Answers
0 must come before 3 in the matrix, so that x will be multiplied with 0.
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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Related Questions
Help me PLEASEEEEEEEEEEEEE
Answers
Answer:
4.0.
Step-by-step explanation:
In sample 1, you do 0.65/1.3 which gets you to 0.5, so then you do the same to the bottom which you also have to divide by 1.3, and 5.2/1.3 is 4.0 or 4.
Answer:
option D. 4.0
Step-by-step explanation:
Mass Volume
Sample 1 0.65 0.5
Sample 2 5.2 x
[tex]\frac{0.65}{5.2} = \frac{0.5}{x}\\\\0.65 \times x = 0.5 \times 5.2\\\\0.65x = 2.6\\\\x =\frac{2.6}{0.65} =4[/tex]
25 POINTS NEED HELP QUICKLY:
Choose the system of inequalities that best matches the graph below.
A.
B.
C.
D.
Answers
Answer: D y>2x-1
y<1/3x+1
Step-by-step explanation: I took the test and got it right
The points (0, 0) and (6/5, 7/5) are solutions to the system of inequalities D y>2x-1 and y<1/3x+1 which is correct options (D).
What is inequality?Inequality is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is not equal.
What is a graph?A graph can be defined as a pictorial representation or a diagram that represents data or values.
Given the system of inequalities as
y>2x-1 and y<1/3x+1.
To determine the solutions, you first have to graph both of the lines in the problem.
y = 2x-1 and y = 1/3x+1. Then, to shift them to inequality, you have to shade the half-plane that they represent.
The solution is the space that they have in common. In this case, it will be on the right side of the graph.
The points (0, 0) and (6/5, 7/5) are included in the shaded region they have in common.
Hence, the points (0, 0) and (6/5, 7/5) are solutions to the system of inequalities y>2x-1 and y<1/3x+1.
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Which equation is part of the same family as 5×4 = 20
Answers
Answer:
4x5=20
20 divided by 5 = 4
Step-by-step explanation:
Answer:
20 ÷ 4 = 5 and 20 ÷ 5 = 4 also 4 x 5 = 20
Step-by-step explanation:
Pizza Uno offers 2/3 of a small pizza for $3.50. Pizza Duo offers % of a small pizza for $4.20. How much does each charge for a whole small pizza?
Show your work and remember to answer the question.
Answers
Answer:
Pizza Uno offers $5.25 for a small pizza and Pizza Duo offers $5.60 for a small pizza.
Step-by-step explanation:
For Pizza Uno:
If 2/3 of a Pizza costs $3.50, divide it by 2.3.50 ÷ 2 = 1.75For each 1/3 it costs $1.75Multiply 1.75 by 3 to get a whole pizza.1.75 × 3 = 5.25For pizza Duo: (the "%" is actually 3/4)
If 3/4 of a pizza costs $4.20, divide it by each 1/4 you get (3).4.20 ÷ 3 = 1.40Each fourth (1/4) costs $1.40 eachMultiply 1.40 by 4 to get a whole pizza1.40 × 4 = 5.60does 2, 5, and 7 make a right triangle
Answers
Answer: No, we don't have a right triangle
==========================================================
Explanation:
If a triangle with sides a,b,c makes the equation a^2+b^2 = c^2 true, where c is the longest side, then this triangle is a right triangle. This is the converse of the pythagorean theorem.
Here we have a = 2, b = 5 and c = 7.
So...
a^2+b^2 = c^2
2^2+5^2 = 7^2
4+25 = 49
29 = 49
The last equation is false, so the first equation is false for those a,b,c values. Therefore, we do not have a right triangle.
------------
In contrast, consider the classic 3-4-5 right triangle
a = 3, b = 4 and c = 5 would make a^2+b^2 = c^2 true because 3^2+4^2 = 5^2 is a true equation (both sides lead to 25).
Solve the Exponential Equation:
[tex]5 { }^{66} = {3}^{42} [/tex]
Answers
.........
Work:
maths question 11 divided by 4 please give me the answer in decimal as fast as u can
Answers
2.75
Step-by-step explanation:
[tex]\sf\purple{2.75}[/tex] ✅
[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]
[tex] \frac{11}{4} \\ = 2.75[/tex]
[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{.ඞ}}}}}[/tex]
ILL GIVE BRAINLIEST AND 10 POINTS
Answers
Answer:
[tex](7m^2+10)^2[/tex]
Step-by-step explanation:
This is a quadratic in disguise. To visualize this better, let [tex]x=m^2[/tex]. We have:
[tex]49x^2+140x+100[/tex]
To factor, we can write out the format [tex](ax+y)(bx+z)[/tex]. We're looking for numbers [tex]a[/tex], [tex]b[/tex], [tex]y[/tex], and [tex]z[/tex] such that the following is true:
[tex]a\cdot b=49[/tex] [tex]a\cdot z+b\cdot y=140[/tex] [tex]y\cdot z=100[/tex]We find the following numbers:
[tex]a=7,\\y=10, \\b=7, \\z=10[/tex]
Thus, we have:
[tex](7x+10)(7x+10)[/tex]
Substitute back [tex]x=m^2[/tex] to get your final answer:
[tex](7m^2+10)(7m^2+10)=\boxed{(7m^2+10)^2}[/tex]
Triangle PQR with area 32cm square and base QR is an enlargement of Triangle ABC with area 8 cm square and base BC=3cm , what is the length of QR in cm?
a) 6
b) 8
c) 10
d) 12
Answers
Answer:
6 cm (Option A)
Step-by-step explanation:
GIVEN :-
ΔPQR whose area is 32 cm² & has base QR.ΔABC whose area is 8 cm² & has base BC = 3 cmΔPQR is an enlarged figure of ΔABC.TO FIND :-
Length of QRFACTS TO KNOW BEFORE SOLVING :-
Lets say there are two triangles ΔABC & ΔXYZ , who are similar to each other.
[tex]=> \frac{Area \: of \: ABC}{Area of XYZ} = (\frac{AB}{XY})^ {2} = (\frac{BC}{YZ})^2 = (\frac{AC}{XZ} )^2[/tex]
SOLUTION :-
In the question it's given that ΔPQR is an enlarged figure of ΔABC.
⇒ ΔPQR is similar to ΔABC.
[tex]=> \frac{Area \: of \: PQR}{Area \: of \: ABC } = (\frac{QR}{BC})^2[/tex]
[tex]=>\frac{32}{8} = (\frac{QR}{3})^2[/tex]
Root squaring both the sides ,
[tex]=> \sqrt{(\frac{QR}{3})^2} = \sqrt{\frac{32}{8} }[/tex]
[tex]=> \frac{QR}{3} = \sqrt{4} =2[/tex]
Multiplying both the sides by 3 ,
[tex]=> \frac{QR}{3} \times 3 = 2 \times 3[/tex]
[tex]=> QR = 6 \:cm[/tex]
Solve the formula Ax + By = C for X
Answers
Answer:
Step-by-step explanation:
Ax+By=C
Ax=C-By
x=C-By/A
[tex] \bf \pink{Define \: the \: decimal \: number \: system \: in \: your \: own \: words. }[/tex]
Answers
Answer:
The decimal number system comprises digits from 0-9 that are 0, 1, 2, 3, 4, 5, 6, 7, 8 & 9. Some of the decimal number system examples are: ... 34110, 5610, 678910, 7810. Now as we know to write decimal numbers till 10 let us use the 3 rules on a decimal system,to write further numbers.
[tex] \bf \pink{Define \: the \: decimal \: number \: system \: in \: your \: own \: words. }[/tex]
Decimal system, also called Hindu-Arabic number system or Arabic number system, in mathematics, positional numeral system employing 10 as the base and requiring 10 different numerals, the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. ... It also requires a dot (decimal point) to represent decimal fractions.
marks)
9 (b). The first two terms of an arithmetic progression are shown.
р
5p
The sum of the first three terms is 90
Work out the value of p.
Answers
9514 1404 393
Answer:
p = 6
Step-by-step explanation:
The difference between the first two terms is ...
5p -p = 4p
Since this is an arithmetic sequence, the next term will be 4p more than the last term:
5p +4p = 9p
Then the sum of the first three terms is ...
p + 5p + 9p = 90
15p = 90 . . . . . . . . . . collect terms
p = 6 . . . . . . . . . . . . divide by 15
_____
The first three terms are 6, 30, 54.
If h(x) = x - 7 and g(x) = x², which expression is equivalent to (gºf)(5?
O (5-7)2
(5)²-7
O (5)? (5 – 7)
O (5-7) x²
Answers
Answer:
(5^2)(5-7)
Step-by-step explanation:
So we know h(x)=x-7.
We also know g(x)=x^2
We need to plug in these values for (g*h)(5)
This would equal:
((x-7)*x^2)(5)
Since parthese can also be considered multipcation symbols, we can think of this as:
(x-7)(x^2)(5)
Lets distrubute the 5 to all the x's:
(5-7)(5^2)
Which is:
([tex]5^{2}[/tex])(5-7)
This looks like answer C.
Hope this helps!
please solve both thank you!
Answers
Answer:
First problem: 24 + 4x = 60
Second problem: 9
Step-by-step explanation:
24 + 4x = 60
4x = 36
x = 9
-2x^2+6x+1=-3x^2 nearest tenth solve to the nearest tenth
Answers
Mmmmmaqq
Which of the following have
a value equal to [-12]?
Answers
Answer:
option 3) ii, iv, v
Step-by-step explanation:
|-12| means write the absolute value, which means just the number without the sign.
Therefore |-12| = 12
So, ii. 12
iv. |12| is also = 12
v. -( -12) is also = 12
Answer:
12.00000000000000000
Help with 5+5-3 please
Answers
Step-by-step explanation:
5+5-3= 7
!!!!!!!!!!!!!!!!!
Answer:
answer is 7 please give a brainliest please
Step-by-step explanation:
a. Find the slope of the line going through the points (-7, 7) and (3.-5).
Answers
Answer:
-1.2
Step-by-step explanation:
In the figure, AB is divided into equal parts. The coordinates of point A are (2, 4), and the coordinates of point Bare (10,6). Match each pair
of coordinates to the corresponding point on AB
(4,4,5)
D
(4,4.75)
E
(9,5.75)
H
(8,5.75)
(8,5.5)
(5,4.75)
(7,5.25)
Answers
Answer: D = 4, 4.5
E = 5, 4.75
H = 8, 5.5
I = 9, 5.75
Step-by-step explanation:Gang
The coordinates of the corresponding points are given below.
C ⇒ (3, 4.25)
D ⇒ (4, 4.50)
E ⇒ (5, 4.75)
F ⇒ (6, 5)
G ⇒ (7, 5.25)
H ⇒ (8, 5.50)
I ⇒ (9, 5.75)
What is coordinate geometry?Coordinate geometry is the study of geometry using the points in space. Using this, it is possible to find the distance between the points, the dividing line is the m:n ratio, finding the mid-point of the line, etc.
AB is separated into equal sections in the picture. Point A's coordinates are (2, 4), and Point Bare's coordinates are (10,6).
There are eight sections of line AB. Then the rise in abscissa after each segment is calculated as,
⇒ (10 - 2) / 8
⇒ 8 / 8
⇒ 1
Then the rise in ordinate after each segment is calculated as,
⇒ (6 - 4) / 8
⇒ 2 / 8
⇒ 0.25
Then the coordinate of the points is written as,
C ⇒ (3, 4.25)
D ⇒ (4, 4.50)
E ⇒ (5, 4.75)
F ⇒ (6, 5)
G ⇒ (7, 5.25)
H ⇒ (8, 5.50)
I ⇒ (9, 5.75)
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solve the following equation 4 x + 10 = 66
Answers
-> 4x= 66-10
-> 4x= 56
-> x= 56/4
-> x= 14
mark me brainliestttt plsss :)))
Answer:
x = 14.
Step-by-step explanation:
4x + 10 = 66
4x + 10 - 10 = 66 - 10
4x = 56
x = 56/4 = 14.
tell whether the ordered pair is a solution of the equation! please help i will mark you brainliest
Answers
Answer:
the answer is
yes to 7 and no to 10
Step-by-step explanation:
7. y = 3x---------> 2*3 = 6
10. y = 7x+2--------------> 2*7=14--> 14+2 = 16
16 does not equal 0
HELP someone please!!!! i dont understand
Answers
Answer:
x = 65.03°
Step-by-step explanation:
To solve for x, we have to apply trigonometric ratio.
Recall: SOH CAH TOA
From the diagram, we know the following:
Reference angle = x
Hypotenuse = 45
Adjacent = 19
Since we know the Hyp and Adj, we would apply CAH, which is:
Cos x = Adj/Hyp
Plug in the values
[tex] cos(x) = \frac{19}{45} [/tex]
[tex] x = cos^{-}(\frac{19}{45}) [/tex]
x = 65.0250346°
x = 65.03° (nearest hundredth)
Please help I am super confused and would really appreciate it ♥️♥️♥️♥️
Answers
x---- independent variable
f(x)--- dependent variable(can also be "y")
The dependent variable (fx) is the output or you can say... For every value of the independent variable (x)...There's a unique value for the dependent variable.
Ok... Lemme explain
Say you have an equation
f(x)=2x+1
let x be take value from all natural Numbers (1,2,3..….)
When x is 1
f(x) = f(1) = 2(1)+1
=3
when x is 2
f(x)=f(2) = 2(2)+1 =5.
So for every x value... There's a unique value for f(x).
You dig?
Now
let's proceed to your question.
We're already given tbe values of x and f(x)
What we now need to find is the equation that corresponds to the values being gotten
From the table
When x =1 ...….f(x)=8
When x=2 .........f(x) = 32
When x=3 ...........f(x)=128
Etc
Which equation from the options will give you these values of f(x)???
You're gonna have to test run it quickly by puttinh values of x and see if they'll give the corresponding value of f(x).
Fun right?
OK. From Observation....
OPTION A WILL DO THE JOB.
f(x)=2.4^t where "t" represents x in this case.
Input your values of x in this
You'll get the exact f(x) value
Eg
when x= 1... f(x)= 2.4¹ =8
x=2 ..….f(x) = 2. 4² = 2.16 = 32.
OPTION A IS OUR ANSWER.
HAVE A GREAT DAY BRO!
help? (i mark brainlist)
Answers
Hope this helps :)
Explanation:
A train leaves a station at 10.15am and
gets to another one at 1.15pm. The
average speed between the stations
is 76km/hr. What is the distance?
Answers
9514 1404 393
Answer:
228 km
Step-by-step explanation:
Traveling 3 hours at 76 km/hour, the train covers a distance of ...
distance = speed × time
distance = (76 km/h)(3 h) = 76×3 km = 228 km
Which of the following elements represents part of the whole? a. percentage b. base c. rate d. both a and b
Answers
Answer:
Percentage
Step-by-step explanation:
Please help and hurry!
Answers
Step-by-step explanation:
6.5+6.5=diameter
Answer:
13 cm
Step-by-step explanation:
The diameter is twice the radius
The radius is 6.5 cm
diameter = 2 * 6.5 = 13 cm
Help!!!!!!!!!!!!!!!!!
Answers
Answer:
the answer is one hundred and eight 108
Step-by-step explanation:
108 bro trust me
(-1) × (-1) × (-1) × (-1) x (-1)
Answers
( - 1 )^5 = - 1
.....................
.....................
.....................
Answer:
the answer is -1 have a nice day
68 - 4 × (6 - 4)4
pls help the answer questions are
16 80 4 or -2