The solution set of the given homogeneous system in parametric vector form is x₁ = 5 = x₂ , x₃ = 1.
What is parametric vector form?
The identity matrix's two columns, which stand in for the two leading coefficients in the row echelon form of the original matrix, are added to create the parametric vector.
We are given set of equations as:
x₁ + 2x₂ - 15x₃ = 0
2x₁ + x₂ - 15x₃ = 0
-x₁ + x₂ = 0
Now, representing this in the matrix form, we get
[tex]\left[\begin{array}{cccc}1&2&-15&0\\2&1&-15&0\\-1&1&0&0\end{array}\right][/tex]
Now, we will reduce the matrix i.e. in row echelon form using elementary operations
From this, we get
[tex]\left[\begin{array}{cccc}1&0&-5&0\\0&1&-5&0\\0&0&0&0\end{array}\right][/tex]
So, we get that x₃ is the free variable.
Now, representing this in the parametric vector form, we get
x₁ - 5x₃ = 0
x₂ - 5x₃ = 0
x₃ = x₃
From this, we get
x₁ = 5x₃
x₂ = 5x₃
x₃ = x₃
So, we now get
x = [tex]\left[\begin{array}{c}x_{1} &x_{2} &x_{3} \end{array}\right][/tex]
This is equal to
x = [tex]\left[\begin{array}{c}5x_{3} &5x_{3} &x_{3} \end{array}\right][/tex]
Thus,
x = [tex]\left[\begin{array}{c}5 &5 &1 \end{array}\right][/tex]
Hence, the solution is x₁ = 5 = x₂ , x₃ = 1.
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Math triangle word problem:
Answer:
2,810 feet
Step-by-step explanation:
Take a look at the diagram
There are two triangles formed with a common side AB
AB represents the vertical height of the plane = 5150 feet
AC represents the distance of car 1 from O
In ΔABC, m∠A = 90°, m∠ABC = 38°
Since the three angles of triangle must add up to 180°
90 + 38 +m∠C = 180
128 + m∠C = 180°
m∠C = 180 - 128 = 52°
In a right angle triangle where one side is the angle ∅, the ratio of the side opposite this angle to the side adjacent to the angle is tan∅
Using the values provided we get
tan(52°) = 5150/AC
AC= 5150/tan(52) = 4,023.62 feet ≈ 4024 feet
This is the horizontal distance of the first car from the plane
Similarly for ΔABD
m∠D = 180 - (90 + 53) = 37°
tan(37) = 5150/AD
AD= 5150/tan(53) = 6,834.28 feet ≈ 6834 feet
This is the horizontal distance of the second car from the plane
The distance between the two cars = 6,834 - 4,024
= 2,810 feet
You have 60m of wire with which you can use to make the frame of
a rectangular block. Find the dimensions (length, width, height) of such a block with
maximum volume.
The dimensions for the block can be 3 x 4 x 5.
What are factors?Factor, in mathematics, a number or algebraic expression that divides another number or expression evenly—i.e., with no remainder.
For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly. The other factors of 12 are 1, 2, 4, and 12.
Given:
We have wire of length 60 m.
Now, to find the length, width and height of block we have to factorize 60.
60 = 3 x 4 x 5
So, the measurement of the block can be length x width x height can be
3 x 4 x 5.
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Order of Operations Consider the numerical expression: 3 + 6 × (5 + 4) ÷ 3 − 7.
Question 1
To evaluate the numerical expression, what is the first step in the order of operations?
A Perform any calculations inside parentheses.
B Perform all additions, working from left to right.
C Perform all multiplications, working from left to right.
D Perform all divisions, working from left to right.
Question 2
Evaluate the given numerical expression.
Responses
A 21
B 14
C 9
D 12
Answer:
Add 5 +4 × 6 ÷ 3 - 7 + 3and you will get 14 and that is your answer
Five more than five times a number is 30, What is the number?
Answer:
5
Step-by-step explanation:
We can set up an equation.
Let x be the number.
So 5x+5 would be equal to 30.
5x+5 = 30
Subtract 5 on both sides:
5x = 25
Divide by 5 on both sides:
x = 5
This graph shows the equations y= - 1/2x + 3 and y=2x-2.
A coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).
What is a linear system of equations?A system of linear equations consists of two or more equations made up of two or more variables such that all equations in the system are considered simultaneously. The solution to a system of linear equations in two variables is any ordered pair that satisfies each equation independently.
a) Given that, the graph shows the equations y= - 1/2x+3 ------(i) and y=2x-2 ------(ii).
From the graph, the solution is (2, 2)
b) Put x=1 in equation (i), we get
y= -1/2(1)+3
y= 2.5
Put x=2 in equation (i), we get
y= -1/2(2)+3
y= 2
Put x=3 in equation (i), we get
y= -1/2(2)+3
y= -1/2 (3)+3
y= -1.5+3
y= 1.5
So, a coordinate that is a solution to the first equation is (3, 1.5)
Therefore, a coordinate that is a solution to the first equation but not a solution to the system of equations is (3, 1.5).
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refers to the consistency of measures, whereas refers to the truthfulness of a measurement.
Reliability refers to the consistency of measures, whereas validity refers to the truthfulness of a measurement.
What do we mean by measure?The size, capacity, or amount of something determined by measurement. Use equal amounts of ingredients. Something used for measurement (such as a ruler or cup). A unit used to measure. A foot is a measure of length.
What is statistics in mathematics?Statistics is a science concerned with developing and studying methods for measure, collecting, analyzing, interpreting, and presenting empirical data.
Significance of statistics:Statistics is the branch of mathematics for collecting, analyzing and interpreting data. Statistics can be used to predict the future, determine the likelihood of certain events occurring, and answer research questions.
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Maddie wrote six different equations based on the triangle below.
60°
Four of the six equations that Maddie wrote are correct. Which four of the equations are correct?
sin 30 = 1
cos 60
12
1/201
tan 60 = √3
sin 60
tan 30-
=
cos 30 =
√2
2
√√2
2
Maddie wrote six different equations based on the triangle below.Four of the six equations that Maddie wrote are correct which are options A, D , E and F.
What is a Triangle?This is referred to as a polygon with three edges and three vertices.
Triangle ABC was given in the picture.
∠A = 60° and ∠B = 90° which is given in the figure
sin 60° = perpendiculer /hypotenuse
√3/2 = BC/10
BC = √3/2 × 10
BC = 5√3
tan 60° = perpendiculer /base
√3 = 5√3/AB
AB = 5√3/√3
AB = 5
sin 60° = 5√3/10 = √3/2
cos 60° = base / hypotenuse
cos 60° = 5/10 = 1/2
tan 60° = perpendicular /base
tan 60° = 5√3/5 = √3
cot 60° = 1 /√3
Therefore the equations which are correct are sin 60° =√3/2, cos 60° = 1/2, tan 60° = √3, and cot 60° = 1 /√3.
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hekp A living room floor measures 11 feet by 18.9 feet as indicated by the solid outline in the diagram below. The owner estimated the floor to be 12 feet by 20 feet as indicated by the dashed outline.
Flooring for the room costs $8 per square foot. What is the approximate difference in cost between the flooring to cover the actual area and the flooring to cover the estimated area of the living room floor?
A) $150
B) $320
C) $50
D) $250
E) $40
Answer: The actual area of the living room floor is 11 feet * 18.9 feet = 208.9 square feet. The estimated area of the living room floor is 12 feet * 20 feet = 240 square feet.
The difference in cost between the flooring to cover the actual area and the flooring to cover the estimated area of the living room floor is 240 square feet - 208.9 square feet = 31.1 square feet.
Therefore, the approximate difference in cost is 31.1 square feet * $8 per square foot = $248.80, which is closest to option (D) $250.
Step-by-step explanation:
Also when you answer can you show work so I know how you got your answer please and thank you
The area covered by the circular spotlight is given as follows:
C. 153.86 square feet.
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr²
π can be rounded to 3.14, hence the equation for the area is given as follows:
A = 3.14r².
The radius is of 7 feet, hence the area is given as follows:
A = 3.14 x 7²
A = 153.86 square feet.
Meaning that option C is the correct option for this problem.
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I need HELP please
Thank you
Answer:
x = 11
Step-by-step explanation:
both the petagons are similar so the sum of their sides will be same
i.e.
sum of ABCDE = sum of JKLMN
ABCDE = sum of all the five sides = 6+2+2+3+3 = 16
thus,
sum of JKLMN = 16
16 = x+1+1+1.5+1.5
16 = x+5
x = 16-5 = 11
What is the equation of a vertical line passing through the point (−5, −1)?
Answer:
x=-5
I think this is right
Step-by-step explanation:
Check the picture below.
2/3y + v = x solve for y
The variable y as the subject formula in the equation (2/3)y + v = x is y = (3/2)(x) - (3/2)(v)
What is y in the given equation?Given the equation in the question;
(2/3)y + v = x
y = ?
Solve for y, we make 'y' the subject of the formula.
(2/3)y + v = x
Subtract v from both sides
(2/3)y + v - v = x - v
(2/3)y = x - v
Multiply both sides by 3/2
(3/2)(2/3)y = (3/2)(x - v)
y = (3/2)(x - v)
Apply distributive property.
y = (3/2)(x) - (3/2)(v)
Therefore, y equals (3/2)(x) - (3/2)(v).
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The population of town X was 220,000 in 2000, and 252,000 in 2010. Project the population in 2020.
Answer: To project the population in 2020, we can use the linear trend line equation.
First, we need to find the equation of the line. Let's use the two given points, (2000, 220,000) and (2010, 252,000), to find the slope of the line:
slope = (252,000 - 220,000) / (2010 - 2000) = 32,000
Next, we can use the slope-intercept form of the line equation: y = mx + b, where m is the slope and b is the y-intercept.
Plug in the first point: 220,000 = 32,000 * 2000 + b
Solve for b: b = 220,000 - 32,000 * 2000 = -44,000,000
The equation of the line is: y = 32,000x - 44,000,000
Finally, we can use the equation of the line to project the population in 2020:
y = 32,000 * 2020 - 44,000,000 = 264,000
So, the projected population in 2020 is 264,000.
Step-by-step explanation:
5. Write the fraction 31415 10000 as a decimal number.
Answer:
To write 31415/10000 as a decimal you have to divide numerator by the denominator of the fraction.
We divide now 31415 by 10000 what we write down as 31415/10000 and we get 3.1415
What is the probability of guessing the top 3 horses in order in a field of 20 horses in the Kentucky derby?
The probability of guessing the top 3 horses in order in a field of 20 horses in the Kentucky derby is, Very low value approximately 0.000145
What is probability?Probability is a mathematical term, which can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event. The possibility that an event will occur is measured by probability.
Probability of Event = Favorable Outcomes/Total Outcomes = X/n
Given that,
There are total 20 horses,
The probability of guessing the top 3 horses in order = ?
The probability of guessing the top 3 horses in order in a field of 20 horses in the Kentucky Derby would be 1 in 20 x 19 x 18 = 6840.
This means that the probability of guessing the top 3 horses correctly would be 1/6840 or approximately 0.000145.
It is a very low probability and requires a lot of knowledge, research, and luck to correctly guess the top 3 horses in order.
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The number of regular season wins for 10 football teams in a given season are given below. Determine the range, mean, variance, and standard deviation of the population data set. 2,10,15,2,,12,13,7,3,8
It falls between: The population mean is 13. 8. The population variance is 192. The population's standard deviation is 13.856.
Why do we calculate population variance?A key measure of dispersion in statistics is population standard deviation. additional reading Statisticians compute variance to determine how various values inside a data collection interact to one another. While calculating the population variance, one may also compute the dispersion in relation to the population means.
The range: 15 - 2 = 13
The population mean is:
Mean = ( 2 + 10 + 15 + 2 + 12 + 13 + 7 + 3 + 8 ) / 9 = 8
The population variance ( S² or Sigma² ):
S ² = 1/9 · ( ( 2 - 8 )² + ( 10- 8 )² + ( 15 - 8 )² + ( 2 - 8 )² + ( 12 - 8 )² + ( 13 - 8 )² + ( 7 - 8 )² + ( 3 - 8 )² + ( 8 - 8 )² )
S ² = 192
The population standard deviation:
S = √(S²) = √192 = 13.856
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width of a triangle is 4 inches more than its width. the area of the rectangle is equal 5 inches more than 2 times the perimeter. find the length and width.
The length and width of the rectangle are 11 and 78 respectively.
What is Area?The area is the entire amount of space occupied by a flat (2-D) surface or an object's form. On a sheet of paper, draw a square using a pencil. It has two dimensions. The area of a form on paper is the area that it occupies.
Given, the length of a rectangle is 4 inches more than its width.
let x be the width of a rectangle.
thus, length = 4 + width
From the general formula of area and perimeter:
Area of rectangle = length*width
Perimeter of rectangle = 2(length + width)
In our case,
Area = x * (4 + x)
Area = x² + 4x
Perimeter = 2( 4 +x+ x)
Perimeter = 8 + 4x
Since the area of the rectangle is equal 5 inches more than 2 times the perimeter.
Thus,
x² + 4x = 5 + 2(8 + 4x)
x² + 4x = 5 + 16 + 8x
x² + 4x = 21 + 8x
x² + 4x -8x -21 = 0
x² - 4x -21 = 0
x = 7 and -3
Thus,
the width of the rectangle = 7
and the length of the rectangle = 11
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Complete question:
length of a rectangle is 4 inches more than its width. the area of the rectangle is equal 5 inches more than 2 times the perimeter. find the length and width.
If the original quantity is 20 and the new quantity is 16 , what is the percent decrease?
The required percent decrease from 20 to 16 is given as 20%.
What is the percentage?The percentage is the ratio of the composition of matter to the overall composition of matter multiplied by 100.
Here,
To find the percent decrease, we can use the formula:
Percent Decrease = (original quantity - new quantity) / original quantity * 100%
Plugging in the values:
Percent Decrease = (20 - 16) / 20 * 100%
= 4 / 20 * 100%
= 20%
So, the percent decrease is 20%.
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92÷3= solving the equation
32.66 repeated :>))))))))))))))
Answer:
30.6666666667
Step-by-step explanation:
92÷3 = 30.6666666667
Find f(0) given the function rule f(x) = 3x - 6.
Responses
Answer:
f(0) = -3
Step-by-step explanation:
1. Insert f(0) into the function of f(x) = 3x-6
2. f(0) = 3 x 0 - 6
3. f(0) = 3 - 6 = -3
Please help quick
(b) Do the sets A, B, and D form a partition of R? If not, which condition of a partition is not satisfied?
(c) Do the sets B, D, and E form a partition of R? If not, which condition of a partition is not satisfied?
a) The sets A, B and D form a partition of the real numbers, as each real number is present in exactly one of of these sets.
b) The sets B, D and E do not form a partition of the real numbers, as the element x = -2 belongs to both sets D and E.
What are the conditions for the partition of a set?The conditions for the partition of a set are given as follows:
No element of the original set is present in more than one of the subsets.Together, the subsets contain all the elements of the original set.More can be learned about partitions of a set at https://brainly.com/question/29495953
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15. ABC is
a. Congruent
b. Similar
c. Neither
to A'B'C'.
Answer:
Step-by-step explanation:
Similar
when the coefficients of polynomials are drawn from a finite field, the set of polynomials constitutes a
The set of polynomials over F is the set of all possible polynomials with coefficients from F, which includes all polynomials with degree up to the size of F.
A polynomial over a finite field is a mathematical expression of the form
[tex]P(x) = a_0 + a_1x + a_2x^2 + ... + a_nx^n[/tex],
where the coefficients a_i are elements of a finite field F. Therefore, the set of polynomials over a finite field F is the set of all possible polynomials with coefficients from F. For example, if F is the field with two elements {0, 1}, then the set of polynomials over F is [tex]{0, 1, x, x + 1, x^2, x^2 + 1, ...}[/tex]. As another example, if F is the field with three elements {0, 1, 2}, then the set of polynomials over F is [tex]{0, 1, 2, x, x + 1, x + 2, x^2, x^2 + 1, x^2 + 2, ...}[/tex]. In general, the set of polynomials over F is the set of all possible polynomials with coefficients from F, which includes all polynomials with degree up to the size of F.
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An automobile dealership has found that for every 170 cars sold, 26 will be brought back to the dealer for major repairs. If the dealership sells 1360 cars this year, approximately how many cars will be brought back for major repairs?
Answer:
208 Cars will be brought back for major repairs.
Step-by-step explanation:
With the simple calculation of:
[tex]\frac{170}{1360}\frac{26}{x}[/tex]
We are solving for x.
We cross-multiply 1360 by 26.
35,360
Then divide that by 170.
which will get us the result of 208.
CAN SOMEONE HELP WITH THIS QUESTION✨
Answer:
m = √3 ≈ 1.7321b = 1 -π√3/6 ≈ 0.0931Step-by-step explanation:
You want the slope-intercept form equation for the tangent line at point (π/6, 1) on the curve y = 2·sin(x).
SlopeThe slope of the line at the point of tangency is the derivative of the curve at that point:
y' = 2cos(x) = 2·cos(π/6) = 2(√3/2)
m = √3 . . . . . approximately 1.7321
Y-interceptSolving the line's equation for b, we have ...
y = mx +b
b = y -mx = 1 -(√3)(π/6)
b = 1 -π√3/6 . . . . . approximately 0.0931
EquationThe equation of the line is ...
y = mx +b
y = (√3)x +1 -(π√3)/6
an inattentive driver is traveling 16.0 m/s m / s when he notices a red light ahead. his car is capable of decelerating at a rate of 3.06 m/s2 m / s 2 .
It will take the inattentive driver 5.22 seconds to come to a complete stop, assuming the car's deceleration remains constant.
An inattentive driver traveling 16.0 m/s when he notices a red light ahead and his car is capable of decelerating at a rate of [tex]3.06 m/s^2[/tex]. To determine how much time it will take for the car to come to a complete stop, we can use the following equation of motion:
v = v0 + at
where v is the final velocity (in this case, 0 m/s), v0 is the initial velocity (16.0 m/s), a is the acceleration (negative, because the car is slowing down), and t is the time.
Rearranging and solving for t, we get:
t = -v0 / a
t = -16.0 / (-3.06)
t = 5.22 seconds
So, it will take the inattentive driver 5.22 seconds to come to a complete stop, assuming the car's deceleration remains constant. This time can be used to determine the minimum distance the driver needs to maintain between himself and the vehicle in front of him to avoid a collision.
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Titing Tunction Rune -3 -2 -1 3 2 1 7 ty A -2 1 2 3 g(x) X Determine the values of h and k in the equation of g(x). g(x)=√√x-h+k
The values of h and k are given as follows:
h = 1.k = -2.What is a translation?A translation happens when either a figure or a function are moved horizontally or vertically.
The four translation rules for functions are given as follows:
Left a units: f(x + a).Right a units: f(x - a).Up a units: f(x) + a.Down a units: f(x) - a.The parent function for this problem is given as follows:
[tex]y = \sqrt[3]{x}[/tex]
Which makes the curve at the origin.
From the graph, the curve is made at point (1,-2), hence the translations are given as follows:
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There is a bag filled with 3 blue and 4 red marbles. A marble is taken at random from the bag, the colour is noted and then it is not replaced. Another marble is taken at random. What is the probability of getting 2 that are different in colour?
Answer: THE ANSWER IS 18/42
Step-by-step explanation:
Which equation would create a line perpendicular to y= 5x +10
Answer:
y=1/5x+10
Step-by-step explanation:
i am a quadratic binomial with only one variable. when written in standard form, my lead coefficient is a 3 and my constant is a -7. who am i?
The quadratic binomial in discuss as described in the task content is; 3x² - 7.
What is the quadratic binomial as discussed?It follows from the task content that the expression in discuss is a quadratic binomial. In essence, there are only 2 terms.
Therefore, the expression should takes the form; ax² + b.
However, since the leading coefficient, a is said to be 3 and the constant, b is said to be -7; we have that;
3x² - 7.
Ultimately, the quadratic binomial is; 3x² - 7.
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