Therefore, the matrix equation represents the system of equations
4x - 2y = -7
0x + 3y = 5 is given by
[tex]\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-7\\5\end{array}\right][/tex].
How to write a system of linear equations in matrix form?Three easy steps must be taken in order to express any system of linear equations in matrix form:
1. First, create a single matrix with all the coefficients. An acronym for this is a coefficient matrix.
2. Multiply this matrix by the system setup variables in a different matrix. The variable matrix is another name for this.
3. In another matrix, place the solutions on the other side of the equal sign. The answer matrix is another name for this.
How to solve this problem?Given system of linear equations:
4x - 2y = -7
0x + 3y = 5
The coefficient matrix is [tex]\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right][/tex].
The variable matrix is [tex]\left[\begin{array}{ccc}x\\y\end{array}\right][/tex].
[ Since [tex]\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4x-2y\\0x+3y\end{array}\right][/tex] ]
The answer matrix is [tex]\left[\begin{array}{ccc}-7\\5\end{array}\right][/tex].
Therefore, the matrix equation represents the system of equations
4x - 2y = -7
0x + 3y = 5 is given by
[tex]\left[\begin{array}{ccc}4&-2\\0&3\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}-7\\5\end{array}\right][/tex]. So, the last option is correct.
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please help! can you explain it to me?
Answer:
It is increasing before x = -2 and from x = 0 to x = 2
Step-by-step explanation:
Option 1 - you can see the line going down starting at -2 and that means the line is decreasing but the choice says "It is increasing before x = 0". This contradicts the actual graph.
Option 2 - The line isn't increasing before x= -1, it's actually decreasing as seen in the graph.
Option 3 - The line doesn't even touch the point before x = -3 so this choice makes no sense.
Option 4 - Since all the other choices were eliminated this is the only choice standing. Looking at the line it is increasing before x = -2.
1 point
A water tank in the form of a rectangular prism is 80 meters long and 50 meters wide. What is the volume of the water in the tank,
if the water is 40 meters deep?
Answer:
160000m³
Step-by-step explanation:
Volume of a rectangular prism= A x h
V= l x b x h
V= 80x 50 x 40
V= 160000m³
What is the product (-2a^2+s)(5a^2 -6s)
PLS HELP
Answer:
-10a^4 + 17a^2s - 6s^2
in other words, your answer is the first one
Answer:
-10a^4 +17a^2s-6s^2
Step-by-step explanation:
see Image below:)
Find the
vertex of this
quadratic.
([?], [ ]
2
1
X
-4 -3 -2 -1 0 1 2 3 4
-1
-2
-3
-4
Answer:
The vertex of the parabola is [tex]V(x,y) = (0, 3)[/tex].
Step-by-step explanation:
In this case, the vertex of the parabola is the absolute maximum of the graph, that is, the point [tex]V(x,y) = (0, 3)[/tex]. Mathematically speaking, the vertex of the parabola is represents the only point of the range ([tex]y[/tex]) which is related to an only value of the domain ([tex]x[/tex]).
Describe the transformation that takes F(x)=x+1 to g(x)=-x+4
Answer:
g(x) = -f(x) +5
Step-by-step explanation:
The sign on the 'x' changes, this implies a reflection.
g(x) = -f(x) = -(x+1) = -x -1
Now apply a vertical translation 'up 5' to f(x)
g(x) = -f(x) + 5 = (-x-1) +5 = -x +4
Ralph rolls a single die two times in a row. What is
the probability that he will roll a "three" both times?
Answer:
1/18 i think
Step-by-step explanation:
The probability of occurring 3 both times will be 1/36.
What is probability?
The probability of an event occurring is defined by probability.
Probability is also called the chance because if you flip a coin then the probability of coming head and tail is nothing but chances that either head will appear or not.
Do not take underestimate probability it has several uses in daily life whether forecasts or like that.
Probability of occurring 3 for the first time ⇒
number of outcomes/number of sample
Sample space {1,2,3,4,5,6} and outcome is 3
So,
P = 1/6
Probability of occurring 3 in second time⇒
number of outcomes/number of sample
Sample space {1,2,3,4,5,6} and outcome is 3
So,
P = 1/6
So,
Probability of occurring 3 both times = 1/6 × 1/6 = 1/36
Hence "The probability of occurring 3 both times will be 1/36".
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make a table where the constant rate of change is 6 inches for every foot
It should be noted that a table where the constant rate of change is 6 inches for every foot will be:
1 foot = 6 inches
2 foot = 12 inches.
3 feet = 18 inches.
4 feet = 24 inches
5 feet = 30 inches.
How to illustrate the information?It should be noted that an expression is used to show the relationship about the numbers given. In this case, it should be noted that there's a constant rate if 6 inches for every foot.
This means that there will be a difference of 6 inches for each foot.
Therefore, 1 foot = 6 inches
2 foot = 2 × 6 = 12 inches.
3 feet = 3 × 6 = 18 inches.
4 feet = 4 × 6 = 24 inches
5 feet = 5 × 6 = 3 inches.
This illustrates that that there is a constant relationship.
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What is one effect of World Bank loans to developing countries?
Answer:
Improved climate for foreign investment
Step-by-step explanation:
I just took the test gs
Which number represents 4%?
Answer:
0.04 or 4/100
Step-by-step explanation:
Think of a percentage as a very lazily written fraction. 4% = 4/100
Just convert the fraction to a decimal.
---
hope it helps
Mark congruent angles. Write down the ratios.
Answer:
ratio=AC/FD=AB/ED=BC/FE
Step-by-step explanation:
Janice has $35.50
She has $10.35 more than Siti
siti has $12.80 less than Amiya
How much money does Amiya
have
siti = x
Janice = 35.50$
Janice = 10.35 + x = 35.50
x = 35.50 - 10.35
x = 25.15
Siti = 25.15$
Amiya = y
Amiya = y - 12.80 = 25.15
y = 25.15 - 12.80
y = 13.25$
The pie chart above shows the percentage of land in Rhode Island split up among the different counties. If Rhode Island has a total of 1,045 square miles of land, how many
square miles does Kent County have?
[tex] \huge{ \mathcal{ \underline{ Answer} \: \: ✓ }}[/tex]
Total land area of Rhode Island is :
[tex] \longmapsto\mathrm{1045 \: \: mi {}^{2} }[/tex]
And from the above pie chart, we can conclude that Kent County comprises 16% of total land area of Rhode Island, that is :
[tex]\longrightarrow \dfrac{16}{100} \times 1045[/tex]
[tex]\longrightarrow \dfrac{16720}{100} [/tex]
[tex]\longrightarrow167.2 \: \: mi {}^{2} [/tex]
Therefore, Total land area of Kent County :
[tex] \boxed{ \large{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 167.2 \: \: \: mi {}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]
_____________________________
[tex]\mathrm{ ☠ \: TeeNForeveR \:☠ }[/tex]
Which phase change takes place when heat is removed from water?
A. Liquid to gas
B. Solid to liquid
C. liquid to solid
Answer:
I don't see an option Gas to liquid but the correct answer will be gas to liquid.
Explanation:
If u heat water will evaporate and form water vapour (gas form). Anytime heat is released from a gas, it will change forms to be a liquid. It is like reverse condensation.
Find m=FGP if m=FGP = x + 8, m=FGH = 100°, and
m=PGH =6x + 8
Please Please help, no links
A blue die and a red die are thrown in a game. If the sum of the two numbers is 7 or 11, the player wins $10. If the sum of the two numbers is 12, then the player wins $20. In all other cases, the player loses a dollar. What are the expected winnings of the player in one game
Answer:
The expected winnings of the player in one game = 2.55
Step-by-step explanation:
Given - A blue die and a red die are thrown in a game. If the sum of the two numbers is 7 or 11, the player wins $10. If the sum of the two numbers is 12, then the player wins $20. In all other cases, the player loses a dollar.
To find - What are the expected winnings of the player in one game ?
Solution -
Given that,
A blue die and a red die are thrown in a game.
The Sample Space becomes -
S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6)
(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6)
(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6)
(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6)
(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)
(6, 1), (6, 2), (6, 3), (4, 4), (6, 5), (6, 6) }
So,
n(S) = 36
Now,
Let A be the outcome that, the sum of the two numbers is 7 or 11
A = {(1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
(6, 5), (5, 6) }
So,
n(A) = 8
So,
P(A) = n(A)/ n(S)
= 8/ 36
= 2/9
⇒P(A) = 2/9
Now,
Let B be the outcome that, the sum of the two numbers is 12
B = {(6, 6)}
So,
n(B) = 1
So,
P(B) = n(B)/ n(S)
= 1/ 36
⇒P(B) = 1/36
Now,
Expected value, E(x) = ∑ x P(x)
= 10 × P(A) + 12 × P(B)
= 10 × 2/9 + 12 × 1/36
= 20/9 + 12/36
= (20×4 + 12)/36
= (80 + 12)/36
= 92/36
= 2.55
⇒Expected value, E(x) = 2.55
∴ we get
The expected winnings of the player in one game = 2.55
What is the answer for this question above
Hello again can anybody help a friend out
Answer:
V= 74.09
Step-by-step explanation:
Multiply the Length, Width & The Height.
So, 4.2x 4.2x 4x2= 74.09
Answer:
74.09 m
Step-by-step explanation:
Volume = width*hight*length
4.2*4.2*4.2 ≈ 74.09
Lucy and Alicia planned to sell 128 glasses (cups) of lemonade,
How many gallons of lemonade would they need to make?
Lucy and Alicia should be planning to make 8 gallongs of lemonade.
If this helps, please mark brainliest!
Have a wonderful day!
What are the domain and range of Y = sin X? select one choice for domain and one for range. (Answers in photo)
Answer: The answers are A and B
Step-by-step explanation:
Ap3x
The domain and range of function Y = sin X will be all the real numbers and [tex]-1\leq y\leq 1[/tex].
What is the domain and range of a function?The domain is the set of values for which the given function is defined.
The range is the set of all values which the given function can output.
We have been given a function Y = sin X.
We need to find the domain and range of function .
Here we can see that the given function is a sine function.
So, the domain of the function would be all the real numbers.
also, The range will be [tex]-1\leq y\leq 1[/tex].
Therefore, options A and B are the correct answer.
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PLS ANSWER ASAP!!person with correct answer will be marked brainliest
Answer:
114
Step-by-step explanation:
angle one is vertical opposite angle and also angle on a straight line
(-6 - 4) divided by 2 simplified
Answer:-5
Step-by-step explanation:
Hello!
-6-4/2 = -10/2=-5
Hope this helps, have a great day!
What is the approximate area, rounded to the nearest square inch, of the frame only? Use 3.14 for 1
Answer:
Step-by-step explanation:
area of square=l^2
=12^2
=144 in.^2
A photograph measuring 4 inches wide and 5 inches long is enlarged to make a wall mural. If the mural is 150 inches wide, how long is the mural?
A. 120 inches
B. 600 inches
C. 750 inches
D. 187.5 inches
please help me i really need help[ please
Answer:
70.69
Step-by-step explanation:
Area = [tex]\pi r (r + \sqrt{h^2+r^2} )[/tex]
Area = [tex]\pi (2.5) (2.5 + \sqrt{(6)^2+(2.5)^2} )[/tex]
Area = 70.68583471
Area = 70.69
11 letters to friends each month for x months in a row. write an expression to show the total number of letters written.
Answer:
11x
Step-by-step explanation:
Each month, 11 letters are written over the course of x months, to find the total, we need to multiply the two:
11 * x
11x
The Drama Club is showing a video of their recent play. The first showing begins at 2:30 pm. The second showing is scheduled at 5:25 pm with a 30-minute break between showings. How long is the video in hours and minutes?
Answer:
the video is 4 hours and 25 minutes
Step-by-step explanation:
first you need to subtract 30 minutes from 5:25 giving you 4:55, then you need to find the difference in minutes from 2:30 to 4:55 by subtracting them or just counting because you cannot subtract units of time like they are real numbers. giving you 4 hours and 25 minutes
The Caudell family went out to dinner. If
their dinner bill came to $52.50 and they
paid $61.95, what percent of a tip did they
leave their waiter?
A. 18%
B. 15%
C. 20%
D. 16.5%
convert 77 ft to yards
Answer:
25.6667
Step-by-step explanation:
Divide the length value by 3.
77 divided 3 =
25.6667
Answer:
Step-by-step explanation:
25.66 SQM
A signalized intersection has a cycle length of 70 seconds. For one traffic movement, the displayed all-red time is set to 2 seconds while the displayed yellow time is 5 seconds. The effective red time is 37 seconds and the total lost time per cycle for the movement is 4 seconds. What is the displayed green time for the traffic movement
Answer:
the displayed green time for the traffic movement is 30 seconds
Step-by-step explanation:
Given the data in the question;
Cycle length; C = 70 seconds
Displayed all-red time; AR = 2 seconds
Displayed yellow time; Y = 5 seconds
Effective red time; r = 37 seconds
total lost time per cycle; [tex]t_L[/tex] = 4 seconds
the displayed green time for the traffic movement; G = ?
First we determine the Effective green time ( g );
Effective red time; r = Cycle length; C - Effective green time ( g )
so,
Effective green time ( g ) = C - r
we substitute
Effective green time ( g ) = 70 seconds - 37 seconds
Effective green time ( g ) = 33 seconds
Now,
Effective green time ( g ) = displayed green time; G + Displayed yellow time; Y + Displayed all-red time; AR - total lost time per cycle; [tex]t_L[/tex]
i.e
g = G + Y + AR - [tex]t_L[/tex]
we substitute
33 = G + 5 + 2 - 4
33 = G + 3
G = 33 - 3
G = 30 seconds
Therefore, the displayed green time for the traffic movement is 30 seconds
y’all pls i’m in pain here
Answer:
it's the first one
Step-by-step explanation:
sorry if im wrong but i think it's right
Answer:
its the first
Step-by-step explanation:
first see how much it increases (1/2x)
and then where on the y line its crossing (+4)
sorry for bad english