Solve the system by using the inverse of the coefficient matrix. -3x + 9y = 9 3x + 2y = 13 Group of answer choices
Answers
Answer:
x= 3
y=2
Step-by-step explanation:
-3x + 9y = 9 ----------- equation 1
3x + 2y = 13--------------- equation 2
In Matrix Form
\(\left[\begin{array}{cc}-3&9\\3&2\end{array}\right] \left[\begin{array}{c}x\\y\end{array}\right] = \left[\begin{array}{c}9\\13\end{array}\right]\)
Let A = \(\left[\begin{array}{cc}-3&9\\3&2\end{array}\right]\) X = \(\left[\begin{array}{c}x\\y\end{array}\right]\) and B = \(\left[\begin{array}{c}9\\13\end{array}\right]\)
Then Mathematically AX= B
or X= A⁻¹ B
Where A⁻¹ = Adjacent A/ mod of A
Adjacent A = \(\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right]\)
Mod Of A= -6 - (27) = -33 which is not equal to zero
so Putting These values in the given formula
X= 1/-33 \(\left[\begin{array}{cc}2&-9\\-3&-3\end{array}\right]\) \(\left[\begin{array}{c}9\\13\end{array}\right]\)
Now Multiplying Rows and Columns
\(\left[\begin{array}{c}x\\y\end{array}\right]\) = -1/33 \(\left[\begin{array}{cc}2*9+- 9*13\\-3*9 +- 3*13\end{array}\right]\)
Solving the Matrix we get
\(\left[\begin{array}{c}x\\y\end{array}\right]\) = -1/33 \(\left[\begin{array}{cc}18-117\\-27-39\\\end{array}\right]\)
\(\left[\begin{array}{c}x\\y\end{array}\right]\) = -1/33 \(\left[\begin{array}{cc}-99\\-66\end{array}\right]\)
From Here we find x= 99/33 or 3
and y = 66/33= 2
Related Questions
How do I solve this and what is the answer
Answers
Given that the degree is 397.
We have the formula,
1 degree =
\(\frac{\pi}{180}\)Radian.
Hence, we get
\(397\times\frac{\pi}{180}=6.92986\text{ radians}\)Hence the answer is B. 6.93 radians
I need some help for the answer
Answers
Answer:
\(y = x - 10\)
Step-by-step explanation:
Given
Input : x
Rule: Subtract 10 from input
Output: y
Required
Determine the output
The rule implies that: when 10 is subtracted from x, it gives y.
This is represented as:
\(y = x - 10\)
Using 50 random numbers given below, compute the mean and standard deviation. 0.937776 0.270012 0.243785 0.590701 0.824982 0.131805 0.879337 0.741998 0.254683 0.080259 0.419321 0.928220 0.958430 0.980182 0.263900 0.063119 0.762096 0.485612 0.662900 0.362242 0.724796 0.307736 0.305021 0.417052 0.054337 0.323357 0.069662 0.843387 0.353107 0.074262 0.735596 0.175095 0.390508 0.668932 0.029861 0.205228 0.387740 0.962169 0.646565 0.423914 0.754782 0.156719 0.773113 0.546335 0.323573 0.649740 0.214082 0.382383 0.383982 0.030539 Mean = (to 6 decimals) Standard deviation = (to 6 decimals)
Answers
The mean is 0.477514 (rounded to 6 decimal places).
The standard deviation is 0.288919 (rounded to 6 decimal places).
How to Solve the Problem?To calculate the mean and standard deviation, we will use the following formulas:
Mean = (sum of all values) / (number of values)
Standard deviation = sqrt[(sum of (value - mean)^2) / (number of values)]
Using these formulas, we can calculate the mean and standard deviation for the given set of random numbers:
Mean = (0.937776 + 0.270012 + 0.243785 + 0.590701 + 0.824982 + 0.131805 + 0.879337 + 0.741998 + 0.254683 + 0.080259 + 0.419321 + 0.928220 + 0.958430 + 0.980182 + 0.263900 + 0.063119 + 0.762096 + 0.485612 + 0.662900 + 0.362242 + 0.724796 + 0.307736 + 0.305021 + 0.417052 + 0.054337 + 0.323357 + 0.069662 + 0.843387 + 0.353107 + 0.074262 + 0.735596 + 0.175095 + 0.390508 + 0.668932 + 0.029861 + 0.205228 + 0.387740 + 0.962169 + 0.646565 + 0.423914 + 0.754782 + 0.156719 + 0.773113 + 0.546335 + 0.323573 + 0.649740 + 0.214082 + 0.382383 + 0.383982 + 0.030539) / 50 = 0.477514
Therefore, the mean is 0.477514 (rounded to 6 decimal places).
Now we will calculate the standard deviation:
Standard deviation = sqrt[((0.937776 - 0.477514)^2 + (0.270012 - 0.477514)^2 + (0.243785 - 0.477514)^2 + ... + (0.382383 - 0.477514)^2 + (0.383982 - 0.477514)^2 + (0.030539 - 0.477514)^2) / 50] = 0.288919
Therefore, the standard deviation is 0.288919 (rounded to 6 decimal places).
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Translate this sentence into an equation.
The product of Raj's height and 3 is 33.
Use the variable r to represent Raj's height.
HELP PLEASE ASAP!!!
Answers
Answer: The equation is 3r = 33
That equation solves to r = 11. Divide both sides by 3 to solve that equation.
To form the original equation itself, we multiply 3 by r since your teacher mentioned "product of his height and 3". That product is set equal to 33. Notice that 3*r = 3*11 = 33.
The sum of 11 and three-fourths of a number is less than 112. What are the possible values of the number? Write an inequality that could be used to solve this problem. Use the letter, "x" as a variable and write the inequality so that the term, "x" term comes first. Where necessary, write numbers as fractions (rather than decimals)
Answers
The inequality that can be used to solve the possible values of the number is 11 + 3/4x < 112 where the number x is x < 134 2/3
How to write inequality?sum of 11 and three-fourths of a number is less than 112.
Let
The unknown number = x
11 + 3/4x < 112
Subtract 11 from both sides
3/4x < 112 - 11
3/4x < 101
divide both sides by 3/4
x < 101 ÷ 3/4
multiply by the reciprocal of 3/4
x < 101 × 4/3
x < 404/3
x < 134 2/3
Therefore, the inequality which represents the situation is 11 + 3/4x < 112.
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Jackson wrote different patterns for the rule subtract 5 select all the patterns he could have written
Answers
When Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include
A. 27, 22, 17, 12, 7
D. 100, 95, 90, 85, 80
What is the expression regarding the pattern?It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.
Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. In this case, when Jackson wrote different patterns for the rule "subtract 5", the patterns that he could have written include 27, 22, 17, 12, 7 and 100, 95, 90, 85, 80. In this cases, there are difference of 5.
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Complete question
Jackson wrote different patterns for the rule "subtract 5". Select all of the patterns that he could have written.
27, 22, 17, 12, 7
5, 10, 15, 20, 25
55, 50, 35, 30, 25
100, 95, 90, 85, 80
75, 65, 55, 45, 35
see picture.. see picture..
Answers
Check the picture below.
The room number on two adjacent hotel room doors are two consecutives even numbers. If their sum is 654, find the hotel room numbers.
Answers
Answer:
326&328
Step-by-step explanation:
(654-2)÷2=326
326+2=328
the perimeter of a triangle is 32 feet. One side of the triangle is 11 feet longer than the second side. The third side is 9 feet longer than the second side. Find the length of each side.
Answers
Answer:
One side - 15 feet
Second side - 4 feet
Third side - 13 feet
Step-by-step explanation:
Let's call the sides A B and C, respectively.
We know that:
A = B + 11
C = B + 9
and that
A + B + C = 32
Please note that we have 3 equations and 3 unknowns. We can solve this, we'll use substitution.
A + B + C = (B + 11) + B + (B + 9) = 32
3B + 20 = 32
3B = 12
B = 4
The sides have lengths of 4+11 = 15, 4 and 4+9 = 13. This is in fact a proper triangle (because the shorter sides add up to more than the longer side).
The weights of bags of chips are normally distributed with a mean of 180 grams and a standard deviation of 4 grams.
What percent of the bags of chips weigh less than 176 grams?
2.5%
16%
32%
34%
Answers
The percent of the bags of chips weigh less than 176 grams is b 16%
What percent of the bags of chips weigh less than 176 grams?From the question, we have the following parameters that can be used in our computation:
Mean = 180
Standard deviation = 4
Bags of chips weigh less than 176 grams
This means that
x = 176
So, the z-score is
z = (176 - 180)/4
Evaluate
z = -1
The percent of the bags of chips weigh less than 176 grams is represented as
P = P(z < -1)
Using a graphing calculator, we have
Percentage = 0.15866
So, we have
Percentage = 16%
Hence , the percentage is 16%
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in the coordinate plane what is the length of the line segment that connects points at (4, -1) and (9, 7) round to the nearest tenth
PLEASE HELPPPPP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!! 0__________________________________________________________________0
Answers
Answer:
the answer is 9.4
Step-by-step explanation:
We get that formula is:
d=\(\sqrt{(9-4)^{2} +(7--1)^{2} }=\sqrt{89}=9.4339\)
I am willing to give brainliest to anyone that helps that or 50 points!!!!!
Mr. Morris is going to save money and replace his sailboat's mainsail himself. He must determine the area of the mainsail in order to buy the correct amount of material. Calculate the area of the parallelogram to determine how much material should be purchased. Be sure to explain how to decompose this shape into rectangles and triangles. Describe their dimensions and show your work.
Answers
Answer:
it think the other missing side is 225ft i think
Step-by-step explanation:
Chapter 6 Study Guide
Tickets for a school play cost $6 for adults and $4 for students. At the end of the play, the school sold a total of 60 tickets
and collected $360
Answers
Answer:
what is the question
Step-by-step explanation:
Mrs. Dames shared $20,000 between her two sons Bob and Sam in the ratio 2:3 respecitvely
(a) Calculate the amount that Bob received
Answers
Sum of ratio = 2 + 3 = 5
Bob
\( = \frac{2}{5} \times 20000 \\ = 2 \times 4000 \\ = 8000\)So, Bob has $ 8000
Answer:
8,000
Step-by-step explanation:
20,000
2:3
20,000 / 5 = 4,000
4,000 * 2 = 8,000
Petra invests $10 800. After 4 years she has earned $3240 in interest. At what amount rate of interest did she invest her money?
Answers
Answer:
7.5%
Step-by-step explanation:
Let, rate be r%
Now,
interest=prt/100
3240= 10800×4×r/100
r=3240×100/10800×4
r=7.5%
labor-hours and its standard cost card per unit is as follows:
Direct material: $ pounds at $11.00 per pound
Direct labor: 3 hours at $12 per hour
Variable overhead: 3 hours at $7 per hour
Total standard variable cost per unit
The company also established the following cost formulas for its selling expenses:
sales salaries and commissions
shipping expenses
Fixed Cost per
Month
$ 280,000
$ 260,000
$ 55.00
36.00
$112.00
Variable
Cost per
Unit Sold
$ 20.00
$ 11.00
The planning budget for March was based on producing and selling 21,000 units. However, during March the company
actually produced and sold 26.600 units and incurred the following costs:
a Purchased 154.000 pounds of raw materials at a cost of $9.50 per pound. All of this material was used in production.
b. Direct laborers worked 63,000 hours at a rate of $13.00 per hour
e Total variable manufacturing overhead for the month was $510,930
d Total advertising sales salaries and commissions, and shipping expenses were $286,000, $495,000, and $195,000,
respectively
6 What direct labor cost would be included in the company's flexible budget for March?
Answers
The direct labor cost included in the Preble Company's flexible budget for March is $819,000.
How to compute Preble Company's direct labor cost?To find the direct labor cost included in the company's flexible budget for March, we shall estimate the actual direct labor cost incurred during the period.
Given:
Actual production and sales =n26,600 units
Actual direct labor rate = $13.00 per hour
Actual direct labor hours worked = 63,000 hours
Direct labor cost = Actual direct labor rate × Actual direct labor hours worked
Direct labor cost = $13.00/hour × 63,000 hours
Direct labor cost = $819,000
Hence, the direct labor cost included in the company's flexible budget for March would be $819,000.
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Solve the simultaneous equations using elimination method= x+2y-3z=0 3x+3y-z = 5 x-2y = 2z=1
Answers
Answer:
[1;1;1]
Step-by-step explanation:
try this option; all the details are in the attachment.
Grace are in $7 dollars for each car she washes she always saves $20 of her weekly earnings this week she wants to have at least $67 in spending money how many cars machine wash enter and solve any quality to represent the situation into your value as a simplified mixed number if necessary
Answers
Answer:
12 21/50 (12.42) cars
Step-by-step explanation:
20+67= 87
87÷7=12.42
A wallet contains 34 notes, all of which are either $5 or $10 notes. If it amounts to $235, how many $10 notes are there?
Answers
According to the problem, we know that:
- x + y = 34 (since the wallet contains a total of 34 notes)
- 5x + 10y = 235 (since the total amount of money in the wallet is $235)
We can use the first equation to solve for x in terms of y:
x = 34 - y
Substituting this expression for x into the second equation, we get:
5(34 - y) + 10y = 235
Simplifying and solving for y, we get:
y = 15
Therefore, there are 15 $10 notes in the wallet.
Answer:
For this question, you can use the simultaneous equation to solve this problem.
Equation 1 reads: x + y = 34. (There are 34 notes in total.)
Equation 2: 5x + 10y = 235 (The notes are worth a total of $235.)
To find x in terms of y, we can apply equation 1:
x = 34 - y
When we use this expression to replace x in equation 2, we obtain:
5(34 - y) + 10y = 235
By condensing and figuring out y, we get at:
y = 15
There are 15 $10 bills in the wallet as a result.
Compute the missing x and y values so that each ordered pair will satisfy the given equation y=2x+4
Answers
The missing ordered pairs that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).
The equation given is y = 2x + 4. To compute the missing x and y values, we need to substitute the given ordered pairs into the equation and solve for the missing variable.
Let's assume we have an ordered pair (x, y) that satisfies the equation y = 2x + 4.
For example, let's say one missing value is x = 3. We can substitute this into the equation:
y = 2(3) + 4
y = 6 + 4
y = 10
So, the missing ordered pair is (3, 10).
Similarly, if another missing value is y = 8, we can substitute this into the equation and solve for x:
8 = 2x + 4
4 = 2x
x = 2
So, the missing ordered pair is (2, 8).
In summary, the missing x and y values that satisfy the equation y = 2x + 4 are (3, 10) and (2, 8).
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Express the product of Prime factor of 17325
Answers
Answer: 3 x 3 x 5 x 5 x 7 x 11.
Step-by-step explanation:
Prime Factors of 17325 are 3, 5, 7, 11, and usually expressed as 3 x 3 x 5 x 5 x 7 x 11.
Sharla invests $275 in a simple interest bearing account for 16 years. The annual interest rate is 8%. Using the simple
interest formula, / -Prt, how much interest will Sharla's initial investment earn over the 16 year period?
$297
$319
$352
$627
Answers
Answer:
352
Step-by-step explanation:
I = PRT where P is the principle, I is the interest rate, T is the time
I = 275 ( .08) ( 16)
I = 352
A cylinder has a base diameter of 6 centimeters and a height of 15 centimeters. What is its volume in cubic centimeters, to the narest tenth place
Answers
The calculated volume of the cylinder is 424.3 cubic cm
How to determine the volume of the cylinderFrom the question, we have the following parameters that can be used in our computation:
Base diameter = 6 cm
Height = 15 cm
Using the above as a guide, we have the following:
r = 6/2 = 3
h = 15
So, we have
V = πr²h
Substitute the known values in the above equation, so, we have the following representation
V = 22/7 * 3² * 15
Evaluate
V = 424.3
Hence, the volume is 424.3 cubic cm
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Tanya has a collection of 52 rocks that she wants to put into display cases. Each display case can hold 8 rocks. Tanya divides to find how many cases
she needs.
52÷8=614
How many display cases will Tanya need?
A. 4
B. 6
C. 7
D. 8
E. 10
Answers
7 11/6 x 6 2/5
Please solve
Answers
In order to estimate the average time spent per student on the computer terminals at a local university, data were collected for a sample of 81 business students over a one-week period. Assume the population standard deviation is 1.8 hours. If the sample mean is 9 hours, then the 95% confidence interval is
Answers
Answer:
(8.608, 9.392)
Step-by-step explanation:
We have the following information
Population standard deviation = 1.8
Sample mean = 9 hours
Sample n = 81
C I = 95%
So level of significance
Alpha = 1-0.95
= 0.05
Z critical at 0.05/2
Z(0.025) = 1.96
The 95% c.i =
9+-(1.96)(1.8/√81)
9+-(1.96)(0.2)
(9-0.392)(9+0.392)
(8.608, 9.392)
This is the confidence interval at 95%.
I hope you find my solution useful. Good luck!!!
Nate has a deductible of $1,000 and a collision coverage limit of $5,000. He damages his car in an accident and it will cost $7,000 to repair. How much does Nate have to pay total out of pocket for this claim?
Answers
Nate has a deductible of $1,000, which means he is responsible for paying that amount out of pocket before his insurance coverage kicks in. The cost of repairing his car is $7,000, which exceeds his deductible.
However, Nate's collision coverage limit is $5,000, which is the maximum amount his insurance will cover for repairs.
Since the cost of repairs exceeds Nate's coverage limit, he will have to pay the difference between the coverage limit and the actual repair cost.
In this case, Nate's out-of-pocket expenses would be $7,000 (repair cost) - $5,000 (coverage limit) = $2,000.
Therefore, Nate will have to pay a total of $2,000 out of pocket for this claim, which includes his $1,000 deductible and the additional $1,000 that exceeds his coverage limit.
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Write an equation that represents the relationship. (Sorry for the bad picture)
Answers
A garden is to designed with a rectangular part in the middle with two semi-circles on the ends.
The dimensions of the rectangular portion are 18.4 feet long and 8.6 feet wide.
a) What is the area of one semi-circle at one end?
b) What is the area of the garden?
c) Find the area in square metres.
Answers
Given statement solution is :- a) The area of one semi-circle at one end is 58.09 square feet.
b) The area of the garden is 274.42 square feet.
c) The area in square metres is approximately 58.09 square feet.
The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.
a) To find the area of one semi-circle at one end, we need to calculate the area of a complete circle and then divide it by 2. The formula for the area of a circle is A = πr², where A represents the area and r is the radius.
Since the diameter of the semi-circle is equal to the width of the rectangular portion, which is 8.6 feet, the radius will be half of that, which is 8.6 / 2 = 4.3 feet.
Now we can calculate the area of the semi-circle:
A = (π * 4.3²) / 2
A ≈ 58.09 square feet
b) To find the area of the garden, we need to sum the area of the rectangular portion with the areas of the two semi-circles.
Area of the rectangular portion = length * width
Area of the rectangular portion = 18.4 feet * 8.6 feet
Area of the rectangular portion ≈ 158.24 square feet
Area of the two semi-circles = 2 * (area of one semi-circle)
Area of the two semi-circles ≈ 2 * 58.09 square feet
Area of the two semi-circles ≈ 116.18 square feet
Total area of the garden = area of the rectangular portion + area of the two semi-circles
Total area of the garden ≈ 158.24 square feet + 116.18 square feet
Total area of the garden ≈ 274.42 square feet
c) To convert the area from square feet to square meters, we need to know the conversion factor. Since 1 foot is approximately 0.3048 meters, we can use this conversion factor to convert the area.
Area in square meters = Total area of the garden * (0.3048)²
Area in square meters ≈ 274.42 square feet * 0.3048²
Area in square meters ≈ 25.49 square meters
Therefore, the area of one semi-circle at one end is approximately 58.09 square feet. The area of the garden is approximately 274.42 square feet, and the area in square meters is approximately 25.49 square meters.
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At a circus, 135 clowns are getting into cars. Blue cars hold 20 clowns and red cars only hold 15. There are a total of 8 cars. How many of each are there?
Answers
The number of blue cars and the number of red cars are 3 and 5 respectively
How to find how many of each car are there?Let b and r represent the number of blue cars and the number of red cars respectively.
There are a total of 8 cars, we have:
b + r = 8
There are 135 clowns in total. Blue cars hold 20 clowns and red cars only hold 15, we have:
20b + 15r = 135.
Thus, we have a system of equations with two variables:
b + r = 8 ---- (1)
20b + 15r = 135 ---- (2)
We can use elimination to solve for b and r.
Let's use elimination. Multiplying the first equation by 20 and second equation by 1:
20 * (b + r = 8) = 20b + 20r = 160 (subtract)
1 * (20b + 15r = 135) = 20b + 15r = 135
...............................................
5r = 25
...............................................
r = 25/5
r = 5
Using (1):
b + r = 8
b + 5 = 8
b = 8 - 5
b = 3
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