Using trigonometric ratios, tree is leaning 106.1°-90° = 16.1° away from the vertical.
Pythagorean identities, reciprocal identities, sum and difference identities, double angle and half-angle identities are the main trigonometric identities. We must apply the sine rule and the cosine rule to the non-right-angled triangles.
6² = 3.5²+4² -2(3.5) (4) cos θ
36 = 12.2.5+16 - 28 cos θ
36 = 28.25 - 28 cos θ
7.75 = -28cos θ
7.75 / 28 = cos θ
Cos⁻¹ (7.75/28) = θ
106.1°=θ
So, the tree is leaning 106.1°-90° = 16.1° away from the vertical
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pls help
me find the volume
Answer:
FIRST
To find the volume of rectangular prism is
Volume = Length x Width x Height
Volume = 20cm x 10cm x 13cm
= 40 x 13
= 520cm cubic or cube
520 is the volume of the rectangular prism
the you divide volume of rectangular prism and volume of solid ball.
Correct me if i am wrong guys.
Answer:
It will take approximately take 17 balls to overflow the container
Step-by-step explanation:
Volume of the rectangle = 20x13x10 = 2600[tex]cm^{3}[/tex]
Volume of the water = 20x10x11 = 2200[tex]cm^{2}[/tex]
Amount of empty space = 2600-2200 = 400[tex]cm^{3[/tex]
Solid ball volume = 23[tex]cm^{3}[/tex] each
To find how many balls can overflow the container = 400/23 = 17.39
A scientist testing the effects of a chemical on apple yield (apples/acre) sprays an orchard with the chemical. A second orchard does not receive the chemical. In the fall, the yield is determined (number of apples harvested per acre). What is the dependent variable
Following are the dependent variables:
1. The amount of water that each orchard receives.
2. The species of trees in the orchard.
Reason:
The exercise scientist is looking for the effects of a chemical between an apple crop to which it is administered and another to which it is not, 4 options are presented, of which it is essential to count as a variable the amount of water each Orchard and tree species in the orchard, since they can generate alterations in the results, the other two variables of the exercise such as number of apples and size of the orchards are not significant and their variations do not affect the scientist's objective.
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Grass the line with the given slope and y-intercept. slope = -4, y-intercept =-5
There will be no change to the grass because the exponential of the function remains the same.
According to the questions,
slope = -4 and y-intercept = -5
Equation of straight line y = mx + c
y = -4x - 5
In order to grass line, there will be no change to the grass because the exponential of the function remains the same.
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Outside temperature over a day can be modelled using a sine or cosine function. Suppose you know the high temperature for the day is 72 degrees and the low temperature of 62 degrees occurs at 3 AM. Assuming t is the number of hours since midnight, find an equation for the temperature, D, in terms of t.
The equation which represents the equation for the temperature, D , in terms of t is D(t)=5°cos{(π/3)t}+67°.
Given that the high temperature is 72 degrees and low temperature is 62 degrees at 3 A.M.
We know that temperature is the intensity of the heat present around us.
We know that,
Maximum temperature=72 degrees,
Minimum temperature=62 degrees, which occurs at t=3 hours
Now we can write the equation as:
D(t)=A cos(ct)+B
Where A, c, B are constants.
We have a minimum at t=3 a minimum means cos(ct)=-1
then we have that D(3)=A cos(c*3)+B
=A*(-1)+b
=35°
Here we solve that ,
Cos(c*3)=-1
this means that
c*3=-1
c*3=π
c=π/3
We also know that the maximum temperature is 72°, the maximum temperature is when cos(c*t)=1
D(t)=0=A(t)+B=72
With this we can find that values of A and b
-A+B=62
A+B=72
B=67
A=5
Equation will be D(t)=5 cos{(π/3)t}+67°.
Hence the equation for the temperature is D(t)=5 cos{(π/3)t}+67°..
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What is the difference? startfraction x 5 over x 2 endfraction minus startfraction x 1 over x squared 2 x endfraction
The difference between the two given fractions is [tex]\frac{x^{2} +4x-1}{x^{2} +2x}[/tex].
What is fraction?Fraction if a part of whole. It is represented in the form of numerator and denominator.
Given that,
[tex]\frac{x+5}{x+2} -\frac{x+1}{x^{2} +2x}[/tex]
= [tex]\frac{x+5}{x+2} -\frac{x+1}{x(x+2)}[/tex]
Take the LCM of the denominators is [tex]x(x+2)[/tex].
= [tex]\frac{x(x+5)-(x+1)}{x(x+2)}[/tex]
= [tex]\frac{x^{2}+5x -x-1}{x^{2} +2x}[/tex]
= [tex]\frac{x^{2}+4x-1}{x^{2} +2x}[/tex]
Thus, the difference between the two given fractions is [tex]\frac{x^{2}+4x-1}{x^{2} +2x}[/tex] .
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The given question is not in correct form.
2sin^2(x)+sin(2x)=2
please help!!
[tex]2sin {}^{2} (x) + sin(2x) = 2 \\ 2sin {}^{2} (x) + 2sin(x)cos(x) = 2 \\ sin {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\1 - cos {}^{2} (x) + sin(x)cos(x) - 1 = 0 \\ - cos {}^{2} (x) + sin(x)cos(x) = 0[/tex]
[tex]cos(x)( - cos(x) + sin(x)) = 0[/tex]
[tex]cos(x) = 0 \\ x = \frac{\pi}{2} + k\pi \\ \\ sin(x) = cos(x) \\ x = \frac{\pi}{4} + k\pi[/tex]
A gym class has $12$ students, $6$ girls and $6$ boys. The teacher has $4$ jerseys in each of $3$ colors to mark $3$ teams for a soccer tournament. If the teacher wants at least one girl and at least one boy on each team, how many ways can he give out the jerseys
Answer:
2700
Step-by-step explanation:
*6*10*9/4!*4*4*6*5/4!
find the volume of these rctangular prisms l=11.5cm w=2.5mm h=6cm
step by step pls
Answer:
172.5cm^3
Step-by-step explanation:
* = multiply or times
volume = length*width*height
Plug in the numbers: 11.5*2.5*6 = 172.5cm^3
Triangle E D F is shown. Angle E D F is 43 degrees and angle D F E is 82 degrees. The length of D F is 15.
What is the measure of angle E?
m∠E =
°
What is the length of EF rounded to the nearest hundredth?
EF ≈
Part 1
Angles in a triangle add to 180 degrees, so
[tex]m\angle E=180^{\circ}-82^{\circ}-43^{\circ}=55^{\circ}[/tex]
Part 2
By the Law of Sines,
[tex]\frac{EF}{\sin 43^{\circ}}=\frac{15}{\sin 55^{\circ}}\\\\EF=\frac{15 \sin 43^{\circ}}{\sin 55^{\circ}}\\\\EF \approx 12.49[/tex]
Answer:
What is the measure of angle E?
m∠E =
✔ 55
°
What is the length of EF rounded to the nearest hundredth?
EF ≈
✔ 12.49
Step-by-step explanation:
A polynomial function has a root of 0 with multiplicity 1, and a root of 2 with multiplicity 4. If the function
has a negative leading coefficient, and is of odd degree, which of the following are true?
The function is positive on (-∞, 0).
The function is negative on (0, 2).
The function is negative on (2, ∞).
The function is positive on (0,0).
Using the Factor Theorem to find the function, the correct statement is:
The function is positive on (0,∞).
What is the Factor Theorem?The Factor Theorem states that a polynomial function with roots [tex]x_1, x_2, \codts, x_n[/tex] is given by:
[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]
In which a is the leading coefficient.
The described roots means that:
[tex]x_1 = 0, x_2 = x_3 = x_4 = x_5 = 2[/tex]
Hence the function is:
f(x) = x(x - 2)^4
(x - 2)^4 is always positive, hence the sign depends on the sign of x, which means that the correct statement is:
The function is positive on (0,∞).
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The square root of the quantity 4 x minus 3 end quantity equals 5.
Answer:
The statement is false.
Step-by-step explanation:
Given,
[tex] \sqrt{4 \times - 3} = 5[/tex]
To Prove
Soln:
[tex] \sqrt{4 \times - 3} [/tex]=[tex]2i \sqrt{3} [/tex]
=>[tex]2i \sqrt{3} ≠5[/tex]
Hence, 2i√3 is not equal (≠) to 5.
A doctor is called to see a sick child. The doctor has prior information that
95% of sick children in that neighborhood have the flu, while the other 5%
are sick with measles. Let F stand for an event of a child being sick with flu
and M stand for an event of a child being sick with measles.
A well-known symptom of measles is a rash (the event of having which is
denoted by R). P(R|M) = 0.93. However, occasionally children with flu also
develop rash, so that P(R|F) = 0.09.Upon examining the child, the doctor
finds a rash. What is the probability that the child has measles?
0.57
0.35
0.65
0.20
The probability that the child has measles is gotten as; 0.35
How to use Baye's Theorem?F is the event of a child being sick with flu.
M is the event of a child being sick with measles.
A is the event that the doctor finds a rash.
B1 is the event that the child has measles
S is the sick children.
P(R|M) = 0.93.
P(R|F) = 0.09
P(S|F) = 0.95
P(S|M) = 0.05
Thus, the probability that the child has measles is;
P(M|R) = [(0.05 * 0.93)/[(0.05 * 0.93) + (0.95 * 0.09)]
P(M|R) = 0.35
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find the value for the given figure
PLS HELP>>>look at pic
Answer:
3x + 2 >= 0
Step-by-step explanation:
Since this is a 4th root, not a cubic root, the radical can only contain 0 or positive numbers. Therefore there is 3x + 2 >= 0.
Diagram 1 shows a tangent to a circle, centre O. Find x and y; 40° y Diagram 1
Answer:
x = 80 , y = 50
Step-by-step explanation:
the angle between the tangent and the radius at the point of contact is 90°
given the angle between the tangent and the chord is 40° , then
angle inside triangle = 90° - 40° = 50°
the triangle has 2 equal radii forming 2 sides thus is isosceles with 2 base angles being congruent, then
y = 50°
the sum of the 3 angles in the triangle = 180° , then
x = 180° - 50° - 50° = 180° - 100° = 80°
Answer:
x = 80°
y = 50°
Step-by-step explanation:
the legs of the inner triangle (tangent to O, and O to point with y angle) are equal because both are the radius of the circle.
that makes the inner triangle an isoceles triangle with both angles on the baseline (tangent to point with y angle) being equal.
the angle of the tangent to the leg "tangent to O" is per definition a right angle (90°). otherwise it would not be a tangent.
one post of the right angle is 40°, so the other part (the triangle inner angle at the tangent point) is then 90-40 = 50°.
since both leg angles must be equal (as described above), y = 50° too.
and as the sum of all angles in a triangle must be 180°, that gives us for x
180 = 50 + 50 + x
x = 180 - 50 - 50 = 80°
PLEASE HELP IM STUCK
Step-by-step explanation:
we have
2y = 4x - 9
and we want it to look like
...x + ...y = -9
simple.
the y term is already on the left side. we need to move the x term to the same side.
what do we do ? we subtract the term we want to get rid of on one side from both sides (we always have to do changes in both sides of the equation, or we change the whole meaning of the equation).
2y = 4x - 9 | -4x on both sides
-4x + 2y = -9
and we are finished. that's it.
Answer:
-4x + 2y = -9
Step-by-step explanation:
Pre-Solving InformationWe are given the equation 2y=4x-9, and we want to convert it into standard form.
Standard form is written as ax+by=c, where a, b, and c are free integer coefficients, however a and b cannot be 0.
SolvingNotice how in standard form, x and y are on the same side. Currently, x and y are on different sides.
Therefore, we first need to get x and y on the same side.
We can do this by subtracting 4x from both sides.
2y = 4x - 9
-4x -4x
_____________
-4x + 2y = -9
As indicated by the -9 on the left side, we have solved the question, and are now done.
Hence, the answer is -4x + 2y = -9.
How many employers ask that employees be skilled in communication and handling money
Based on the Venn diagram, the number of employers who ask employees to be skilled in both communication (C) and handling money (M) is equal to 47 employers.
What is a Venn diagram?A Venn diagram is a circular graphical tool that is used to graphically show, logically compare and contrast two (2) or more finite data set or samples in a given population.
From the Venn diagram, we can deduce that the number of employers who ask employees to be skilled in both communication (C) and handling money (M) is given by:
C∩M = 22 + 25
C∩M = 47 employers.
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Prove that 41 is congruent to 21 (mod 3). Explain using words, symbols, as you wish
From the proof of modular congruence below, it has been shown that;
41 ≡ 21 (mod 3).
How to Solve Modular Arithmetic?We want to use the definition of modular congruence to prove that;
41 is congruent to 21 (mod 3) i.e if a ≡ b (mod m) then b ≡ a (mod m).
We are trying to prove that modular congruence mod 3 is a symmetric relation on the integers.
First, if we recall the definition of modular congruence:
For integers a, b and positive integer m,
a ≡ b (mod m) if and only if m|a–b
Suppose 41 ≡ 21 (mod 3).
Then, by definition, 3|41–21, so there is an integer k such that 41 – 21 = 3k.
Thus;
–(41 – 21) = –3k
So
21 – 41 = 3(–k)
This shows that 3|21 – 41.
Thus;
21 ≡ 41 (mod 3) and the proof is complete
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The test scores of 1,200 students are normally distributed with a mean of 83 and a standard deviation of 5.5. Under which interval did approximately 978 students score?
Select one:
a. 72
b. 77.5
c. 83
d. 72
Using the Empirical Rule, it is found that the interval in which approximately 978 students scored was:
A. 72 < x < 88.5.
What does the Empirical Rule state?It states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.The percentage that 978 is of 1200 is:
978/1200 x 100% = 81.5%.
Considering the symmetry of the normal distribution, two outcomes are possible involving 81.5% of the measures:
Between one standard deviation below the mean and two above, which in the context of this problem is between 77.5 and 94.Between two standard deviations below the mean and one above, which in the context of this problem is between 72 and 88.5, which is option A in this problem.More can be learned about the Empirical Rule at https://brainly.com/question/24537145
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if the ordered pairs (x, -1) and (5, y) belong to the set {(a, b): b = 2a-3}, find x and y.
What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}
The domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}
How to determine the domain?The function is given as
g(x) = –⌊x⌋ + 3
The above is a step function, and the domain is the set of input values it can accept
Step functions of the given form can accept any real value of x
Hence, the domain of the function g(x) = –⌊x⌋ + 3 is (a) {x| x is a real number}
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Complete question
The graph of the step function g(x) = –⌊x⌋ + 3 is shown. What is the domain of g(x)? {x| x is a real number} {x| x is an integer} {x| –2 ≤ x < 5} {x| –1 ≤ x ≤ 5}
Answer:
A
Step-by-step explanation:
52 = -5x - 3 i need help with a math test and this one question i do not understand
Answer:
x=-52/5-i3/5Step-by-step explanation:
[tex]52 = - 5x - 3i...given \: expression \\ - 5x - 3i = 52...switch \: sides \\ - 5x - 3i + 3i = 52 + 3i...add \: 3i \: to \: both \: sides \\ - 5x = 52 + 3i...simplify \\ \frac{ - 5x}{ - 5} = \frac{52}{ - 5} + \frac{3i}{ - 5} ...divide \: both \: sides \: by \: - 5 \\ x = \frac{ - 52}{5} - i \frac{3}{5} ...simplified[/tex]
Find the indefinite integral by making a change of variables. (hint: let u be the denominator of the integrand. remember to use absolute values where appropriate. use c for the constant of integration.) 1 9 2x dx
The value of the indefinite integral is
Given:- The integration of is given whose lower limit is and upper limit is .
To Find:- We have to find the value of the integration of is given whose lower limit is and upper limit is .
By using the concept of indefinite integral it will be solved.
According to the problem,
Therefore, the value of the indefinite integral is .
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Which equation represents this number sentence?
Nine more than the quotient of a number and 3 is 21.
n3+9=21
fraction n over 3 end fraction plus 9 equals 21
3n+9=21
fraction 3 over n end fraction plus 9 equals 21
n+93=21
fraction numerator n plus 9 end numerator over 3 end fraction equals 21
9n+3=21
The equation which represents the number sentence given in the task content is; n/3 + 9 = 21.
Which equation correctly represents the number sentence?According to the task content, it follows that the sentence given is; Nine more than the quotient of a number and 3 is 21.
Since, the quotient of a number and 3 can be written as; n/3.
Consequently, the correct equation is; n/3 +9 = 21.
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Prove the statement using a two-column proof or paragraph proof.
M
L
Given: JKLM is a parallelogram; KL≈ LM; JL MK
Prove: JKLM is a rhombus.
Complete your proof in the box below. You will be awarded 5 points for your
statements and 5 points for your reasons.
1) JKLM is a parallelogram, [tex]\overline{KL} \cong \overline{LM}[/tex] (given)
2) JKLM is a rhombus (a parallelogram with a pair of consecutive congruent sides is a rhombus)
Please someone help me, I don't get it
Answer:
a) x = 1.5 and x = -0.3
b) x = -8 and x = 5
Step-by-step explanation:
a)
The given equation follows the general structure: ax² + bx + c = 0.
Therefore, if a = 5, b = -6, and c = -2, you can substitute the values into the quadratic formula and solve for "x".
b)
Another way of solving polynomials is through factorization. After rearranging the equation to fit the general structure of a quadratic (as seen above), you can factor by asking yourself the question, which 2 numbers multiply to "c" (-40) and add to "b" (3)? The answers will make up your factors.
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\huge\textbf{Equation \#1. }[/tex]
[tex]\mathsf{5x^2 - 6x - 2 = 0}[/tex]
[tex]\huge\textbf{Use the quadratic formula to solve:}[/tex]
[tex]\mathsf{x = \dfrac{-(-6)\pm \sqrt{(-6)^2 - 4(5)(-2)}}{2(5)}}[/tex]
[tex]\huge\textbf{Simplify it: }[/tex]
[tex]\mathsf{x = \dfrac{6 \pm \sqrt{76}}{10}}[/tex]
[tex]\huge\textbf{Simplify that as well:}[/tex]
[tex]\mathsf{x = \dfrac{3}{5} + \dfrac{1}{5}\sqrt{19}\ or\ x = \dfrac{3}{5} + (-\dfrac{1}{5})\sqrt{19}}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x \approx 1.5 \ or\ x\approx -0.3{}\ }}\huge\checkmark[/tex]
[tex]\huge\textbf{Equation \#2.}[/tex]
[tex]\mathsf{x^2 + 3x = 40}[/tex]
[tex]\huge\textbf{Subtract 40 to both sides:}[/tex]
[tex]\mathsf{x^2 + 3x - 40 = 40 - 40}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x^2+ 3x - 40 = 0}[/tex]
[tex]\huge\textbf{Factor the left side of the equation:}[/tex]
[tex]\mathsf{(x - 5)\times (x + 8) = 0}[/tex]
[tex]\mathsf{(x - 5)(x + 8) = 0}[/tex]
[tex]\huge\textbf{Set the factors to equal to 0:}[/tex]
[tex]\mathsf{x - 5 = 0 \ or\ even\ x + 8 = 0}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = 5\ or\ x = -8}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = 5\ or \ x = -8}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
insert a monomial so that each result is an identity( *− 3b4)(3b4 +*) = 121a10 − 9b8
Answer:
(11a^5 - 3b^4) (3b^4 + 11a^5) = 121a^10 - 9b^8
Step-by-step explanation:
I got the 11 part by doing √121 = 11
I got the a^5 by knowing that a needs to have the same exponent both times and 5+5=10. Thats how I got the a^5 part.
Answer: (11a^5 - 3b^4) (3b^4 + 11a^5) = 121a^10 - 9b^8
PR=
Help me please thanks so much
Formula: U*V=R*T
3*1=4*x
3=4x
x=3/4
Hope it helps!
Answer:
[tex]\sf PR =\dfrac{3}{4}[/tex]
Step-by-step explanation:
Intersecting chords theorem:It two chords or secants intersect inside the circle, then the product of the length of the segments of one chord is equal to the product of the lengths of the segments of the other chords.
TP * PR = UP * PV
4 * PR = 3 * 1
[tex]\sf PR = \dfrac{3}{4}[/tex]
A solid box is 15 cm by 10 cm by 8 cm. A new solid is formed by removing a cube 3 cm on a side from each corner of this box. What percent of the original volume is removed
Percent of the original volume that is removed is; 18%
How to find the Volume of a box?
Formula for volume of a box is;
V = lbh
where;
l is length
b is breadth
h is height
Thus;
V_original = 15 * 10 * 8
V_original = 1200 cm³
Volume for each cube removed = 3 * 3 * 3 = 27 cm³
Since there are 8 corners on the box, then 8 cubes are removed.
So the total volume removed is; 8 * 27 = 216
Thus;
Percent of the original volume that is removed is;
216/1200 * 100% = 18%
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Match each system of equations to the inverse of its coefficient matrix, A-1, and the matrix of its solution, X.
The system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X is shown in the figure.
Given that the system of equations are shown in given figure.
The first system of equations are
[tex]\begin{aligned}4x+2y-z&=150\\x+y-z&=-100\\-3x-y+z&=600\\\end[/tex]
By writing in matrix AX=b, we get
Coefficient matrix [tex]A=\left[\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right][/tex] and [tex]B=\left[\begin{array}{l}150&-100&600\end{array}\right][/tex]
Firstly, we will find the A⁻¹ by finding the determinant and adjoint of A and divide the adjoint with determinant, we get
[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}4&2&-1\\1&1&-1\\-3&-1&1\end{array}\right|\\ &=4(1-1)-2(1-3)-1(-1+3)\\&=4(0)-2(-2)-1(2)\\ &=2\neq 0\end[/tex]
[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}0&2&2\\-1&1&-2\\-2&3&2\end{array}\right]^T\\&=\left[\begin{array}{lll}0&-1&-2\\2&1&3\\2&-2&2\end{array}\right]\end[/tex]
[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0&-0.5&-0.5\\1&0.5&1.5\\1&-1&1\end{array}\right]\end[/tex]
For a solution Consider [A B] and apply row operations, we get
[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{lll1}4&2&-1&150\\1&1&-1&-100\\-3&-1&1&600\end{array}\right]\\ R_{2}&\rightarrow 4R_{2}-R_{1},R_{3}\rightarrow 4R_{3}+3R_{1}\\ &\sim \left[\begin{array}{lll1}4&2&-1&150\\0&2&-3&-550\\0&2&1&2850\end{array}\right]\\ R_{3}&\rightarrow R_{3}-R_{2}\\ &\sim \left[\begin{array}{llll}4&2&-1&150\\0&2&-3&-550\\0&0&4&3400\end{array}\right]\end[/tex]
Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}-250\\1000\\850\end{array}\right][/tex]
The second system of equations are
[tex]\begin{aligned}x+y-z&=220\\5x-5y-z&=-640\\-x+y+z&=200\\\end[/tex]
Similarly, we will find for second system of equations
[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}1&1&-1\\5&-5&-1\\-1&1&1\end{array}\right|\\ &=1(-5+1)-1(5-1)-1(5-5)\\&=1(-4)-1(4)-1(0)\\ &=-8\neq 0\end[/tex]
[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}-4&-4&0\\-2&0&-2\\-6&-4&-10\end{array}\right]^T\\&=\left[\begin{array}{lll}-4&-2&-6\\-4&0&-4\\0&-2&-10\end{array}\right]\end[/tex]
[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.5&0.25&0.75\\0.5&0&0.5\\0&0.25&1.25\end{array}\right]\end[/tex]
[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}1&1&-1&220\\5&-5&-1&-640\\-1&1&1&200\end{array}\right]\\ R_{2}&\rightarrow R_{2}-5R_{1},R_{3}\rightarrow R_{3}+R_{1}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&2&0&420\end{array}\right]\\ R_{3}&\rightarrow 5R_{3}+R_{2}\\ &\sim \left[\begin{array}{llll}1&1&-1&220\\0&-10&4&-1740\\0&0&4&360\end{array}\right]\end[/tex]
Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}100\\210\\90\end{array}\right][/tex]
The third system of equations are
[tex]\begin{aligned}2x+2y-z&=290\\x+y-3z&=500\\x-y+2z&=600\\\end[/tex]
Similarly, we will find for third system of equations
[tex]\begin{aligned}|A|&=\left|\begin{array}{lll}2&2&-1\\1&1&-3\\1&-1&2\end{array}\right|\\ &=2(2-3)-2(2+3)-1(-1-1)\\&=2(-1)-2(5)-1(-2)\\ &=-10\neq 0\end[/tex]
[tex]\begin{aligned}Adj A&=\left[\begin{array}{lll}-1&-5&-2\\-3&5&4\\-5&5&0\end{array}\right]^T\\&=\left[\begin{array}{lll}-1&-3&-5\\-5&5&5\\-2&4&0\end{array}\right]\end[/tex]
[tex]\begin{aligned}A^{-1}&=\frac{Adj A}{|A|}\\ &=\left[\begin{array}{lll}0.1&0.3&0.5\\0.5&-0.5&-0.5\\0.2&-0.4&0\end{array}\right]\end[/tex]
get
[tex]\begin{aligned}\left[A\right.\text{ }\left.B\right]&=\left[\begin{array}{llll}2&2&-1&290\\1&1&-3&500\\1&-1&2&600\end{array}\right]\\ R_{2}&\rightarrow 2R_{2}-R_{1},R_{3}\rightarrow 2R_{3}-R_{1}\\ &\sim \left[\begin{array}{llll}2&2&-1&290\\&0&-5&710\\0&-4&5&910\end{array}\right]\end[/tex]
Thus, [tex]x=\left[\begin{array}{l}x\\y\\z\end{array}\right]=\left[\begin{array}{l}479\\-405\\-142\end{array}\right][/tex]
Hence, each system of equations to the inverse of its coefficient matrix, A⁻¹, and the matrix of its solution, X.
Learn more about the system of equations from here brainly.com/question/1761142
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