Solve for x, y and z
2x – y + 3z = 10
x + 3y – 2z = 5
3x – 2y + 4z = 12
Answer:
Given system of linear equations are
2x+3y+3z=5
x−2y+z=−4
3x−y−2z=3.
Represent it in matrix form
⎣
⎢
⎢
⎡
2
1
3
3
−2
−1
3
1
−2
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
5
−4
3
⎦
⎥
⎥
⎤
which is in the form of AX=B
A=
⎣
⎢
⎢
⎡
2
1
3
3
−2
−1
3
1
−2
⎦
⎥
⎥
⎤
∣A∣=10+15+15=40
=0
∴ A
−1
exists
To find adjoint of A
A
11
=5,A
12
=5,A
13
=5
A
21
=3,A
22
=−13,A
23
=11
A
31
=9,A
32
=1,A
33
=−7
Adj(A)=co-factor
⎣
⎢
⎢
⎡
5
3
9
5
−13
1
5
11
−7
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
A
−1
=
∣A∣
1
Adj(A)
=
40
1
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
X=A
−1
B
=
40
1
⎣
⎢
⎢
⎡
5
5
5
3
−13
11
9
1
−7
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
5
−4
3
⎦
⎥
⎥
⎤
X=
40
1
⎣
⎢
⎢
⎡
25−12+27
25+52+3
25−44−21
⎦
⎥
⎥
⎤
X=
40
1
⎣
⎢
⎢
⎡
40
80
−40
⎦
⎥
⎥
⎤
⎣
⎢
⎢
⎡
x
y
z
⎦
⎥
⎥
⎤
=
⎣
⎢
⎢
⎡
1
2
−1
⎦
⎥
⎥
⎤
Hence, x=1,y=2 and z=−1
The solution to the system of equations is
x = 3
y = 2
z = 2
How to solve the simultaneous linear equation?To solve for x, y, and z, we can use the elimination method or substitution method. Here, we will use the elimination method.
First, we will eliminate y from the equations by multiplying the first equation by 3 and the second equation by 1, and then adding them:
(3) (2x – y + 3z = 10)
6x – 3y + 9z = 30
(1) (x + 3y – 2z = 5)
x + 3y – 2z = 5
Adding the two equations gives:
7x + 7z = 35
Simplifying, we get
x + z = 5 (Equation 1)
Next, we will eliminate y again by multiplying the second equation by 2 and the third equation by 3, and then adding them:
(2) (x + 3y – 2z = 5)
2x + 6y – 4z = 10
(3) (3x – 2y + 4z = 12)
9x – 6y + 12z = 36
Adding the two equations gives:
11x + 8z = 46
Substituting x + z = 5 from Equation 1 into the above equation, we get:
11(x + z) + 8z = 46
11x + 19z = 46
Solving for z, we get:
z = 2
Substituting z = 2 into x + z = 5 from Equation 1, we get:
x + 2 = 5
x = 3
Finally, substituting x = 3 and z = 2 into any of the original equations, we can solve for y:
2x – y + 3z = 10
2(3) – y + 3(2) = 10
6 – y + 6 = 10
y = 2
Therefore, the solution to the system of equations is:
x = 3
y = 2
z = 2
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Three cakes are sliced into 20 pieces each. Each cake contains 1 gold ring What is the
probability one person who eats one piece of cake from each of the 3 cakes will find 3 gold
rings?
Answer:
1/60
Step-by-step explanation:
For each cake, there is a 1/20 chance to find the gold ring since it is in one of the 20 slices. The probability for each cake is independent of each other, so we multiply
1/20 x 1/20 x 1/20
=1/60
PLEASE LOOK AT PICTURE
The numeric ratio of the segment ratio are:
CD: DB | √5:10 | part:partCE: CA | 2:10 | part:wholeDE: BA | 1:5 | part:partCD: CB | √5:√181 | part:wholeHow to find numeric ratio?To find the numeric ratios of the given segment ratios, to calculate the distances between the given points.
CD: DB
The distance between C(6,2) and D(4,3) is:
CD = √[(6 - 4)² + (2 - 3)²] = √5
The distance between D(4,3) and B(-4,7) is:
DB = √[(4 + 4)² + (3 - 7)²] = 10
Therefore, the numeric ratio of CD:DB is:
CD:DB = √5:10
CE: CA
The distance between C(6,2) and E(4,2) is:
CE = √[(6 - 4)² + (2 - 2)²] = 2
The distance between A(-4,2) and C(6,2) is:
CA = √[(-4 - 6)² + (2 - 2)²] = 10
Therefore, the numeric ratio of CE:CA is:
CE:CA = 2:10
DE: BA
The distance between D(4,3) and E(4,2) is:
DE = √[(4 - 4)² + (3 - 2)²] = 1
The distance between B(-4,7) and A(-4,2) is:
BA = √[(-4 + 4)² + (7 - 2)²] = 5
Therefore, the numeric ratio of DE:BA is:
DE:BA = 1:5
CD: CB
The distance between C(6,2) and D(4,3) is:
CD = √[(6 - 4)² + (2 - 3)²] = √5
The distance between C(6,2) and B(-4,7) is:
CB = √[(6 + 4)² + (2 - 7)²] = √181
Therefore, the numeric ratio of CD:CB is:
CD:CB = √5:√181
Based on the numeric ratios, determine the type of ratio for each segment ratio:
CD: DB is a part:part ratio
CE: CA is a part:whole ratio
DE: BA is a part:part ratio
CD: CB is a part:whole ratio
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what is the value of t
Find the magnitude and direction angle for each vector. Give the measure of the direction angle as an angle in [0,360]
Answer:
(b) 10; 150°
Step-by-step explanation:
You want the polar coordinate equivalent of (-5√3, -5).
ConversionThe polar form of (a, b) is ...
(a, b) = (r; θ)
where ...
r = √(a² +b²)
θ = arctan(b/a) . . . . . with attention paid to quadrant
ApplicationFor the given values, the polar form is ...
r = √((-5√3)² +5²) = √(75 +25) = 10
θ = arctan(5/(-5√3)) = arctan(-1/√3) = 150°
The angle is a quadrant II angle with a reference angle of 30°.
The polar form is (10; 150°).
__
Additional comment
Some calculators will do the coordinate conversion based on a vector or ordered pair. Others require the coordinates of the point to be expressed as a complex number, as in the attachment. (Note the calculator mode is set to DEGrees.)
can you please help me with the answer?
The dimension is gioven as 69.26 feet
How to solve for the dimensionxy = 1836
This is the area
The cost of fence = 2x + 2y
cost of interior fencing
2x + 4y
C = 20.40(C1) + 12.00(C2)
We have to put the vakues in the formula above
C = 20.40(2x + 2y) + 12.00(2x + 4y)
= 40.80x + 40.80y + 24.00x + 48.00y
= 64.80x + 88.80y
from xy = 1836
y = 1836 / x
We have to put the value in C
C = 64.80x + 88.80(1836/x)
= 64.80x + 164236.80/x
Take the deriveative with respect to x
64.80 - 164236.80/x^2 = 0
x = √(164236.80/64.80)
= 69.26 feet
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if u were to flip a coin 15 times how many times will the coin land on tails
Find s(t), where s(t) represents the position function, v(t) represents the velocity function, and a(t) represents the acceleration function.a(t)= -30t+6, with v(0)=8 and s(0)=2
The position function is s(t) = -5t³ + 3t² + 8t + 2.
We have,
To find s(t), we need to integrate the velocity function v(t) since velocity is the rate of change of position with respect to time.
To do this, we need to first find the velocity function v(t) by integrating the acceleration function a(t):
a(t) = -30t + 6
Integrating with respect to t, we get:
v(t) = -15t² + 6t + C1
We are given that v(0) = 8, so we can use this to solve for the constant C1:
v(0) = -15(0)² + 6(0) + C1 = C1
C1 = 8
Now we have the velocity function:
v(t) = -15t² + 6t + 8
To find s(t), we need to integrate v(t) with respect to t:
s(t) = -5t³ + 3t² + 8t + C2
We are given that s(0) = 2, so we can use this to solve for the constant C2:
s(0) = -5(0)³ + 3(0)² + 8(0) + C2 = C2
C2 = 2
Now we have the position function:
s(t) = -5t³ + 3t² + 8t + 2
Therefore,
The position function is s(t) = -5t³ + 3t² + 8t + 2.
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what’s the answer bro what is the answer
Answer:
7
Step-by-step explanation:
a= a+b/2*h
pls help ............ explain
Answer:
Step-by-step explanation:
help me please fr i just need these questions
a) The base area of the cylinder is given as follows: 78.54 ft².
b) The height of the cylinder is given as follows: 2 ft.
How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
The base area is given as follows:
Ab = πr².
Considering the radius of 5 ft, the base area is of:
Ab = 3.1416 x 5²
Ab = 78.54 ft².
Considering the volume of 157.08 ft³, the height of the cylinder is obtained as follows:
78.54h = 157.08
h = 157.08/78.54
h = 2 ft.
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Graph with x axis labeled Quantity Demanded and numbered in hundreds, 100 to 500. Y axis is Price, with prices 0 to 6. A line representing the Demand Curve starts at 100, 5 and drops at an angle down to 500, 1. Solid lines extend upward from the x axis to the green line at points 100, 5, 200, 4, 300, 3, 400, 2, and 500, 1. Public Domain Based on the graph, how is quantity demanded related to price? (5 points) Quantity demanded decreases as price decreases. Quantity demanded is equal to the product's price. Quantity demanded decreases as price increases. Quantity demanded increases as price increases.
Based on the information, the correct information regarding the graph is that C. Quantity demanded decreases as price increase.
How to explain the graphThe graph shows that for every increase of 100 units of the goods demanded, price reduces by 1 unit.
When 500 units was demanded, the price was at 1. Therefore, if 550 units are demanded, the price will reduce by half, which means the price would drop to 0.5.
The price would drop to 0.5. In this case, the the correct information regarding the graph is that Quantity demanded decreases as price increase.
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If m varies jointly as p and the square root of w and m=21 when p=5 and w=36, find m when p=9 and w=225
When p = 9 and w = 225, the value of m is 94.5
How to find the value of m?We know that m varies jointly as p and the square root of w, then we can write.
m = k*p*√w
Where k is a constant.
We know that m=21 when p=5 and w=36, replacing that we will get:
21 = k*5*√46
21 = k*30
21/30 = k
7/10 = k
Then the equation is:
m = (7/10)*p*√w
Then when p = 9 and w = 225 we will have:
m = (7/10)*9*√225
m = 94.5
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How knows how do this help me please
Answer:
Step-by-step explanation:
Lois is planning to retire from her job. She has been working there for 27 years. If she retires this year, her monthly pension will be calculated with a flat benefit formula using the flat amount of $52 for each year of
service. She was informed that if she works another 4 years that the flat amount would increase to $60 for each year of service. How much more would her pension be if she waited the 4 years?
If Lois is retiring from her job after 27 years, then if she waited for 4 years, her pension will be $38 higher than if she retires this year.
If Lois retires this year, the flat-amount is $52, So, her monthly pension can be calculated as follows;
⇒ Monthly pension = (52 × 27)/12,
⇒ Monthly pension = $117,
If Lois works for another 4 years, the flat amount used to calculate her monthly pension will increase to $60 for each year of service.
So, her monthly pension will be calculated as follows:
⇒ Monthly pension = (60 × 31)/12,
⇒ Monthly pension = $155,
So, The difference in monthly pension between retiring this year and retiring after working another 4 years can be calculated as follows:
⇒ Difference in monthly pension = $155 - $117,
⇒ Difference in monthly pension = $38,
Therefore, if Lois waits another 4 years before retiring, her monthly pension will be $38 higher than if she retires this year.
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6. It takes Ms. Singleton 36 minutes to get ready
for school. This is 4 times as long as it takes Ms.
Mullaney to get ready for school. How long does
it take Ms. Mullaney to get ready for school?
Two sets of data have the same measures of central tendency. Are the data sets the same? Explain.
Sample Response/ Explanation: The data sets could be the same, but not necessarily. It is possible for data sets to differ in their spread but still have the same measures of center. The measures of spread could be different.
The data sets could be the same, but not really. It is possible for the data sets to differ in their spread but still have the same measures of center. The measures of spread could be different though.
Abby is collecting data for her science fair project about nutrition. She gathers data about the number of grams of fat and the number of calories in a serving of fruit.
Describe patterns in the data
There is no association between the number of fat grams and the number of calories because there are no outliers or clusters.
What does no association mean ?To make this clear, when we claim that there is no correlation between two variables, it indicates a lack of comprehensible patterns or connections. Put another way, adjustments in one factor do not seem to impact the other.
In relation to the inquiry at hand, if fat grams and calorie figures have no notable outliers or groupings, there might be an inference that these two variables are not related.
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Five sevenths of the fifty six images used as backgrounds on julia iPad were photos from dance class that she took herself. How many photos are of julia dance class? **Make sure you provide Your final answer as a fraction with a denominator of 56
The number of photos from Julia dance class = 5/7 or 40/56 photos.
We shall use mathematical operations to calculate the photos that are of Julia dance class
How do we use mathematical operations to calculate the photos?Five sevenths of the images are photos from dance class, meaning that 5/7 x 56 = 40 photos from dance class.
We express the answer as a fraction with a denominator of 56 like this:
Number of photos / Total number of photos = 40/56
Number of photos from dance class / Total number of photos = 5/7
Therefore, the fraction of photos that are of Julia dance class (as a fraction with a denominator of 56) = 5/7 or 40/56.
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The histograms display the frequency of temperatures in two different locations in a 30 day period. A histogram titled “Temps in Desert Landing” with When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature?
The measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is:
Range, because Flower Town is symmetric
How to Interpret the Histogram?A histogram is a visual representation of statistical data that makes use of rectangles to illustrate the frequency of data points over a range of successive numerical intervals of equal width. The independent variable and dependent variable are plotted along the horizontal axis and the vertical axis, respectively, in the most typical type of histogram.
Now, from the given histograms, we can see that Desert landing is skewed while Flower town is symmetrical entirely.
Thus, The measure of variability that should be used for both sets of data to determine the location with the most consistent temperature is:
Range, because Flower Town is symmetric
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Happy Motor® is a company producing specialty vehicles. The company operates
several departments and each of the department is responsible for building a particular
type of vehicles, including large transport trucks, mini-bus, race car, motorcycle... etc.
Happy Motor® wants to create a database to keep track the orders to improve the
purchase and deliver process.
Each vehicle requires at least one or more different specific components, and each
department makes order to buy the components from the vendors. The vendors may
provide more than one type of the components.
All the orders are handled by the purchasing department. Each order may contain of
several different components, but all components should be come from the same vendor.
The quantity for each component requested may be different If the components needed
by the department are come from different vendors, the department need to place one
order per vendor. Each component is provided by a specified vendor.
To provide the frequently requested components immediately, an inventory is
maintained. That means the quantity on hand (QOH) for each component is recorded.
When an order comes in, it is checked to determine whether the requested component
is in inventory. If a component is not in inventory, it must be ordered from a vendor.
For each department, department code, name and email are recorded. For each order,
order number, date and total amount are recorded. For each component, component
code, name and price are recorded. Some components may not have been ordered by
any departments yet. For each vendor, vendor code, name and email are recorded. Some
vendors are newly introduced and has no order or component provided.
Given that functional description of the processes encountered at Happy Motor®
purchasing department, create the appropriate fully attributed Crow's Foot ERD.
I am not able to create visual content such as an ERD diagram, but I can guide you through the process of creating an ERD for Happy Motor's purchasing department based on the functional description provided.
First, let's identify the entities in the description:
Department (with attributes: department code, name, email)
Vehicle Type (which is produced by each department)
Component (with attributes: component code, name, price)
Vendor (with attributes: vendor code, name, email)
Order (with attributes: order number, date, total amount)
Next, let's identify the relationships between the entities:
Each department produces one or more types of vehicles
Each vehicle type requires at least one or more different specific components
Each department makes orders to buy components from vendors
Each vendor provides one or more types of components
Each order contains several different components, but all components should be from the same vendor
Each component is provided by a specified vendor
An inventory is maintained to keep track of the quantity on hand (QOH) for each component
Based on these relationships, we can create an ERD with the following entities and relationships:
Department (department code, name, email) with a one-to-many relationship with Vehicle Type
Vehicle Type (vehicle type code, name) with a many-to-many relationship with Component
Component (component code, name, price) with a many-to-one relationship with Vendor
Vendor (vendor code, name, email) with a one-to-many relationship with Component and Order
Order (order number, date, total amount) with a many-to-many relationship with Component
To show the inventory relationship, we can add an attribute to the Component entity for QOH.
Note that this is just a general outline of the ERD, and there may be additional details that need to be considered based on the specific requirements of Happy Motor's purchasing department.
To represent the inventory maintained for each component, the Component entity would have an attribute for quantity on hand (QOH).The ERD for Happy Motor® purchasing department would have the following entities and relationships:
Entities:
1. Department - with attributes: department code (PK), name, email
2. Vehicle Type - with attributes: type code (PK), name
3. Component - with attributes: component code (PK), name, price
4. Vendor - with attributes: vendor code (PK), name, email
5. Order - with attributes: order number (PK), date, total amount
Relationships:
1. Department orders Component - one-to-many (1:N) relationship between Department and Component
2. Component belongs to Vehicle Type - many-to-one (N:1) relationship between Component and Vehicle Type
3. Component is provided by Vendor - many-to-one (N:1) relationship between Component and Vendor
4. Order contains Component - many-to-many (M:N) relationship between Order and Component
5. Order is placed by Department - many-to-one (N:1) relationship between Order and Department
6. Order is placed with Vendor - many-to-one (N:1) relationship between Order and Vendor
Additionally, to represent the inventory maintained for each component, the Component entity would have an attribute for quantity on hand (QOH).
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Hurry up (time limit )
State the domain and range and tell if the graph is a function yes or no?
What’s the domain and range?
In this problem, we have that the graph in fact represents a function, as there are no vertically aligned points, that is, each input is mapped to a single output.
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Lily Starbright, a singer-songwriter, released her first album at the beginning of March. By the
end of March, she had sold 1,040 copies. In April, she sold 1,352 copies. Several of the songs
on the album are now trending, so Lily expects her sales to continue to increase.
Write an exponential equation in the form ya(b) that can model the expected monthly
number of albums sold, y, x months after release.
Answer: 1040
Step-by-step explanation: y=ab
The exponential equation is: y = 1040(1.3^x)
How to solve
Calculate the value of y, which stands for the albums sold, and x represents the months passed from their release. For an exponential equation structured as y = a(b^x), identify the base b to solve it mathematically.
By analyzing the last month after launch, known as March, 1040 copies were made available for public consumption. One month further down the line, in April, the gross profit jumped up to 1352 units sold.
When we divide the copies traded throughout April by those resold in March, the value identifies the base:
b=1352/1040 ≈ 1.3
Thus, applying the coefficient a for the initial sales registered during March - totaling 1,040 copies - leads us to define the following form for our equations:
y = 1040(1.3^x)
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Jake just learned to identify the difference between an oak tree and a
maple tree. He was curious about the concentration of these trees in his
neighborhood, so he went out and identified several trees that were either
by the pond or in the field.
Unfortunately, he smudged his data tables and can't read some of the
values. The absolute and relative frequency tables below show Jake's
salvaged data. Can you help him figure out the rest?
Fill in the missing values from each table.
The value of row total of the column total's is 165.
The value of row total of field is 91
How to calculate the valueColumn total of maple can be found by:
(46.32 /100) * y =44
Or y = (44 *100)/46.32
Or y = 94.991 =95 (approx)
Now we get value of field under maple by
Value of field under maple = (column total - value of pond under maple) = (95 - 44) = 51
Value of row total of the column total's = (column total of oak + column total of maple = (70 + 95) = 165 (total data)
Value of row total of field = ( value of field under oak + value of field under maple) = (40 + 51) = 91
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on the map , a line of length 5cm represents 40km, how many kilometers would a line of length 7 1/2 cm represents
How many ways to paint a house with 3 different colors from a pool of 12 distinct colors
Please help i will mark brainliest
Use the graph to answer the question.
graph of triangle ABC with vertices at negative 2 comma negative 7, 3 comma negative 2, 2 comma negative 10 and a second triangle A prime, B prime C prime with vertices at 2 comma 7, negative 3 comma 2, negative 2 comma 10
Determine the direction and degree of rotation used to create the image.
90° counterclockwise rotation
270° counterclockwise rotation
90° clockwise rotation
180° clockwise rotation
Answer:
(d) 180° clockwise rotation
Step-by-step explanation:
Given points A(-2, -7), B(3, -2), C(2, -10) and A'(2, 7), B'(-3, 2), C'(-2, 10), you want to know the angle and direction that rotates ∆ABC to ∆A'B'C'.
SignsWe notice the signs of each of the coordinates of ABC have been reversed for the coordinates A'B'C'. For example, A(-2, -7) became A'(2, 7).
A line joining these points is a straight line through the origin. The measure of its angle at the origin is 180°. This is the angle of rotation of A'B'C' with respect to ABC.
The image is created by 180° clockwise rotation, choice D.
__
Additional comment
When rotation is 180°, the direction is immaterial. A clockwise rotation gets you to the same place as a counterclockwise rotation.
<95141404393>
mary read 1/7 pages on monday.there are 490 pages. how many pages did she read?
Answer: 70 pages
Step-by-step explanation: If she read 1/7 pages on monday and the book is 490 pages, divide. 490 ÷ 1/7 = 70. 70 × 7 is 490. So use these operations in future problems. Just make sure to read carefully!
(1 point) (a) Find a vector parametric equation for the part of the saddle = z = x y inside the cylinder 2+2=9 x 2 + y 2 = 9 .
Which set of ordered pairs gives the polygon shown?
(-4.2), (-4, -5), (1.5, -5), (1.5, 2)
(1.5, 2), (1.5, -4.5), (-4.5, -4), (2, -4)
(-4, -4.5), (-4.5, 1.5), (1.5, 2), (-4, 2)
(1.5, -4.5), (-4, -4.5), (-4, 2), (1.5, 2)
The points of the polygon are:
(1.5, 2)
(-4, 2)
(-4, -4.5)
(1.5, -4.5)
Option D is the correct answer.
We have,
From the coordinate plane,
There are 4 points that form the polygon,
The points are all in ordered pairs.
So,
(1.5, 2)
(-4, 2)
(-4, -4.5)
(1.5, -4.5)
Thus,
The points of the polygon are:
(1.5, 2)
(-4, 2)
(-4, -4.5)
(1.5, -4.5)
Learn more about coordinates here:
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