Which system of equations is represented by this graph?

We solved the following equation using an appropriate cofunction identity as x = π/18 and x = -π/18.

To solve the equation sin(4π/9) = cos(x) using an appropriate cofunction identity, we can start by recognizing that the sine and cosine functions are cofunctions of each other. This means that the sine of an angle is equal to the cosine of its complement, and vice versa.

In other words, sin(x) = cos(π/2 - x) and

cos(x) = sin(π/2 - x).

In this case, we have

sin(4π/9) = cos(x),

so we can rewrite the equation as

cos(π/2 - 4π/9) = cos(x).

Now, we need to find the value of π/2 - 4π/9. To simplify this, we can find a common denominator for π/2 and 4π/9, which is 18.

So, π/2 - 4π/9 can be written as

(9π/18) - (8π/18) = π/18.

Therefore, the equation simplifies to

cos(π/18) = cos(x).

Since the cosine function is an even function,

cos(x) = cos(-x),

we can say that

x = π/18 or x = -π/18.

Hence, the solutions to the equation sin(4π/9) = cos(x) using an appropriate cofunction identity are x = π/18 and x = -π/18.

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Answer:

The probability is 0.5 tiles will be green

Step-by-step explanation:

Hope this helps

(a) If f(x) is a convex function with x ∈ ℝⁿ, then all local minima of f(x) are also global minima. In other words, if there exists a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo, then f(x) ≥ f(xo) for all x ∈ ℝⁿ.

(b) A graph of a non-convex function can be visualized to understand why the statement in part (a) is not true. It will show a scenario where a local minimum is not a global minimum.

(a) To prove that all local minima of a convex function are also global minima, we can utilize the property of convexity. Suppose there is a point xo such that f(x) ≥ f(xo) for all x in a neighborhood of xo. We assume that xo is a local minimum. Now, consider any arbitrary point x in ℝⁿ. We can express x as a convex combination of xo and another point y in the neighborhood, using the convexity property: x = λxo + (1 - λ)y, where λ is a scalar between 0 and 1. Using this expression, we can apply the convexity property of f(x) to get f(x) ≤ λf(xo) + (1 - λ)f(y). Since f(x) ≥ f(xo) for all x in the neighborhood, we have f(y) ≥ f(xo). Therefore, f(x) ≤ λf(xo) + (1 - λ)f(y) ≤ λf(xo) + (1 - λ)f(xo) = f(xo). This inequality holds for all λ between 0 and 1, implying that f(x) ≥ f(xo) for all x ∈ ℝⁿ, making xo a global minimum.

(b) A graph of a non-convex function can demonstrate a scenario where the statement in part (a) is not true. In such a graph, there may exist multiple local minima, but one or more of these local minima are not global minima. The non-convex nature of the function allows for the presence of multiple valleys and peaks, where one of the valleys may contain a local minimum that is not the overall lowest point on the graph. This occurs because the function may have other regions where the values are lower than the local minimum in consideration. By visually observing the graph, it becomes apparent that there are points outside the neighbourhood of the local minimum that have lower function values, violating the condition for a global minimum.

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Answer:

x = 5

Step-by-step explanation:

to find the value of x that makes the expressions equal, equate them

8x - 24 = 4x - 4 ( subtract 4x from both sides )

4x - 24 = - 4 ( add 24 to both sides )

4x = 20 ( divide both sides by 4 )

x = 5

then

4x - 4 = 4(5) - 4 = 20 - 4 = 16

8x - 24 = 8(5) - 24 = 40 - 24 = 16

the value x = 5 makes the 2 expressions equal

The option (a) 12 ounces of beer (360ml) contain more alcohol

Alcohol content is something that is important to understand, especially if you are of legal drinking age. It can affect your health and your ability to make sound decisions.

First, let's start with 12 ounces of beer. A typical beer has an alcohol content of around 5%, which means that 12 ounces of beer contains 0.6 ounces (18 ml) of alcohol. This is the same as the fourth option.

Next, let's consider 4 ounces of wine. The alcohol content of wine varies depending on the type and brand, but a typical wine has an alcohol content of around 12%. This means that 4 ounces of wine contains 0.48 ounces (14.2 ml) of alcohol.

Finally, we have 1.5 ounces of spirits. The alcohol content of spirits is generally higher than beer and wine, with a typical range of 40-50%. For the sake of this comparison, let's assume the spirits have an alcohol content of 40%. This means that 1.5 ounces of spirits contains 0.6 ounces (18 ml) of alcohol, the same amount as 12 ounces of beer.

So, in summary, 12 ounces of beer and 1.5 ounces of spirits contain the same amount of alcohol, which is 0.6 ounces (18 ml). 4 ounces of wine contains less alcohol, with 0.48 ounces (14.2 ml).

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Answer:

3(3x - 2y)

Step-by-step explanation:

9x - 6y

Factor out 3 from the expression

3(3x - 2y)

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY

Answer:

option 2 is correct given diagrm

Answer:

w = 18

Step-by-step explanation:

6(33 - w) = 90

33 - w = 15

-w = -18

w = 18

Answer:

4 per hour

Step-by-step explanation:

32➗8=4

Answer:

4 chapters per hour

Step-by-step

32/8=4 and we know that because

1h per 4

2h per 8

3h per 12

4h per 16

5h per 20

6h per 24

7h per 28

8h per 32

Answer:

The correct mean is 30.875

Step-by-step explanation:

Mean Value

Given n observations of a specific magnitude, the mean value of the random experiment is:

\(\displaystyle \bar x=\frac{\sum x_i}{n}\)

Where xi is each individual value.

Henry made 16 observations and found the mean was 30. Replacing that into the formula, we have

\(\displaystyle 30=\frac{\sum x_i}{16}\)

Operating:

\(\sum x_i=480\)

We know the sum of all the individual values is 480. Knowing that Henry made a mistake and used 28 and 18 instead of 32 and 28, the correct mean should include the correct sum. Since 32 is 4 more than 28, and 28 is 10 more than 18, the correct sum is 480 + 4 + 10 = 494. This gives us the corrected mean:

\(\displaystyle \bar x'=\frac{494}{16}= 30.875\)

The correct mean is 30.875

Answer:

i think the answer is SAS . i am not sure becoz i have learned this long ago

Answer:

sss

Step-by-step explanation:

Because DB is = to DB by the reflexive proporty and it shows that AB = DC and AD = BC

If you mean "factor over the rational numbers", then this cannot be factored.

Here's why:

The given expression is in the form ax^2+bx+c. We have

a = 3

b = 19

c = 15

Computing the discriminant gives us

d = b^2 - 4ac

d = 19^2 - 4*3*15

d = 181

Note how this discriminant d value is not a perfect square

This directly leads to the original expression not factorable

We can say that the quadratic is prime

If you were to use the quadratic formula, then you should find that the equation 3x^2+19x+15 = 0 leads to two different roots such that each root is not a rational number. This is another path to show that the original quadratic cannot be factored over the rational numbers.

Based on the given linear equations, the number of 7th-grade students and 8th-grade students is 120 students and 150 students respectively. Hence, Mia's solution is correct.

The value of h in the given linear equation is determined as follows:

9 rectangles = 270 students

1 rectangle = 30 students

7 + h = 11

h = 11 - 7

h = 4

The number of 7th-grade students and 8th-grade students is then determined as follows:

7th-grade students:

4 * 30 = 120 students

8th-grade students:

5 * 30 = 150 students

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Answer:

5/6 of the players are at the game.

Step-by-step explanation:

There are 54 players.

54 is 6 groups of 9.

6 × 9 = 54

9 people are in each group. Each of the 6 groups is one-sixth of the total.

9 people are out. 1/6 are out.

5/6 are attending.

OR, think 54 - 9 is 45. 45 are attending the game.

present/total

= 45/54

= 5/6

The simplest way to perform a division is long division and synthetic division.

What is division?

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on.

There are two methods to perform division:

Long division: The mathematical procedure for splitting big numbers into more manageable groups or sections is known as long division. A difficulty can be solved by breaking it down into manageable parts. Dividends, divisors, quotients, and remainders all exist in long divisions.

Synthetic division: In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

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Yes.  

Being quadratic has nothing to do with the quadrants of the x-y graph.  It's more related to the geometry of a four-sided shape.

Answer:

Fraction = \(\frac{1}{20}\) and Decimal = 0.05

Step-by-step explanation:

Percent means, some number over a hundred.

in this case we have 5%

\(\frac{5}{100} = \frac{1}{20}\)

and for decimal form we just move the decimal 2 places to the left because our denominator is a 100 and we get 0.05.

In statistics, p hat is used as an estimator of the population proportion (p) of a categorical variable. It is the sample proportion of the variable, which is calculated as the number of occurrences of a particular category in the sample divided by the total sample size.

The reason why p hat is used is that it provides an estimate of the unknown population proportion based on a representative sample. By using p hat, we can draw inferences about the population proportion with a certain level of confidence. This is important in hypothesis testing and confidence interval estimation, where we want to make statements about the population based on the information gathered from a sample.

Using p hat as an estimator of p is also beneficial because it has desirable statistical properties, such as being an unbiased estimator, having a sampling distribution that approaches normality, and having a known standard error.

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Answer:

x = -3

Step-by-step explanation:

5x + 4y = 1

y = 1 - x

• Substitute (1 - x) into y:

5x + 4(1 - x) = 1

• Distribute:

5x + 4 - 4x = 1

• Combine like terms:

x + 4 = 1

• Subtract the 4 to solve for x:

x = -3

Answer:

Step-by-step explanation:

x^3+3x^2<x+3

(-∞,-3)∪(-1,1)

Yes, each vector in R4 can be written as a linear combination of the columns of matrix A.

To explain this, first, we must convert matrix A into its reduced row echelon form. This is done by performing row operations so that the leading (i.e. leftmost non-zero) entry in each row is a 1.

By doing this we can see that the columns of the matrix A form a basis for R4, which means that any vector in R4 can be written as a linear combination of the columns of A.

To be more specific, we can show that the columns of A span R4 by showing that the columns are linearly independent. To do this, we solve the equation Ax = 0, where x is the vector of unknowns. We can see that the only solution to this equation is x = 0, which implies that the columns of A are linearly independent and therefore span R4.

This means that any vector in R4 can be written as a linear combination of the columns of A. In other words, any vector in R4 can be expressed as a linear combination of the columns of A, which means that the columns of A span R4.

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The complete question is attached below.

Answer:

The y intercept of f(x) is 8 and the equation of the horizontal asymptote is y = 0

Answered by GAUTHMATH

Two scenarios that create right angle are 3 and 4.

In both the situations, Pythagoras theorem get satisfy with the sides which theorem is only applicable when there is right angle in the triangle.

Here's the explanation using 3 as an example :

From the statement we can assume that height of the window as the perpendicular(P) and distance from base(B) of the building to William as base of the triangle and line distance from Tom to William as hypotenuse(H) of the triangle.

Therefore, H = 130, B= 36.4 and P = 124.8

By Pythagoras theorem,

H² = P² + B²;

130² = 124.8² + 36.4²,

16900 = 15575.04 + 1324.96,

16900 = 16900

Hence satisfy the Pythagoras theorem, therefore triangle is right angle.

Similarly for the 4 statement.

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1) Point slope form equations are written according to this general formula:

2) Since we've got the slope and one point we can plug them into the formula:

That yields the equation of the line y=4/3x -4 (slope-intercept form). So in Point Slope form, the answer is:

(y-0)=4/3(x-3)

The reasonable solutions for this situation is (1, 3.5) and (2, 2)

A graph is a visual representation of data or information, typically used to display the relationship between two or more variables. Graphs are used to make it easier to understand and analyze data, and can be used to convey information in a clear and concise manner.

Audrey has x pounds of red grapes and y pounds of green grapes.

She has less than 5 pounds of grapes in all, hence:

x + y < 5

Also, x ≥ 0, y ≥ 0

a) The option (–1, 2) is wrong because x = -1 < 0

b) The option (1, 3.5) is correct because 1 + 3.5 = 4.5 < 5

c) The option (2, 2) is correct because 2 + 2 = 4 < 5

d) The option (4.5, 0.5) is wrong because 4.5 + 0.5 = 5 which is not less than 6.

e) The option (5, 0) is wrong because 5 + 0 is not less than 5

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The game field is 350 40 percent for 250 is 100 and 250 plus 100 is 350

The probability of Todd winning the game on his next turn is 1/48 or approximately 0.02 or 2%.

Probability is the study of the chances of occurrence of a result, which are obtained by the ratio between favorable cases and possible cases.

Assuming that the die and spinner are fair, the probability of Todd rolling a 2 and spinning a 5 on his next turn are independent events, so we can multiply their probabilities to get the overall probability:

P(rolling a 2) = 1/6 (since there is only one 2 on the die)

P(spining a 5) = 1/8 (since there is only one 5 on the spinner)

Therefore, the probability of Todd winning the game on his next turn is:

P(winning) = P(rolling a 2) x P(spining a 5) = (1/6) x (1/8) = 1/48

Hence, the probability of Todd winning the game on his next turn is 1/48 or approximately 0.02 or 2%.

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Answer:

2 2/3

Step-by-step explanation:

we know that the kg in each bag is 2 2/3