![Given: A = [ 1 -1 -2 3] B = [ 1 5 8 -8 ] C = [ 1 2 3 4 ] Solve: AX + B = C](https://brainimage.s3.us-east-005.backblazeb2.com/contents/attachments/bzkCs6aEW4e0AMYm76HZ220uInUWX2J1.jpeg)
Answers
Given in the question the matrix
A = [ 1 -1 B = [ 1 5 C = [ 1 2
-2 3 ] 8 -8 ] 3 4]
after solving AX + B = C, we get the value of x
x = [ 1 -21/5
-1 8/5] ..........(ii)
Given A = [ 1 -1 B = [ 1 5 C = [ 1 2
-2 3 ] 8 -8 ] 3 4]
find x, if AX + B = C
AX + B = C
AX = C -B = [ 1 2 [ 1 5
-
3 4] 8 -8 ]
AX = [ 1-1 2-5 = [ 0 -3
3-8 4+8 ] -5 12]
X = A -1 [ 0 -3
-5 12] .........(i)
A = [1 1 |A| = {3*1 - 1 *(-2)}
-2 3] = 5
A-1 = [tex]\frac{adj A}{|A|}[/tex]
Adj A = [cofactor A]^1 = [ [tex]a_{11}[/tex] = 3 [tex]a_{12}[/tex] = 2
[tex]a_{21}[/tex] = -1 [tex]a_{22}[/tex] = 1 ] ^1
adj A = [ 3 -1 A -1 = 1/5 [ 3 -1
2 1] 2 1]
x = 1/5 [3 -1 [ 0 -3
2 1] -5 12]
= 1/5 [ 5 -21 = [ 1 -21/5
-5 8] -1 8/5] ..........(ii)
Hence, required solution of the given matrix is equation (ii)
Therefore, Given the matrix A = [ 1 -1 B = [ 1 5 C = [ 1 2
-2 3 ] 8 -8 ] 3 4]
after solving AX + B = C, we get the value of x
x = [ 1 -21/5
-1 8/5] ..........(ii)
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Related Questions
find c for this equation!
ab + c = d
Answers
Answer:
c=d-ab
Step-by-step explanation:
ab+c=d
move over to the other side
change sides change signs
c=d-ab
Answer:
c=d−ab
Subtract ab from both sides of the equation
Show that quadrilateral ABCD is a parallelogram.
Answers
Slope of AB = 2; Slope of DC = 2
Slope of AD = -1/2; Slope of BC = -1/2
Both pairs of opposite sides are parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.
What is a Parallelogram?A parallelogram is a quadrilateral that has two pairs of opposite sides that have the same lengths and are parallel to each other.
Since the opposite sides of a parallelogram are parallel, therefore, they have the same slope value.
Slope = change in y / change in x.
Find the slope of AB and DC. then AD and BC:
Slope of AB = (-2 - 2)/(-3 -(-1)) = -4/-2
Slope of AB = 2
Slope of DC = (-3 - 1)/(-1 - 1) = -4/-2
Slope of DC = 2
Slope of AD = (-3 -(-2))/(-1 -(-3)) = -1/2
Slope of AD = -1/2
Slope of BC = (2 - 1)/(-1 - 1) = 1/-2
Slope of BC = -1/2
Therefore, since AB and DC have the same slope, they are parallel, so also is AD and BC parallel because they have the same slope, therefore, quadrilateral ABCD is a parallelogram.
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I will give brainliest
Answers
The algebraic equation and the original price is:
original price - discount = sales price
x - 27 = 89
x = 116
What is the original price?An algebraic equation is made up of two expressions that are made up of variables or numbers that are connected by an arithmetic operation.
A discount reduces the price of a good or service. In order to determine the price of a good after the discount has been applied, subtract the amount of the discount from the original price of the item.
original price - discount = sales price
x - 27 = 89
Combine similar terms: x = 89 + 27
Add similar terms together: x = 116
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Which of the following is an arithmetic sequence?
A) 3, -3, 4, -4, 5, -5
B)1, 2, 4, 7, 10
C) 4, 7, 10, 13, 16
D)2, 4, 8, 16, 32
Answers
Answer:
The answer is C
Step-by-step explanation:
The increase between the numbers in a arithmetic sequence is always the same, in this case the number always increased by 3.
Here is a another example
3, 5, 7, 9
The difference between the consecutive terms is always 2
Read the screenshot, please.
Answers
Answer:
You need at least 101 cans of food in order to meet or surpass the goal.
Step-by-step explanation:
a.
135+89=224
224+c>=325
b.
224-224+x>=325-224
x>=101
You need at least 101 cans of food in order to meet or surpass the goal.
Which system of inequalities is graphed below?
Answers
A group of two or more inequalities in one or more variables is referred to as a system of inequalities. The system of inequalities graphed is y > x² - 4 and y < x² + 6.
What is meant by system of inequalities?A group of two or more inequalities in one or more variables is referred to as a system of inequalities. When a problem demands a variety of solutions and those solutions must satisfy many constraints, systems of inequalities are used.
A system of inequalities is one where the total number of inequalities is greater than or equal to the number of variables.
A system of inequalities may have,
Zero solutionOne solutionInfinite solutionThe equation of the vertical parabola with y-intercept -4 is equal to
y = x² - 4.
The solution of the inequality is the shaded area above the dashed line.
The inequality must be y > x² - 4
2) The equation of the vertical parabola with y-intercept 6 is equal to y = x² + 6.
The solution of the inequality exists the shaded area below the dashed line. The inequality must be y < x² + 6
The system of inequalities graphed is
y > x² - 4
y < x² + 6
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Kevin has x dollars in an account that pays 2.2% interest, compounds quarterly. Express his balance after one quarter algebraically
Answers
Balance of Kevin after 1 quarter will be 1.0055(x)
What is quarterly compounded compound interest?Compound interest is interest that is calculated using both the starting amount and the interest that has accrued over time.
Interest is considered to be compounded quarterly if it is compounded four times each year.
If interest is compounded four times or quarterly each year, the formula for the amount at time t is as follows.
A = P( ( 1 + (r/4))⁴ⁿ
A = Accumulated amount
P= Principal amount
r = interest rate
n = time
Given that Kevin has x dollars in an account that pays 2.2% interest, compounds quarterly
∴ P = x
r = 2.2% = 2.2/100
To find balance after one quarter , i.e. time n = 1/4 year
⇒ Balance = accumulated amount =$ x(1 + 2.2/400)¹ = $ 1.0055(x)
Therefore, Balance of Kevin after 1 quarter will be 1.0055(x)
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Write 360 as a product of primes.
Use index notation when giving your
answer
Answers
Answer:
2³ * 3² * 5
Step-by-step explanation:
Prime factorize 360 and find how many times each number is repeated and write in index notation.
360 = 36 * 10
= 6 * 6 * 2 * 5
= 2 * 3 * 2 * 3 * 2 * 5
= 2 * 2 * 2 * 3 * 3 * 5
= 2³ * 3² * 5
a nursery decides to make a grass-seed blend by mixing rye seed that sells for $6.50 per pound with bluegrass seed that sells for $3.50 per pound. the final mix is 180 pounds and sells for $5.33 per pound. how much of each type was used?
Answers
The amount of rye seed and bluegrass seed used in the mixture is 109.8 and 70.2 pounds respective.
What exactly is the substitution method?The substitution method is an algebraic approach to solving simultaneous linear equations.As the name implies, the value with one variable from one equation is replaced in the other equation.In response to the given question;
Let's say the amount of rye seed is 'x.'
The cost of rye seed = $6.50 per pound
Let's say the amount of bluegrass seed is 'y.'
The cost of bluegrass seed = $3.50 per pound.
The total seeds are 180 pounds.
Thus,
x + y = 180
x = 180 - y .......eq 1.
The other equation for the total cost of $5.33 per pound is;
6.50x + 3.50y = 5.33×180
Put the value of x from eq 1.
6.50(180 - y) + 3.50y = 959.4
1170 - 6.50y + 3.50y = 959.4
3y = 210.6
y = 70.2
x = 180 - 70.2 = 109.8
Thus, the amount of rye seed and bluegrass seed used in the mixture is 109.8 and 70.2 pounds respectively.
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pls help with these i need them quick
Answers
1. The transformation is: A. rotation 90° clockwise about the origin.
2. Based on the alternate exterior angles theorem, the value of x is: 2.
3. x = 10
4. The slope of the given line is: A. 2
How to Find the Slope of a Line?The slope of a line = change in y/change in x.
What is the Alternate Exterior Angles Theorem?The theorem states that alternate exterior angles are congruent if they each lie on lines that are parallel to each other.
1. The transformation that took UVWX to U'V'W'X' is: A. rotation 90° clockwise about the origin.
2. 26x - 2 = 50 [based on the alternate exterior angles theorem]
Solve for x
26x = 50 + 2
26x = 52
x = 52/26
x = 2
The value of x is: D. 2.
3. 9x + 15 + 6x + 15 = 180 [based on the same-side interior angles theorem]
Solve for x
15x + 30 = 180
15x = 180 - 30
15x = 150
x = 150/15
x = 10
The value of x is: C. 10
4. Using two points on the line, (1, 1) and (-1, -3), we have:
Slope of the line = (-3 - 1)/(-1 - 1) = -4/-2
Slope of the line = 2
The slope is: A. 2
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On a certain hot summer's day, 435 people used the public swimming pool. The daily prices are 1.25 for children and 2.00 for adults. The receipts for admission totaled 818.25 How many children and how many adults swam at the public pool that day?
Answers
The number of children and the number of adults that swam in the swimming pool that day are 69 and 366 respectively.
Given that:-
Total number of people that swam in the swimming pool = 435
Price for children = 1.25
Price for adults = 2
Total receipts = 818.25
We have to find the number of children and the number of adults that swam in the swimming pool that day.
Let the number of children that swam that day be x and,
the number of adults that swam that day be y.
Hence, we can write,
1.25x + 2y = 818.25 ...(1)
x + y = 435 ... (2)
Solving the linear equation in two variable by elimination method
Multiplying (2) by 2 , we get
2x + 2y = 870 ... (3)
(3) - (1)
0.75x = 870 - 818.25
0.75x = 51.75
x = 51.75/0.75
x = 69
From (2), we can write,
69 + y = 435
y = 435 - 69
y= 366
Hence, the number of children and the number of adults that swam that day are 69 and 366 respectively.
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Draw and label center D at (-4,-2)
Answers
PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
32
Step-by-step explanation:
this expression cannot be simplified because there are no like terms to combine with the numbers in the expression.
the number that goes in the ? is 32
PLEASE HELP!!
SEE PICTURES!
Answers
Answer: G=62, I = 62, H =54
Step-by-step explanation:
3x+26=4x+14
x=12
G=36+26 = 62
180-62-62=54
We know that
G= (3x+26)°
I= (4x+14)°
Since G°=I°,
4x+14=3x+26
4x-3x=26-14
X= 12
Now, angle G=(3x+26)°
Since X=12,
G= (3(12)+26)°
G=62°
Since G=I, I would also be 62°
We know that all angles in a triangle must add up to 180°,
Therefore
angle H = 180-(2(62))
H= 180-124
H = 56°
And therefore we know that
Angle G = angle I = 62°
Angle H = 180-(Angle G + Angle I) = 56°
Write a complete two-column proof for following information.
B
C
Given: AB = 3y - 1, BC = 7y, AC = 29
Prove: AB = 8
Answers
Hence proved that triangle AB = 3(3) - 1 = 9 - 1 = 8.
What is triangle?A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space). In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle. All triangles are enclosed in a single plane if all of geometry is the Euclidean plane, however this is no longer true in higher-dimensional Euclidean spaces. Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.
Given that,
AB + AC = AC
3y - 1 + 7y = 29
10y = 29 + 1 = 30
y = 30/10 = 3
Therefore, AB = 3(3) - 1 = 9 - 1 = 8.
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Find the 10th term of the geometric sequence 8,-16,32,…
Answers
Answer: -4096
Step-by-step explanation: Use the geometric sequence formula to find the 10th term (image attached). So, the 10th term = 8(-2)^9
Note: the common ratio can be found by 2ndterm/1stterm
Answer:
a₁₀ = -4096
Step-by-step explanation:
Geometric sequence
General form of a geometric sequence:
[tex]\boxed{a_n=ar^{n-1}}[/tex]
where:
aₙ is the nth term.a is the first term.r is the common ratio.n is the position of the term.Given terms of the geometric sequence:
a₁ = 8a₂ = -16a₃ = 32To find the common ratio (r), divide consecutive terms:
[tex]\implies \dfrac{a_3}{a_2}=\dfrac{32}{-16}=-2[/tex]
Substitute the values of a and r into the formula to create an equation for the nth term of the sequence:
[tex]\implies a_n=8(-2)^{n-1}[/tex]
To find the 10th term of the sequence, substitute n = 10 into the equation:
[tex]\begin{aligned}\implies a_{10}&=8(-2)^{10-1}\\&=8(-2)^{9}\\&=8(-512)\\&=-4096\end{aligned}[/tex]
Therefore, the 10th term of the given geometric sequence is -4096.
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find the sum by using a number line -9+8=
Answers
Hello! So...
We are given the following to solve:
[tex]-9+8=?[/tex]
In order to solve this, we simply need to add.
[tex]-9+8=-1[/tex]
Hence, our solution is -1, and would be marked -1 on a number line. Graph is displayed below.
____________________________________
Hope this helps! If so, lmk! Thanks and good luck!
Please help me
I need this at least in 5 hours
Answers
The area of the parallelogram based on the given parameters is 0.0324 m²
The total cost of Lilian's apple if a pound cost $1.77 is $2.3364.Ethan is more correct because he moved the decimal point 4 places to the left.The total mass of the green rope given the length and weight is 3.146 kgThe product of 0.102 × 7.3 is 0.7446Area of a parallelogramHeight = 0.09mBase = 0.36 mArea of the parallelogram = Base × height
= 0.36 m × 0.09m
= 0.0324 m²
Cost of each pound of apple = $1.77Weight of Lilian's apple = 1.32 lbTotal cost of Lilian's apple = Cost of each pound of apple × Weight of Lilian's apple
= $1.77 × 1.32 lb
= $2.3364
Ethan:
3.045 × 1.3
= 3.9585
Anica:
3.045 × 1.3
= 39.585
Ethan is more correct because he moved the decimal point 4 places to the left.
Length of the green rope = 60.5 mMass of each meter of the rope = 0.052 kgTotal mass of the green rope = Length of the green rope × Mass of each meter of the rope
= 60.5 × 0.052
= 3.146 kg
0.102 × 7.3
= 0.7446
Therefore, the area of the parallelogram when calculated is 0.0324 m²
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PLSSS HELP IF YOU TURLY KNOW THISS
Answers
Answer:
19
Step-by-step explanation:
Answer:
9d :)
Step-by-step explanation:
So, we have the equation 5c + 9d - 5c
We combine our like terms which are 5c and -5c bc they both have the variable "c"
When we do 5c + -5c we get 0 since were adding a negative and a positive. This leaves us with just 9d, therefore, that's your answer!
A triangle has three sides: AB, BC, CA. We know that angle A is greater than angle C. Find the range for side AC.
A) AB< CA< BC
B) BC- AB < CA < AB + BC
C) BC< CA< AB
D) AB + BC < CA < BC- AB
Answers
Answer:
BC- AB < CA < AB + BC
Step-by-step explanation:
The sides opposite the larger angles are longer than the sides opposite smaller angles.
So, BC (opposite < A) is longer than AB (opposite < C) so,
BC > AB
The other side AC cannot be greater than AB + BC, otherwise the triangle would not exist, so,
AC < AB + BC
Also, CA > BC - AB
The range for AC is
BC- AB < CA < AB + BC
ANSWER ASAP
Select the correct answer from each drop-down menu.
Answers
Considering the concepts of the diameter and the radius of a circle, it is found that the correct statement is:
The ratio of the lengths of EF and AD is 2:1.
What are the diameter and the radius of a circle?The radius of a circle is given by the length of the line segment from the center of the circle towards an edge of the circle.The diameter of a circle is given by the length of the segment between two opposite edges of the circle, passing through the center, hence it is twice the radius.In the context of the circle given in this problem, we have that:
The center is of A.The radius is of AD.The diameter is of EF.hence:
EF = 2AD, meaning that the ratio is of 2:1.
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Marco needs to buy some cat food. At the nearest store, 3 bags of
cat food cost $17.25. How much would Marco spend on 6 bags of
cat food?
Marco would spend $ on 6 bags of cat food.
Answers
Answer: 34.50
Step-by-step explanation: Since 3 bags cost 17.25 and Marco would buy 6, 3 times 2 is 6 so 17.25 times 2 is 34.50
40 point question!! Functions. (ignore pencil marks)
Answers
Answer:
[tex]\textsf{D)} \quad P(n)=0.024n^2-0.3n+4.3[/tex]
Step-by-step explanation:
From inspection of the graph, when the number of coils is 10, the length of the spring is between 0 cm and 20 cm.
Substitute n = 10 into the equation of each given answer option:
[tex]\begin{aligned}\textsf{Option A}: \quad P(10)&=10^2+4.3\\ & =100+4.3\\&=104.3\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Option B}: \quad P(10)&=10^2-0.3(10)+4.3\\ & = 100-3+4.3\\&=97+4.3\\&=101.3\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Option C}: \quad P(10)&=0.24(10^2)+4.3\\&=0.24(100)+4.3\\&=24+4.3\\&=28.3\end{aligned}[/tex]
[tex]\begin{aligned}\textsf{Option D}: \quad P(10)&=0.024(10^2)-0.3(10)+4.3\\ & = 0.024(100)-3+4.3\\&=2.4-3+4.3\\&=-0.6+4.3\\&=3.7\end{aligned}[/tex]
Therefore, as 0 < P(10) < 20, the only suitable equation is Option D:
[tex]\boxed{P(n)=0.024n^2-0.3n+4.3}[/tex]
Select three names for the angle.
Answers
Answer:
Step-by-step explanation:
Here, what they're really saying is to find 3 different ways to rearrange the letters A, B, and C. Then, put them together to give the angle a combination of "names"
(1 ABC
(2 BAC
(3 CAB
Hope this helps! :D
Find a term that results in 66x^9 when multiplied by 22x^-3
Answers
Answer: 3x^12
Step-by-step explanation:
66 / 22 = 3
We can add exponents when multiplying them.
-3 + 12 = 9
find the value x in the triangle
Answers
Answer:
x = 5
Step-by-step explanation:
Comment
The three sides need to add up to 23 (the perimeter is given as 23)
Givens
The sides are
x (x + 3)2xThe perimeter is 23Solution
x + x + 3 + 2x = 23 Combine
4x + 3 = 23 Subtract 3 from both sides
4x + 3-3 = 23-3 Combine
4x = 20 Divide by 4
4x/4 = 20/4
x = 5
The three sides of a triangle is x, x+3 and 2x. If the perimeter is 23 feet. Find the value of x.
Explanation -:In this question we are given
the perimeter of a triangle is 23 feet.sides of the triangle xx+3 2x.We are asked to calculate the value of x.
To solve this problem first we have to form an equation.
Let us solve this question.
We know that the perimeter of a triangle is the sum of all three sides.
According To Question
x + x + 3 + 2x = 23
→ 2x + 3 + 2x = 23
→ 4x + 3 = 23
→ 4x = 23 - 3
→ 4x = 20
→ x = 20/4 = 5
x = 5
The value of x is 5.
[tex] \rule{70mm}{2pt}[/tex]
Write an equivalent expression for 10 6 power divided by 10 4 power
Answers
The equivalent expression for 10⁶ / 10⁴ will be equal to 10²
Given,
Exponents: 10⁶ and 10⁴
We have to find an equivalent expression for 10⁶ / 10⁴
Equivalent expression:
In general, something is considered equal if two of them are the same. Similar to this, analogous expressions in mathematics are those that hold true even when they appear to be different. However, both forms provide the same outcome when the values are plugged into the formula.
Here,
aˣ / aⁿ = x - n
So,
10⁶ / 10⁴ = 6 - 4 = 2
That is,
The equivalent expression for 10⁶ / 10⁴ will be equal to 10²
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billy had 15 apples. His mom took 2 and his dad took 5 for his cooking. How many apples does he have
Answers
Answer:
8
Step-by-step explanation:
Billy started with 15 apples.
Lost 2, and another 5, In total 7 apples were taken.
" Lost " Indicates subtraction.
The equation would look like this: 15 - 7.
Subtract.
Hence, your answer should be 8.
Hopes this helps!
Have a good day :).
Answer: 8
Step-by-step explanation: 15 - 2 = 13 and 13 - 5 = 8.
the sum of simple interest and compound interest of a certain interest on a sum of money for 2 years at the rate of 7% p.a is Rs 85470. by how much percent the compound interest is more than the simple interest?
Answers
Answer: 3.3%
Step-by-step explanation:
Principal not given.
SI = PRT/100
CI = P(1+R/100)^T -
SI + CI = 85470
[P×7×2]//100 + P [1+ (7/100)]^2 = 85470
on solving: P = 3,00,000
P = 300000 SI for 2 years = 42000
CI = Rs 43470
The difference= Rs 1470
as percentage to CI = [1470/ 43470] ×100
= 3.38%
Is my friend correct or incorrect
Answers
Answer:Your friend is incorrect
x=-2
Step-by-step explanation:
Add 6 to both sides
-6+2x=-10
+6 +6
2x=-4
Then divide each side
2x/2=-4/2
x=-2