Answers
The answer is A. The game is strictly determined and the value of the game is -7.
What is matrix?A rectangular array of characters, numbers, or phrases arranged in rows and columns is known as a matrix.
Given matrix, where we have to find out, is the game strictly determined for the following matrix or not?
[tex]\left[\begin{array}{ccc}-7&7&-3\\3&8&6\\1&3&-3\end{array}\right][/tex]
Using the minimax theorem, we know that if the game is strictly determined, the value of the game is equal to the value of the saddle point. If the game is not strictly determined, the value of the game may not exist or may be a range of values.
We can check each row and column for minimum and maximum values:
The minimum value in the first row is -7.
The maximum value in the second column is 7.
The minimum value in the third row is -3.
We can see that the element in the first row and second column is both the minimum in its row (-7) and the maximum in its column (7), so it is a saddle point. Therefore, the game is strictly determined and the value of the game is -7.
The answer is A. The game is strictly determined and the value of the game is -7.
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Related Questions
Your firm purchases large shipments of a component, subject to the requirement that not more than 4% of a shipment may be defective. If a random sample of 200 parts from a new shipment reveals 12 defectives, can you reject this shipment as not meeting requirements, at the 5% level of significance?
Answers
Answer:
see the attachment
Step-by-step explanation:
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the shipment does not meet requirements.
Given the function I need to evaluate question a)
Answers
Answer:
a) p(-6) = 30
b) c = -2 ,1
Step-by-step explanation:
[tex]p(c)=c^2+c[/tex]
a) Evaluate p(-6)
This mean input -6 into the equation to solve for p(-6) =
[tex]p(-6)=(-6)^2+(-6)\\\\p(-6)=36-6\\\\p(-6)=30\\[/tex]
(b) Solve for p(c) = 2.
[tex]p(c)=c^2+c\\\\2=c^2+c\\\\c^2+c=2\\\\c^2+c-2=0\\\\Factoring\\(c+2)(c-1)=0\\(c+2)=0,(c-1)=0\\c = -2 , 1[/tex]
P(-4)
P(-4)=(-4)^2+(-4)
P(-4)=16-4
P(-4)=12
Divide 240g in the ratio 5: 3: 4.method
Answers
To divide 240g in the ratio 5:3:4, we need to find out the total number of parts of the ratio:
5 + 3 + 4 = 12
Now, we can find the value of one part of the ratio by dividing the total quantity by the total number of parts:
240g ÷ 12 = 20g
So, one part of the ratio is equal to 20g.
To find the quantities of each part of the ratio, we multiply the value of one part by the respective ratio number:
5 parts x 20g = 100g (for the first part)
3 parts x 20g = 60g (for the second part)
4 parts x 20g = 80g (for the third part)
Therefore, the quantities of 240g divided in the ratio 5:3:4 are 100g, 60g, and 80g respectively.
NEED HELP ASSIGNMENT DUE IN AN HOUR WOULD BE MUCH APPRECIATED!
Answers
Let y = f(x). Then we have:
y = 3/(7x + 1)
Multiplying both sides by 7x + 1, we get:
y(7x + 1) = 3
Expanding the left side, we get:
7xy + y = 3
Subtracting y from both sides, we get:
7xy = 3 - y
Dividing both sides by 7y, we get:
x = (3 - y)/(7y)
Therefore, the inverse of f(x) is:
f^-1(x) = (3 - x)/(7x)
Explanation: To find the inverse function, we set y = f(x) and solve for x. By isolating x on one side of the equation in terms of y, we obtain the inverse function.
B. Let g(x) = (3 - x)/(7x). We need to verify that (f(g(x))) = x for all values of x in the domain of f(x) and g(x).
We have:
f(g(x)) = f((3 - x)/(7x)) = 3/(7((3 - x)/(7x)) + 1) = 3/(3 - x + 7x)/(7x) = 3/(3 + 6x)/(7x) = (21x)/(3 + 6x) = 7x/(1 + 2x)
To show that (f(g(x))) = x, we need to show that:
7x/(1 + 2x) = x
Multiplying both sides by (1 + 2x), we get:
7x = x(1 + 2x)
Expanding the right side, we get:
7x = x + 2x^2
Subtracting 7x from both sides, we get:
0 = x + 2x^2 - 7x
Simplifying, we get:
2x^2 - 6x = 0
Dividing both sides by 2x, we get:
x - 3 = 0
Therefore, x = 3.
Since we have shown that (f(g(x))) = x for x = 3 (which is in the domain of both f(x) and g(x)), we can conclude that g(x) is the inverse of f(x).
C. We cannot answer part C of the question because no function is given. The table provided only shows a set of input-output pairs, but we need the function itself to perform any further analysis.
The domain and range of the inverse function f^-1(x) = (3 - x)/(7x) depend on the domain and range of the original function f(x) = 3/(7x + 1).
The domain of f(x) is all real numbers except -1/7 (since division by zero is undefined). Therefore, the range of f^-1(x) is all real numbers except 0, since division by zero is also undefined.
To find the domain of f^-1(x), we can consider the denominator of the expression for f^-1(x), which is 7x. Since division by zero is undefined, we need to exclude any value of x that makes the denominator equal to zero. Therefore, the domain of f^-1(x) is all real numbers except 0.
In summary:
Domain of f^-1(x): All real numbers except 0
Range of f^-1(x): All real numbers except 0
3x(x-3)=12 How do you solve this
Answers
Step-by-step explanation:
3x squared -9 = 12
3x squared = 12 + 9
3x squared = 21
am i doing the wrong maths?
is it find what 3x squared is or....
point z is the circumcenter of triangle tub what is the value of uv
Answers
The measure of angle ZUB is 32.8°.
What precisely is a triangle?A triangle is a closed, double-symmetrical object composed of three line segments known as sides that intersect at three points known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides.
Triangles are classified as acute (all angles are less than 90 degrees), okay (one angle is equal to 90 degrees), or orbicular (all angles are greater than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighborhood, b is the triangle's base, and h is the triangle's height.
Since the angles given are 90 degrees and 57.2 yοu can add thοse tοgether then subtract them frοm 180 tο find the answer.
180 - 90 + 57.2 = 32.8
Thus,
32.8° is the answer.
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Complete question:
Point Z is the circumcenter of ΔTUV.
Point Z is the circumcenter of triangle T U V. Lines are drawn from each point of the triangle to point Z. Lines are drawn from point Z to each side to form right angles and line segments Z A, Z B, and Z C. The line segments cut the sides into 2 equal parts. Angle Z T B is 32.8 degrees and angle B Z U is 57.2 degrees.
What is m Angle ZUB?
23.7°
32.8°
33.5°
57.2°
If cos 55° = p determine the value of cos 5° in terms of p.
Answers
Answer:
Step-by-step explanation:
We can use the identity for the cosine of the sum of two angles:
cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
In this case, we can write:
cos(60°) = cos(55° + 5°) = cos(55°)cos(5°) - sin(55°)sin(5°)
We know that cos(60°) = 1/2, and we also know that cos(55°) = p. We can solve for cos(5°):
1/2 = p cos(5°) - sin(55°)sin(5°)
sin(55°)sin(5°) = p cos(5°) - 1/2
We also know that sin²(55°) + cos²(55°) = 1, so:
sin²(55°) = 1 - cos²(55°) = 1 - p²
Substituting this into the previous equation:
(1 - p²)sin(5°)² = p cos(5°) - 1/2
Rearranging and factoring:
p cos(5°) = 1/2 - (1 - p²)sin(5°)²
Using the fact that sin²(5°) + cos²(5°) = 1, we can substitute cos²(5°) = 1 - sin²(5°):
p cos(5°) = 1/2 - (1 - p²)(1 - cos²(5°))
Simplifying:
p cos(5°) = 1/2 - (1 - p²) + (1 - p²)cos²(5°)
p cos(5°) = 1 - 2p² + (2p² - 1)cos²(5°)
Solving for cos²(5°):
cos²(5°) = (1 - p cos(5°) + 2p²) / (2p² - 1)
Substituting the value we found for p, cos²(55°) = p²:
cos²(5°) = (1 - p cos(5°) + 2cos²(55°)) / (2cos²(55°) - 1)
Finally, substituting p = cos(55°):
cos²(5°) = (1 - cos²(55°) cos(5°) + 2cos²(55°)) / (2cos²(55°) - 1)
cos²(5°) = (2cos²(55°) - cos²(55°) cos(5°) + 1) / (2cos²(55°) - 1)
cos²(5°) = (cos²(55°) + 1) / (2cos²(55°) - 1)
Therefore, the value of cos 5° in terms of p = cos 55° is:
cos 5° = ±sqrt[(cos²(55°) + 1) / (2cos²(55°) - 1)]
Note that the sign of the square root is determined by the quadrant in which 5° lies. Since 5° is in the first quadrant, cos 5° is positive.
Devon wants to plant 84 tomato plants in his garden.
He wants to put 7 plants in each row. How many rows
will he need?
Answers
84 tomatos/7 in each row
What referents would you use to estimate the length, in both SI units and imperial units, of the Victoria (Old Traffic) Bridge in Saskatoon? Explain how you could measure the length in both units.
Answers
Step-by-step explanation:
The Victoria (Old Traffic) Bridge in Saskatoon, Canada, has a length of approximately 230 meters (755 feet). To estimate the length of the bridge in both SI and imperial units, you can use the following referents:
SI Units:
To estimate the length of the bridge in SI units, you can use meters as the referent. The length of the Victoria Bridge can be measured using a distance measuring device such as a surveyor's wheel, a laser distance meter, or a tape measure. You can start at one end of the bridge and measure the distance to the other end. This will give you an accurate measurement of the length of the bridge in meters.
Imperial Units:
To estimate the length of the bridge in imperial units, you can use feet as the referent. You can use a tape measure or a distance measuring wheel that measures in feet. You can start at one end of the bridge and measure the distance to the other end. This will give you an accurate measurement of the length of the bridge in feet.
To convert the length from meters to feet or vice versa, you can use the following conversion factors:
1 meter = 3.28 feet
1 foot = 0.3048 meters
Therefore, to convert the length of the Victoria Bridge from meters to feet, you can multiply the length in meters by 3.28. For example, 230 meters x 3.28 = 754.4 feet (rounded to the nearest tenth).
To convert the length of the Victoria Bridge from feet to meters, you can multiply the length in feet by 0.3048. For example, 755 feet x 0.3048 = 230.1 meters (rounded to the nearest tenth).
Marilou,a buyer of lot,pays Php10,000 every month for ten years.If money is 8%compoundef annually,how much is the cash value of the lot?
Answers
Answer:1,200,000
Step-by-step explanation:
Which of the loans should you try to pay off first?
A. a loan for $3,400 at 16%
B. a loan for $3,500 at 15%
C. a loan for $3,600 at 14%
D. a loan for $3,700 at 13%
Answers
A loan for $3,400 at 16% should be paid first as it has the highest interest rate.
What is loan?A loan is a financial agreement in which one party (the lender) agrees to give money, property, or other assets to another party (the borrower) in exchange for the promise of repayment with interest or other charges. Loans are typically used by individuals, businesses, or governments to finance specific projects, make purchases, or cover expenses.
Assuming that all other factors such as minimum payments and penalties are the same, the loan that you should try to pay off first is the one with the highest interest rate, as it will be accruing interest at a faster rate than the others.
Based on this reasoning, the loan that you should try to pay off first is option A, which has a higher interest rate of 16%.
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Find each angle measure to the nearest degree.
Answers
Answer:
5) A = 70°
6) X = 55°
7) Y = 8°
8) A = 51°
Step-by-step explanation:
There really no way to explain. All you ahve to do is inverse function to solve for the angle. Use a calculator.
5) sin(A) = 0.9397
[tex]A=sin^-1(0.9397)\\\\A=69.701...\\\\A = 70\\[/tex]
6) cos(X) = 0.5763
[tex]X=cos^-1(0.5763)\\\\X=54.998...\\\\X=55\\[/tex]
7) tan(Y) = 0.1405
[tex]Y=tan^-1(0.1405)\\\\Y=7.997...\\\\Y = 8\\[/tex]
8) sin(A) = 0.7771
[tex]A=sin^-1(0.7771)\\\\A=50.995...\\\\A = 51\\[/tex]
6.5 practice the measure of the exterior of a triangle is equal to the sum of the remote interior angles?
Answers
Answer:
Step-by-step explanation:
Yes, that is correct. The measure of the exterior angle of a triangle is equal to the sum of the two remote interior angles. In other words, if you extend one side of a triangle to form an exterior angle, then the measure of that exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to the exterior angle. This property is known as the Exterior Angle Theorem.
Mathematically, we can express this as:
Exterior angle = Sum of remote interior angles
Or, in symbols:
∠ABC = ∠A + ∠C
where ∠ABC is the exterior angle formed by extending side BC of triangle ABC, and ∠A and ∠C are the two remote interior angles.
Here are two more examples that illustrate the Exterior Angle Theorem:
Example 1:
Consider a triangle ABC with angles A, B, and C as shown below. If we extend side AC to form an exterior angle, then we can label the exterior angle as ∠DCE. The remote interior angles are ∠B and ∠A.
css
Copy code
C
/ \
/ \
/ \
/ \
/ \
/______\
A B
D
According to the Exterior Angle Theorem, we have:
∠DCE = ∠B + ∠A
HELP ME ASAP I NEED A NUMERICAL ANSWER
Owen's Muffin Extravaganza recorded how many of each type of muffin it recently sold.
bran muffins 25
blueberry muffins 12
poppy seed muffins 3
chocolate chip muffins 10
Considering this data, how many of the next 16 muffins sold would you expect to be bran muffins?
Answers
After answering the given query, we can state that Therefore, we can function anticipate that 8 to 16 of the upcoming pastries will be bran muffins.
what is function?Mathematicians research numbers, their variations, equations, associated structures, shapes, and possible configurations of these. The relationship between a group of inputs, each of which has a corresponding outcome, is referred to as a "function." A function is a relationship between inputs and outputs where each input results in a unique, distinct output. Each function has a domain, codomain, or scope assigned to it. Functions are commonly denoted by the letter f. (x). An cross is entered. On functions, one-to-one capabilities, so several capabilities, in capabilities, and on functions are the four main categories of available functions.
We must determine the percentage of muffins that were bran muffins in the prior sales in order to determine how many of the subsequent 16 muffins sold would be bran muffins.
In the prior auction, the following amount of muffins were sold in total:
25 + 12 + 3 + 10 = 50
The percentage of muffins that were wheat muffins is as follows:
25/50 = 0.5
This indicates that wheat muffins accounted for 50% of all sales.
This ratio can be used to make a forecast about how many bran muffins will be sold over the course of the following 16 muffins. Therefore, we anticipate that roughly 50% of the subsequent 16 batches of muffins sold will be wheat muffins:
0.5 x 16 = 8
Therefore, we can anticipate that 8 to 16 of the upcoming pastries will be bran muffins.
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The road is 7m wide. The Corner is in the shape of a quarter of a Cude the inside radius of the Corner is 70m. Ali Walks round the Corner on the inside, from A to B, Obi walks round the Corner On Obe Outside from C Go D. How much further does Obi walk than Ali? use the Value 22 for To- 7
Answers
C = 2πr = 2π(70) ≈ 439.82 m
Since the corner is a quarter of a cube, its length is equal to one-fourth of the cube's edge length, which is:
l = (1/4) x 22 = 5.5 m
The distance Ali walks from A to B is equal to the length of the inside of the corner, which is approximately 439.82 m.
To find the distance Obi walks from C to D, we need to calculate the length of the path around the outside of the corner. The outside radius of the corner is equal to the sum of the inside radius and the width of the road, which is:
r' = r + w = 70 + 7 = 77 m
The length of the path around the outside of the corner is:
L = 2πr' = 2π(77) ≈ 483.43 m
Since Obi walks around the outside of the corner, he walks a distance that is greater than the distance Ali walks on the inside. Therefore, Obi walks:
483.43 m - 439.82 m = 43.61 m
further than Ali.
The following events occur for The Turner Corporation during 2024 and 2025, its first two years of operations.
June 12, 2024 Provide services to customers on account for $35,000.
September 17, 2024 Receive $20,000 from customers on account.
December 31, 2024 Estimate that 40% of accounts receivable at the end of the year will not be received.
March 4, 2025 Provide services to customers on account for $50,000.
May 20, 2025 Receive $10,000 from customers for services provided in 2024.
July 2, 2025 Write off the remaining amounts owed from services provided in 2024.
October 19, 2025 Receive $40,000 from customers for services provided in 2025.
December 31, 2025 Estimate that 40% of accounts receivable at the end of the year will not be received.
Required:
1. Record transactions for each date.
2. Post transactions to the following accounts: Cash, Accounts Receivable, and Allowance for Uncollectible Accounts.
3. Calculate net accounts receivable reported in the balance sheet at the end of 2024 and 2025
How to calculate
July 2, 2025 Write off the remaining amounts owed from services provided in 2024.
Answers
Net accounts receivable is calculated by subtracting allowance for uncollectible from gross accounts receivable.
1- The journal entries are used to record the business transactions.
2- Ledger accounts are used to summarize thee recorded transactions.
3- Net accounts receivable (2024) = 8,640
Net accounts receivable (2025) = 4,280
1. The Turner Corporation's transactions are recorded as follows:
Date Account Title Debit Credit Journal Entries
Accounts Receivable $35,000 on June 12, 2024
$35,000 in revenue from services
Cash $20,000, September 17, 2024
$20,000 in accounts receivable
Bad Debt Cost $5,760 as of December 31, 2024
Uncollectible Allowance: $5,760
Accounts Receivable $46,400 on March 4, 2025
$46,400 in revenue from services
Cash $10,000, May 20, 2025
$10,000 in Accounts Receivable
Allowance for Uncollectible $4,400 on July 2, 2025
$4,400 in Accounts Receivable
On October 19, 2025, the cash value is $40,000.
$40,000 in accounts receivable
Bad Debts Cost $2,400 on December 31, 2025
Uncollectible Allowance: $2,400
2. The following is the procedure for posting transactions to the chosen accounts:
Account Titles Debit Credit Cash Account Date Account Titles Debit Credit
Accounts Receivable $17,000 on September 17, 2024
Accounts Receivable $10,000 on May 20, 2025
The date is October 19, 2025 $37,000 in accounts receivable
Date Account Titles Debit Credit Accounts Receivable
Service Revenue of $31,400 on June 12, 2024
17th of September, 2024, $17,000 cash
$46,400 in service revenue on March 4, 2025
$10,000 cash, May 20, 2025
Allowance for Uncollectible Accounts $4,400 on July 2, 2025
On October 19, 2025, a cash payment of $37,000 is made.
Balance $9,400 on December 31, 202 $77,800
Provision for Uncollectible Accounts
Debit Credit Date Account Titles
Bad debt expense of $5,760 as of December 31, 2024
Accounts Receivable $4,400 on July 2, 2025
Bad Debts Cost $2,400 as of December 31, 2025
Balance of $3,760 at the end of December 2025
3. The balance sheet net accounts receivable at the end of 2024 and 2025 include:
Net accounts receivable = $8,640 in 2024
Net accounts receivable = $5,640 in 2025.
Transaction Analysis: Accounts Receivable $31,400 on June 12, 2024 $31,400 in service revenue September 17, 2024, $17,000 Cash Accounts Receivable $17,000
Bad Debt Cost $5,760 as of December 31, 2024 Provision for Uncollectible Accounts $5,760 ($31,400 minus $17,000 multiplied by 40%)
Accounts Receivable $50,000 on March 4, 2025 $50,000 in service revenue
May 20, 2025, $10,000 Cash Accounts $10,000 is available for receipt.
Allowance for Uncollectible Accounts $4,400 Accounts Receivable $4,400 July 2, 2025
The date is October 19, 2025. $37,000 in cash and accounts Receivable: $37,000
Bad Debts Cost $2,400 on December 31, 2025 Uncollectible Accounts Allowance $2,400
Net Accounts Receivable: $8,640 in 2024 ($14,400 - $5,760)
2025: $5,640 ($9,400 - $3,760).
can someone please help me
please show work
Answers
The arc length and area of each circle sector is:
Case 1: s = 121π / 12 yd, A = 1331π / 24 yd²
Case 2: s = 35π / 3 in, A = 245π / 3 in²
Case 3: s = 17π / 6 ft, A = 17π / 4 ft²
Case 4: s = 11π / 2 in, A = 33π / 2 in²
Case 5: s = 116π / 9 yd, A = 928π / 9 yd²
Case 6: s = 13π / 12 ft, A = 13π / 8 ft²
How to determine the arc length and the area of a circle sector
In this problem we need to determine the arc length (s), in yards or inches, and the area (A), in square yards or square inches, of a circle sector, whose formulas are listed below:
Arc length
s = (θ / 180) · π · r
Area
A = 0.5 · (θ / 180) · π · r²
Where:
θ - Measure of the central angle, in degrees. r - Radius, in yards or inches.Now we proceed to determine the arc length and the area for each case:
Case 1 (r = 11 yd, θ = 165°)
s = (165 / 180) · π · 11
s = 121π / 12 yd
A = 0.5 · (165 / 180) · π · 11²
A = 1331π / 24 yd²
Case 2 (r = 14 in, θ = 150°)
s = (150 / 180) · π · 14
s = 35π / 3 in
A = 0.5 · (150 / 180) · π · 14²
A = 245π / 3 in²
Case 3 (r = 3 ft, θ = 170°)
s = (170 / 180) · π · 3
s = 17π / 6 ft
A = 0.5 · (170 / 180) · π · 3²
A = 17π / 4 ft²
Case 4 (r = 6 in, θ = 165°)
s = (165 / 180) · π · 6
s = 11π / 2 in
A = 0.5 · (165 / 180) · π · 6²
A = 33π / 2 in²
Case 5 (r = 16 yd, θ = 145°)
s = (145 / 180) · π · 16
s = 116π / 9 yd
A = 0.5 · (145 / 180) · π · 16²
A = 928π / 9 yd²
Case 6 (r = 3 ft, θ = 65°)
s = (65 / 180) · π · 3
s = 13π / 12 ft
A = 0.5 · (65 / 180) · π · 3²
A = 13π / 8 ft²
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What is the area of this trapezoid?
Enter your answer in the box.
Answers
Answer:
80
Step-by-step explanation:
In triangle ABC, the length of side AB is 16 inches and the length of side BC is 25 inches. Which of the following could be the length
of side AC?
A. 29 inches
B. 46 inches
C. 43 inches
D. 7 inches
Answers
After answering the presented question, we can conclude that triangle Therefore, the answer is A. 29 inches, since it falls within this range.
What precisely is a triangle?A triangle is a closed, double-symmetrical shape composed of three line segments known as sides that intersect at three places known as vertices. Triangles are distinguished by their sides and angles. Triangles can be equilateral (all factions equal), isosceles, or scalene based on their sides. Triangles are classified as acute (all angles are fewer than 90 degrees), good (one angle is equal to 90 degrees), or orbicular (all angles are higher than 90 degrees) (all angles greater than 90 degrees). The region of a triangle can be calculated using the formula A = (1/2)bh, where an is the neighbourhood, b is the triangle's base, and h is the triangle's height.
So, for triangle ABC with sides AB, BC, and AC, we have:
[tex]AB + BC > AC\\16 + 25 > AC\\41 > AC\\BC + AC > AB\\25 + AC > 16\\AC > -9 \\AB + AC > BC\\16 + AC > 25\\AC > 9\\[/tex]
So, the possible lengths of side AC are between 9 and 41 inches.
Therefore, the answer is A. 29 inches, since it falls within this range.
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work out the question
23 - 81 =
Answers
The mathematical expression 23 - √81 has a value of 14 when evaluated, mathematically
How to evaluate the expressionGiven the following expression
23 - √81
The expression 23 - √81 involves finding the difference between the number 23 and the square root of 81.
We know that the square root of 81 is 9, so we can simplify the expression to:
23 - √81 = 23 - 9
Evaluate the difference
23 - √81 = 14
Therefore, the value of the expression is 14.
In evaluating expressions like these, it is important to be familiar with basic arithmetic operations and the rules of exponents and radicals.
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) Using matrix method solve the following simultaneous equations 1x + 4y = 9 2x – 3y = 7
Answers
Answer: To solve the system of equations using the matrix method, we first need to set up the corresponding coefficient matrix and augmented matrix:
Coefficient matrix:
[1 4]
[2 -3]
Augmented matrix:
[1 4 | 9]
[2 -3 | 7]
To solve the system using matrix method, we perform row operations on the augmented matrix to get it into row echelon form, and then back substitute to obtain the solutions.
Performing row operations:
Multiply the first row by 2 and subtract the result from the second row:
[1 4 | 9]
[0 -11| -11]
Divide the second row by -11:
[1 4 | 9]
[0 1 | 1]
Subtract 4 times the second row from the first row:
[1 0 | 5]
[0 1 | 1]
The row echelon form of the augmented matrix is:
[1 0 | 5]
[0 1 | 1]
Therefore, the solution is x = 5 and y = 1.
So the solution of the system of equations is x = 5 and y = 1.
Step-by-step explanation:
Find the length of side � x in simplest radical form with a rational denominator. 30° 60° x 2
Answers
The length οf side x can be any value, as lοng as it is nοt 0.
We can use the trigοnοmetric ratiοs fοr 30°-60°-90° triangles tο sοlve fοr the value οf x.
In a 30°-60°-90° triangle, the sides are in the ratiο:
1 : √3 : 2
In this case, we have the side οppοsite the 60° angle (which is the lοnger leg) equal tο x√3 and the side οppοsite the 30° angle (which is the shοrter leg) equal tο x.
Sο we can set up the fοllοwing equatiοn:
x√3 = 2x sin 60°
Simplifying the right side:
sin 60° = √3/2
2x sin 60° = 2x(√3/2) = x√3
Substituting back intο the equatiοn:
x√3 = x√3
This is true fοr any value οf x, as lοng as x is nοt equal tο 0. Therefοre, the length οf side x can be any value, as lοng as it is nοt 0.
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The suspension cable that supports a footbridge hangs in the shape of a parabola. The height h, in feet, of the cable above the bridge is given by the function
h(x) = 0.25x ^ 2 - 0.8x + 30, 0 < x < 3.2
where x is the distance in feet measured from the left tower toward the right tower. What is the minimum height of the cable above the bridge? (Round your answer to two decimal places.)
Answers
Step-by-step explanation:
The height of the cable above the bridge is given by the function:
h(x) = 0.25x^2 - 0.8x + 30
To find the minimum height of the cable above the bridge, we need to find the vertex of the parabola, which is the lowest point.
The x-coordinate of the vertex is given by:
x = -b / 2a
where a = 0.25 and b = -0.8. Substituting these values, we get:
x = -(-0.8) / 2(0.25) = 1.6
So the vertex is at x = 1.6.
To find the height of the cable at the vertex, we substitute x = 1.6 into the equation for h(x):
h(1.6) = 0.25(1.6)^2 - 0.8(1.6) + 30 = 29.48
Therefore, the minimum height of the cable above the bridge is approximately 29.48 feet (rounded to two decimal places).
Which pizza can represent 3/4 of a pizza remaining?
Answers
Answer:
Step-by-step explanation:
C.
Find a quadratic function that includes the set of values below.
(0,7), (2,17), (3,16)
The equation of the parabola is Y
Answers
Y = aX^2 + bX + c
where Y is the output (dependent variable), X is the input (independent variable), and a, b, and c are constants that we need to solve for.
We can plug in the three sets of values given into this equation to get three equations:
7 = a(0)^2 + b(0) + c
17 = a(2)^2 + b(2) + c
16 = a(3)^2 + b(3) + c
Simplifying each equation, we get:
7 = c
17 = 4a + 2b + c
16 = 9a + 3b + c
Substituting c = 7 from the first equation into the other two equations, we get:
17 = 4a + 2b + 7
16 = 9a + 3b + 7
Simplifying these equations, we get:
4a + 2b = 10
9a + 3b = 9
We can solve this system of equations using substitution or elimination to find the values of a and b. I'll use elimination:
Multiplying the first equation by 3 and the second equation by -2, we get:
12a + 6b = 30
-18a - 6b = -18
Adding the two equations, we get:
-6a = 12
a = -2
Substituting a = -2 into one of the equations we got earlier (e.g. 4a + 2b = 10), we get:
4(-2) + 2b = 10
-8 + 2b = 10
2b = 18
b = 9
So the values of a and b are -2 and 9, respectively. Substituting these values into the general form of the quadratic function, we get:
Y = -2X^2 + 9X + 7
Therefore, the equation of the parabola is:
Y = -2X^2 + 9X + 7
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Replace the by >, < 0o = to make the sentence -4/9* -5/9
Answers
The inequality to replace the symbol is > and the expression is -4/9 > -5/9.
How to determine the inequality to replace the symbolWe can utilize the following parameters in our calculation based on the question:
-4/9* -5/9
Represent the symbol * as a blank
This gives
-4/9 [ ] -5/9
Evaluate the quotients
-0.44444444444 [ ] -0.55555555555
By comparison, 0.44444444444 is greater than -0.55555555555
Using the above as a guide, we have the following:
-0.44444444444 [ > ] -0.55555555555
So, we have
-4/9 > -5/9
Hence, the inequality is >
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please helpppp asap thank you !!:)
Answers
[tex]f(-11) = 3(-11)^{2} - 5 = 3(11)^{2} - 5 = 3(121) - 5 = 363-5= \bf 358[/tex]
Answer:D
Step-by-step explanation:
if x==-11
then,
f(-11) means you should write -11 in every x you see.
[tex]f(-11)=3*(-11)^{2} -5=3*121-5=363-5=358[/tex]
if i had 1000 apples and gave 39 away
how many wouldd i have left
Answers
Answer:
1000-39=961
so 961 apples are left.
x + 5 < 2
the solution is ??
Answers
Answer:
x < -3
Step-by-step explanation:
x + 5 < 2
x < -3
So, the answer is x < -3
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A) 3
B) 6
C) 9
D) 12
Answers
The value of x, considering the similar triangles, is given as follows:
B) 6.
What are similar triangles?Similar triangles are triangles that share these two features listed as follows:
Congruent angle measures, as both triangles have the same angle measures.Proportional side lengths, which helps us find the missing side lengths.Considering that the triangles for this problem are similar, the proportional relationship for the side lengths is given as follows:
9/3 = 12/4 = x/2.
Since the constant is of 3, the value of x is obtained with cross multiplication as follows:
x/2 = 3
x = 6.
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