:
ax + b = 0
Explanation:
The number of slices of cheese Diego uses to make x sandwiches is equal to 2x (since he uses 2 slices of cheese for each sandwich). If he starts with a package of cheese that has 24 slices, then the number of slices of cheese remaining, y, after making x sandwiches is:
y = 24 - 2x
This equation shows that the number of slices of cheese remaining depends on the number of sandwiches Diego makes. As he makes more sandwiches, he will use more cheese and the number of slices of cheese remaining will decrease.
To clarify, the equation is:
y = 24 - 2x
where y represents the number of slices of cheese remaining, and x represents the number of sandwiches Diego makes.
For example, if Diego makes 5 sandwiches, then the number of slices of cheese he uses is 2 times 5, or 10. The number of slices of cheese remaining would be:
y = 24 - 2(5) = 24 - 10 = 14
So, if Diego makes 5 sandwiches, he will have 14 slices of cheese left over.
Similarly, if Diego makes 10 sandwiches, then the number of slices of cheese he uses is 2 times 10, or 20. The number of slices of cheese remaining would be:
y = 24 - 2(10) = 24 - 20 = 4
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what is 23 out of 25 as a percentage
Answer:
92%
Step-by-step explanation:
Find the dimensions of the cube
Answer: DBSB272 PONTA DEM
Step-by-step explanation: Find a answer
PLEASE HELP I RLY RLY NEED HELP
Answer: x= 155 degrees
Step-by-step explanation:
All angles in a triangle add up to 180. That is how we find angle a
a + b = 120 degrees as 60 degrees is taken for a straight angle or 180 degrees.
Use Algebra to find angle b
To find c we do the same thing as for a.
x is everything remaining from 180 degrees after c is taken from it.
x = 155 degrees
Multiply the following rational expressions. Remember to fully simplify your answer.
(x^2-1)/(2x-3) ∙ (2x^2+x-6)/(x^2+3x+2)
PLEASE SHOW ALL WORK FOR BRAINLIEST
Answer:
Answered By Unish ©
Verified Answer ✅
Step-by-step explanation:
Multiply the following rational expressions. Remember to fully simplify your answer.
(x^2-1)/(2x-3) ∙ (2x^2+x-6)/(x^2+3x+2)
First, let's factor the expressions in both numerators and denominators to simplify the multiplication:
scss
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(x^2 - 1)/(2x - 3) = (x + 1)(x - 1)/(2x - 3)
scss
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(2x^2 + x - 6)/(x^2 + 3x + 2) = (2x - 3)(x + 2)/(x + 1)(x + 2)
Notice that the factor (x + 2) appears in both the numerator and denominator of the second expression. We can cancel this factor and simplify the expression:
scss
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(x^2 - 1)/(2x - 3) ∙ (2x^2 + x - 6)/(x^2 + 3x + 2)
= [(x + 1)(x - 1)/(2x - 3)] ∙ [(2x - 3)/(x + 1)]
= (x - 1)
Therefore, the simplified product of the two rational expressions is x - 1.
what is grain to gram ?
Although both grains and grams are weight-measuring units, they are not interchangeable.
The weight of gunshots, arrows, and gunpowder is often measured in the United States using a unit of mass called a grain. A grain weighs around 0.06479891 grams.
In contrast, a gram is a mass unit in the International System of Units (SI) that is often employed in scientific and practical contexts. There are 15.4323584 grains in one gram.
You may multiply the total number of grains by 0.06479891 to convert grains to grams. If you have 500 grains, for instance, you would convert them to grams as follows: 500 grains x 0.06479891 grams per grain = 32.399455 grams.
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What is value of sin 1?
The value of sin 1 is 0.841.
It is needed to find the value of the sine function of 1.
Let's take it in radians since it is not mentioned whether the angle is in degrees or radians.
The sine function is the function which is defined as the ratio of the opposite to the hypotenuse o a right triangle.
So consider the right triangle with one of the angles as 1 radian or 57.296 degrees, then find the ratio of the opposite side to the hypotenuse.
The value is :
sin(1 radian) = 0.841
Hence the sine of 1 is 0.841.
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How do you write a homogeneous system in parametric vector form?
A homogeneous system in parametric vector form:
(x1,x2,x3) = (s,s,-0.25s)
Parametric vector Form:
Any equation expressed as a parameter is a parametric equation. The general equation y = mx + b (where m and b are parameters) of a straight line in the form of a slope intersection is an example of a parametric equation. Example: one of the variables to t(x = t). Then we can rewrite this equation as y = t²+5.
So the set of parametric equations is x = t and y=t²+5.
According to the Question:
We are to solve them in parametric form.
X₁ + 2X₂ + 12X₃ = 0 ----------------------- (1)
2X₁ + X₂ + 12X₃ = 0 ----------------------- (2)
-X₁ + X₂ = 0 ----------------------- (3)
From equation 3 we get
x₁ = x₂
Substitute in 1 and 2 to get
3x₁ + 12x₃ = 0 and
3x₁ + 12x₃ = 0
Thus, we find these two equations are dependent. So we can have infinite solutions in parametric form only.
No unique solution is possible
Let x₁ = x₂ = s
Since 3x₁ +12x₃ = 0
x₁ = -4x₃
Or x₃ = -0.25s
So solution in parametric form is
(x1,x2,x3) = (s,s,-0.25s) for all real values.
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