Consider the equation x 5 − 2 = 11. Each of these values might be the solution to this equation. Verify the correct solution by substituting each value into the equation. Which is the correct solution?

The radius of the circle is approximately 22.9 meters when rounded to the nearest tenth.

To find the radius of the circle, we need to use the formula:

arc length = radius x central angle (in radians)

Since the central angle is given in degrees, we need to convert it to radians by multiplying it by π/180.

First, let's convert the central angle:

258° x π/180 ≈ 4.5 radians

Now we can plug in the values into the formula and solve for the radius:

102.9 = r x 4.5

r = 102.9 / 4.5

r ≈ 22.9

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Answer:

1.  x = mp - mn

2. g = (x-2)/3

Step-by-step explanation:

Making a variable the subject of the equation means finding the equation for x in terms of all the other variables.

1. Make x the subject of the equation.

\(m =n+\frac{x}{p}\\ mp = mn + x\\x = mp-mn\)

2. Make g the subject of the equation.

\(x = 3g+2\\x-2 = 3g\\g = \frac{x-2}{3}\)

Answer:

For the first image, to find the value of x, we need to use the fact that the angles in a triangle add up to 180 degrees.

We can see that the angle measures for the two angles shown are x and 70 degrees. The third angle is not shown but is opposite the 85-degree side. So, we know that:

x + 70 + 35 = 180

Simplifying the equation, we get:

x = 75

Therefore, the value of x is 75 degrees.

For the second image, we can see that we have a system of two equations with two variables:

x + y = 8

2x - y = -1

We can solve for one of the variables in terms of the other by rearranging one of the equations. For example, from the first equation, we have:

y = 8 - x

We can substitute this expression for y into the second equation to get:

2x - (8 - x) = -1

Simplifying the equation, we get:

3x = 7

So, x = 7/3.

To find the value of y, we can substitute the value of x into either equation, for example:

x + y = 8

7/3 + y = 8

Simplifying the equation, we get:

y = 17/3

Therefore, the values of x and y are 7/3 and 17/3, respectively.

Answer:

d

Step-by-step explanation:

m= 6-10 / -1-(-5) = -2

Hope this Helps :)

The complete factorization of the equation is \[6x^3 - 24x^2 - 66x + 180 = 6(x - 5)(x + 3)(x - 2)\].

We are given that one of the roots of the cubic equation \[ 6x^3 - 24x^2 - 66x + 180 = 0\] is 5. We can use this information to factor the equation completely using synthetic division.

First, we write the equation in the form \[(x - 5)(ax^2 + bx + c) = 0\], where a, b, and c are constants that we need to determine. We know that 5 is a root of the equation, so we can use synthetic division to divide the equation by \[(x - 5)\] and find the quadratic factor.

Performing synthetic division, we get:

5 | 6 - 24 - 66 180

| 0 -24 - 450

----------------

6 - 24 - 90 0

So, we have \[6x^3 - 24x^2 - 66x + 180 = (x - 5)(6x^2 - 24x - 90)\]. Now, we can factor the quadratic factor using either factoring by grouping or the quadratic formula. Factoring out a common factor of 6, we get:

\[6(x^2 - 4x - 15) = 6(x - 5)(x + 3)\]

Therefore, the complete factorization of the equation is \[6x^3 - 24x^2 - 66x + 180 = 6(x - 5)(x + 3)(x - 2)\].

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Answer:

64 square centimeters

Step-by-step explanation:

The surface are of a pyramid is found by finding the sum of the area of the four sides and the base.

Finding the triangular face:

Area of triangle = \(\frac{1}{2} b h\) = \(\frac{1}{2}*4*6 = 12\)

12 * 4 (4 sides) = 48 square cm

Finding the Base = \(w * l = 4 * 4 = 16\)

Finally, we add it together. 48 + 16 = 64

To calculate the standard deviation of the sampling distribution of p-hat, the answer will be 59 students.

By calculating,

600/10=60 and 59 students which is less than 10% of the population.

A sampling distribution, also known as a finite-sample distribution, in statistics is the probability distribution of a given random-sample-based statistic. The sampling distribution is the probability distribution of the values that the statistic takes on if an arbitrarily large number of samples, each involving multiple observations (data points), were used separately to compute one value of a statistic (such as, for example, the sample mean or sample variance) for each sample. Although only one sample is frequently observed, the theoretical sampling distribution can be determined.

Because they offer a significant simplification before drawing conclusions using statistics, sampling distributions are crucial in the field. They enable analytical decisions to be made based on the probability distribution of a statistic rather than the combined probability distribution of all the individual sample values

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We have that the prime factors of 84 are:

2, 2, 3 & 4.

For the formulas given, we will have:

84 = 7 * 12.

84 = 3 * 4 * 7

84 = 2 * 2 * 3 * 7

Answer: No

Step-by-step explanation:

There are infinitely many numbers. Numbers so big that they are beyond our comprehnsion. Numbers can also be infinitly small. A fraction is something less than a whole. So the answer is no you can't list them all.

The greatest profit that can be earned is given by profit(c) = 2P - kQ(c).

To get the greatest profit that can be earned from a commuter railway with a certain number of passengers per day and a fare of two dollars per day, follow these steps:

Step 1: Let the number of passengers per day be denoted by P.

Step 2: The amount earned from the fare each day is calculated as 2P dollars.

This is the revenue earned by the commuter railway.

Step 3: Let the fare be increased by x cents.

Therefore, the new fare per day is (200 + x) cents, or (2 + x/100) dollars.

Note that the original fare is 200 cents, or 2 dollars.

Step 4: Let the number of passengers who travel by the train after the fare is increased by x cents be denoted by Q(x).

Step 5: It is assumed that the fewer people travel by train as the fare increases.

Therefore, Q(x) is a decreasing function of x, i.e. as x increases, Q(x) decreases.

Additionally, Q(0) = P, since the number of passengers traveling when the fare is unchanged is P.

Step 6: Let C(x) denote the cost of running the commuter railway after the fare is increased by x cents.

This cost is assumed to be proportional to the number of passengers traveling by the train, since a higher number of passengers would require more trains and staff to run them.

Therefore, C(x) = kQ(x),

where k is a constant of proportionality.

Step 7: The profit earned by the commuter railway after the fare is increased by x cents is calculated as the difference between the revenue earned and the cost of running the train.

Therefore, profit(x) = 2P - kQ(x).

Step 8: The greatest profit that can be earned is obtained by finding the value of x that maximizes the profit.

This is equivalent to finding the value of x that minimizes the cost, since the revenue is fixed.

Therefore, we need to find the value of x that minimizes C(x). This is achieved by minimizing Q(x), since C(x) is proportional to Q(x).Step 9: To minimize Q(x), we can use the mean value theorem.

This theorem states that for any decreasing function f(x) and any value of a, there exists a unique value of x between 0 and a such that f(x) = f(a)/a * x.

This value of x is denoted by m(a) and is called the mean value of f(x) on [0, a].

Step 10: Applying this theorem to Q(x), we get Q(x) = Q(0) * (200 + x)/200 * m(x/200).

Therefore, to minimize Q(x), we need to find the value of x that maximizes m(x/200).

This value is denoted by c and is called the critical value of x. It satisfies the equation Q(c) = Q(0)/2.

Step 11: To find c, we need to solve the equation Q(c) = Q(0)/2 for c.

This is equivalent to solving the equation kQ(c) = kQ(0)/2 for c,

since C(x) = kQ(x).

Therefore, we need to find the value of c that satisfies the equation 2P - kQ(c) = P.

This is equivalent to solving the equation Q(c) = P/k.

Therefore, we need to find the value of c that satisfies the equation Q(c) = P/k/2.

Step 12: To find the greatest profit that can be earned, we need to substitute c into the expression for profit(x).

This gives the value of the profit that can be earned when the fare is increased by the critical value c.

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Answer:

B is correct I hope this helps.

Answer:

rounded to the nearest tenth is 0.4

The limit is equal to -5/9 as x approaches negative infinity.

To evaluate the limit, we can divide the numerator and denominator by the highest power of x, which is x^2. This gives:

lim (63/x^2 + 36/x + 9 - 5/x^2) / (6/x^2 + 36 + 9/x - 5/x^2)

As x approaches negative infinity, all the terms in the numerator and denominator tend to zero except for the constant terms. Therefore, the limit is equal to:

lim (-5/x^2) / (-5/x^2) = 1

Multiplying by the constant -5/9, we get:

lim (-5/9) * (1) = -5/9

Therefore, the limit is -5/9 as x approaches negative infinity.

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Answer:

The two solutions of the equation is (0,-4)(6,0).

The measure of the arc length of the sector will be 103.62 centimeters.

Let r be the radius of the sector and θ be the angle subtends by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

The central angle is 11π / 6 radian and the radius is 18 cm. Then the measure of the arc length is given as,

Arc = {(11π / 6)/2π} 2π (18)

Arc = 0.9167 x 2 x 3.14 x 18

Arc = 103.62 cm

The measure of the arc length of the sector will be 103.62 centimeters.

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Answer:

45

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Step-by-step explanation:

Step 1: Define

g(x) = 10 - 7g

g(-5) is x = -5

Step 2: Evaluate

Answer:

C

Step-by-step explanation:

The y-intercept is approximately 191.1. The correct option is (B).

To compute the y-intercept, we need to use the equation of the regression line, which is:

y = a + bx

where a is the y-intercept, b is the slope, x is the independent variable (in this case, x-bar), and y is the dependent variable (in this case, y-bar).

The formula for the slope of the regression line is:

b = r * (sy/sx)

where r is the correlation coefficient, sx is the standard deviation of x, and sy is the standard deviation of y.

Substituting the given values, we get:

b = 0.341 * (37/12) = 1.05025

Now, we can use the formula for the y-intercept:

a = y-bar - b * x-bar

Substituting the given values, we get:

a = 251 - 1.05025 * 57 = 191.10925

Therefore, the y-intercept is approximately 191.1.

The answer is B) 191.1.

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The context that could be modeled by a linear function is A. A smartphone data plan charges $65/month and $0.46/GB of data used.

The total cost of the data plan depends linearly on the amount of data used.  The monthly fixed cost of $65 represents the y-intercept, and the variable cost of $0.46/GB represents the slope of the linear function.

A linear function is a rule in Maths that links two things on a graph using a straight line.

For instance: y = mx + b

In this equation

y = the thing that depends on something else (like time),

x = the thing it depends on (like distance),

m = how much y changes when x changes and

b = where the line starts on the up-and-down axis.

So, the slope (m) shows how y changes when x changes and the starting point (b) tells us where the line begins.

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Answer:

47.49%

Step-by-step explanation:

profit / selling price ×100% = gain percent

profit =selling price - cost price

therefore profit = 155.63 - 105.52 = 50.11

50.11/105.52 ×100% = gain percent

47.49% = gain percent

The correct option is A. Write-in adjustments All above-the-line adjustments that do not have corresponding input lines on Schedule 1 (Form 1040) are indicated as write-in adjustments.

All above-the-line adjustments that do not have corresponding input lines on Schedule 1 (Form 1040) are referred to as write-in adjustments. Line 36 of Schedule 1 is where all write-in adjustments are reported. You have to provide a brief explanation of the adjustment and the corresponding amount for each write-in adjustment.If the IRS has developed an input line for a particular write-in adjustment, taxpayers must use that input line to report the adjustment. 

When writing in adjustments, taxpayers must ensure that the amount they enter is calculated and that they have a reasonable explanation for the adjustment. Taxpayers may be required to provide documentation to support the adjustment if the IRS requests it.

Miscellaneous adjustments and miscellaneous deductions are not used to describe all above-the-line adjustments that do not have corresponding input lines on Schedule 1 (Form 1040).

Therefore, options C and D are incorrect. The correct option is A. Write-in adjustments.

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The equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3.Given two points (-8, 9) and (2, -6). We are supposed to find the equation of the line that passes through these two points.

We can find the equation of a line that passes through two given points, using the slope-intercept form of the equation of a line. The slope-intercept form of the equation of a line is given by, y = mx + b,Where m is the slope of the line and b is the y-intercept.To find the slope of the line passing through the given points, we can use the slope formula: m = (y2 - y1) / (x2 - x1).Here, x1 = -8, y1 = 9, x2 = 2 and y2 = -6.

Hence, we can substitute these values to find the slope.m = (-6 - 9) / (2 - (-8))m = (-6 - 9) / (2 + 8)m = -15 / 10m = -3 / 2Hence, the slope of the line passing through the points (-8, 9) and (2, -6) is -3 / 2.

Now, using the point-slope form of the equation of a line, we can find the equation of the line that passes through the point (-8, 9) and has a slope of -3 / 2.

The point-slope form of the equation of a line is given by,y - y1 = m(x - x1)Here, x1 = -8, y1 = 9 and m = -3 / 2.

Hence, we can substitute these values to find the equation of the line.y - 9 = (-3 / 2)(x - (-8))y - 9 = (-3 / 2)(x + 8)y - 9 = (-3 / 2)x - 12y = (-3 / 2)x - 12 + 9y = (-3 / 2)x - 3.

Therefore, the equation of the line that passes through the points (-8, 9) and (2, -6) is y = (-3 / 2)x - 3. Thus, the answer is (-3/2)x - 3.

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Answer:

180⁰

Step-by-step explanation:

Since the angle of straight line is 180⁰

Answer:

A and B = 180 degrees

Step-by-step explanation:

this is because a circle is 360 and a line wich would be cutting the line in half is 180. so the two andles must add up to 180 degrees.

Option B pair of triangles cannot be proved congruent.

Congruence in two or more triangles depends on the measurements of their sides and angles. Two triangles are said to be congruent if pairs of their corresponding sides and their corresponding angles are equal. They are of the same shape and size.

SSS Criterion for Congruence

SSS criterion stands for Side-Side-Side criterion. Under this criterion, two triangles are congruent if three sides of a triangle are equal to the corresponding sides of the other triangle.

SAS Criterion for Congruence

SAS criterion stands for Side-Angle-Side criterion. Under this criterion, two triangles are congruent if the two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

ASA Criterion for Congruence

ASA criterion stands for Angle-Side-Angle criterion. Under the ASA criterion, two triangles are congruent if any two angles and the side included between them of one triangle are equal to the corresponding angles and the included side of the other triangle.

AAS Criterion for Congruence

AAS criterion stands for Angle-Angle-Side criterion. Under the AAS criterion, two triangles are congruent if any two angles and the non-included side of one triangle are equal to the corresponding angles and the non-included side of the other triangle.

According to the question

Option A :

SAS : A triangle with equal sides and equal angles.

Option C :

SSS : A triangle with equal sides.

Option D :

AAS : A triangle with two equal angles and one equal side.

Option B :

These pair of triangles cannot be proved congruent.

Two triangles with equal corresponding angles may not be congruent to each other because one triangle might be an enlarged copy of the other. Hence, there is no AAA criterion for congruence.

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Answer:

8/81

Step-by-step explanation:

8/18 x 4/18 = 32/324 = 8/81

The probability of drawing a blue and then a green and replacing the candy after the draw is 8/81.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

It is given that in a bag of M&MS there are 4 green, 6 yellow, and 8 blue candies.

The probability for blue = 8/18

The probability for green = 4/18

The probabilities of drawing a blue then green if you replace the candy after the draw will be calculated as below:-

Probability = 8/18 x 4/18

Probability = 32/324

Divide the number 32 by 324 to get the probability.

Probability = 8/81

Therefore, the probability of drawing a blue and then a green and replacing the candy after the draw is 8/81.

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Answer:

πr + (4+6+6+8) = 2π+24=30.28

Answer:

135, 137, 139

Step-by-step explanation: My bad, I did not see that it said consecutive odd integers

x+x+2+x+4=411

3x+6=411

3x=405

x=135

x+2+137

x+4=139

Represent 3 consecutive odd integers as follows.

X ⇒ first odd integer

X + 2 ⇒ second odd integer

X + 4 ⇒ third odd integer

Since their sum in this problem is 411, x + (x + 2) + (x + 4) = 411.

Now combine like terms to get 3x + 6 = 411.

No subtract 6 from both sides to get 3x = 405.

Now divide both sides by 3 and x = 135.

So x + 2 would be 137 and x + 4 would be 139.

So our consecutive odd integers are 135, 137, and 139.

The correct answer is option B that is polynomial h(x) = (x - 3)³(x² - 2x + 2).

A polynomial may be defined as an expression containing variables and their coefficients along with powers of the variables. A polynomial having 5 zeroes will be called a fifth-degree polynomial that can be represented as ax⁵ + bx⁴ + cx³ + dx² + ex + f = 0 where a, b, c, d, e and f are coefficients and x is the independent variable. It is given that the polynomial has 3 real zeroes and 2 imaginary zeroes. If we take the polynomial h(x) = (x - 3)³(x² - 2x + 2) we see that the first term (x - 3)³ when equated to zero gives three real zeroes equal to 3. Now, in the second term that is (x² - 2x + 2), if we equate this to zero then the value of discriminant that is b² - 4ac = 4 - 8 = -4 is negative so this term will have two imaginary roots. So, this function h(x) = (x - 3)³(x² - 2x + 2) is the required polynomial.

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Answer: 22 mor packages.

Give me brainlyest please.

Step-by-step explanation: