Write the matrix equation as a system of linear equations without matrices.
5
-1 -5
X
-7
- 6
6
3
y
8
-6-8-2
Z
2
Equation 1
SHO
1
Answers
The system of equations is 5x - y - 5 = -7, -6x + 6y + 3z = 8 and -6x - 8y - 2z = 2
How to determine the system of equations?The matrix is given as:
\(\left[\begin{array}{ccc}5&-1&-5\\-6&6&3\\-6&-8&-9\end{array}\right] \left[\begin{array}{c}x&y&z\end{array}\right] = \left[\begin{array}{c}-7&8&2\end{array}\right]\)
Next, we multiply the matrices
\(\left[\begin{array}{c}5x - y - 5&-6x + 6y + 3z&-6x -8y -2z\end{array}\right] = \left[\begin{array}{c}-7&8&2\end{array}\right]\)
By comparing the position of the cells, we have
5x - y - 5 = -7
-6x + 6y + 3z = 8
-6x - 8y - 2z = 2
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The system of equations is 5x - y - 5z = -7, -6x + 6y + 3z = 8, and -6x -8y -2z = 2 which is represented by the matrix in the provided picture.
What is the matrix?It is defined as the group of numerical data, functions, and complex numbers in a specific way such that the representation array looks like a square, rectangle shape.
We have given matrices in the picture that represents the system of the equation.
\(\rm \left[\begin{array}{ccc}5&-1&-5\\-6&6&3\\-6&-8&-2\end{array}\right] \rm \left[\begin{array}{ccc}x\\y\\z\end{array}\right] = \left[\begin{array}{ccc}-7\\8\\2\end{array}\right]\)
After the multiplication of two matrices:
\(\rm \left[\begin{array}{ccc}5x-y-5z\\-6x+6y+3z\\-6x-8y-2z\end{array}\right] = \left[\begin{array}{ccc}-7\\8\\2\end{array}\right]\)
On comparing:
5x - y - 5z = -7
-6x + 6y + 3z = 8
-6x -8y -2z = 2
Thus, the system of equations are 5x - y - 5z = -7, -6x + 6y + 3z = 8, and -6x -8y -2z = 2 which is represented by the matrix in the provided picture.
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Related Questions
Need help with puzzle
Answers
Answer:
x = 4
Step-by-step explanation:
The two angles A and C added together equal 88
5x + 3 + 15x + 5 = 88 Combine like terms
20x + 8 = 88 Subtract 8 from both sides
20x + 8 - 8 = 88 - 8
20x = 80 Divide both sides by 20
x = 4
Helping in the name of Jesus.
Solve each equation by completing the square.
d² - 24d + c
Answers
Answer:
d² - 24d + c = (d - 12)² - 144 + c
there are 8 circles and 6 squares. what is the simplest ratio of squares to circles?
Answers
Answer:
4:3
Step-by-step explanation:
Given function:
8 circle by 6 squaresDivide similar factor by each term:
\(8=4\)·\(2\) \(6=3\)·\(2\)Rewrite:
\(4:3\)Therefore, the simplest ratio for 8 circles and 6 squares would be 4:3..
Consider a tree T with n vertices, where n is an odd integer greater than or equal to 3. Let v be a vertex of T. Prove that there exists a vertex u in T such that the distance between u and v is at most (n-1)/2
Answers
There must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
To prove the existence of a vertex u in tree T such that the distance between u and v is at most (n-1)/2, we can employ a contradiction argument. Assume that such a vertex u does not exist.
Since the number of vertices in T is odd, there must be at least one path from v to another vertex w such that the distance between v and w is greater than (n-1)/2.
Denote this path as P. Let x be the vertex on path P that is closest to v.
By assumption, the distance from x to v is greater than (n-1)/2. However, the remaining vertices on path P, excluding x, must have distances at least (n+1)/2 from v.
Therefore, the total number of vertices in T would be at least n + (n+1)/2 > n, which is a contradiction.
Hence, there must exist a vertex u in T such that the distance between u and v is at most (n-1)/2.
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what is the answer of 180 x 586 estimate
Answers
Answer:105,500
Step-by-step explanation:Siri
The result of multiplication 180 x 586 is 105480.
Given, that multiply 180 x 586.
Multiplication: It is basic mathematical operation among addition, subtraction and division. Multiplication is the basic operation in BODMAS.
BODMAS:
B = Bracket
O = Of
D = Division
M= Multiplication
A = Addition
S = Subtraction
Multiplication rule:
The rules for multiplication are:
(1) positive × positive = positive
(2) positive × negative = negative
(3) negative × negative = positive
Here both the numbers are positive . So apply rule number 1,
180 x 586
= 105480
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Please answer this question for me
Answers
The criterion that she should use to prove that triangles RST and XYZ are congruent are:
i. Hypotenuse Leg (HL)
ii. Side-Angle-Side (SAS)
What are congruent triangles?When the corresponding properties i.e. length of sides and measure of internal angles of two or more triangles are equal, then the triangles are said to be congruent. The relations can be shown using some theorems.
From the given triangles RST and XYX, it can be observed that;
TR ≅ XZ
RS ≅ XY
<R ≅ <X (given)
<T ≅ <Z (given)
Angles R and X are included angle of the triangles. Thus, the criterion that can be used to show that triangles RST and XYZ are congruent at;
i. Hypotenuse Leg (HL)
ii. Side-Angle-Side (SAS)
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Find an equivalent expression for the expression below using the distributive property.8 - 1/2 (4s - 1/2 + 12s - 1/4)
Answers
Distribution property is given by,
\(a\times(b+c)=a\times b+a\times c\)Now, using the distributive property, the expression can be written as,
\(\begin{gathered} 8-\frac{1}{2}(4s-\frac{1}{2}+12s-\frac{1}{4})=8-\frac{1}{2}\times4s-\frac{1}{2}\times(-\frac{1}{2})-\frac{1}{2}\times12s-\frac{1}{2}\times(-\frac{1}{4}) \\ =8-2s+\frac{1}{4}-6s+\frac{1}{8} \\ =8-8s+\frac{1}{4}+\frac{1}{8} \\ =8-8s+\frac{12}{32} \\ =8-8s+\frac{3}{8} \end{gathered}\)Therefore
What is greater 1.0275 or 1.029
Answers
Answer:
1.029 is greater than 1.0275
Step-by-step explanation:
Answer:
1.029
Step-by-step explanation:
What is greater 1.0275 or 1.029
.027 < .029
So, 1.029 is greater.
Simplify: 35( 1/7n + 3/5n ) + n
Answers
Answer:
Simplified: 27n
Step-by-step explanation:
help with the question please
Answers
24. There are 10 pupils in a class. Half of them are
girls. What is the probability of selecting a girl
from the class for a trip to the zoo?
Answers
A town's population is currently 6,595. If the population doubles every 29 years, what will the population be 145 years from now?
Answers
Answer:
Below
Step-by-step explanation:
145 yr / 29 yr/double = 5 doubles
6595 x 2 ^5 = 211 040 ppl
Find the intercepts and the vertical and horizontal asymptotes
Answers
The x and y-intercepts of the rational function are; (-3, 0) and (0, -3/25).
The vertical asymptotes of the function are; x = ± 5.
The horizontal asymptotes of the function is f(x) = 0.
What are the intercepts?For x-intercept; let f (x) = 0;
0 = (x + 3) / (x² - 25)
x + 3 = 0; x = -3 or (-3, 0).
For the y-intercept; let x = 0.
f (0) = (0 + 3) / (0² - 25)
= -3/25 or (0, -3/25).
For the vertical asymptotes;
x² - 25 = 0
x² = 25
x = ±5.
For the horizontal asymptote;
Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is; f (x) = 0.
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I need help on C, D, E, F, G, and H. The mean is 27, and the Standard Deviation is 15.01
Answers
(a) Mean of the distribution.
The mean of a uniform distribution is
\(\begin{gathered} \mu=\frac{a+b}{2} \\ \mu=\frac{1+53}{2} \\ \mu=\frac{54}{2} \\ \mu=27 \\ \\ \text{The mean of the distribution is 27} \end{gathered}\)(b) Standard deviation
The standard deviation is calculated as
\(\begin{gathered} \sigma=\frac{b-a}{\sqrt[]{12}} \\ \sigma=\frac{53-1}{\sqrt[]{12}} \\ \sigma=\frac{52}{\sqrt[]{12}} \\ \sigma=15.0111 \end{gathered}\)(c) Probability of Pr( x = 5 )
\(\begin{gathered} \text{Since week 1 up to week 53 is uniformly distributed, they have the same probability} \\ \text{all throughout} \\ \\ \text{There are 52 spreads }(53-1) \\ \text{the probability is} \\ \Pr (x=5)=\frac{1}{52}\approx0.0192 \end{gathered}\)(d) Probability of Pr( 11 < x < 16 )
\(\begin{gathered} \Pr (11\le x\le16)=\frac{16-11}{53-1} \\ \Pr (11\le x\le16)=\frac{5}{52}\approx0.0962 \end{gathered}\)(e) Probability of Pr( x > 13)
\(\begin{gathered} \Pr (x>13)=\frac{53-13}{52-1} \\ \Pr (x>13)=\frac{40}{52}\approx0.7692 \end{gathered}\)(f) Probability of Pr ( 18 < x < 42 )
\(\begin{gathered} \Pr (18(g) Find the 23rd percentile.The area of the 23rd percentile is 0.23
the area is solved by
\(\begin{gathered} A=k\cdot\frac{1}{52} \\ \\ \text{Since area is 0.23, then} \\ 0.23=k\cdot\frac{1}{52} \\ \frac{0.23}{\frac{1}{52}}=\frac{k\cdot\cancel{\frac{1}{52}}}{\cancel{\frac{1}{52}}} \\ k=11.96 \\ \\ \text{Therefore, the 23rd percentile is 11.96 weeks} \end{gathered}\)(h) Find the minimum for the lower quartile
The lower quartile, or first quartile (Q1), is the value under which 25% of data points are found when they are arranged in increasing order. It starts with the smallest number, for our uniform distribution which starts at week 1, the MINIMUM for the lower quartile is week 1.
Joe has saved $30. He earns $7.50 per hour at his job. He plans to buy a plane ticket to Florida for $300. Enter the minimum number of hours Jon must work in order to buy the plane ticket to Florida.
Answers
Answer:
30 hours
Step-by-step explanation:
300 - 30
270/7.5
You are setting up a part-time business with an initial investment of $12,000. The unit cost of the product is $11.50, and the selling price is $19.00.Required:a. Find equations for the total cost C (in dollars) and total revenue R (in dollars) for x units.b. Find the break-even point by finding the point of intersection of the cost and revenue equations units.c. How many units would yield a profit of $1000?
Answers
Answer:
Given Initial investment = $12,000
Cost per unit = $11.50
Selling price per unit = $19
a. For x unit
Total cost = Initial investment + Cost per unit * no of unit
= 12,000 + 11.50(x)
c(x) = 12,000 + 11.50(x)
R(x) = Selling price per unit * no of items
R(x) = 19 * x
R(x) = 19x
b. Break even point = R(x) = C(x)
19x = 12,000 + 11.50x
19x - 11.5x = 12,000
7.5x = 12,000
x = 12,000 / 7.5
x = 1600
So, break even point x = 1,600
c. For Profit = $1,000
P(x) = 1,000
P(x) = R(x) - C(x)
1000 = 19x - (12,000 + 11.5x)
1000 =19x - 11.5x - 12000
7.5x = 12000 + 1000
7.5x = 13000
x = 13000/7.5
x = 1733.33
So x = 1733 units
Hence, 1733 units will yield for $1,000 profit
2 3/4 of 500grams in step by step calculator
Answers
Answer:
To calculate 2 3/4 of 500 grams, follow these steps:
1. Convert the mixed number to an improper fraction:
2 3/4 = (2 x 4 + 3)/4 = 11/4
2. Multiply the improper fraction by 500:
11/4 x 500 = (11 x 500)/4 = 2,750/4
3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:
2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2
Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.
Step-by-step explanation:
3x^2+5x+2 help me solve this
Answers
Answer:
(3x +2)(x +1)
Step-by-step explanation:
A number of different ways are suggested for doing this. One that seems straightforward is this.
For ax^2 +bx +c, look for factors of ac that total b. Here we have ...
ac = 3·2 = 6
b = 5
It is easy to see that the factors we just multiplied to get 6 are ones that total 5: 3+2 = 5.
Now, rewrite the "bx" term using this sum.
3x^2 +3x +2x +2
Factor each pair of terms.
3x(x +1) +2(x +1)
And factor out the common factor:
(3x +2)(x +1)
Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.
Pick the diagram that models the ratio in the story.
If the choir has learned 9 classical songs, how many modern songs have they learned?
Answers
Answer:
prolly 12
Step-by-step explanation:
it is probably 12 thank you
Answer:
15
Step-by-step explanation:
All you gotta do is divide 9/3 for the ratio.
Once you get 3 all you have to do is multiply that to the 5
And you get 15 easy
Use OZ with VWXY
What is XY ?
A 30
B. 35
C. 40
D. 50
Answers
Answer:
Step-by-step explanation:
Chords having equal measures are equidistant from the center of the circle.
Since, VW = XY
Therefore, ZP = ZR = 15 units
A perpendicular line drawn from the center of a circle to the chord is the bisector of the chord.
VR = WR = 20 units
By applying Pythagoras theorem in ΔZRV,
ZV² = ZR² + VR²
ZV² = (15)² + (20)²
ZV = √(225 + 400)
ZV = √625
ZV = 25 units
Therefore, measure of radius ZV = 25 units.
VW = XY [Given]
Therefore, XY = 2(20)
= 40 units
What is the volume of a solid that is 2 cm wide, 2 cm long, and 2 cm high?
Answers
The volume of a solid with the given dimensions is 8 cm³.
The dimensions of a solid that is 2 cm wide, 2 cm long, and 2 cm high.
What is the volume of solid?The volume of a solid is the measure of how many regions of space is occupied by an object. It is measured by the number of unit cubes it takes to fill up the solid. It is decided by counting the unit cubes in the solid.
The volume of the solid can be solid using length × Width × Height.
That is, 2 × 2 × 2 = 8 cm³
Therefore, the volume of a solid with the given dimensions is 8 cm³.
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Determine the interval(s)
on which the given function is-decreasing.
Answers
A function assigns the values. The interval for which the given function will be decreasing is (-∞, -1)∪(0,∞).
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The interval for which the given function will be decreasing is from point A to point B, and then from point C to point D. Therefore, the interval will be (-∞, -1) and (0,∞). Hence, The interval for which the given function will be decreasing is (-∞, -1)∪(0,∞).
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What is the value of the digit in the ones place?
2,615
A. 50
B. 5
OC. 2,000
OD. 100
Answers
(12x)
D
A
E
(17x - 14)°
В
(2x + 5)°
с
Answers
The value of x for the given equation (2x+5)=(17x-14) will be 19/15.
What is the equation?An equation is a statement that two expressions, which include variables and/or numbers, are equal. In essence, equations are questions, and efforts to systematically find solutions to these questions have been the driving forces behind the creation of mathematics.
It is given that,
(2x+5)=(17x-14)
We have to rearrange the equation by applying the arithmetic operation for the like term, the terms which are similar, and we can perform arithmetic operations on it like addition and subtraction.
17x-2x=5+14
15x=19
x=19/15
Thus, the value of x for the given equation (2x+5)=(17x-14) will be 19/15.
The question is incomplete, the complete question is"solve the value of x for the given equation,
(2x+5)=(17x-14)
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Directions - Find the sector areas of both the grey and white areas:
*Use 3.14 in place of
285⁰
8 in
in²
in
(round to two decimal places)
(round to two decimal places)
E
Answers
The sector areas of the grey and white areas are 159.09 in² and 41.87 in²
Finding the sector areas of the grey and white areas:From the question, we have the following parameters that can be used in our computation:
Radius, r = 8 inchesCentral angle,= 45 degreesThe area of shaded sector is calculated as
Area = Central angle/360 * π * Radius^2
Substitute the known values in the above equation, so, we have the following representation
Gray = 285/360 * 3.14 * 8^2 = 159.09White = (360 -285)/360 * 3.14 * 8^2 = 41.87Hence, the area is 159.09
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ASAP plz I need help
Answers
Answer: 30
Step-by-step explanation:
Plug in x for the expression
6^2 + x - x^2
36 + (3) - (3)^2
36 + 3 - 9
39 - 9
= 30
Cassie earns $11.40 an hour up to 8 hours, and then she gets paid $12.50 for overtime hours. How much will she get paid if she worked 8.5 hours?
Answers
Answer:
$97.45
Step-by-step explanation:
Answer:
$97.45
Step-by-step explanation:
8 hours x 11.4
0.5 hour x 12.5
(11.4 x 8) + (12.5 x 0.5) =
(91.2) + ( 6.25) =
$97.45
how many like terms are in the expression 4j^2 +3j^2-9j^2
Answers
Answer: 16j^3+2
Step-by-step explanation:
graph the line with slope -3/4 passing through the point (2,-1)
Answers
Answer:
Step-by-step explanation:
Slope of the line:
\(m = \frac{y-y1}{x-x1} \\\)
Given:
slope = -3/4
point (x1,y1) = (2, -1)
Substitute and solve
\(m = \frac{y-y1}{x-x1} \\-\frac{3}{4} = \frac{y-(-1))}{x-2} \\-3(x-2) = 4(y+1)\\-3x + 6 = 4y + 4 \\Transpose\\4y = -3x + 6 - 4\\4y = -3x + 2 \\y = -3/4x + 2/4\\y = -3/4x + 1/2\\OR\\4y +3x - 2 = 0\)
1/2 is the y-intercept
(0,1/2)
Since we have 2 points already, we can then graph the line.
(2, -1) and (0, 1/2)
Which equation is true?
O 9x²-25= (3x - 5)(3x - 5)
O9x2-25= (3x - 5)(3x + 5)
+ 5)(3x + 5)
O9x²-25=-(3x
O9x²-25=-(3x
+ 5)(3x - 5)
Answers
Answer:
B. 9x² - 25 = (3x - 5)(3x + 5)