What will be the result of substituting 2 for x in both expressions below?
+4
x+6-x-2
O Both expressions equal 5 when substituting 2 for x because the expressions are equivalent.
O Both expressions equal 6 when substituting 2 for x because the expressions are equivalent.
O One expression equals 5 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.
One expression equals 6 when substituting 2 for x, and the other equals 2 because the expressions are not
equivalent.

In a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case).

The experimental probability and theoretical probability can be compared in a trial of 10 versus 500 by understanding the concepts behind each type of probability.

Theoretical probability is based on mathematical calculations and is determined by analyzing the possible outcomes of an event. It relies on the assumption that the event is equally likely to occur, and it can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. Theoretical probability is often considered the expected or ideal probability.

On the other hand, experimental probability is determined through actual observations or experiments. It involves conducting the event multiple times and recording the outcomes to determine the relative frequency of a specific outcome. The experimental probability is an estimation based on the observed data.

In the given trial of 10 versus 500, we can expect the experimental probability to be closer to the theoretical probability when the number of trials (or repetitions) is larger. In this case, with 500 trials, the experimental probability is likely to be a more accurate representation of the true probability.

When the number of trials is small, such as only 10, the experimental probability may deviate significantly from the theoretical probability. With a smaller sample size, the observed outcomes may not accurately reflect the expected probabilities calculated theoretically.

In summary, in a trial of 10 versus 500, the experimental probability is expected to be closer to the theoretical probability when there are more trials (500 in this case). As the number of trials increases, the observed frequencies are likely to converge towards the expected probabilities calculated theoretically.

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The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

To represent the relationship between the number of hours Steven babysits (x) and the amount he charges (y), we can use a linear equation in the form of y = mx + b, where m is the slope and b is the y-intercept.

From the given information, we can identify two data points:

(4, 31.00) and (8, 62.00)

Using these points, we can calculate the slope (m) using the formula:

m = (y2 - y1) / (x2 - x1)

m = (62.00 - 31.00) / (8 - 4)

m = 31.00 / 4

m = 7.75

Now, we can substitute one of the points and the slope into the equation to find the y-intercept (b).

Using the point (4, 31.00):

31.00 = 7.75(4) + b

31.00 = 31.00 + b

b = 0

Therefore, the equation that represents the relationship between the number of hours Steven babysits (x) and the amount he charges (y) is:

y = 7.75x

The equation is y = 7.75x, where x is the number of hours Steven babysits and y is the amount he charges.

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The calculated value of m in the triangular prism is 13

From the question, we have the following parameters that can be used in our computation:

The triangular prism

Where, we have

Volume = 1170

The volume of the triangular prism is calculated as

Volume = Base area * Height

So, we have

1/2 * m * 18 * 10 = 1170

Evaluate the products

This gives

90m = 1170

So, we have

m = 13

Hence, the value of m is 13

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Answer:

[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]

Step-by-step explanation:

The graph of the solid black line is the cosine parent function, y = cos(x).

The standard form of a cosine function is:

[tex]\boxed{y = A \cos(B(x + C)) + D}[/tex]

where:

From inspection of the graph, the x-values of the turning points (peaks and troughs) of the parent function and the new function are the same. Therefore, the period of both functions is the same, and there has been no horizontal shift. So, B = 1 and C = 0.

The mid-line of the new function is y = 3. Therefore, D = 3.

The y-value of the peaks is y = 5. The amplitude is the distance from the mid-line to the peak. Therefore, A = 2.

Substituting these values into the standard formula we get:

[tex]y = 2 \cos(1(x + 0)) + 3[/tex]

[tex]y=2 \cos (1(x))+3[/tex]

[tex]y= 2 \cos(x) + 3[/tex]

Therefore, the equation of the trigonometric graph is:

[tex]y=\boxed{2}\:\cos \left(\boxed{1}\;x\right)+\boxed{3}[/tex]

1.) The exponential form for the number of yo-yos, 1,000,000,000, is [tex]10^9[/tex]. This represents 10 raised to the power of the number of zeros in the original number.

2.) For Mrs. Penn's vegetable garden, with 8 rows and 8 columns of 1cm squares, the total number of small squares is 64. This can be expressed as [tex]2^6[/tex] , where 2 is the base number and 6 represents the exponent obtained from repeated multiplication.

1.) To write the number of yo-yos in exponential form, we can use the base 10 since we have a decimal system. The given number of yo-yos is 1,000,000,000. We can express it as 10 raised to the power of a certain exponent that represents the number of zeros in the original number.

In this case, the number has 9 zeros, so we can write it as [tex]10^9[/tex]. The exponential form for the number of yo-yos is [tex]10^9.[/tex]

2.) In Mrs. Penn's vegetable garden, there are 8 rows and 8 columns in each bed. Each row and column is 1cm wide. We need to calculate the number of small squares, each measuring 1cm by 1cm, in the grid.

Since there are 8 rows and 8 columns, we can multiply these two numbers together to find the total number of small squares. 8 multiplied by 8 equals 64.

The exponential form represents repeated multiplication of the base number. In this case, the base number is 64 since we have 64 small squares. To write it in exponential form, we need to determine the exponent that represents the number of times 64 is multiplied by itself.

Since 64 is 2 raised to the power of [tex]6 (2^6)[/tex], we can express it as [tex](2^6)^1[/tex]. Simplifying this, we get [tex]2^(6*1)[/tex] which equals [tex]2^6.[/tex]

Therefore, the exponential form for the number of small squares in the grid is [tex]2^6.[/tex]

In summary, the number of yo-yos in exponential form is [tex]10^9[/tex], and the number of small squares in the grid is [tex]2^6.[/tex]

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Answer:

x = 0.39 or

x = -1.72

Step-by-step explanation:

The quadrateic formula is:

[tex]x = \frac{-b\pm\sqrt{b^2 - 4ac} }{2a}[/tex]

eq: 3x² + 4x - 2

which is of the form ax² + bx + c = 0

where a = 3, b = 4 and c = -2

sub in quadratic formuls,

[tex]x = \frac{-4\pm\sqrt{4^2 - 4(3)(-2)} }{2(3)}\\\\=\frac{-4\pm\sqrt{16 + 24} }{6}\\\\=\frac{-4\pm\sqrt{40} }{6}\\\\=\frac{-4\pm2\sqrt{10} }{6}\\\\=\frac{-2\pm\sqrt{10} }{3}\\\\=\frac{-2+\sqrt{10} }{3} \;or\;=\frac{-2-\sqrt{10} }{3}\\\\=0.39 \;or\; -1.72[/tex]

Answer:

I wish you good luck in finding your answer

Answer: 115

Step-by-step explanation:

Answer : Focus is (0,3)

To find the focus of the parabola defined by the equation (y - 3)² = -8(x - 2), we can compare it with the standard form of a parabolic equation: (y - k)² = 4a(x - h).

In the given equation, we have:

(y - 3)² = -8(x - 2)

Comparing it with the standard form, we can determine the values of h, k, and a:

h = 2

k = 3

4a = -8

Solving for a, we get:

4a = -8

a = -8/4

a = -2

Therefore, the vertex of the parabola is (h, k) = (2, 3), and the value of 'a' is -2.

The focus of the parabola can be found using the formula:

F = (h + a, k)

Substituting the values, we get:

F = (2 + (-2), 3)

F = (0, 3)

Therefore, the focus of the parabola defined by the equation (y - 3)² = -8(x - 2) is at the point (0, 3).

Answer:

Focus = (0, 3)

Step-by-step explanation:

The focus is a fixed point located inside the curve of the parabola.

To find the focus of the given parabola, we first need to find the vertex (h, k) and the focal length "p".

The standard equation for a sideways parabola is:

[tex]\boxed{(y-k)^2=4p(x-h)}[/tex]

where:

If p > 0, the parabola opens to the right, and if p < 0, the parabola opens to the left.

Given equation:

[tex](y-3)^2=-8(x-2)[/tex]

Compare the given equation to the standard equation to determine the values of h, k and p:

The formula for the focus is (h+p, k).

Substituting the values of h, p and k into the formula, we get:

[tex]\begin{aligned}\textsf{Focus}&=(h+p,k)\\&=(2-2,3)\\&=(0,3)\end{aligned}[/tex]

Therefore, the focus of the parabola is (0, 3).

By conducting a statistical test with the provided data and using a significance level of 0.05 and a critical value of 0.811, the educator can determine whether the number of absences significantly affects the final grade of the students.

To analyze the relationship between the number of absences and the final grade of students, an educator collected data from a sample. The obtained data reveals that for 10 absences, the corresponding final grade was 70. In order to determine whether the number of absences significantly impacts the final grade, a statistical test is needed.

The information provided, "Test at α = 0.05, XCV = 0.811," suggests that the educator is referring to a significance level (α) of 0.05 and the critical value (XCV) associated with this level is 0.811.

To conduct a hypothesis test, the educator needs to set up the null (H0) and alternative (Ha) hypotheses. In this case, the null hypothesis would assume that the number of absences does not have a significant effect on the final grade. The alternative hypothesis would assume that the number of absences does have a significant effect on the final grade.

Using the obtained data, the educator would perform the statistical test, such as a correlation analysis or a regression analysis, to determine the strength and significance of the relationship between absences and final grade.

If the test statistic (such as the correlation coefficient or regression coefficient) exceeds the critical value, the null hypothesis would be rejected, suggesting that the number of absences does have a significant impact on the final grade.

The educator can then interpret the results, considering factors such as the direction and strength of the relationship. Additionally, they may explore other variables or factors that could be influencing the final grade and further refine their analysis.

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Answer:

f(x) = 4x² - 2x + 11

f'(x) = 8x - 2

m = f'(3) = 8(3) - 2 = 24 - 2 = 22

41 = 22(3) + b

41 = 66 + b

b = -25

y = 22x - 25

Answer:

(- 4, - 4 )

Step-by-step explanation:

x - 5y = 16 → (1)

4x - 2y = - 8 → (2)

multiplying (1) by - 4 and adding to (2) will eliminate x

- 4x + 20y = - 64 → (3)

add (2) and (3) term by term to eliminate x

(4x - 4x) + (- 2y + 20y) = - 8 - 64

0 + 18y = - 72

18y = - 72 ( divide both sides by 18 )

y = - 4

substitute y = - 4 into either of the 2 equations and solve for x

substituting into (1)

x - 5(- 4) = 16

x + 20 = 16 ( subtract 20 from both sides )

x = - 4

solution is (- 4, - 4 )

The measure of angle of arc UB is 46°

An arc is a part of the circumference.

If two arcs in circles with equal radii have the same length, then their central angles (and measures) will be equal.

To find the measure of angle of arc UB, we use the theorem that says;

angle I = 1/2( angle ZC - angle UB)

angle I = 48°

angle ZC = 142°

Therefore ;

represent angle UB by x

48 = 1/2( 142-x)

142 - x = 96

x = 142 -96

x = 46°

Therefore the measure of angle of arc UB is 46°

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Answer:

Step-by-step explanation:

The correct statement about the mean is:

The mean equals the sum of all observations divided by the number of observations.

The mean is a commonly used measure of central tendency. It is calculated by summing up all the observations and then dividing the sum by the total number of observations. It provides an average value that represents the typical value of the data set.

To calculate the mean, it is not necessary to order the observations from least to most. The order of the observations does not affect the mean calculation.

The mean is not necessarily a whole number. It can be a decimal or a fraction, depending on the data set and the values of the observations. The mean represents the balance point of the data set and can take on any real number value.

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Answer:

he spent 2hours 50minutes snowboarding

the time he spent skiing and snowboarding minus the time he skied

5hours minus 2hours 10minutes

The opposite of -5 can be represented by situations such as a temperature increase of 5 degrees and a financial gain of $5. Additionally, it can also represent a distance traveled of 5 miles and a weight gain of 5 pounds.

The opposite of -5 is 5. The opposite of a number represents the number with the opposite sign. Here are three situations that can be represented by the opposite of -5:

Situation 1: Temperature Change

If the temperature is currently -5 degrees Celsius and it undergoes a change in the opposite direction, it means it increases by 5 degrees. Therefore, the opposite of -5 represents a temperature increase of 5 degrees.

Situation 2: Financial Gain

Suppose you owe someone $5, and you receive the opposite of that amount. The opposite of owing $5 would be gaining $5. So, the opposite of -5 represents a financial gain of $5.

Additional situations that can be represented by the opposite of -5:

Situation 3: Distance Traveled

If a car has traveled -5 miles, indicating it has moved in the opposite direction, the opposite of that distance would be 5 miles. So, the opposite of -5 represents a distance traveled of 5 miles.

Situation 4: Weight Gain

Imagine someone loses 5 pounds (which can be represented as -5). The opposite of losing 5 pounds would be gaining 5 pounds. Thus, the opposite of -5 represents a weight gain of 5 pounds.

In each of these situations, the opposite of -5 denotes a change in the opposite direction or the reverse of the initial value.

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For a collection of numbers to be considered a sequence, it is essential that they have a law of formation, are ordered in a specific manner, and can be either finite or infinite.

B: They have a law of formation:

A sequence is a set of numbers arranged in a specific order according to a rule or pattern. The numbers in a sequence are not random but follow a specific law of formation.

This law can be a mathematical formula, a recursive relationship, or any other systematic pattern that determines the values of the sequence. Without a well-defined law of formation, a collection of numbers cannot be considered a sequence.

C: They are ordered:

In a sequence, the numbers are arranged in a specific order or sequence. The order of the numbers is crucial and defines the pattern and structure of the sequence.

Each number in the sequence has a unique position or index that determines its place in the sequence. The order of the numbers allows us to identify the next number or predict the pattern of the sequence. Without the concept of order, the numbers would simply be a set of unrelated elements and not a sequence.

A: They may or may not be infinite:

Sequences can be finite or infinite. A finite sequence has a specific number of terms, and once the pattern or rule is established, the sequence ends.

On the other hand, an infinite sequence continues indefinitely, and its terms extend infinitely in one direction or both directions. Whether a sequence is finite or infinite depends on the context and the specific rule or pattern that governs its formation.

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Note: the translated question is:

To have a sequence it is essential that the numbers that form it:

A: be infinite

B: they have a law of formation C: they are ordered

The equation of the normal line to the curve x^2y^2 = 4 at the point (-1,-2) is y = x - 1.

To find the tangent line and normal line to the curve x^2y^2 = 4 at the point (-1,-2), we need to determine the derivative of the curve equation with respect to x and evaluate it at the given point.

First, let's differentiate the equation x^2y^2 = 4 implicitly with respect to x using the chain rule:

2x * (y^2) + 2y * (2xy * dy/dx) = 0

Simplifying the equation, we have:

2xy^2 + 4xy(dy/dx) = 0

Now, let's find the value of dy/dx at the point (-1,-2). Substitute x = -1 and y = -2 into the equation:

2*(-1)(-2)^2 + 4(-1)*(-2)(dy/dx) = 0

Simplifying further:

8 + 8(dy/dx) = 0

8(dy/dx) = -8

dy/dx = -1

We have found the derivative dy/dx at the point (-1,-2), which is -1. This represents the slope of the tangent line to the curve at that point.

Using the point-slope form of a line, we can write the equation of the tangent line as:

y - y₁ = m(x - x₁)

Substituting the values of (-1,-2) and dy/dx = -1 into the equation, we have:

y - (-2) = -1(x - (-1))

y + 2 = -1(x + 1)

y + 2 = -x - 1

y = -x - 3

Therefore, the equation of the tangent line to the curve x^2y^2 = 4 at the point (-1,-2) is y = -x - 3.

To find the normal line, we know that the slope of the normal line is the negative reciprocal of the slope of the tangent line. Therefore, the slope of the normal line is 1.

Using the point-slope form of a line again, we can write the equation of the normal line as:

y - y₁ = m'(x - x₁)

Substituting the values of (-1,-2) and m' = 1 into the equation, we have:

y - (-2) = 1(x - (-1))

y + 2 = x + 1

y = x - 1

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Answer:  Choice C.   [tex]\displaystyle \boldsymbol{-\frac{\sqrt{5}}{3}}[/tex]

===================================================

Work Shown:

Part 1

[tex]\sin^2(\theta)+\cos^2(\theta) = 1\\\\\cos^2(\theta) = 1-\sin^2(\theta)\\\\\cos(\theta) = -\sqrt{1-\sin^2(\theta)} \ \ \text{ ..... cosine is negative in Q2}\\\\\cos(\theta) = -\sqrt{1-\left(\frac{2}{3}\right)^2}\\\\\\cos(\theta) = -\sqrt{1-\frac{4}{9}}\\\\[/tex]

Part 2

[tex]\cos(\theta) = -\sqrt{\frac{9}{9}-\frac{4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{9-4}{9}}\\\\\cos(\theta) = -\sqrt{\frac{5}{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{\sqrt{9}}\\\\\cos(\theta) = -\frac{\sqrt{5}}{3}\\\\[/tex]

a)In a typical week, Maybelle will earn a total of: $600 + $250 = $850

b) Her total earnings for the week would be: $600 + $300 = $900

c)  Her paycheck will be reduced by $100.

d) Her wage earnings should remain the same assuming she still works at least 40 hours per week.

To calculate Maybelle's earnings in a typical week, we first need to determine the minimum number of hours she works. Since she earns $15 per hour for at least 40 hours per week, her minimum wage earnings are:

$15 x 40 = $600

In addition to her wage earnings, Maybelle earns a commission of 10% for each pair of shoes she sells. Since she is expected to sell $2,500 worth of shoes every week, her commission earnings are:

$2,500 x 0.10 = $250

b) If Maybelle sells $3,000 worth of shoes in one week, her commission earnings would be:

$3,000 x 0.10 = $300

On top of her wage earnings of $600 (based on working at least 40 hours at $15 per hour)

c) If customers return $1,000 worth of shoes the next week, Maybelle's commission earnings will not be affected. However, her wage earnings will be reduced by the amount of the returned shoes, which is $1,000 x 0.10 = $100.

d) With an economic downturn and sales slump, Maybelle's earnings from commission will likely decrease since she will sell fewer shoes. However, her total earnings will likely decrease due to the decrease in commission earnings.

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The number of wheelbarrow loads of soil required for this project is 71.

The landscaper uses a wheelbarrow to transport soil to a particular region of the garden. A wheelbarrow can accommodate roughly 6 cubic feet of soil. Once the pile has a diameter of 13 feet and a height of 3 feet, the landscaper determines that there will be enough soil for the project.

Area of a cone =1/3πr²hwhere r = 13/2 feet and h = 3 feet.

Substituting the given values to find the area of the cone.1/3 x 3.14 x (6.5)² x 3 = 422.55 cubic feet.Then, divide the total amount of soil required by the volume of soil that a wheelbarrow can hold to determine the number of wheelbarrow loads required.

Number of wheelbarrow loads = (Volume of soil needed) / (Volume of one wheelbarrow)Volume of one wheelbarrow = 6 cubic feet.The total volume of soil required is 422.55 cubic feet.

Therefore, the number of wheelbarrow loads required is:Number of wheelbarrow loads = (422.55) / (6) = 70.42 ≈ 71 wheelbarrow loads, which is the final answer.

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The period of the trigonometric function is -2π/3.

To determine the period of the trigonometric function based on the given information, we need to consider the pattern of the graph and identify the interval over which it repeats.

Given that the maximum point is at (-π, 7.7) and the minimum point is at (-1/3π, -6.7), we can observe that the graph completes one full oscillation between these two points.

The distance between the maximum and minimum points corresponds to half of the period. Therefore, the full period of the function can be found by doubling this distance.

The distance between (-π, 7.7) and (-1/3π, -6.7) can be calculated as follows:

Δx = -1/3π - (-π) = π/3π - π = -π/3

Since the full period is twice this distance, we multiply by 2:

2 * (-π/3) = -2π/3

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Answer:

Step-by-step explanation:

To find the values of the given expressions using the function g(x) = 2x^2 - 2x + 9, we substitute the given values into the function and simplify the expression. Let's calculate each of the following:

a) g(0)

To find g(0), substitute x = 0 into the function:

g(0) = 2(0)^2 - 2(0) + 9

g(0) = 0 - 0 + 9

g(0) = 9

b) g(-1)

To find g(-1), substitute x = -1 into the function:

g(-1) = 2(-1)^2 - 2(-1) + 9

g(-1) = 2(1) + 2 + 9

g(-1) = 2 + 2 + 9

g(-1) = 13

c) g(2)

To find g(2), substitute x = 2 into the function:

g(2) = 2(2)^2 - 2(2) + 9

g(2) = 2(4) - 4 + 9

g(2) = 8 - 4 + 9

g(2) = 13

d) g(-x)

To find g(-x), substitute x = -x into the function:

g(-x) = 2(-x)^2 - 2(-x) + 9

g(-x) = 2x^2 + 2x + 9

e) g(1 - t)

To find g(1 - t), substitute x = 1 - t into the function:

g(1 - t) = 2(1 - t)^2 - 2(1 - t) + 9

g(1 - t) = 2(1 - 2t + t^2) - 2 + 2t + 9

g(1 - t) = 2 - 4t + 2t^2 - 2 + 2t + 9

g(1 - t) = 2t^2 - 2t + 9

Therefore:

a) g(0) = 9

b) g(-1) = 13

c) g(2) = 13

d) g(-x) = 2x^2 + 2x + 9

e) g(1 - t) = 2t^2 - 2t + 9

Answer:

Step-by-step explanation:

To find the time it takes for the turtle to reach the pond, we can use the formula:

Time = Distance / Speed

Given that the turtle travels at a speed of 1/12 mile per hour and the distance to the pond is 5/6 mile, we can substitute these values into the formula:

Time = (5/6) / (1/12)

To simplify this, we can multiply the numerator by the reciprocal of the denominator:

Time = (5/6) * (12/1) = (5 * 12) / 6 = 60 / 6 = 10

Therefore, it will take the turtle 10 hours to reach the pond.

The missing statement 4 of the two column proof of AD ║ BC is:

Statement 4: m∠1 + m∠4 = 180°

The complete two column proof to show that AD || BC is as follows:

Statement 1: AD ║ DC

Reason 1: Given

Statement 2: m∠2 = m∠4

Reason 2: Given

Statement 3: ∠1 and ∠3 are supplements

Reason 3: Same side interior angles theorem

Statement 4: m∠1 + m∠4 = 180°

Reason 4: Def. of Supplementary angles

Statement 5: m∠1 + m∠2 = 180°

Reason 5: Substitution

Statement 6: ∠1 and ∠2 are supplements

Reason 6: Def. of Supplementary angles

Statement 7: AD ║ BC

Reason 7: Converse same side interior angles thm

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The equations of the asymptotes of the hyperbola are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

To find the equations of the asymptotes of the hyperbola defined by the equation:

[tex]-25x^2 + 81y^2 + 100x + 1134y + 1844 = 0[/tex]

We can rewrite the equation in the standard form by isolating the x and y terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y + 1844 = 0[/tex]

Rearranging the terms:

[tex]-25x^2 + 100x + 81y^2 + 1134y = -1844[/tex]

Next, let's complete the square for both the x and y terms:

[tex]-25(x^2 - 4x) + 81(y^2 + 14y) = -1844\\-25(x^2 - 4x + 4 - 4) + 81(y^2 + 14y + 49 - 49) = -1844\\-25((x - 2)^2 - 4) + 81((y + 7)^2 - 49) = -1844[/tex]

Expanding and simplify

[tex]-25(x - 2)^2 + 100 - 81(y + 7)^2 + 3969 = -1844\\-25(x - 2)^2 - 81(y + 7)^2 = -1844 - 100 - 3969\\-25(x - 2)^2 - 81(y + 7)^2 = -4913[/tex]

Dividing both sides by -4913:

[tex](x - 2)^2/(-4913/25) - (y + 7)^2/(-4913/81) = 1[/tex]

Comparing this equation to the standard form of a hyperbola:

[tex](x - h)^2/a^2 - (y - k)^2/b^2 = 1[/tex]

We can determine that the center of the hyperbola is (h, k) = (2, -7). The value of [tex]a^2[/tex] is (-4913/25), and the value of [tex]b^2[/tex] is (-4913/81).

The equations of the asymptotes can be found using the formula:

y - k = ±(b/a)(x - h)

Substituting the values we found:

y + 7 = ±(√(-4913/81) / √(-4913/25))(x - 2)

Simplifying:

y + 7 = ±(√(4913) / √(81)) × √(25/4913) × (x - 2)

y + 7 = ±(√(4913) / 9) × √(25/4913) × (x - 2)

Rationalizing the denominators and simplifying:

y + 7 = ±(5/9) ×(x - 2)

Finally, rearranging the equation to isolate y:

y = ±(5/9)x - 10/9 - 7

Simplifying further:

y = ±(5/9)x - 79/9

In light of this, the equations for the hyperbola's asymptotes are y = (5/9)x - 79/9 and y = -(5/9)x + 79/9.

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Answer:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]

Step-by-step explanation:

First, rewrite the given equation in the standard form of a hyperbola by completing the square.

Given equation:

[tex]-25x^2+81y^2+100x+1134y+1844=0[/tex]

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side:

[tex]-25x^2+100x+81y^2+1134y=-1844[/tex]

Factor out the coefficient of the x² term and the coefficient of the y² term:

[tex]-25(x^2-4x)+81(y^2+14y)=-1844[/tex]

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

[tex]-25(x^2-4x+4)+81(y^2+14y+49)=-1844-25(4)+81(49)[/tex]

Factor the two perfect trinomials on the left side and simplify the right side:

[tex]-25(x-2)^2+81(y+7)^2=2025[/tex]

Divide both sides by the number of the right side so the right side equals 1:

[tex]\dfrac{-25(x-2)^2}{2025}+\dfrac{81(y+7)^2}{2025}=\dfrac{2025}{2025}[/tex]

      [tex]\dfrac{-(x-2)^2}{81}+\dfrac{(y+7)^2}{25}=1[/tex]

        [tex]\dfrac{(y+7)^2}{25}-\dfrac{(x-2)^2}{81}=1[/tex]

As the y²-term is positive, the hyperbola is vertical (opening up and down).

The standard equation of a vertical hyperbola is:

[tex]\boxed{\dfrac{(y-k)^2}{a^2}-\dfrac{(x-h)^2}{b^2}=1}[/tex]

Therefore, comparing this with the rewritten equation:

The formula for the equations of the asymptotes of a vertical hyperbola is:

[tex]\boxed{y=\pm \dfrac{a}{b}(x-h)+k}[/tex]

Substitute the values of h, k, a and b into the formula:

[tex]y=\pm \dfrac{5}{9}(x-2)-7[/tex]

Therefore, the equations for the asymptotes are:

[tex]\boxed{y=\dfrac{5}{9}x-\dfrac{73}{9}}\;\; \textsf{and} \;\;\boxed{ y=-\dfrac{5}{9}x-\dfrac{53}{9}}[/tex]

Answer:

x=-24

Step-by-step explanation:

2/3*1/2x = 2/6x
2/3*12=8
1/2*1/3x=1/6x
1/2*14=7
2/6x+8=1/6x+7-3
2/6x+8=1/6x+4
Takeaway 1/6x both sides to make x on one side
1/6x+8=4
take away 8 both sides to make x on its own
1/6x=-4
divide 1/6 both sides
x=-24
Hope this helps, (brainliest pleasee thanks)

Answer:

In the given equation, V(r) represents the volume of the air inside a basketball when the radius of the basketball is r.

Step-by-step explanation:

The function V(r) represents the volume of the basketball when the radius is r. So, the correct interpretation is that V(r) represents "the volume of the basketball when the radius is r."

Answer:    -8 ≥ x

Step-by-step explanation:

Let x be the number, we set up an inequality:

-183 ≥ 9 + 24x    [we use ≥ to present "at least"]

-192 ≥ 24x

  -8 ≥ x