The graph below shows the solution to which system of inequalities?

The minimum value of the expression x^2 + y^2 - 6x + 4y + 18 for real x and y is 13.

The minimum value of the expression x^2 + y^2 - 6x + 4y + 18 for real x and y can be found by completing the square.

Step 1: Rearrange the expression by grouping the x-terms and y-terms together:
x^2 - 6x + y^2 + 4y + 18

Step 2: Complete the square for the x-terms. Take half of the coefficient of x (-6) and square it:
(x^2 - 6x + 9) + y^2 + 4y + 18 - 9

Step 3: Complete the square for the y-terms. Take half of the coefficient of y (4) and square it:
(x^2 - 6x + 9) + (y^2 + 4y + 4) + 18 - 9 - 4

Step 4: Simplify the expression:
(x - 3)^2 + (y + 2)^2 + 13

Step 5: The minimum value of a perfect square is 0. Since (x - 3)^2 and (y + 2)^2 are both perfect squares, the minimum value of the expression is 13.

Therefore, the minimum value of the expression x^2 + y^2 - 6x + 4y + 18 for real x and y is 13.

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Answer:

-135, -134, -133

Step-by-step explanation:

Hi there!

Let x be equal to the first integer in the set of three consecutive integers.

Let x+1 and x+2 be the consecutive integers.

We're given that they have a sum of -402.

We can construct an equation:

\((x)+(x+1)+(x+2)=-402\)

Combine like terms:

\(x+x+1+x+2=-402\\x+x+x+1+2=-402\\3x+3=-402\\3x=-405\\x=-135\)

Therefore the first integer is -135.

The next two consecutive integers after -135 is -134 and -133.

Therefore, the three consecutive integers are -135, -134 and -133.

I hope this helps!

There are 840 ways for NASA to make this selection. Total number of ways melissa and wade can sit together is 96.

We can use the combination formula to solve this problem. The number of ways to choose 2 men from 6 is C(6,2) = 15, and the number of ways to choose 3 women from 8 is C(8,3) = 56. To find the total number of ways to make the selection, we multiply these values together: 15 x 56 = 840.

To solve this problem, we can treat Melissa and Wade as a single unit and then arrange the other 3 people and the Melissa-Wade unit in 4 seats. There are 4 ways to arrange Melissa and Wade (MW, WM, AMW, WMA). After that, we have 4 seats left, and we need to arrange 3 people (Anna, Chris, and Nora) and the Melissa-Wade unit in those seats. There are 4 people to arrange in 4 seats, so there are 4! = 24 ways to do this. Therefore, the total number of ways to seat Melissa and Wade together is 4 x 24 = 96.

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The mean and standard deviation of the number of seats filled on an airplane is 240 and 6.93 respectively.

The load factor given is 80%

Hence the probability that the seat s filled with a paying passenger is 0.8.

Therefore, here we are given a no. of seats and we need to find the mean and standard deviation of the number of seats actually filled.

Here for every seat, there can be two possibilities:-

The seat is filled

The seat is not filled.

Hence this clearly models into a Binomial distribution with the no. of samples n = 300

probability of success = p = 0.8

Mean of a binomial distribution = np

Therefore, the mean of the above problem is

300 X 0.8

= 240.

The variance of a binomial distribution is np(1 - p)

Hence the standard deviation will be √{np(1 - p)}

= √(300 X 0.8 X (1 - 0.8))

√(300 X 0.16)

= √48

= 4√3

= 6.93

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Answer:

There needs to be 300 liters of Drink A and 270 liters of Drink B

Step-by-step explanation:

Let a = the amount of Drink A and b = the amount of Drink B

Multiplying a number by 0.2 is the same as calculating 20% of it and same goes with 15% and 0.15. This makes our equation for the amount of fruit juice:

0.2a + 0.15b = 100.5

We know what the difference between a and b will be 30 liters so:

a - b = 30

Now we have our system of equations

To cancel out a, we can multiply the first equation by -5 so we will now have:

-a - 0.75b = -502.5

a - b = 30

Adding these two equations together, we get:

-1.75b = -472.5

Both sides are negative, so we can take the negative signs away.

1.75b = 472.5

Now divide both sides by 1.75

b = 270

Plugging 270 into b, we have:

a - b = 30

a - 270 = 30

Add 270 to both sides

a = 300

There needs to be 300 liters of Drink A and 270 liters of Drink B

The system of linear equations which could be used to find the amount in litres of drinks A and B are :

Let :

Amount of drink A = a

Amount of drink B = b

Percentage of real fruit juice for drink A = 20%

Percentage of real fruit juice for drink B = 15%

Total litres made = 100.5

(Amount of drink A × percentage) + (Amount of drink B × percentage) = Total litres

The difference between the amount of drink A and B made :

Drink A is 30 liters more than B :

The system of equations required to determine the amount of drink A and B made are :

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The angle between the vectors u = <-7, 12> and v = <-3, 3> is approximately 1.151 radians.

To find the angle, a, between two vectors, u and v, we can use the dot product formula:

u · v = |u| |v| cos(a)

where u · v is the dot product of vectors u and v, |u| and |v| are the magnitudes (or lengths) of vectors u and v, and cos(a) is the cosine of the angle, a, between the vectors.

First, let's calculate the magnitudes of the given vectors u and v:

|u| = √((-7)^2 + 12^2) = √(49 + 144) = √193

|v| = √((-3)^2 + 3^2) = √(9 + 9) = √18 = 3√2

Next, let's calculate the dot product of u and v:

u · v = (-7)(-3) + 12(3) = 21 + 36 = 57

Now we can substitute these values into the dot product formula:

57 = (√193)(3√2) cos(a)

To solve for cos(a), we divide both sides of the equation by (√193)(3√2):

cos(a) = 57 / ((√193)(3√2))

Now, we can calculate the value of cos(a) using a calculator:

cos(a) ≈ 0.401

To find the angle, a, we take the inverse cosine (arccos) of cos(a):

a ≈ arccos(0.401) ≈ 1.151 radians (approximately)

The angle between the vectors u = <-7, 12> and v = <-3, 3> is approximately 1.151 radians.

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Area: (4 * 2) + (4 *2) = 16cm^2

Perimeter: (4 + 2 )+ 6 + (2 + 2 + 4) = 20

Answer:I think -0.4

Step-by-step explanation:

Answer:

i think 80m

Step-by-step explanation:

because if it is in 30° it is 40m and 60° means double of it

The height of the tower from the given parameters is; 20√3 m

I have attached a drawing showing the triangle formed by the tower and the shadow.

We can use trigonometric ratios on Triangle ABC of the attached image to get; AB = BC * tan 60°

AB = BC√3

Where AB is the height of tower

For Triangle ABD, using trigonometric ratios again, we will have;

tan 30° = AB/(BC + 40)

1/√3 = (BC√3)/(BC + 40)

Cross multiply to get;

BC + 40 = 3BC

3BC - BC = 40

2BC = 40

BC = 40/2

BC = 20 m

Thus;

Height of tower; AB = 20√3 m

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Answer:

its 9

Step-by-step explanation:

19-1 divided by 2

so 19-1=18

18/2 equals 9

and thats your answer

Answer:

6n^3

Step-by-step explanation:

3/3 *9^10/453*7+sqrt175

The polynomial expression is \($B=6 n^{3}\) ; where, \(\quad n \neq 0\).

Given:

\($\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}} \div \frac{2 n^{2}+18 n}{B}=1$\)

To find:

the value of B is a polynomial expression.

Step 1

Let, \($\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}} \div \frac{2 n^{2}+18 n}{B}=1$\)

\($\frac{\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}}}{\frac{2 n^{2}+18 n}{B}}=1$$\)

Simplifying the above equation as

\($\frac{\frac{n^{2}+12 n+27}{3 n^{3}+9 n^{2}}}{\frac{2 n^{2}+18 n}{B}}: \frac{B}{6 n^{3}}$\)

then, we get

\($\frac{B}{6 n^{3}}=1$$\)

Step 2

Multiply both sides by \($6 n^{3}$\), then we get

\($\frac{B}{6 n^{3}} \cdot 6 n^{3}=1 \cdot 6 n^{3} $$\) where, \(\quad n \neq 0\)

Simplifying the equation as

\($B=6 n^{3}\) ; where, \(\quad n \neq 0\)

The value of \($B=6 n^{3}\) ; where, \(\quad n \neq 0\).

Therefore, the polynomial expression is \($B=6 n^{3}\) ; where, \(\quad n \neq 0\).

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Answer:

.2 Cm

Step-by-step explanation:

Answer:

Points B,C and D

Step-by-step explanation:

1:10 = 3:30 = 5:50

Answer: The answer is B, C, D!

Step-by-step explanation: Correct on Edg. 2021! Please mark brainlist! Have a wonderful day!

Answer:

50%

Step-by-step explanation:

5/10*100

=50%

So the answer is 1.3 after rounding to 10.

Answer:

22

Step-by-step explanation:

Just plug in

2(15 - 5) + 2 (Solve what's in the parenthesis)

2(10) + 2 (multiply 2*10)

20 + 2 (collect like terms)

22

The evaluation of the expression, 2(a - 5) + 2 when a = 15 is; 22

According to the question;

To evaluate 2(a - 5) + 2. when a = 15.

We have;

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Itrs is known that the sum of the internal angles of a triangle is 180°.

So, if a triangle has angles A, B and C, we have:

a)

In this case, we know that values of the angles 68° and 53°. Let the missing one be x, so:

So, the missing angles is 59°.

Answer:

f(x) = x ³ shifted 4 units to the right will be g(x) = f(x-4) = (x - 4)³

Step-by-step explanation:

If a function f(x) is shifted right 4 units every x coordinate will become x - 4

g(x)  = f(x - 4) = (x - 4)³

To be complementary, the angles need to add to 90 degrees. But 55+45 = 100, so the angles are not complementary.

The angles are not adjacent either. Adjacent angles share a common line, line segment or ray. There cannot be a gap between the angles if you want adjacent angles. Think of adjacent rooms in a house in that they share the same wall.

Therefore, the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM is approximately 0.1755, rounded to four decimal places.

To calculate the probability of getting exactly 4 calls between 8:00 AM and 9:00 AM, we need to use the Poisson distribution formula. The Poisson distribution is commonly used to model the number of events occurring in a fixed interval of time or space. In this case, the mean (λ) is given as 5. The formula for the Poisson distribution is:

P(X = k) = (e*(-λ) * λ\(^k\)) / k!

Where:

P(X = k) is the probability of getting exactly k calls

e is the base of the natural logarithm (approximately 2.71828)

λ is the mean number of calls (given as 5)

k is the number of calls (in this case, 4)

k! is the factorial of k

Let's calculate the probability using the formula:

P(X = 4) = (e*(-5) * 5⁴) / 4!

P(X = 4) ≈ 0.1755

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Answer:

Step-by-step explanation:

You can use the slope formula:

\(y = mx + b \\ m = slope , b = y-intercept\)

So if the function is :

\(f(x) = \frac{-2}{3} x - 4\)

Then m (the slope) is -2/3

This is a translation of 2 units to the left and 5 units up, so the correct option is the first one.,

Remember that a vertical translation of N units is:

g(x) = f(x) + N

if N < 0 the translation is down.

if N > 0 the translation is up.

And a horizontal translation of N units is:

g(x) = f(x + N)

If N > 0 the translation is to the right.

if N < 0 the translation is to the left.

Here we have the transformation:

f(x) = x²

g(x) = (x + 2)² + 5

So this is a translation of 2 units to the left and 5 units up.

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A reflection in the line y = -2 and then translation of 2 units right will create the same area so option (C) will be correct.

f we shift the triangle anywhere then there will be no change in the area but if we apply the scale factor then since the dimension changes so its area will also change.

In all options, there is a scale factor so it will change area but in option C

A reflection in the line y = -2 reflection gives a mirror image about y = -2 but no changes in area then translation of 2 units right will shift triangle 2 units right but no effect in the area.

Hence "A reflection in the line y = -2 and then translation of 2 units right will create the same area".

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Answer:

D. Normality of the estimator (e.g., sample mean)

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The question was incomplete. Check below the complete question.

Which of the following is the necessary condition for creating confidence intervals for the population mean? A. Known population parameter B. Normality of the population C. Known standard deviation of the estimator D. Normality of the estimator (e.g., sample mean)

Let's write the ration as a fraction:

1 cm to 1.5 cm

Ratio : 1/1.5 but we need to write it without decimals,

1/1.5 = 2/3 (multiplying by 2 numerator and denominator)

K, the correct answer is 2/3

Answer:

I think it's D:)

Step-by-step explanation:

The union of two sets is to avoid counting the same elements twice.

The mathematical logic subfield of set theory investigates sets, which can be loosely defined as collections of objects. Although any object can be combined into a set, set theory, as a mathematical discipline, focuses primarily on those that are relevant to mathematics as a whole.

Given union of set

(A ∪ B),

The set of all objects that are members of either A or B, or both, is the union of the sets A ∪ B.

let us take example,

A = { 1, 2, 3, 4}

B = {3, 4, 5, 6, 7}

(A ∪ B) = { 1, 2, 3, 4} ∪  {3, 4, 5, 6, 7}

we can simply write all of A and B's elements in a single set to avoid duplicates to find A U B.

(A ∪ B) = {1, 2, 3, 4, 5, 6, 7}

Hence the  union of two sets is a set that contains all the elements of both set and avoid duplicates.

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In each scenario, the choice between mean and median as a representative measure of central tendency depends on the nature of the data and the specific context..

1. Scenario: Income distribution of a population

- If the income distribution is skewed or contains extreme values (outliers), the median would be a better representation of the central tendency. This is because the median is not influenced by outliers and provides a more robust estimate of the "typical" income level. However, if the income distribution is approximately symmetric without outliers, the mean can also be an appropriate measure.

2. Scenario: Exam scores in a class

- If the exam scores are normally distributed without significant outliers, the mean would be a suitable measure as it takes into account the value of each score. However, if there are extreme scores that deviate from the majority of the data, the median may be a better representation. This is especially true if the outliers are indicative of errors or exceptional circumstances.

3. Scenario: Housing prices in a city

- In this case, the median would be a more appropriate measure to represent the central tendency of housing prices. This is because the housing market often exhibits a skewed distribution with a few high-priced properties (outliers). The median, being the middle value when the data is sorted, is not influenced by these extreme values and provides a better understanding of the typical housing price in the city.

Ultimately, the choice between mean and median depends on the specific characteristics of the data and the objective of the analysis. It is important to consider the distribution, presence of outliers, and the context in which the data is being interpreted.

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Answer: x=17

Step-by-step explanation:

1.Identify relationship

Since both the angles are on the inside of both parallel lines and on the same side of the transversal you know that you have a same side interior relationship that makes them supplementary

2. set up equation

because they are supplementary you know that they are equal to 180 which gives the equation: 3x+6+123=180

3. solve the equation

3x+6+123=180

3x+129=180 | combine like terms

3x=51 | subtract 123 from both sides

x=17 | divide by 3 on both sides

Answer:

AGDB

Step-by-step explanation:

1: 1 is alternate interior because the angles are on opposite sides of the interior of the transversal. (A)

2: 2 is alternate exterior because the angles are on opposite sides of the exterior of the transversal. (G)

3: 3 is same-side interior because the angles are on the same side of the interior of the transversal. (D)

4: 4 is same-side exterior because the angles are on the same side of the exterior of the transversal. (B)