The complete question is:
Create a matrix for this linear system:
what is the solution of the system?
[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]
The solution straight from the matrix as
[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]
[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex]
and z = r
What is the solution of the system?A solution to a system of equations exists a set of values for the variable that satisfy all the equations simultaneously.
Given:
[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]
By applying two more row operations, we get
[tex]$&{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}} \\[/tex]
[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2} \\[/tex]
simplifying the above matrix, we get
[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1} \\[/tex]
[tex]$&\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$$[/tex]
The solution straight from the matrix as
[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]
[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex] and
z = r
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Which of the following expressions is equivalent to ab2 + 6ab + 7a3 – 14a?
(b + 7)(b + 6)(a2 – 2)
b(b + 6) + 7(a2 – 2)
a[b(b + 6) + 7(a2 – 2)]
a[(b + 7)(b + 6)(a2 – 2)]
Answer:
3rd answer is correct
Step-by-step explanation:
Take the common factor out.
[tex]a {b}^{2} + 6ab + 7a ^{3} - 14a \\ a[ {b}^{2} + 6b + 7 {a}^{2} - 14] \\ \blue{ a[b(b + 6) + 7( {a}^{2} - 2)]}[/tex]
The correct option is: a(b² + 7a² + 6b - 14), which matches the factorized form of the given expression.
The expression ab² + 6ab + 7a³ - 14a can be factored as follows:
ab² + 6ab + 7a³ - 14a
a(b² + 6b + 7a² - 14)
a(b² + 7a² + 6b - 14)
The expression b(b + 6) + 7(a² - 2) does not appear to be directly related to the given expression.
The expression a[(b + 7)(b + 6)(a² - 2)] is not equivalent to the given expression either.
The correct option is: a(b² + 7a² + 6b - 14), which matches the factorized form of the given expression.
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Angles 1 and 2 form a right angle. 2 lines form a right angle. another line extends between the 2 lines to form 2 angles. the top angle is labeled 1, and the bottom angle is labeled 2. which word describes their measures?
The word complementary describes the their measures of ∠1 and ∠2.
According to the statement
we have given that the some conditions like
Angles 1 and 2 form a right angle. 2 lines form a right angle. another line extends between the 2 lines to form 2 angles. the top angle is labeled 1, and the bottom angle is labeled 2.
And we have to find the word that describes all about the given angles.
So, For this purpose,
According the given conditions, we recall that:
Angles that are complementary angles whose sum equals 90 degrees.
A right angle equals 90 degrees.
From the information given, we know that:
m∠1 and m∠2 forms a right angle.
Since a right angle = 90 degrees, therefore:
m∠1 + m∠2 = 90° (complementary)
So, The word complementary describes the their measures of ∠1 and ∠2.
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Answer: complementary
Step-by-step explanation: took the test on edge!
What is next year's expected cash flow if there is a 50/50 probability that it will be either $10 million or $60 million?
The next year's expected cash flow if there is a 50/50 probability that it will be either $10 million or $60 million is $35 million.
What is probability?Probability refers to possibilities. This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. The probability formula states that the ratio of positive outcomes to all other outcomes determines how likely an event is to occur.
Sum of outcomes= 410+$60=$70 million
Number of outcomes=2
As the probability is 50/50, the next year’s expected cash flow will be
10+60/(2)
=70/2
=35 million dollars.
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two trains are moving towards each other on the same railroad track. From this track there's an offshot peice of railroad- the length of whice is shorter than the length of the train but longer than the length of one train car. How can the trains pass eash other?
If the length of whice is shorter than the length of the train but longer than the length of one train car then the train can pass one car at a time.
Given that two trains are moving towards each other on the same railroad track. From this track there's an offshot peice of railroad- the length of whice is shorter than the length of the train but longer than the length of one train car.
We are required to find how the trains pass each other.
Two cases are there:
For each car in the shorter train
Train A leaves one of its cars on the offshot.Both trains move until train B car move the car from the offshoot the portion of track away from train A.Train B moves to allow the cycle to repeat.We assume that cars can be decoupled at any point in the train,so that any required order of cars can be preserved.We further assume that train can move any one of the A's car in addition to all of them.
The total number of cars lengths that must pass the off shoot is the product of the number of cars in both the trains.So,it does not seems to matter which train makes use of the offshoot.
Hence if the length of whice is shorter than the length of the train but longer than the length of one train car then the train can pass one car at a time.
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Can someone help me out? :) The answer choices are:
A) 20.0
B) 21.2
C) 22.4
D) 23.6
Answer:
20.0
Step-by-step explanation:
We can use the distance formula, d = [tex]\sqrt{(x_{1}-x_{2}) ^{2} +(y_{1}-y_{2}) ^{2}}[/tex] to find the length of three sides separately.
AB = [tex]\sqrt{(-4+2) ^{2} +(1-3}) ^{2}}[/tex] = [tex]\sqrt{8}[/tex]
BC = [tex]\sqrt{(-2-3) ^{2} +(3+4) ^{2}}[/tex] = [tex]\sqrt{74}[/tex]
CA = [tex]\sqrt{(3+4) ^{2} +(-4-1) ^{2}}[/tex] = [tex]\sqrt{74}[/tex]
Perimeter = [tex]\sqrt{74}[/tex] + [tex]\sqrt{8}[/tex] + [tex]\sqrt{74}[/tex] = 20.0330776588 units
Answer:
Step-by-step explanation:
I cant figure this out
24 is the answer! Its all about isolation, i tried to show it a little better in the image attached. Hope this helps!!
quien me hace una canción de ley de los cosenos de C por favor le doy 100 estrellas y corona
Answer:
..........................................
Confused about this question
Answer:
17.1
Step-by-step explanation:
Plug in -1 for x, this gets you -4.
Solve 2^-4 and get .0625.
Add .0625 to 17 and get 17.0625.
The question says answer to the nearest tenth so you round the 6 up to a 1 giving you 17.1
If f (x) = x² - 7, evaluate the following: f(12) f(-7)
Answer: f(12) = 137, f(-7) = 42
Step-by-step explanation: In a function, what you want to do is plug in the value they give you for x. This means you substitute x with the value they are looking for.
In this case, they are looking at 12 and -7. Let's do 12 first.
The equation becomes (12^2) - 7. 12^2 is 144, and 144-7 is 137.
Now we do -7. The equation becomes (-7)^2 - 7. -7^2 is 49, and 49 - 7 is 42.
Hope this helped!
Pls solve this with step by step.
Step-by-step explanation:
-x+5+6x-7x-14
6x-8x+5-14
-2x-9
о
О A. y< x
у>4
О B. y< x
y<4
( C. y> x
у>4
о D. y> x
y<4
-5
5
5
Answer:
b
Step-by-step explanation:
B
HELPP!!!!! PLSSSS!!!!
Consider functions f and g. Select the correct answer.
f(x)=(x^4)+9x²-3
g(x)=(1/2)^(x-2)
Using a table of values, what are the approximate solutions to the equation f(x)=g(x) to the nearest quarter of a unit?
A.) x congruent to -0.25 and x congruent to 2.5
B.) x congruent to -1 and x congruent to 0.75
C.) x congruent to -0.5 and x congruent to 0.5
D.) x congruent to -0.25 and x congruent to 1.5
which expression is simplified form of 24/27
Answer:
8/9
Step-by-step explanation:
I'm pretty sure it's that
The answer is 8/9.
First, find the HCF of 24 and 27.
24 = 8 x 327 = 9 x 3Hence, the HCF of the numbers is 3.
Then, divide both sides of the fraction by 3.
(24/3)/(27/3)8/9PLEASE I NEED HELP PLEASE
Answer:
i'll give you answer.Dont worry. Since i came back from school
The table shows the first five terms for two number sequences with different rules. Select the coordinate plane that has the ordered pairs properly plotted. (4 points)
A table with three columns, with the first column titled Sequence One, the second column titled Sequence Two, and the third column titled Ordered Pair. There are five rows below the heading row. Under Sequence One is the numbers six, eight, ten, twelve, fourteen. Under Sequence Two is the numbers sixteen, thirteen, ten, seven, and four. Under Ordered Pairs is the ordered pairs six and sixteen, eight and thirteen, ten and ten, twelve and seven, and fourteen and four.
The linear function of the table of values is y = -1.5x + 25
How to plot the ordered pairs?The table of values is given as:
Sequence One Sequence Two Ordered Pair
6 16 (6, 16)
8 13 (8, 13)
10 10 (10, 10)
12 7 (12, 7)
14 4 (14, 4)
From the above table of values, we can see that:
As x constantly increases by 2 i.e. +1y constantly decreases by 3 i.e. -3This means that the table represents a linear function, and the slope of the function is
m = -3/+2
This gives
m = -1.5
A linear function is represented as:
y = mx + c
This gives
y = -1.5x + c
Using the table of values, we have
16 = -1.5 * 6 + c
Evaluate the product
16 = -9 + c
Add 9 to both sides
c = 25
Substitute c = 25 in y = -1.5x + c
y = -1.5x + 25
Hence, the linear function of the table of values is y = -1.5x + 25
See attachment for the graph of the table
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Some randomly selected high school students were asked to name their favorite sport to watch. The table displays the distribution of results. A 2-column table with 5 rows. Column 1 is labeled sport with entries football, basketball, baseball, soccer, none. Column 2 is labeled probability with entries 0.23, 0.18, 0.26, 0.17, 0.16. What is the probability that a student chose football given that they like watching sports? 0.16 0.23 0.27 0.77
The probability that a student chose football given that they like watching sports is: c. 0.27.
Conditional ProbabilityUsing this formula
P[Like (Football)/Like (Sport)]
Where:
P=Probability
Like (Football)=0.23
Like (Sport)=0.23+0.18+0.26+0.17=0.84
Let plug in the formula
P[Like (Football)/Like (Sport)]=0.23/0.84
P[Like (Football)/Like (Sport)]=0.27
Therefore the probability that a student chose football given that they like watching sports is: c. 0.27.
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Answer:
C.
Step-by-step explanation:
What is the exponential function that best models the number of gnats the scientists have
gathered after the number of hours listed in the table below?
Answer:
(b) f(x) = 12.5(1.6^x)
Step-by-step explanation:
An exponential model is generally of the form ...
f(x) = a·b^x
where 'a' is the initial value (for x=0), and 'b' is the growth factor, the multiplier when x increases by 1.
Growth factorThe ratio of the f(x) values for x=0 and x=1 is 20/12 ≈ 1.67. A number close to this will be the growth factor in the exponential function. There is only one answer choice showing a growth factor near 1.6. (Eliminates choices A, C, D.)
An exponential regression model can be produced by many graphing calculators and spreadsheets. The attachment shows a model that has the values matching choice B.
For the transformation t, what is t-1? t : (x, y) (x 4, y 3) t-1: (x, y) (x - 4, y - 3) (-4x, -3y) (x 3, y 2)
The transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as
[tex]$T^{-1}:(x, y) \rightarrow(x-4, y-3)$$[/tex]
The value of a exists -4 and value of b exists -3.
How to determine the value of [tex]$\mathrm{T}^{-1}$[/tex]?
The transformation T exists given as
[tex]$T:(x, y) \rightarrow(x+4, y+3)[/tex]
Let the transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as
[tex]$T^{-1}:(x, y) \rightarrow(x+a, y+b)$$[/tex]
If T and [tex]$T^{-1}$[/tex] exists inverses each other, then
[tex]$&T\left(T^{-1}(x)\right)=x \\[/tex]
[tex]$&T(x+a)=x \\[/tex]
[tex]$&x+a+4=x \\[/tex]
[tex]$&a=-4[/tex]
The value of a exists -4.
If T and [tex]$\mathrm{T}^{-1}$[/tex] exists inverses each other, then
[tex]$&T\left(T^{-1}(y)\right)=y \\[/tex]
[tex]$&T(y+b)=y \\[/tex]
[tex]$&y+b+3=y \\[/tex]
b = -3
The value of b exists -3.
The transformation [tex]$\mathrm{T}^{-1}$[/tex] exists described as
[tex]$T^{-1}:(x, y) \rightarrow(x-4, y-3)$$[/tex].
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solve the following system {y=x^2-3 and {y=3x-3 graphically and algebraicallyPLEASE HELP ME IM BEGGING
Answer:
There are two solutions:
x = 0, y = -3 Point (0, -3)
x = 3, y = -6 Point (3, 6)
The solutions are at the intersections of the two individual graphs corresponding to each of the two equations (see attached figure)
Step-by-step explanation:
Use a graphing calculator or tool to plot each equation. The point of intersection of the two is the solution to the system of equations. See attached image
Algebraically
The first equation must be equal to the second equation for a unique value of y and x
[tex]y = x^2 - 3 = 3x -3\\x^2 - 3 = 3x - 3[/tex]
Subtract 3x - 3 from both sides giving
[tex]x^2 - 3 - (3x -3) = 0\\x^2 -3 -3x + 3 = 0\\x^2 - 3x = 0\\[/tex]
Factoring out x we get
[tex]x(x-3) = 0[/tex]
This means that x = 0 and also
x -3 = 0, or x = 3
Substituting for x = 0 in y = 3x-3 gives
y = 3.0 - 3 = -3
So x= 0, y = -3 is one solution (0,-3)
Substituting for x = 3 in the same equation gives
y = 3(3) - 3 = 6
So x = 3, y = 6 is another solution (3, 6)
Use the slope formula to find the slope of the line in the graph shown above.
Question 19 options:
A)
–2
B)
2
C)
–1∕2
D)
1∕2
According to the slope formula, the slope of the line shown in the picture is equal to - 1 / 2. (Correct choice: C)
How to find the slope of a line shown in a graph
In this problem we should determine the slope associated to a line described on a Cartesian plane. This information can be found by knowing the coordinates of two points and substituting on the secant line formula:
m = Δy / Δx (1)
Where:
m - SlopeΔx - Change in the independent variable.Δy - Change in the dependent variable.After a quick inspection, we find that the points (0, 3) and (6, 0) lie on the line and the slope according to the secant line formula is:
m = (0 - 3) / (6 - 0)
m = - 3 / 6
m = - 1 / 2
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Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to tariqareesha2, tysm for the help!
Please help answer my questions like these I have many more quick algebra 1 questions that are all due in 2 days so it would be much appreciated if you check them out. Once again, tysm!
The line is parallel to y axis
We know that if a line is parallel to y axis
slope=tan90=undefinedSo there is no slope
Here it has constant x value as -2
So the equation is
x=-2Option A
Answer:
x = -2
Step-by-step explanation:
The line is crossing the x-axis at -2, The graph is attached
Since it is identical to the graph given in the problem, x=-2 is the correct answer
Please answer correctly
Answer:
Option (1)
Step-by-step explanation:
We need a recursive formula.
Eliminate option 3.The common ratio is 2.
Eliminate options 2 and 4.So, the answer is option 1.
20 POINTS TO SOLVE THIS ANSWER!!!
Answer:
V₁ = 104 in.³ , S₂ = 650 in. ²
Step-by-step explanation:
⇒ Ratio = 4/10 = 2/5
⇒ V₁ : V₂ = (ratio)³ = 8/125 {geometric scale}
⇒ S₁ : S₂ = (ratio)² = 4/25
∴ V₁ = 8/125 × V₂ = 1,625 in³ × 8/125 = 104 in.³
⇒ S₂ = 25/4 × S₁ = 104 in² × 25/4 = 650 in.²
If f(3x)=f(3) + f(x) then show that f(1)-f(3)-f(9) -f(27) = f (81).
The claim is wrong, or your question is incorrectly entered.
[tex]x=1 \implies f(3) = f(3) + f(1) \implies f(1) = 0[/tex]
[tex]x=3 \implies f(9) = f(3) + f(3) = 2f(3)[/tex]
[tex]x=9 \implies f(27) = f(3) + f(9) = 3 f(3)[/tex]
[tex]x=27 \implies f(81) = f(3) + f(27) = 4f(3)[/tex]
Then
[tex]f(1) - f(3) - f(9) - f(27) = 0 - f(3) - 2f(3) - 3f(3) = -6f(3) \neq 4f(3) = f(81)[/tex]
at least if [tex]f(3)\neq0[/tex].
In △MDK, m=16.4, d=22, and k=19. Identify m∠D rounded to the nearest degree. The figure shows triangle M D K. The length of side M D is k units. The length of side D K is m units. The length of side K M is d units.
Answers;
a) 46°
b) 58°
c) 76°
d) 14°
The length of the sides,MD, DK, and KM gives the measure of the angle m<D as c) 76°
Which method can be used to find the measure of angle m<D?In triangle ∆MDK, we have;
m = 16.4
d = 22
k = 19
Using cosine rule, we get;
d² = m² + k² - 2•m•k•cos(D)
Therefore;
2•m•k•cos(D) = m² + k² - d²
[tex]D = arccos \left( \frac{ {m}^{2} + {k}^{2} - {d}^{2} }{2 \cdot m \cdot k} \right)[/tex]
Which gives;
[tex]D = arccos \left( \frac{ {16.4}^{2} + {19}^{2} - {22}^{2} }{2 \times 16.4 \times 19} \right) \approx {76}^{ \circ} [/tex]
m<D = 76°The correct option is therefore;
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Answer:
76
Step-by-step explanation:
Use the Law of Cosines to find m∠D
.The figure shows the same triangle as in the beginning of the task. Angle M D K is highlighted in red.
Set up the equation for the Law of Cosines.
d2=k2+m2−2kmcosD
Substitute the given values and solve for m∠D
.222=192+16.42−2(19)(16.4)cosD
Simplify.
484=629.96−623.2cosD
Subtract 629.96
.−145.96=−623.2cosD
Divide by −623.2
0.234=cosD
Use the inverse cosine function to find m∠D
and round to the nearest degree.
The figure shows a screen of a graphical calculator. The inverse cosine of 0 point 2 3 4 is calculated. The result is 76 point 4 6 7 3 1 6 4 6.
m∠D=cos−1(0.234)≈76∘
Therefore, m∠D≈76∘
hope it helps you!
.
35 Points + Brainest
Answer:
5/12a + 1/3b
Step-by-step explanation:
2/3a + 1/6b + (-1/6a) + 3/18b + (-1/12a)
[2/3a + (-1/6a) + (-1/12a)] + [3/18b + 1/6b]
5/12a + 1/3b
How many 5-letter words can be made using exactly 5 of the letters from
TEXAS and MEXICO? Letters may only be used as many times as they appear. (For
example, XETEX is allowed. However, MATEA is not allowed, since the A appears twice
in MATEA but only once in the given words.)
The total number of ways by words are formed is 35 ways.
According to the statement
We have given that the 5 letters and we have to make word from them and the letters are repeated as equal to letters in given words.
And we have to find the possible ways.
So, The given words are:
TEXAS and MEXICO
Here X = 2 and E = 2 and all other words are one time used words.
We can find possible ways by use of combination and permutation.
So,
Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]
here 3 because three letters are not repeatable and 2 letters are repeated for 2 times.
So,
Total number of ways = [tex]3C_{1} ^{5} + 2C_{2} ^{5}[/tex]
Total number of ways = [tex]3(\frac{5!}{1!} ) + 2(\frac{5!}{2!*3!} )[/tex]
Total number of ways = [tex]3(5) + 2(10)[/tex]
Total number of ways = 15 + 20
Total number of ways = 35.
So, The total number of ways by letters are formed is 35 ways.
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Volume=
Help me please thanks so much asap
Answer:
600
Step-by-step explanation:
since it is a right triangle based pyramid, 2 of them will make a cube. so, it is bwh / 2.
base = 24
width = 10
height = 5
volume = 1200
volume of pyramid = 600
The following table represents a relation. X Y -3 0 0-2 5 -3 11-2 Does the table represent y as a function of c? Why or why not? No, because a number in the input is the same as a number in the output. Yes, because there are no x-values with more than one y-value. Yes, because every x-value has at least one y-value. No, because there are two inputs that have the same output.
The table represent y as a function of c, Yes because every x-value has at least one y-value.
According to the question,
X -3 0 5 11
Y 0 2 -3 -2
In order to find the table represent y as a function of c, When x = -3; y=0; x= 0 ;y=2; x= 0 y=2; x= 5 y=-3; x= 11 y=-2.
No, because a number in the input is the same as a number in the output.⇒ Above option is wrong, because a number in the input is not same as a number in the output.
Yes, because there are no x-values with more than one y-value.⇒ Above option is wrong, because there are many x-values with more than one y-value.
Yes, because every x-value has at least one y-value.⇒ Above option is correct, because every x-value has at least one y-value.
No, because there are two inputs that have the same output.⇒ Above option is wrong, because there are not two inputs that have the same output
Hence, the table represent y as a function of c, Yes, because every x-value has at least one y-value. Above option is correct, because every x-value has at least one y-value.
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Select the correct answer. What is the value of the limit ? lim x 5 square x^2 +4
By direct evaluation, we will see that the limit is equal to 29.
How to find the limit?Here we want to find the limit of the given expression when x tends to 5.
[tex]\lim_{x \to \ 5} x^2 + 4[/tex]
We can directly evaluate the expression in x = 5 and see if we get a real value different than zero.
By direct evaluation, we get:
[tex]\lim_{x \to \ 5} x^2 + 4 = 5^2+ 4 = 29[/tex]
Notice that the limit does give a whole number, then in this way, we conclude that the limit of the given expression when x tends to 5 is equal to 29.
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Answer:
square 29
Step-by-step explanation:
