Hello, let's note A the matrix, we need to find [tex]\lambda[/tex] such that A[tex]\lambda[/tex]=[tex]\lambda[/tex] I, where I is the identity matrix, so the determinant is 0, giving us the characteristic equation as
[tex]\left|\begin{array}{cc}1-\lambda&3\\-3&1-\lambda\end{array}\right|\\\\=(1-\lambda)^2+9\\\\=\lambda^2-2\lambda+10\\\\=0[/tex]
We just need to solve this equation using the discriminant.
[tex]\Delta=b^2-4ac=2^2-40=-36=(6i)^2[/tex]
And then the eigenvalues are.
[tex]\lambda_1=\dfrac{2-6i}{2}=\boxed{1-3i}\\\\\lambda_2=\boxed{1+3i}[/tex]
To find the basis, we have to solve the system of equations.
[tex]A\lambda_1-\lambda_1 I=\left[\begin{array}{cc}3i&3\\-3&3i\end{array}\right] \\\\=3\left[\begin{array}{cc}i&1\\-1&i\end{array}\right] \\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}ai+b=0\\-a+bi=0\end{cases}\\\\\text{(1,-i) is a base of this space, as i-i=0 and -1-}i^2\text{=-1+1=0.}[/tex]
[tex]A\lambda_2-\lambda_2 I=\left[\begin{array}{cc}-3i&3\\-3&-3i\end{array}\right] \\\\=3\left[\begin{array}{cc}-i&1\\-1&-i\end{array}\right]\\\\\text{For a vector (a,b), we need to find a and b such that.}\\\\\begin{cases}-ai+b=0\\-a-bi=0\end{cases}\\\\\text{(1,i) is a base of this space as -i+i=0 and -1-i*i=0.}[/tex]
Thank you
The solution to the compound inequality are____
Answer:
-1 < x ≤ 2
Step-by-step explanation:
-2 < 2x ≤ 4
Divide by 2
-2/2 < 2x/2 ≤ 4/2
-1 < x ≤ 2
Open circle at -1 line going to the right to a closed circle at 2
PLZZZZZZZZ HELP ME I WILL GIVE BRAINLIEST TO THE FASTEST AND MOST ACCURATE
HELP!! 30 POINTS!!! 2 and 3!!!
Replace x with each value and solve :
2 x 2^1 = 2 x 2 = 4
2 x 2^2 = 2 x 4 = 8
2x 2^3 = 2 x 8 = 16
2x 2^4 = 2 x 16 = 32
2 x 2^5 = 2 x 32 = 64
Now mark two points on the graph: (1,4) and (2,8) and draw a straight line though both points
The image is not rotated correctly...
Answer:
Q#2 y;; 4 8 16 32 64
Q#3 given below;
Step-by-step explanation:
Which of the following is the correct formula for distance?
(A.) d= (x2-x1)^2+(y2-y1)^2, where d is the distance between points (x1,y1) and (x2,y2).
(B.) d= sqrt (x2+x1)^2+(y2+y1)^2, where d is the distance between points (x1,y1) and (x2,y2).
(C.) d= sqrt (x2-x1)^2+(y2-y1)^2, where d is the distance between points (x1,y1) and (x2,y2).
(D.) d= sqrt (x2-x1)+(y2-y1), where d is the distance between points (x1,y1) and (x2,y2).
Answer:
(C.) d= sqrt (x2-x1)^2+(y2-y1)^2, where d is the distance between points (x1,y1) and (x2,y2).
Step-by-step explanation:
Answer:
[tex]\Huge \boxed{\mathrm{C }}[/tex]
Step-by-step explanation:
[tex]\sf The \ distance \ formula \ is \ given \ as:[/tex]
[tex]d=\sqrt{(x_2-x_1)^2 +(y_2-y_1)^2 }[/tex]
[tex]d \Rightarrow \sf distance[/tex]
[tex](x_1,y_1) \Rightarrow \sf Coordinates \ of \ the \ first \ point[/tex]
[tex](x_2,y_2) \Rightarrow \sf Coordinates \ of \ the \ second \ point[/tex]
A zookeeper divided 3,570 pounds of food equally among 7 elephants.
How many pounds of food did each elephant receive?
Each elephant received
pounds of food.
Answer:
[tex] \boxed{\sf Amount \ of \ food \ each \ elephant \ receive = 510 \ pounds} [/tex]
Given:
Total amount of food = 3,570 pounds
Total number of elephants = 7
To Find:
Amount of food each elephant receive
Step-by-step explanation:
7 elephants receive = 3,570 pounds
[tex] \sf 1 \: elephant \: receive = \frac{3570}{7} \: pounds[/tex]
= 510 pounds
So,
Amount of food each elephant receive = 510 pounds
What is the difference between 4 and 62
2.
Answer:
6214
Step-by-step explanation:
you round up 62 and 4 20 times and that is your answer but for give me if this answer wrong
A candy box is to be made out of a piece of cardboard that measures 8 by 12 inches. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a rectangular box. What size square should be cut from each corner to obtain a maximum volume
Answer:
Length of square cut = 1.569 inches
Step-by-step explanation:
given data
Length of cardboard = 12 inches
Breadth of cardboard = 8 inches
solution
we will consider here side of the square = x
when we cutting out the square then there Length and breadth of candy box will be
Length of box = (12 - x - x)
Length of box = (12 - 2x) inches.
and
Breadth of box = (8 - x - x)
Breadth of box = (8 - 2x) inches.
and Height of candy box wil be = x inches
so
Volume of a cuboid = L × b × h .....................1
Volume of a cuboid = (12 - 2x) × (8 - 2x) × x
Volume of a cuboid = 96x - 40x² + 4x³
now we Differentiate with respect to x
V' = 96 - 80x + 12x²
and for maximum volume we put V' = 0
0 = 96 - 80x + 12x²
solve it we get
x = 5.097
x = 1.569
when x = 5.097 inches
Breadth of candy box = 8 - 10.194 = -2.194 inches
but we know breadth never be negative,
so we take
Length of square cut = 1.569 inches
Alewuya recently hired a landscaper to do some necessary work. On the final bill, Alewuya was charged a total of $361. $265 was listed for parts and the rest for labor. If the hourly rate for labor was $32, how many hours of labor was needed to complete the job?
Answer:
361-265＝96
96÷32＝3
3hours of labor was needed to complete the job
What is the Area of the region shown below?
Answer:
B) 47 units²
Step-by-step explanation:
It can be done by finding the area of the black, but it will be much easier to find the area of the white and subtract.
Total area of the grid equals 10x8=80
There are two rectangles at the bottom. 6+8=14
There are 4 triangles that each equal 4.5. 4.5*4=18
There is 1 small triangle at the top that equals 1.
80-14-18-1=47
Interpret the results. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. nothing% of all random samples of people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints. B. It can be said that nothing% of the population has a driving distance to work (in miles) that is between the interval's endpoints. C. With nothing% confidence, it can be said that most driving distances to work (in miles) in the population are between the interval's endpoints. D. With nothing% confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints.
Answer:
With 99 % confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints [19.91 miles, 31.49 miles] .
Step-by-step explanation:
The complete question is: In a random sample of six people, the mean driving distance to work was 25.7 miles and the standard deviation was 6.7 miles. Assuming the population is normally distributed and using the t-distribution, a 99% confidence interval for the population mean mu is left parenthesis 14.7 comma 36.7 right parenthesis (and the margin of error is 11.0).
Through research, it has been found that the population standard deviation of driving distances to work is 5.5 . Using the standard normal distribution with the appropriate calculations for a standard deviation that is known, find the margin of error and construct a 99 % confidence interval for the population mean mu .
Interpret the results. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.)
A. nothing % of all random samples of six people from the population will have a mean driving distance to work (in miles) that is between the interval's endpoints.
B. With nothing % confidence, it can be said that most driving distances to work (in miles) in the population are between the interval's endpoints.
C. It can be said that nothing % of the population has a driving distance to work (in miles) that is between the interval's endpoints.
D. With nothing % confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints.
We are given that in a random sample of six people, the mean driving distance to work was 25.7 miles and the standard deviation was 6.7 miles.
Through research, it has been found that the population standard deviation of driving distances to work is 5.5 .
Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;
P.Q. = [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\bar X[/tex] = sample mean driving distance to work = 25.7 miles
[tex]\sigma[/tex] = population standard deviation = 5.5 miles
n = sample of people = 6
[tex]\mu[/tex] = population mean driving distance to work
Here for constructing a 99% confidence interval we have used a One-sample z-test statistics because we know about the population standard deviation.
So, 99% confidence interval for the population mean, [tex]\mu[/tex] is ;
P(-2.58 < N(0,1) < 2.58) = 0.99 {As the critical value of z at 0.5% level
of significance are -2.58 & 2.58}
P(-2.58 < [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] < 2.58) = 0.99
P( [tex]-2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]{\bar X-\mu}[/tex] < [tex]2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.99
P( [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] < [tex]\mu[/tex] < [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ) = 0.99
99% confidence interval for [tex]\mu[/tex] = [ [tex]\bar X-2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] , [tex]\bar X+2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex] ]
= [ [tex]25.7-2.58 \times {\frac{5.5}{\sqrt{6} } }[/tex] , [tex]25.7+2.58 \times {\frac{5.5}{\sqrt{6} } }[/tex] ]
= [19.91, 31.49]
Therefore, a 99% confidence for the population mean is [19.91, 31.49] .
The margin of error here is = [tex]2.58 \times {\frac{\sigma}{\sqrt{n} } }[/tex]
= [tex]2.58 \times {\frac{5.5}{\sqrt{6} } }[/tex] = 5.793
With 99 % confidence, it can be said that the population mean driving distance to work (in miles) is between the interval's endpoints [19.91, 31.49] .
What is the area of a circle with a diameter of 6?
Answer:
[tex] \boxed{ \bold{ \huge{ \boxed{ \sf{28.28 \: }}}}}[/tex]
Step-by-step explanation:
Given, diameter of a circle = 6
pi ( π ) = 22 / 7
Finding the radius of the circle
We know that the radius of a circle is just half of the diameter. So, 6 / 2 = 3
Finding the area of circle having radius of 3
[tex] \boxed{ \sf{area \: of \: circle = \pi \: {r}^{2} }}[/tex]
plug the values
⇒[tex] \sf{area \: of \: circle = \frac{22}{7} \times {3}^{2} }[/tex]
Evaluate the power
⇒[tex] \sf{area \: of \: circle = \frac{22}{7} \times 9}[/tex]
Calculate
⇒[tex] \sf{area \:of \: circle = 28.28 \: }[/tex]
Hope I helped!
Best regards! :D
give another name for r
I would have to say its AB<----
But im not 100% sure I wish you luck.
You take the four Aces, four $2$'s, and four $3$'s from a standard deck of 52 cards, forming a set of $12$ cards. You then deal all $12$ cards at random to four players, so that each player gets three cards. What is the probability that each player gets an Ace, a $2$, and a $3$?
Answer:
Probability each player gets an ace, a $2 and a $3 = 0.0374
Step-by-step explanation:
The total number of ways to divide the card in triples among four players = 369600 ways
The total number of ways to share the cards such that no card is repeated in each triple = 13824 ways
Probability each player gets an ace, a $2 and a $3 = 13824/369600
Probability each player gets an ace a $2 and a $3 = 0.0374
Note: Further explanation is provided in the attachment.
Please, can someone help me with this problem? I would really appreciate it if you could explain the process too.
I’m really struggling, someone please help!
Hi there! :)
Answer:
[tex]\huge\boxed{C.}[/tex]
We can examine each answer choice individually:
A. 569 × 10² = 569 × (10 · 10) = 569 · 100 = 56,900. Therefore, this choice is incorrect.
B. 569 · 10 = 5,690. This choice is incorrect.
C. 10³ · 569 = (10 · 10 · 10) ·569 = 1000 · 569 = 569,000. This choice is correct.
D. 10² · 569 = (10 · 10) · 569 = 56,900. This choice is incorrect.
Therefore, the correct option is C.
Answer:
A. 569 × 10² = 569 × (10 · 10) = 569 · 100 = 56,900.
B. 569 · 10 = 5,690.
C. 10³ · 569 = (10 · 10 · 10) ·569 = 1000 · 569 = 569,000.
D. 10² · 569 = (10 · 10) · 569 = 56,900.
So your answer is C
Which statement about the two values of the digits 4 is correct 10 times more, 40 times more, 100 times more, 400 times more
In the number 1,034,456
Answer:
10 times more
Step-by-step explanation:
Step 1: Find the 2 '4' values
Value 1 is 400
Value 2 is 4,000
Step 2: Divide the lager number with the smaller number
4,000 / 400 = 10
Therefore the first digit is 10 times more than the second digit(Looking from left to right)
Perform the operation. (Write fractional answers in simplest form.) 8x/3 ÷ 6/7
Answer:
[tex]\frac{28x}{9}[/tex]
Step-by-step explanation:
Order of Operations: BPEMDAS
Step 1: Write out equation
[tex]\frac{8x}{3} /\frac{6}{7}[/tex]
Step 2: KCF (Keep Change Flip)
[tex]\frac{8x}{3} (\frac{7}{6})[/tex]
Step 3: Multiply
[tex]\frac{56x}{18}[/tex]
Step 4: Simplify
[tex]\frac{28x}{9}[/tex]
Answer:
28x/9
Step-by-step explanation:
Dividing a fraction by fraction is the same as multiplying a fraction by the other fraction's reciprocal:
Here is the formula:
[tex]\frac{x}{y} / \frac{a}{b} = \frac{x}{y} * \frac{b}{a}[/tex]
Thus, [tex]\frac{8x}{3} / \frac{6}{7} = \frac{8x}{3} * \frac{7}{6}[/tex]
8x * 7 = 56x and 3* 6 is 18, so:
[tex]\frac{56x}{18}[/tex]
It can be further simplified by dividing both numerator and denominator by 2:
[tex]\frac{28x}{9}[/tex]
round 5.36909546581 to 5 decimal places.
Answer:
5.36910
Step-by-step explanation
whatever you see like 95 can round up to 100.
5.369095... you just round up 95 to 100.
5 decimal is 5.36910
The number 5.36909546581 which is needed to be rounded off up to 5 decimal places is 5.36910.
What are decimal numbers?The decimal numeral system is the most widely used system for representing both integer and non-integer values. It is the Hindu-Arabic numeral system's expansion to non-integer numbers. The method of representing numbers in the decimal system is commonly referred to as decimal.
Given the number 5.36909546581 which is needed to be rounded off up to 5 decimal places. Therefore, if we look at the sixth place after the decimal it is equal to 5.
Thus, fifth place is needed to be rounded off to the next number.
Hence, the number 5.36909546581 which is needed to be rounded off up to 5 decimal places is 5.36910.
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Find the heigt and width of the box. PLEASE HELP I’m having a lot of trouble on this.
Answer:
The height and width are both 12 inches.
Step-by-step explanation:
2304/16=144
√144=12
What is the sum of ( − 5.5) and the product of 5 3 and the number that is 100 greater than (− 5.5)?
Answer:
- 5.5 + ( 5/3 ) x( 100-5.5) ( as per statement given)
-5.5 + (5/3)x(94.5) = -5.5 + 5x31.5 = -5.5 + 157.5
=152
Step-by-step explanation:
. Which sentence contains a proper noun? Users of electronic databases can check a library’s catalog to see which books are available. Using computers, people can obtain goods directly from manufacturers in other countries. The Internet is a communication network that gained popularity in the 1990s. With the capabilities provided by the computer, users can research products, services, and companies online.
Step-by-step explanation:
A proper noun is a specific name for a particular person, place, or thing.
The Internet is a communication network that gained popularity in the 1990s.
A proper noun should always start with a capital letter, whether at the start or middle of a sentence.
Convert 8 centimeters into yards. Round your answer to the nearest hundredth
Answer: 0.08 yards
Step-by-step explanation: 1 centimeter equals to about 0.01 yards. You have to multiple 0.01 to 8 and it will give 0.08 yards.
Answer:
x = 0,087489064
Step-by-step explanation:
1 cm = 0.010936133 yards
8 cm = x
x = 8 cm x 0.010936133 yards/ 1 cm
x = 0,087489064
Let L1 be the line containing points (8, -4) and (2, -5), and let L2 be the line containing points (10, 9) and (15, -21). Find the slope of each line.
x +x= telllllllllkkkll
Answer: X + X= 2x or X squared.
Step-by-step explanation:
Which is closest to the distance between A and B on the number
line?
A) -9
B) -5
C) 13
D) 5
E) 12
Answer:
C) 13
Step-by-step explanation:
A on the number line is about -5 and B is 8. Act as if there wasn't a negative sign in front of the 5. Add the two numbers together the get the distance.
claire and her classmates placed the colored block on a scale during a science lab the blue block weighed 0.9 pounds and the green block weighed 0.07 how much more did the blue block weigh than the green block?
Answer:
0.83
Step-by-step explanation:
.9 which is .90 minus the weight of the blue block which is.07 is equal to .83 thus making it your answer.
The blue block weighs 0.2 pounds more than the green block.
What is a numerical expression?A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.
The difference between the weights of the colored blocks is how more the blue block weighs than the green block which is,
= (0.9 - 0.7).
= 0.2 pounds.
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Sally had 150 dollars to spend on 9 books. After
buying them she had 15 dollars. How much did each book cost
Answer:
Each book costs $15 dollars
Step-by-step explanation
150-15=135
135/9=15
$15
At the sixth-grade school dance, there are 132 boys, 89 girls, and 14 adults. Write the ratio of the number of boys to the number of girls. Type your answer either in the format: 3:4 with no spaces, OR in the format 3 to 4.
Answer:
the ratio will be 132 to 89
The ratio is 132 : 89.
What is ratio?A comparison of two quantities by division is called a ratio and the equality of two ratios is called proportion. A ratio can be written in different forms like x : y or x/y and is commonly read as, x is to y.
Ratio is the comparison of two quantities which is obtained by dividing the first quantity by the other. If a and b are two quantities of the same kind and with the same units, such that b is not equal to 0, then the quotient a/b is called the ratio between a and b. Ratios are expressed using the symbol of the colon (:). This means that ratio a/b has no unit and it can be written as a : b
Given:
Boys= 132
girls= 89
adults= 14
So,
the ratio of number of boys to number of girls is
= 132/89
=132 : 89
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Video Example EXAMPLE 3 Find the local maximum and minimum values and saddle points of f(x, y) = x4 + y4 − 4xy + 1. SOLUTION We first locate the critical points:
Answer:
(0, 0) is a saddle point
(1, 1) is a local minimum
(-1, -1) is another point of local minimum
Step-by-step explanation:
We first locate the critical points. In order to get the critical points we need to find the first derivatives and then set them to zero.
f(x, y) = x⁴ + y⁴ - 4 xy + 1
Find the first derivatives wrt to x and y
[tex]f_{x}(x,y)[/tex] = 4x ³ - 4y --> (1)
[tex]f_{y}(x,y)[/tex] = 4y³ - 4x --> (2)
Solve (1) for y
4x ³ - 4y = 0
x ³ = y
y = x ³ ---> (3)
Solve (2) for x
4y³ - 4x = 0
4y³ = 4x
y³ = x
x = y³ ----> (4)
Plug (3) into (2)
4y³ - 4x
4(x ³)³ - 4x = 0
4x⁹ - 4x = 0
4x (x ⁸ - 1) = 0
4x (x ⁴ - 1)(x⁴ + 1) = 0
4x (x ² - 1)(x ² + 1)(x ⁴ + 1) = 0
4x (x - 1)(x + 1)(x ² + 1)(x ⁴ + 1) = 0
So
x = 1 , -1 , 0
In order to find values of y, Plug each x value in (3)
For
x = 0
corresponding y value
y = x ³
y = 0 ³
y = 0
For
x = 1
y = x ³
y = 1 ³
y = 1
For
x = -1
y = x ³
y = (-1 )³
y = -1
Hence we get the critical points which are:
(0, 0)
(1, 1) and
(-1, -1)
Now for each critical point, we have to compute D(x,y)
For a critical point (x,y), D computed as:
D(x, y) = [tex]f_{xx}[/tex] (x, y) - [tex]f_{yy}[/tex] (x, y) - ([tex]f_{xy}[/tex] (x, y))²
After computing D(x,y) check:
If D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) > 0:
f(x, y) is a local minimum.
If D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) < 0:
f(x, y) is a local maximum.
If D(x, y) < 0:
then f(x, y) is a saddle point
Here first compute the second derivative in order to get [tex]f_{xx}[/tex] , [tex]f_{yy}[/tex] and [tex]f_{xy}[/tex]
we have already computed:
[tex]f_{x}(x,y)[/tex] = 4x ³ - 4y --> (1)
[tex]f_{y}(x,y)[/tex] = 4y³ - 4x --> (2)
Now
[tex]f_{xx}(x,y)[/tex] = 12x²
[tex]f_{yy}(x,y)[/tex] = 12y²
[tex]f_{xy}(x,y)[/tex] = -4
Compute D(x,y)
Critical Point (0, 0):
[tex]D(0, 0) = f_{xx} (0,0) f_{yy}(0,0)-(f_{xy}(0,0))^{2}[/tex]
Putting values of [tex]f_{xx}(x,y)[/tex] , [tex]f_{yy}(x,y)[/tex] and [tex]f_{xy}(x,y)[/tex] in above equation:
D(0,0) = 12(0)² * 12(0)² - (-4)²
= 0 * 0 -16
D(0,0) = -16
We know that if D < 0, the critical point f(x, y) is a saddle point.
D(0,0) < 0 because D(0,0) = -16
Hence (0, 0) is a saddle point
Compute D(x,y)
Critical Point (1, 1):
[tex]D(1, 1) = f_{xx} (1,1) f_{yy}(1,1)-(f_{xy}(1,1))^{2}[/tex]
Putting values of [tex]f_{xx}(x,y)[/tex] , [tex]f_{yy}(x,y)[/tex] and [tex]f_{xy}(x,y)[/tex] in above equation:
D(1,1) = 12(1)² * 12(1)² - (-4)²
= 12 * 12 - 16
D(1,1) = 128
We know that if D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) > 0 then f(x, y) is a local minimum.
D(1,1) > 0 because D(1,1) = 128
[tex]f_{xx}[/tex] (x, y) > 0 because [tex]f_{xx}[/tex] (x, y) = 12
Hence (1,1) is the local minimum
Compute D(x,y)
Critical Point (-1, -1):
[tex]D(-1, -1) = f_{xx} (-1,-1) f_{yy}(-1,-1)-(f_{xy}(-1,-1))^{2}[/tex]
Putting values of [tex]f_{xx}(x,y)[/tex] , [tex]f_{yy}(x,y)[/tex] and [tex]f_{xy}(x,y)[/tex] in above equation:
D(-1,-1) = 12(-1)² * 12(-1)² - (-4)²
= 12 * 12 - 16
D(-1,-1) = 128
We know that if D(x, y) > 0 and [tex]f_{xx}[/tex] (x, y) > 0 then f(x, y) is a local minimum.
D(-1,-1) > 0 because D(-1,-1) = 128
[tex]f_{xx}[/tex] (x, y) > 0 because [tex]f_{xx}[/tex] (x, y) = 12
Hence (-1,-1) is the local minimum
Write the following relation as a linear equation in standard form. Include a space between terms and operations.
B={(x, y): (2, 3), (4,4), (6,5), ...}
Answer:
In the form of
Y= mx+c
Y= 1/2x +2
m = 1/2
Step-by-step explanation:
A linear equation in it's standard form is in the format
Y= mx+c
Where m is the slope and c is the y intercept
Let's use these two points to determine both the slope and the equation
(2, 3), (4,4)
Slope= (y2-y1)/(x2-x1)
Slope= (4-3)/(4-2)
Slope= 1/2
Equation of the linear function
(Y-y1)/(x-x1)= m
(Y-3)/(x-2)= 1/2
2(y-3) = x-2
2y -6 = x-2
2y= x-2+6
2y= x+4
Y= 1/2x +2