Is a graph a function or not?

The quotient A/B is equal to 42 + 84j, which corresponds to option b: 4 + j7.45.

To find the quotient A/B, we can perform complex division. Let's proceed with the calculation:

A/B = (68 + j16) / (2 - j4)

To simplify the expression, we can multiply the numerator and denominator by the conjugate of the denominator:

A/B = ((68 + j16) * (2 + j4)) / ((2 - j4) * (2 + j4))

Expanding the numerator and denominator:

A/B = ((68 * 2) + (68 * j4) + (j16 * 2) + (j16 * j4)) / ((2 * 2) + (2 * j4) - (j4 * 2) - (j4 * j4))

= (136 + j272 + j32 + j64) / (4 + j8 - j8 - j16)

= (136 + j272 + j32 + j64) / 4

Simplifying further:

A/B = (136 + j272 + j32 + j64) / 4

= (136 + j272 + j32 + j64) / 4

= (136 + 32) / 4 + (272 + 64) / 4j

= 168 / 4 + 336 / 4j

= 42 + 84j

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Answer:

B 2x - 31 = -2x - 31 have exactly one solution

Step-by-step explanation:

Which of the following equations have exactly one solution?

Choose all answers that apply:

A 2x - 31 = 2x - 31

B 2x - 31 = -2x - 31

C 2x + 31 = 2x - 31

D 2x - 2 = 2x - 31

A. 2x - 31 = 2x - 31

2x-31=2x-31

Collect like terms

2x-2x= -31+31

0=0

Infinite number of solutions

B 2x - 31 = -2x - 31

2x - 31 = -2x - 31

Collect like terms

2x+2x=-31+31

4x=0

x=0

One solution

C 2x + 31 = 2x - 31

2x + 31 = 2x - 31

Collect like terms

2x-2x= -31-31

0= -62

No solution

D 2x - 2 = 2x - 31

2x - 2 = 2x - 31

Collect like terms

2x-2x= -31+2

0= -29

No solution

Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.

An isomorphism is a bijective linear transformation, that is both one-to-one and onto. The determinant of a linear transformation can help determine if it is an isomorphism. If the determinant is non-zero, the linear transformation is invertible, and therefore an isomorphism. A linear transformation is an isomorphism if and only if its determinant is nonzero.
Additionally, another way to check if a linear transformation is an isomorphism is to check if the kernel, which is the set of all vectors that get mapped to zero, is equal to only the zero vector. If the kernel is only the zero vector, then the linear transformation is one-to-one and therefore an isomorphism.

Therefore, to determine if a linear transformation is an isomorphism, we can check if the determinant is non-zero or if the kernel is only the zero vector.

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Answer:

7

Step-by-step explanation:

Mean is all of your numbers added up and then divided by the amount of numbers in total there are. So 2+4+6+9+14 = 35 35÷5 = 7

Hope this helped <3

Answer:

Step-by-step explanation:

I think that you cut off the leading number in the BD segment 8cm appears to be truncated....

if that number was in the image....

BC would be sqrt(52.3 ^2 + ?.8^2)

if you  have BC then

sin(θ)/BC = sin(90)/18.6

Answer:

C

Step-by-step explanation:

give brainliest

Answer:

I believe it's SAS, but I am not 100% sure. I say this because you see the angle then in between is a side then another angle

The most direct way to measure how dispersed a set of scores is, is by using the range. The range is calculated by subtracting the lowest score from the highest score in the dataset, which gives a quick and easy measure of the spread of the scores.

However, the range can be influenced by extreme scores and may not provide a complete picture of the variability. Other measures of variability, such as the standard deviation and variance, take into account the variability of all scores in the dataset and provide a more robust measure of variability.

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When Cedric walked into a party, two-thirds of those invited had already arrived. Six more people arrived just after Cedric, bringing the number at the party to of those invited. The total number of invited guests is 18 by Linear equations

What was the total number of invited guests?

There are different methods of solving the problem, and we will use the following steps to get the solution of the problem: Let the total number of invited guests be x.Let's solve the problem with a step-by-step explanation.

Step 1: At the time Cedric arrived, two-thirds of the guests were already present.Let the number of guests present at the party when Cedric arrived be A. Therefore, A = (2/3)x

Step 2: Six more people arrived after Cedric got there. Therefore, the total number of guests after the six people arrived is A + 6.

Step 3: The total number of guests present was also x, which is the total number of guests invited. Therefore A + 6 = x.

Step 4: Substitute A = (2/3)x from Step 1 into A + 6 = x from Step 3 to obtain: (2/3)x + 6 = xStep 5: To solve for x, we will get rid of the fraction by multiplying every term by 3x.

Then we will simplify. 3x * (2/3)x + 3x * 6 = 3x * x Simplifying further  2x + 18 = 3x Subtracting 2x from both sides of the equation 18 = x.

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Answer:

Its the 2nd Dot

Step-by-step explanation:

Answer:

Solution given:

A(a,b) lie in 6x-y =1

substituting value of A in equation ,we get

6a-b=1...................(1)

B(b,a) lie in 2x - 5y = 5

substituting value of B in equation ,we get

2b-5a=5

b=5(a+1)/2............(2)

substituting value of b in equation 1 ,we get

6a-5(a+1)/2=1

12a-5a-5=2

7a=2+5

a=\( \frac{7}{7} \)=1

substituting value of a in equation 1 ,we get

6×1-b=1

6-1=b

b=5

so points are A(1,5) and B(5,1)

we have

equation of line having two points

\((y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1) \)

\((y - 5) = \frac{1-5}{5-1} (x - 1) \)

\((y - 5) = -1 (x - 1) \)

y-5=1-x

x+y=6 is a required equation of line AB.

Answer:

d/2 = r if you are talking about circles, if that's the case then the r would be 5

The final value of x when (x = 1 ; x<10; x ),in this case will be 9.

This is because the initial value of x is set to 1, and the condition for the loop is that x must be less than 10.

Therefore, the loop will continue to execute as long as x is less than 10, and will stop when x is equal to 10. However, since the final value of x is not included in the loop, the final value of x will be one less than the stopping value, or 9.

Steps include:-
1. Set the initial value of x to 1: x = 1
2. Check if x is less than 10: x<10
3. If x is less than 10, execute the loop and increase the value of x by 1: x++
4. Repeat steps 2 and 3 until x is no longer less than 10
5. The final value of x will be one less than the stopping value, or 9.

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Answer:

48 drops of red food coloring

Step-by-step explanation:

32/8 = 4

SO she uses 4x as much yellow food coloring meaning you need to use 4x as much red food coloring.

4 x 12 = 48 so she needs to add 48 drops of red food coloring

Answer:

Mya will need 48 drops of red food coloring

Answer:

Area of trapezoid = 200 m²

Step-by-step explanation:

Parallel side1 a= 15m

Parallel side2 b= 25m

Perpendicular distance h = 10 m

We need to find area of the trapezoid.

The formula used to find area of the trapezoid is: \(Area \ of \ trapezoid=\frac{a+b}{2}h\)

Putting values and finding area of the trapezoid:

\(Area \ of \ trapezoid=\frac{a+b}{2}h\\Area \ of \ trapezoid=\frac{15+25}{2}\times 10\\Area \ of \ trapezoid=40\times5\\Area \ of \ trapezoid=200 \ m^2\)

So, area of trapezoid = 200 m²

Cindy gets 117 Canadian dollars as exchange.

A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0.

Given that in 2003 the exchange rate between the United States and Canada was three Canadian dollars to two US Dollars

Cindy has 78 US dollars to exchange when she visits Canada

We need to find the number of Canadian dollars could she get in exchange

Let the unknown value be x

Formulate a proportion

3/2=x/78

Apply cross multiplication

3×78=2x

234=2x

Divide both sides by 2

x=117

Hence, Cindy gets 117 Canadian dollars as exchange.

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Answer:

do it got a picture

Step-by-step explanation:

The car will cost $ 800 after a depreciation time of approximately 6 years.

Herein we are informed about the case of a car bought in 2011 at a cost of $ 36,000 and that depreciates linearly every year. Then, the depreciation function is described below:

c(t) = c' + m · t

Where:

If we know that c(0) = 36,000, c(4) = 12,000 and c(t) = 800, then the depreciation rate is:

m = (12,000 - 36,000) / (4 - 0)

m = - 24,000 / 4

m = - 6,000

800 = 36,000 - 6,000 · t

6,000 · t = 35,200

t = 35,200 / 6,000

t = 5.867

The expected depreciation time is approximately 6 years.

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Answer:

(5, -3)

Step-by-step explanation:

when you reflect across x axis the y changes symbols.

Answer:

frequcy: 1/1080

b in the equation: 1/3

Which could be an equation for this function? -- y=cos(x/3)

Step-by-step explanation:

The number of students that are in both the Categories A and B are 16 students.

In the question ,

it is given that ,

the total number of students in category A and category B is 32 students .

which is represented as A union B ,

that is n(AUB) = 32 ,

the number of students in category A = n(A) = 24

the number of students in category B = n(B) = 24

we need to find the number of students that are in both category ,

that is n(A∩B) .

we know that ,

n(AUB) = n(A) + n(B) - n(A∩B)

Substituting the values , we get

n(A∩B) = 24 + 24 - 32

= 48 - 32

= 16

Therefore , The number of students that are in both the Categories are 16 students.

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Answer:

The correct answer is C.

Step-by-step explanation:

C. ✓ No, the Large Counts condition is not met.

A response variable in statistics is a variable that is being measured or observed in a study. It is thought to be affected by the explanatory variable.

Response variable in statistics is a variable that is being measured or observed in a study. It is also known as the dependent variable or the outcome variable.

This variable is thought to be affected by the explanatory variable, also known as the independent variable.

This allows us to understand if the changes involved are significantly related or not or whether it is due to certain factors.

For example, if a study is examining the effect of exercise on weight loss, the response variable would be weight loss and the explanatory variable would be exercise. The response variable is typically plotted on the y-axis of a graph, while the explanatory variable is plotted on the x-axis.

In summary, a response variable in statistics is a variable that is being measured or observed in a study.

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Answer: y = 3x - 2

Step-by-step explanation:

slope intercept: y = mx + b, where m is the slope and b is the y-intercept.

Thus, because you already know the slope, you can simplify the equation to

y = 3x + b.

Then plug in the provided point to get, 4 = 3(2) + b

4 = 6 + b

-2 = b

Thus,

y = 3x - 2

Hope it helps :)

The only value of x in the interval [0,4] for which the function f(x) equals its average value of 2/3 is approximately x = 0.139.

To find the average value of the function f(x) = x - 2√x over the interval [0,4], we can use the formula:

Average value of f(x) over [a,b] = 1/(b-a) * integral of f(x) from a to b

Using this formula, we have:

Average value of f(x) over [0,4] = 1/(4-0) * integral of (x - 2√x) dx from 0 to 4

                                 = 1/4 * (1/2 x^2 - 4/3 x^(3/2)) evaluated from 0 to 4

                                 = 1/4 * ((1/2 * 4^2 - 4/3 * 4^(3/2)) - (1/2 * 0^2 - 4/3 *

                                                                                                           0^(3/2)))                            

                                 = 1/4 * (8/3 - 0)

                                 = 2/3

Therefore, the average value of f(x) over [0,4] is 2/3.

To find all values of x in the interval [0,4] for which the function f(x) equals its average value, we can set f(x) = 2/3 and solve for x:

x - 2√x = 2/3

Multiplying both sides by 3, we have:

3x - 6√x = 2

Rearranging, we get:

6√x = 3x - 2

Squaring both sides, we have:

36x = 9x^2 - 12x + 4

Simplifying, we get:

9x^2 - 48x + 4 = 0

Using the quadratic formula, we have:

x = (48 ± sqrt(48^2 - 4*9*4))/2*9

 = (48 ± sqrt(2292))/18

Since x must be between 0 and 4, we can ignore the root that is greater than 4:

x = (48 - sqrt(2292))/18

 ≈ 0.139

Therefore, the only value of x in the interval [0,4] for which the function f(x) equals its average value of 2/3 is approximately x = 0.139.

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The parent function f(x) = |x| is a V-shaped graph that represents the absolute value of x. When the value of x is negative, the function returns the opposite positive value of x, while when the value of x is positive, it remains the same.

To match this parent function with its translations, we need to understand the effects of different constants added or multiplied to x within the function.

1. f(x - 2): This translation shifts the graph 2 units to the right. The V-shape remains the same, but it is now centered at x = 2.

2. 3f(x): This translation stretches the graph vertically by a factor of 3. The V-shape becomes taller and narrower, but it still passes through the origin.

3. -f(x + 1): This translation reflects the graph across the y-axis and shifts it 1 unit to the left. The V-shape is now flipped to the left side of the y-axis, centered at x = -1.

4. f(2x): This translation compresses the graph horizontally by a factor of 2. The V-shape becomes shorter and wider, but it still passes through the origin.

In summary, each of these translations affects the shape and position of the V-shaped graph of the absolute value function, but the basic characteristics of the function remain the same.

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Answer:

1

Step-by-step explanation:

y2-y1 divided by x2-x1

12-3 divided by 20-11

which equals to 9/9 which equals to 1

The equation is separated in terms of variables.

The given equation is y' + x√(x² + 1) = ex + 1.

Rewriting the equation with the variables separated:

Subtract x√(x² + 1) from both sides, we get:y' = ex + 1 - x√(x² + 1)

Thus, the equation is separated in terms of variables.

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