Solve the triangle. Round lengths to the nearest tenth and angle measures to the nearest degree.
a = 6, b = 9, C = 106° A) c = 17.9, A = 26°, B = 48° B) c = 12.1, A = 28°, B = 46°
C) c = 15, A = 30°, B = 44° D) no triangle

Let's simplify the expression step by step: Expand the squared term:

(x - 3y)² = (x - 3y)(x - 3y) = x² - 6xy + 9y²

Expand the second term:

3(x + y)(x − 4y) = 3(x² - 4xy + xy - 4y²) = 3(x² - 3xy - 4y²)

Expand the third term:

x(3x + 4y + 3) = 3x² + 4xy + 3x

Now, let's combine all the expanded terms:

(x - 3y)² + 3(x + y)(x − 4y) + x(3x + 4y + 3)

= x² - 6xy + 9y² + 3(x² - 3xy - 4y²) + 3x² + 4xy + 3x

Combining like terms:

= x² + 3x² + 3x² - 6xy - 3xy + 4xy + 9y² - 4y² + 3x

= 7x² - 5xy + 5y² + 3x

The simplified form of the expression is 7x² - 5xy + 5y² + 3x.

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The simplest radical form. 2√5 (√6 +2).

Given that

To find

We know that

Simplest radical form is the expression in radical form that, after rationalizing the denominator, leaves no more square roots, cube roots, fourth roots, or other roots to find

So, according to the question

We have

To find the simplest radical form of the given problem, we must first solve those brackets, then multiply under root numbers in root and without root numbers with without root numbers. 

So now, let's follow that process

We will get,

       2√5 (√6 +2)  = 2√5 ×√6 +2√5 ×2

                              = 2√(5×6) + 2×2×√5

                              = 2√(30) + 4√5

So the radical form of that given problem is B) 2√(30) + 4√5

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Given the equation:

8x + 7y = -50

We will check the options to find which order pair is the solution of the equation

Point (-6 , -1)

8 * -6 + 7 * -1 = -48 - 7 = -55 ≠ -50

Point ( 0 , -6)

8 * 0 + 7 * - 6 = -42 ≠ -50

Point (-6, 0 )

8 * - 6 + 7 * 0 = -48 ≠ -50

Point (-1 , -6)

8 * -1 + 7 * -6 = -8 - 42 = -50

so, the order pair which is a solution for the equation is (-1 , -6 )

Answer: Thx for the answer

Step-by-step explanation:

Answer:

Step-by-step explanation:

the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

To write the system of ordinary differential equations (ODEs) for the transition probabilities Pᵢⱼ(t) of the given continuous-time Markov chain, we need to consider the rate at which the system transitions between different states.

Let Pᵢⱼ(t) represent the probability that the Markov chain is in state j at time t, given that it started in state i at time 0.

The ODEs for the transition probabilities can be written as follows:

dP₁₂(t)/dt = q₁₂ * P₁(t) - q₂₁ * P₂(t)

dP₁₃(t)/dt = q₁₃ * P₁(t) - q₃₁ * P₃(t)

dP₂₁(t)/dt = q₂₁ * P₂(t) - q₁₂ * P₁(t)

dP₂₃(t)/dt = q₂₃ * P₂(t) - q₃₂ * P₃(t)

dP₃₁(t)/dt = q₃₁ * P₃(t) - q₁₃ * P₁(t)

dP₃₂(t)/dt = q₃₂ * P₃(t) - q₂₃ * P₂(t)

where P₁(t), P₂(t), and P₃(t) represent the probabilities of being in states 1, 2, and 3 at time t, respectively.

Now, let's consider the second part of the question: Suppose that the initial state is 1. We want to find the probability that after the first transition, the process X(t) enters state 2.

To calculate this probability, we need to find the transition rate from state 1 to state 2 (q₁₂) and normalize it by the total rate of leaving state 1.

The total rate of leaving state 1 can be calculated as the sum of the rates to transition from state 1 to other states:

total_rate = q₁₂ + q₁₃

Therefore, the probability of transitioning from state 1 to state 2 after the first transition can be calculated as:

P(X(t) enters state 2 after the first transition | X(0) = 1) = q₁₂ / total_rate

In this case, the transition rate q₁₂ is 1, and the total rate q₁₂ + q₁₃ is 1 + 2 = 3.

Therefore, the probability of transitioning from state 1 to state 2 after the first transition is:

P(X(t) enters state 2 after the first transition | X(0) = 1) = 1 / 3

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(a) With 10 rectangles using left endpoints, 5 rectangles are contributing negative area values to the estimated net area. This means that the function is below the x-axis in those intervals.

The remaining 5 rectangles are contributing positive area values, as the function is above the x-axis in those intervals.

When using midpoints, the number of positive and negative rectangles may not be the same. It depends on the behavior of the function within each subinterval. The use of midpoints can result in a different distribution of positive and negative rectangles compared to using left endpoints.

(b) The error when using midpoints with 10 subintervals can be determined by calculating the difference between the estimated net area using midpoints and the actual net area.

To calculate the error, we need to evaluate the definite integral of the function over the given interval and subtract the estimated net area using midpoints.

Error = Actual Net Area - Estimated Net Area using Midpoints

Since the exact values are not provided, the specific error value cannot be determined without further information or calculations.

Using left endpoints with 10 rectangles, 5 rectangles contribute negative area values and 5 contribute positive area values. When using midpoints, the distribution of positive and negative rectangles may differ. The error when using midpoints can be calculated by subtracting the estimated net area using midpoints from the actual net area, but the exact error value cannot be determined without further information or calculations.

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Answer:

980

Step-by-step explanation:

900+80=980

The three points that represents the proportional relationship will be;

⇒ (2 , 4) (3, 6) and (5, 10)

What is mean by Ratio?

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y.

Where, x and y are individual amount of two quantities.

And, Total quantity gives after combine as x + y.

Given that;

The number cards are,

0, 1, 2, 3, 4, 5, 6, 7, 8, 9

Now,

Since the proportions represents the equivalent ratios.

Hence,

We can take the points which represents the equivalent ratio.

So, We get the points as;

⇒ (2 , 4) (3, 6) and (5, 10)

Because all the ratio between every points represents the equivalent ratio.

That is;

2 : 4 = 1 : 2

3 : 6 = 1 : 2

5 : 10 = 1 : 2

Therefore,

The three points that represents the proportional relationship will be;

⇒ (2 , 4) (3, 6) and (5, 10)

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Converting mL (milliliters) to L (liters).

5,450 mL is equal to 5.45 L.

We have,

In the metric system, there are different units of measurement for volume, such as milliliters (mL) and liters (L).

One liter is equal to 1000 milliliters.

So, to convert a volume measurement from milliliters to liters, you need to divide the volume in milliliters by 1000.

This is because there are 1000 milliliters in one liter.

So, to convert 5,450 mL to L, you would divide by 1000 as follows:

5,450 mL ÷ 1000

= 5.45 L

Therefore,

5,450 mL is equal to 5.45 L.

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Here's link\(^{}\) to the answer:

bit.\(^{}\)ly/3gVQKw3

Answer:

42/6 = 7

7 - 4 = 3

Step-by-step explanation:

The coordinate of point P is -8.

We are given that the endpoints of AB are -16 and -4.

This means that A is at -16 and B is at -4

Therefore, the total length of the line AB will be-

-16 - (-4) = -12 units

But since length cannot be negative, we take only the absolute value, the length of AB comes out to be 12 units.

Now, point P divides AB in the ratio 2:1

The length of these two parts will be

12 × 2/3 and 12 x 1/3

= 8 units and 4 units

This means that AP = 8 units and PB = 4 units

Hence the coordinate of P will be (-16 + 8) or (-4 - 4)

Thus, the coordinate of point P is -8.

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The coordinate notation of the translation that maps JKLM to PQRS is:

(x,y) -> (x + 5, y + 3).

Transformations in the graph of a function involve operations such as multiplication/division or sum/subtraction, either in the domain of the function, involving values of x, or the range, involving values of y.

One such case of transformation is a translation, when the function is moved down, up, left or right, keeping it's orientation, just changing the position.

To find the rule for this problem, we look at equivalent vertices J and P, with coordinates given by:

Hence the rule is:

(x,y) -> (x + 5, y + 3).

Meaning that the function was translated:

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Answer:

C

Step-by-step explanation:

AA postulate because we are given 2 of the 3 angles of each triangle. They are both the same in each triangle. Also, we can find the 3rd angle in each triangle. Since both triangles have the exact same angles, they are similar.

The given triangles ΔABC and ΔLMN are similar by AA postulate.

A triangle is a three sided polygon that consist of three edges and three vertices .

Here two given triangles are ΔABC and ΔLMN. In these two triangles ∠A=∠L=53° and ∠B=∠M= 72°.

Therefore, the two corresponding angles of triangles ΔABC and ΔLMN are equal . So the third angle of ΔABC is also equal to the corresponding angle of ΔLMN.

Hence two triangles are similar by AA postulate.

Thus two triangles are similar by AA postulate. So option (C) is correct.

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Answer:

t = 5 years

online readership will exceed physical sales in 5 years

Step-by-step explanation:

The number of physical readership can be represented by the equation;

P(t) = 120 - 6t

The number of Online readership can be represented by the equation;

K(t) = 60 + 8t

For online readership to exceed physical sales

K(t) > P(t)

60 + 8t > 120 - 6t

Collecting the like terms;

8t+6t > 120-60

14t>60

t > 60/14

t > 4.29

To the nearest year greater than 4.29.

t = 5 years

online readership will exceed physical sales in 5 years

you will be on floor no. -8 and your friend will be in floor no. 5 if you and your friend started at floor no. 0

YOU CAN ALSO VISUALISE THIS WAY

Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

What is the mean and standard deviation?

The standard deviation is a summary measure of the differences of each observation from the mean. If the differences themselves were added up, the positive would exactly balance the negative and so their sum would be zero. Consequently, the squares of the differences are added.

To test the claim about the population mean μ at the level of significance α, we can perform a one-sample t-test.

Given:

Claim: μ > 29 (right-tailed test)

α = 0.05

σ = 1.2 (population standard deviation)

Sample statistics: x = 29.3 (sample mean), n = 50 (sample size)

We can follow these steps to conduct the hypothesis test:

Step 1: Formulate the null and alternative hypotheses.

The null hypothesis (H₀): μ ≤ 29

The alternative hypothesis (Hₐ): μ > 29

Step 2: Determine the significance level.

The significance level α is given as 0.05. This represents the maximum probability of rejecting the null hypothesis when it is actually true.

Step 3: Calculate the test statistic.

For a one-sample t-test, the test statistic is given by:

t = (x - μ) / (σ / √(n))

In this case, x = 29.3, μ = 29, σ = 1.2, and n = 50. Plugging in the values, we get:

t = (29.3 - 29) / (1.2 / √(50))

= 0.3 / (1.2 / 7.07)

= 0.3 / 0.17

≈ 1.76

Step 4: Determine the critical value.

Since it is a right-tailed test, we need to find the critical value that corresponds to the given significance level α and the degrees of freedom (df = n - 1).

Looking up the critical value in a t-table with df = 49 and α = 0.05, we find the critical value to be approximately 1.684.

Step 5: Make a decision and interpret the results.

If the test statistic (t-value) is greater than the critical value, we reject the null hypothesis; otherwise, we fail to reject the null hypothesis.

In this case, the calculated t-value is approximately 1.76, which is greater than the critical value of 1.684. Therefore, we reject the null hypothesis.

hence, Based on the sample data and the hypothesis test, there is sufficient evidence to support the claim that the population mean μ is greater than 29 at the significance level of 0.05.

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Combine like terms , we get \(g^3+3g^2+2g\).

In Algebra, the like terms are defined as the terms that contain the same variable which is raised to the same power. In algebraic like terms, only the numerical coefficients can vary. We can combine the like terms to simplify the algebraic expressions so that the result of the expression can be obtained very easily.

For example, 4x + 10x is an algebraic expression with like terms. In order to simplify this algebraic expression, we can add the like terms. Thus, the simplification of the given expression is 14x. In the same way, you can perform all the arithmetic operations on the like terms.

Collect like terms:

\(g^3+g^2+g+2g^2+g\)

Combine like terms:

\(g^3+3g^2+2g\)

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650 adult tickets were sold.

Let's denote the number of adult tickets sold by A and the number of child tickets sold by C.

From the problem, we know that:

A + C = 1000 (the total number of tickets sold is 1000)

8.50A + 4.50C = 7100 (the total revenue from ticket sales is $7100)

We can use the first equation to solve for A in terms of C:

A = 1000 - C

Substituting this expression for A into the second equation, we get:

8.50(1000 - C) + 4.50C = 7100

Expanding and simplifying:

8500 - 8.50C + 4.50C = 7100

4C = 1400

C = 350

So 350 child tickets were sold. We can use the first equation to find the number of adult tickets sold:

A + 350 = 1000

A = 650

Therefore, 650 adult tickets were sold.

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Answer:

$1,008.15

Step-by-step explanation:

550÷30= 18.33

18.33×55= 1,008.15

hope this helped !

Answer:

$1,008.15

Step-by-step explanation:

The matrix of a quadratic form is always a symmetric matrix.A quadratic form is a mathematical expression that consists of variables raised to the power of two, multiplied by coefficients, and added together.

It can be represented in matrix form as Q(x) = x^T A x, where x is a vector of variables and A is the matrix of coefficients. The matrix A is known as the matrix of the quadratic form.

To show that the matrix of a quadratic form is symmetric, let's consider the expression Q(x) = x^T A x. Using the properties of matrix transpose, we can rewrite this expression as Q(x) = (x^T A^T) x. Since the transpose of a matrix A is denoted as A^T, we can see that A^T is the same as A, as A is already a matrix.

Therefore, we have Q(x) = x^T A x = x^T A^T x. This implies that the matrix of the quadratic form A is symmetric, as A^T = A. In other words, the elements of the matrix A are symmetric with respect to the main diagonal. This property holds true for any quadratic form, regardless of its coefficients or variables, making the matrix of a quadratic form symmetric.

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Answer:

262,144

Step-by-step explanation:

2^0 = 1

(2^6)^3 = 2^18 = 262,144

Answer: 262,144.

Step-by-step explanation: (26)3(20)

=(643)(20)

=262144(20)

=(262144)(1)

=262144

Answer: 11.4 cm

Step-by-step explanation:

190/25 = 7.6

7.6 x 1.5 = 11.4

Answer

the two cities are 11.4 cm apart on the map

Step-by-step explanation:

f(7) = 34

7² -5(7) +k = 34

49-35+k =34

14+k = 34

k = 34-14

k = 20

Step-by-step explanation:

f(7) = 34

7² -5(7) +k = 34

49-35+k =34

14+k =34

k = 34-14

k = 20

hope it's help

Answer:

C) (0,1)

Step-by-step explanation:

What is a y-intercept?

A y-intercept is a value when x=0, so up and down the y-axis of a graph.

Given this, we can see that x must be equal to 0 to have a y-intercept number.

The first option, (1,1), is located in the first quadrant, making this incorrect.

The second option, (1,0) is when y=0, so the point would be on the x-axis, making this also incorrect.

The third option, (0,1), is when x=0, meaning that the point would be on the y-axis, making this the correct option.

Hope this helps! :)

The correct response is d) All the above. The arithmetic mean is equal to the median, the median is equal to the mode, and the mode is equal to the arithmetic mean.

If the data are graphed symmetrically, the distribution demonstrates 0% skewness regardless of how long or fat the tails are. When the median of a data set is utilized, 50% of the data points in the collection have values lower than or equal to the median, and 50% of them have values greater than or equal to the median. The middle score in the set is known as the median. The first step in calculating the median is to order the data points from smallest to greatest. The median in an odd-numbered set will be the value that falls exactly in the middle of the list. You must determine the average of the two middle numbers in a set of even numbers. The average is determined by summing up each value individually and dividing that sum by the total number of observations.

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Answer:

\( 5\sqrt{3} \)

Step-by-step explanation:

here

tan(60)= p/b

\( \sqrt{3 } = \frac{y}{5} \)

\(y = 5\sqrt{3} \)

On solving the provided question, we can say that in the quadrilateral BD = 11, BC = 8, DC = 8 and perimeter of ABCD is = 38

A quadrilateral is a four-sided polygon in geometry that has four edges and four corners. The word is a derivative of the Latin words quadri and latus (meaning "side"). Having four sides, four vertices, and four corners, a rectangle is a two-dimensional form. Concave and convex come in primarily two varieties. Additionally, there are several subclasses of convex quadrilaterals, including trapezoids, parallelograms, rectangles, rhombuses, and squares. Four straight sides make up a rectangle, which is a two-dimensional form. There are several different types of quadrilaterals, including parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.

in the quadrilateral

BD = 11 ( equal angle have equal sides)

BC = 8

DC = 8

perimeter of ABCD is = 38

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Answer:

the answer should be b and e

Answer:

its B and D.

Step-by-step explanation:

Michelle's score is given by the following formula

where, S is her final score and C represent the number of correct answers.

Since she must get at least a 92, then S = 92

therefore,

She must get at least 46 correct questions.

The height of the 10th bounce of the ball will be 0.6 feet.

A geometric sequence is a sequence in which each term is found by multiplying the preceding term by the same value.

The nth term of the geometric sequence is given by

\(\sf T_n=ar^{n-1}\)

Where,

According to the given question.

During the first bounce, height of the ball from the ground, a = 4.5 feet

And, the each successive bounce is 73% of the previous bounce's height.

So,

During the second bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 10\)

\(=\dfrac{73}{100}(10)\)

\(\sf = 0.73 \times 10\)

\(\sf = 7.3 \ feet\)

During the third bounce, the height of ball from the ground

\(\sf = 73\% \ of \ 7.3\)

\(=\dfrac{73}{100}(7.3)\)

\(\sf = 5.33 \ feet\)

Like this we will obtain a geometric sequence 7.3, 5.33, 3.11, 2.23,...

And the common ratio of the geometric sequence is 0.73

Therefore,

The sixth term of the geometric sequence is given by

\(\sf T_{10}=10(0.73)^{10-1\)

\(\sf T_{10}=10(0.73)^{9\)

\(\sf T_{10}=10(0.059)\)

\(\sf T_{10}=0.59\thickapprox0.6 \ feet\)

Hence, the height of the 10th bounce of the ball will be 0.6 feet.

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