Using Gaussian elimination, the solution to the given system of equations is given as follows:
x = 5, y = -11, z = 3.
What is a system of equations?A system of equations is when multiple variables are related, and equations are built to find the values of each variable, according to the relations given in the problem.
For this problem, the equations are given as follows:
2x - y + 4z = 33.x + 2y - 3z = -26.-5x - 3y + 5z = 23.(I suppose there was a typing mistake on the first equation, as Gaussian elimination can only be applied to solve linear systems).
For Gaussian elimination, the first step is building the matrix of the system, in which:
The first three columns contain the coefficients of x, y and z, respectively.The last column contains the results of the operations.Hence, the matrix of the system is given as follows:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\1&2&-3&-26\\-5&-3&5&23\end{array}\right][/tex]
Then, we need to make the coefficient of x zero in the second and third rows, hence:
R2 -> 2R2 - R1.R3 -> 5R1 + 2R3.Then the matrix will be given by:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&-11&30&211\end{array}\right][/tex]
Now we need to make the coefficient of y on the third row zero, hence:
R3 -> 11R2 + 5R3.
Then:
[tex]\left[\begin{array}{cccc}2&-1&4&33\\0&5&-10&-85\\0&0&40&120\end{array}\right][/tex]
From the third row, we have that:
40z = 120
z = 120/40
z = 3.
From the second row, we have that:
5y - 10z = -85
5y - 30 = -85
5y = -55
y = -11.
From the first row, we have that:
2x - y + 4z = 33
2x + 11 + 12 = 33
2x = 10
x = 5.
Hence the solution of the system is given by:
x = 5, y = -11, z = 3.
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Half the difference of k and 18
Answer:
k and 16
Step-by-step explanation:
I will cry
Nan
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Nan
Determine the distance between each pair of points. Then determine the coordinates of the midpoint M of the segment joining the pair of points.
P(-2,-5,8) and Q(3,-2,-1)
The midpoint is at (1/2 , -3, 7/2 )
In the given statement is
To find the midpoint of the line segment joining the pair of points
P(-2,-5,8) and Q(3,-2,-1)
Midpoint:
The coordinates of the midpoint of a line segment are the average of the coordinates of the end points.
m = (A +B)/2
If we are given three points and we wish to find the midpoint of those points, we need to use the midpoint formula m =( [tex]\frac{x_{1}+x_{2} }{2}[/tex] ,[tex]\frac{y_{1}+y_{2} }{2}[/tex] , [tex]\frac{z_{1}+z_{2} }{2}[/tex])
where:
(x1 , y1 ,z1) are the coordinates of the first point:
(x2 , y2 , z2) are the coordinates of the second point:
Now, We are given the three points P(-2,-5,8) and Q(3,-2,-1)
Solving for the midpoint , we have,
m = ([tex]\frac{-2 + 3}{2} , \frac{-5+ (-2)}{2} , \frac{8 +(-1)}{2}[/tex])
m = (1/2 , -3, 7/2 )
Therefore, the midpoint is at (1/2 , -3, 7/2 )
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The mean income of households in the US is $75,000 per year. The median household income in the US is $42,000 per year. Describe the shape of income in the US. skewed left, mean > median skewed left, mean < median skewed right, mean > median skewed right, mean < median
Answer:
skewed right, mean > median
Step-by-step explanation:
just did it
Answer:
skewed right, mean>median
Step-by-step explanation:
edge 2023
Message instructor about this question
-Match each part of the explicit formula relating the term values and term positions in an arithmetic sequence with the best description of what it
represents.
Note that you might use some choices more than once and might not use all choices.
ar+d(n-1)
11
Submit
a. the change in the term value when the position changes from the first term to the nth term
b. the change in the term value when the position changes by 1
c. the value of the term a
d. the value of the term at position n
e, the value of the term 0-1
f. the position of the term an
g. the change in the term position from the first term to the nth
Using arithmetic sequence concepts, the matching terms are given as follows:
[tex]a_n[/tex]: d.[tex]a_1 + (n - 1)d[/tex]: a.n: f.d: b.d(n - 1): e.n - 1: g.What is an arithmetic sequence?In an arithmetic sequence, the difference between consecutive terms is always the same, called common difference d.
The nth term of an arithmetic sequence is given by:
[tex]a_n = a_1 + (n - 1)d[/tex]
In which [tex]a_1[/tex] is the first term.
Hence, in this problem, the terms are classified as follows:
[tex]a_n[/tex]: value of the term at position n, hence it matches with item d.[tex]a_1 + (n - 1)d[/tex]: change in the term value when the position changes from the first term to the nth term, hence item a.n: position of the term [tex]a_n[/tex], hence item f.d: common ratio, which is the change in the term value when the position changes by 1, hence item b.d(n - 1): value at the position n - 1, hence item e.n - 1: the change in the term position from the first term to the nth, hence item g.More can be learned about arithmetic sequence concepts at https://brainly.com/question/6561461
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Find the midpoint of the line segment with the given
endpoints.
(-4, 5) and (2, 5).
Answer:
Midpoint = (-1, 5)
Step-by-step explanation:
x₁ + x₂ y₁ + y₂
Midpoint = (--------------- , -----------------)
2 2
-4 + 2 5 + 5
Midpoint = (--------------- , -----------------)
2 2
-2 10
Midpoint = (--------------- , -----------------)
2 2
Midpoint = (-1, 5)
I hope this helps!
Factor the expression: 3x² - 7x + 2
Answer:
2 or 1/3
Step-by-step explanation:
by getting the product and sum,then the roots
Write an algebraic proof.
Given: Δ XYZ with medians XR , YS, ZQ
Prove: XP/PR=2
According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.
What is meant by Centroid Theorem?The triangle's centroid is the point where the three medians intersect. According to the centroid theorem, the centroid is 23 times the distance from each vertex to the midpoint of the opposite side.
Consider the algebraic relationships that exist for triangle medians.
The centroid of a triangle is 2/3 the distance from one vertex to the midpoint of the opposite side, according to the Centroid Theorem.
Given: [tex]$\triangle XYZ[/tex] with medians [tex]$\overline{X R}[/tex], [tex]\overline{Y S}$[/tex], and [tex]$\overline{Z Q}$[/tex].
By using Centroid Theorem, we get
1. XP = 2/3 XR
2. XR = XP + PR( Segment Addition Postulate)
3. XP = 2/3(XR+PR) (Substitution Property)
4. XP = 2/3 XP + 2/3 PR (Distributive Property)
5. 1/3 XP = 2/3 PR(Subtraction Property)
6. XP = 2PR (Multiplication Property)
7. XP/PR = 2 (Division Property)
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Amy hiked due east for 2 miles and then hiked due south for 3 miles.
b. How far and in what direction is Amy from her starting position?
The distance between Amy's initial and final position is 1 mile and she is facing South direction
It is given that,
Amy first moves towards East direction in reference to her initial position for 2 miles
The distance covered by Amy in East direction = 2 miles
Then,
Amy moves towards South direction in reference to her initial position(facing East side) for 3 miles
The distance covered by Amy in South direction = 3 miles
We need to find,
The distance between Amy's initial and final position which will be given by the displacement between both points
Let's say that the positive direction is East and the negative direction is south.
The distance covered by Amy in East direction = + 2 miles
The distance covered by Amy in South direction = - 3 miles
Then , +2 +(-3) = -1
Hence, the distance between Amy's initial and final position is 1 mile and she is facing South direction
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The measure of the supplement of an angle is four times the measure of the angle. Find the measures of the angle and it's supplement.
The measures of the angle and it's supplement are144° and 36° respectively.
supplementary angles are those angles that sum up to 180°. The supplement of an angle is calculated by subtracting the value of the angle from 180°.The measure of the supplement of an angle is four times the measure of the angle. (given)
Let us consider the value of the supplement be X°.
Therefore the value of the angle is 4X°
180 - X = 4X
X = 36° (The value of supplement)
180°-X = 144°( The value of angle)
Hence the angles are 36° and 144° .
The measures of the angle and it's supplement are144° and 36° respectively.
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okay can someone help me with this question please! it says look at the given exponents 7 and 4 how can we easily combine them to get our result?
Choices are
[7] [4]
7/4
7-4
7+4
Answer:
7+4 (11)
Step-by-step explanation:
I think you are asking about an equation that looks like this
x^7*x^4
When multiply exponents they are added together and the sum is what the new exponent is.
7+4=11
11 is the new exponent
x^11
So I believe the answer would be 7+4? But I don't fully understand what your question is.
If P Q R S is translated along <3,-2 >, reflected in y=-1, and rotated 90° about the origin, what are the coordinates of P''' Q''' R''' S''' ?
P'''( 1 , -2 ) Q'''( 0 , 1) R'''( -1 , 3 ) S'''( -2 , 0) are the coordinates of P''' Q''' R''' S''' .
What does the term "coordinates" mean?
Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ). Mathematicses, scientists, and engineers frequently employ a variety of coordinate systems.( x , y) → ( x + 3 , y - 2 )
p' ( -2, -1 ) Q' ( 1 , 0) R'( 3, -3 ) S'(0, -4 )
( x , y ) → ( x , -2 - y)
p''(-2 , - 1 ) Q''( 1 , 0 ) R''( 3 , 1 ) S''( 0,2 )
( X , Y ) → ( -Y , X )
P'''( 1 , -2 ) Q'''( 0 , 1) R'''( -1 , 3 ) S'''( -2 , 0)
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Are 1 divided by 3/4 and 1/3 divided by 4 equivalent fractions?
Answer:
No Because 1/1 : 3/4 = 4/3 and 1/3 : 4/1 = 1/12
The garden and a walkway around its perimeter have an area of 378. Find the width of the walkway if the garden measures 12 feet wide 15 feet long
The width of walkway is 3 feet.
What is rectangle ?
A rectangle has 2 congruent diagonals, that is the two diagonals are equal to each other. The diagonals of a rectangle bisects each other into equal segments.
We have been given that the garden and the walkway around its perimeter have an area of 378 square feet.
Let us suppose the width of the walkway is x feet.
the length of garden and the walkway will be = 15+2x
and, the breadth of garden and the walkway will be = 12+2x
Now, area of the garden and the walkway around its perimeter is given by :
A = (15+2x)(12+2x)
A = 4x^2 + 54x + 180
Now, the area is given is given as 378 square feet. Hence, we have
4x^2 + 54x + 180 = 378
4x^2 + 54x -198 = 0
Using quadratic formula to find the roots of above equation we get :
x = 3, -33/2
Taking positive value of x that is 3 as area cannot be negative.
Therefore, the width of walkway is 3 feet.
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In right AABC with mzC-90°, mzB-75°, and AB = 12 cm. Find the area
of AABC.
The area of triangle ΔABC with ∠C = 90°, ∠B = 75° an AB = 12 cm will be 18.16 square centimeters.
We have a right - angled triangle ΔABC.
We have to find the area of ΔABC.
What is Pythagoras theorem ?Pythagoras theorem states - In a right - angled triangle ΔABC, the square of the hypotenuse is equal to the sum of the squares of the base and perpendicular. Mathematically -
h² = b² + p²
According to the question -
(Refer to the image attached)
∠C = 90°
∠B = 75°
AB = 12 cm
Now -
sin 75° = AC/AB
AC = AB sin(75°) = 12 sin(75°) = 12 x 0.97 = 11.64 cm
and
tan 75° = AC/BC
BC = AC/tan(75°) = 11.64/3.73 = 3.12 cm
Therefore, the area of triangle ΔABC -
A = 1/2 (AC x BC) = 0.5 x 3.12 x 11.64 = 18.16 cm²
Hence, the area of triangle ΔABC will be 18.16 cm².
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PLEASEEE HELP!!!!!!!!
Answer:
108°
Step-by-step explanation:
Since angle WYT and angle UYW lie on the same line, we can use linear pair fidn the answer.
That is: 180-72= angle UYW
Therefore angle UYW=108°
-Hence proved:)
Is 7√56 rational or irrational? Explain.
What is Irrational Number?
An Irrational number is areal number that cannot be expressed as a ratio of integers; for example [tex]\sqrt{2}[/tex] is an irrational number. We cannot express any irrational number in the form of ratio, such as p/q, where p and q are integers, q[tex]\neq[/tex] 0. Again, the decimal expansion of an irrational number in neither terminating nor recurring.
Let us assume [tex]7\sqrt{56}[/tex] is rational.
So, we can write this number as
[tex]7\sqrt{56}[/tex] = a/b __(1)
Here, a and b are two co-prime numbers and b is not equal to zero.
Simplify the equation (1) divide by 7 both sides, we get
[tex]\sqrt{56}=\frac{a}{7b}[/tex]
Here, a and b are integers, so a/7b is a rational number, so [tex]\sqrt{56}[/tex] should be a rational number.
But [tex]\sqrt{56}[/tex] is a irrational number, so it is Contradictory.
Therefore, [tex]7\sqrt{56}[/tex] is irrational number.
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What is the common ratio in the geometric sequence 4,10,25,62.5, . . . . . ?
(A) 0.4 (B) 2.5 (C) 15 (D) 25
The common ratio of the geometric sequence 4, 10, 25, 62.5, . . . is 2.5. The answer is B.
A geometric sequence refers to a sequence of numbers, which the next term is obtained by multiplying the previous term with a constant, called a common ratio.
a(n) = a r^(n-1)
Where:
a(n) = nth term
a = first term
r = common ratio
The common ratio must be the same for all pairs of succeeding term to be called a geometric sequence.
To find the common ratio, use the formula
a(n) = a r^(n-1)
let n = 2, a = 4, a(2) = 10
10 = 4(r^(2 - 1)
10 = 4(r)
r = 2.5
Or just simply divide each succeeding pairs of the sequence.
r = 10/4 = 2.5
r = 25/10 = 2.5
r = 62.5/25 = 2.5
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Write an equation of the line with the given slope and y -intercept. Use slope-intercept form. Then rewrite the equation in standard form. m=-6, b=9
The slope-intercept form is y = mx + b.
If the value of m = -6 and b = 9 then 6x + y = 9 be the standard form.
What is meant by slope intercept form?Y = mx + b is the general formula for the slope-intercept form, where m stands for the line's slope and b for the y-value of the line's y-intercept. We may more easily determine a line's slope and its y-axis intersection using the slope-intercept form of a linear equation.
Let the value of m = -6(slope)
b = 9 (y -intercept)
The slope-intercept form is given by,
y = mx + b
y = -6x + 9
Therefore, y = -6x + 9 is the slope-intercept form
Standard form is given by, Ax + By = C
Since, slope-intercept form is y = -6x + 9
⇒ 6x + y = 9
Therefore, 6x + y = 9 is the standard form.
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Marc wants to qualify for the 200-meter dash at the school championship.
In order to qualify, his mean running time for 5 races must be no greater than 22.8 seconds.
A list of Marc's running times, in seconds, for his first 4 races is shown.
23.1, 23.2. 22.8, 21.9
What is the maximum running time, in seconds, Marc can have in his last race in order to qualify for the championship? Round the answer to
the nearest tenth.
______ seconds
the maximum time that he can have in his last race is 23 seconds.
What is the maximum running time, in seconds?
We know that the average can not be greater than 22.8 seconds, then if x represents the time of the last race, the maximum value that x can take is given by the equation:
(23.1 + 23.2 + 22.8 + 21.9 + x)/5 = 22.8
(That is the equation for the mean of the 5 times)
Solving that for x we will get:
(23.1 + 23.2 + 22.8 + 21.9 + x) = 5*22.8
91 + x = 114
x = 114 - 91 = 23
So the maximum time that he can have in his last race is 23 seconds.
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I need help with the answer for Geometry, could someone help?
Answer:
48
Step-by-step explanation:
ABC is a right triangle so the masure of ∠A = 90°
The sum of interior angles in a triangle is equal to 180 so we will write an equation accordingly to find the
missing angle:
90 + 2x + 14 + 4x - 26 = 180 add like terms
78 + 6x = 180 subtract 78 from both sides
6x = 102 divide both sides by 6
x = 17
Now replace x with 17 to calculate the measure of m∠B
2*17 + 14 = 48
Determine the truth value of the given conditional statement. If true, explain your reasoning. If false, give a counterexample.
If a number is divisible by 6 , then it is divisible by 3 .
The given conditional statement is true that is If a number is divisible by 6, then it is divisible by 3".
What are conditional statement?A conditional statement involves 2 propositions, p and q. The conditional statement, is a proposition which we write as;
p⇒q, and read "if p then q"
An example of a conditional statement is : p⇒q, that is:
if Triangle ABC is a right triangle with m(C)=90° then The sides of triangle ABC are such that AB^2 = BC^2 + AC^2
"If a number is divisible by 3, then it is divisible by 6." is the inverse of the conditional statement "
Thus If a number is divisible by 6, then it is divisible by 3".
Therefore, the given conditional statement is true that is If a number is divisible by 6, then it is divisible by 3".
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Determine whether the equation below has a one solution no solution or an infinite number of solutions afterwords determine two values of X I support your conclusion X -2 equals -2+ X
The given equation is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.
How many solutions has the given equation?Here we have the linear equation:
x - 2 = -2 + x
And we want to see how many solutions it has, so let's solve it.
IF we add 2 in both sides we will get:
x - 2 + 2 = -2 + x + 2
x + (-2 + 2) = x + (-2 + 2)
x = x
Now, that is an identity, so it is true for any value of x, and x can take infinite values, thus, the linear equation has infinite solutions.
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Determine the slope of the line that contains the given points.
J(7,-3), K(-8,-3)
The slope of the line containing (7,-3) and (-8,-3) is Zero(0).
The slope of a straight line can be written as follows,
m = [tex](y_{2} - y_{1} )/(x_{2} - x_{1} )[/tex] equation1
The line is containing the points (-3,3) and (4,3). So, we can write
[tex]y_{2}[/tex] = -3 , [tex]y_{1}[/tex] = -3 , [tex]x_{2}[/tex] = -8 , and [tex]x_{1}[/tex] = 7 .
On substituting the values of variables in equation1, we will get
m = ( (-3)-(-3) ) / ( (-8)-(7) ) = (0/(-15)) = 0.
As the slope of a line is Zero(0), so we can conclude that the given line is a straight line.
Here:
m = the slope of the line
( [tex]x_{1}[/tex] , [tex]y_{1}[/tex] ) are the first coordinates.
( [tex]x_{2}[/tex] , [tex]y_{2}[/tex] )are the second coordinates.
The slope of the line containing (7,-3) and (-8,-3) is Zero(0).
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Evaluate the equation: 6w = 180
w =
Answer: Evaluate
6w=180
Divide both sides
6
6w = 6
180
Simplify
6
6w =30
Solution
w=30
Step-by-step explanation: hope this helps
Read the problem. Identify what you need to know. Then organize the data to solve the problem.
Alana has the letter tiles A, H, M , and T in a bag. If she selects a permutation of the tiles at random, what is the probability she will spell the word MATH?
A. 1/4
B. 1/12
C. 3/50
D. 1/24
The probability she will spell the word MATH P(MATH) is 1/12
What is the probability?Probability refers to a possibility that deals with the occurrence of random events.
The probability of all the events occurring need to be 1.
The formula of probability is defined as the ratio of a number of favorable outcomes to the total number of outcomes.
Given ; Alana has the letter tiles A, H, M , and T in a bag. If she selects a permutation of the tiles at random.
The different arrangements which can be made out of a given number of objects by taking out some or all at a time are called permutations.
Permutations of "MATH"
4P4 = 4! = 24
Two of the 'MATH" s we can get as a result
Then the probability she will spell the word MATH
P(MATH) = 2/24 = 1/12
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Four friends are sitting at a table together at the prom. What is the probability that a particular one of them will sit in the chair closest to the dance floor?
The probability that a particular one of them will sit in the chair closest to the dance floor is 1/4.
Linear Permutation:
Linear permutation defines the number of ordered arrangement of objects in a line while circular permutations is an ordered arrangement of objects in a circular manner.
Given,
Four friends are sitting at a table together at the prom.
Here we need to find the probability that a particular one of them will sit in the chair closest to the dance floor.
Since the samples are arranged with a fixed reference point, this is a linear permutation.
So there are 4! or 24 ways in which the samples can be arranged.
The number of favorable outcomes is the number of permutations of the other 3 people given that a particular one of them will sit in the chair closest to the dance floor, 3! or 6.
Therefore, the probability is
=> 6/24
=> 1/4.
Therefore, the probability that a particular one of them will sit in the chair closest to the dance floor 1/4.
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A room has an area of 32 square feet. How many square inches is that? How many square
yards?
Answer:
In bold below.
Step-by-step explanation:
There are 12*12 = 144 square inches in a square foot.
So, there are 144 in^2 per 1 ft^2
So, we have:
144 in^2
32 ft^2 ----------- = 4608 in^2.
1 ft^2
For yards it is 1 yd^2 per 9 ft^2 :-
1 yd^2
32 ft^2 = ------------ = 3.56 yd^2.
9 ft^2
HELP WITH THIS PROBLEM PLS PLS
Answer:
Here,
MP=MN+NP=17+3y
or, 5y+9=17+3y
Now do equation and find the value of y.
Answer:
MP = 29
mp = mn + np
17 + 3y = 5y + 9
2y = 8
y= 4, NP = 3(4) = 12
so, MP = mn + np.... 12 + 17
MP = 29
Evaluate the expression when a= -6 and c=4
-c +6a
Answer:
x=3: 2(3) = 6.
Step-by-step explanation:
1. Find a rule for the following table. Write your rule as a
sentence relating the input and the output.
Rule:
C
Input
O
Output
59
29
39
119
No output
39
Step-by-step explanation:
The attached image should be what you're looking for.
