What is the equation of the line that passes through (-3, -1) and has a slope of 3/5?

(slope-intercept form)


A: y = 3/5x + 4/5

B: y = 3/5x - 4/5

C: y = -3/5x - 4/5

Answer:

A. To find the derivative of h(x), we can use the chain rule:

h(x) = a(-2x + 1)^5 - b

h'(x) = a * 5(-2x + 1)^4 * (-2) = -10a(-2x + 1)^4

To find the second derivative, we can again use the chain rule:

h''(x) = -10a * 4(-2x + 1)^3 * (-2) = 80a(-2x + 1)^3

B. To show that h is monotonic, we need to show that h'(x) is either always positive or always negative. Since h'(x) is a multiple of (-2x + 1)^4, which is always non-negative, h'(x) is always either positive or negative depending on the sign of a. If a > 0, then h'(x) is always negative, which means that h(x) is decreasing. If a < 0, then h'(x) is always positive, which means that h(x) is increasing.

C. To find the critical points, we need to find where h'(x) = 0:

h'(x) = -10a(-2x + 1)^4 = 0

-2x + 1 = 0

x = 1/2

Thus, the critical point is at x = 1/2. This value is independent of a and b, as neither a nor b appear in the calculation of the critical point.

The Sunday game brought in $2232.50, while the Thursday game brought in $1832.00.

A company's income, costs, and profit are compiled in a profit and loss (P&L) statement, a financial report. It provides information to investors and other interested parties about a company's operations and financial viability.

The issue informs us that the combined revenue from the two games was $4064.50.

S + (S - 400.50) = 4064.50

Simplifying the left side, we get:

2S - 400.50 = 4064.50

Adding 400.50 to both sides, we get:

2S = 4465

Dividing both sides by 2, we get:

S = 2232.50

So the Sunday game generated $2232.50, and the Thursday game generated $2232.50 - $400.50 = $1832.00.

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Answer:

Step-by-step explanation:

If the zeros and their multiplicities are given, we can write the polynomial as the product of linear factors corresponding to each zero.

For this problem, the polynomial has zeros of -9 (multiplicity 1) and -1 (multiplicity 2), so the linear factors are:

(x + 9) and (x + 1)^2

To find the third factor, we use the fact that the degree of the polynomial is 3. We can multiply the linear factors together and then simplify:

(x + 9)(x + 1)^2 = (x^2 + 10x + 9)(x + 1)

= x^3 + 11x^2 + 19x + 9

Therefore, the polynomial with zeros of -9 (multiplicity 1), -1 (multiplicity 2), and degree 3 is:

f(x) = x^3 + 11x^2 + 19x + 9

"I am 95% convinced that the true population mean corresponds to this confidence interval," is the appropriate sentence to use when interpreting the confidence interval.

Each whole group that shares at least one trait is referred to be a population. People do not make up all populations. Individuals, animals, groups, organisations, edifices, edifices, buildings, houses, farms, items, or events can all be considered populations.

As a rough estimate, the true mean monthly rent is $1,235.

At a 95% confidence level, the critical value (Z) for a two-tailed test is 1.96. The margin of error can be calculated as follows:

The 95% confidence interval can be obtained as follows:

CI = 1235 1.96*(150/36) CI = X Z*(n/n)

Lower value: 1.96 * (150/36) * 1235 = $1,175.20

Higher value: $1,294.80 = 1235 + 1.96 * (150/36).

Higher value: $1,294.80; Lower value: $1,175.20

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The steps for finding out the third derivative of y (given as y''') are explained and given below.

To find the third derivative of y (y'''), you would need to differentiate the function y three times with respect to the independent variable. Here are the steps:

Start by differentiating y once to get the first derivative, y'.

Differentiate y' again to get the second derivative, y''.

Finally, differentiate y'' to get the third derivative, y'''.

You can use the chain rule, product rule, quotient rule, and other differentiation rules as needed to find each derivative.

Here's an example of finding the third derivative of y for the function y = x^4 + 2x^3 - 5x:

y' = 4x^3 + 6x^2 - 5

y'' = 12x^2 + 12x

y''' = 24x + 12

So the third derivative of y is y''' = 24x + 12.

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Answer:

[tex] {y}^{6} {x}^{ - 2} [/tex]

Step-by-step explanation:

4 will get multiplied to the exponents of x and y inside the bracket.

The correct numerical expression for the given statement "multiply the sum of 7 and 6 by the sum of 4 and 5" is (7 + 6) x (4 + 5).

Mathematical statements are called expressions if they have at least two words that are related by an operator and contain either numbers, variables, or both. There are two sorts of expressions in mathematics: numerical expressions, which only contain numbers, and algebraic expressions, which also include variables. A mathematical expression is a phrase that has a minimum of two numbers or variables and at least one mathematical operation.

The given statement, "multiply the sum of 7 and 6 by the sum of 4 and 5", can be represented as:

sum of 7 and 6 = (7 + 6)

sum of 4 and 5 = (4 + 5)

multiply: (7 + 6) x (4 + 5)

Hence, the correct numerical expression for the given statement is (7 + 6) x (4 + 5).

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Answer:

(7 + 6) x (4 + 5).

Step-by-step explanation:

hope this helps!

Using binomial theorem, the generating function is G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256 while the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.

To find the generating function of (x+4)^4, we expand it using the binomial theorem:

[tex](x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)[/tex]

where C(n,k) denotes the binomial coefficient "n choose k".

Simplifying the terms, we get:

[tex](x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]

Therefore, the generating function of (x+4)^4 is:

[tex]G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256[/tex]

The associated sequence can be read off by finding the coefficients of each power of x:

To find the generating function of (x+4)^4, we expand it using the binomial theorem:

(x+4)^4 = C(4,0)x^4 + C(4,1)x^3(4) + C(4,2)x^2(4^2) + C(4,3)x(4^3) + C(4,4)(4^4)

where C(n,k) denotes the binomial coefficient "n choose k".

Simplifying the terms, we get:

(x+4)^4 = x^4 + 16x^3 + 96x^2 + 256x + 256

Therefore, the generating function of (x+4)^4 is:

G(x) = x^4 + 16x^3 + 96x^2 + 256x + 256

The associated sequence can be read off by finding the coefficients of each power of x:

The coefficient of x^k is the k-th term of the sequence.

In this case, the sequence is given by the coefficients of G(x):

a₀ = 256

a₁ = 256

a₂ = 96

a₃ = 16

a₄ = 1

Therefore, the associated sequence of (x+4)^4 is {1, 16, 96, 256, 256}.

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The surface area is  1305. 96 square units

It is important to note that the formula for calculating the surface area of a cylinder is expressed with the equation;

SA = 2πrh + 2πr²

Given that the parameters are;

Now, substitute the values, we have;

Surface area = 2 × 3.14 × 9 ×14 + 2 × 3.14 × 9²

Multiply the values

Surface area = 791. 28 + 508. 68

add the values

Surface area = 1305. 96 square units

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Answer:

The right answer is below

Step-by-step explanation:

4.7 is the length of LJ

The relationship between AB and BC is given as follows:

AB > BC.

Two angles are defined as supplementary angles when the sum of their measures is of 180º.

The supplementary angles for this problem are given as follows:

By the law of sines, we have that:

AB/sin(110º) = BC/sin(70º).

As sin(110º) > sin(70º), the inequality for this problem is given as follows:

AB > BC.

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Answer:

AB>BC

Step-by-step explanation:

AI-generated answer

Based on the given information, the relationship between AB and BC depends on the measure of angle ZADB. If mZADB is 110°, we can determine the relationship as follows:

Since triangle ABD and triangle CBD share side AB, the larger the angle ZADB, the longer the side AB will be compared to side BC. Therefore, if mZADB is 110°, we can conclude that AB is greater than BC.

In summary, when mZADB is 110°, the relationship between AB and BC is:

AB > BC.

Step-by-step explanation:

240g divided in ratios.

divide 240g in the ratio 5:4:3

To divide 240g in the ratio 5:4:3, we need to determine the amount of each part of the ratio.

First, we need to find the total number of parts in the ratio, which is 5 + 4 + 3 = 12.

Next, we divide the total amount (240g) by the total number of parts (12) to find the value of one part:

240g ÷ 12 = 20g

Therefore, one part of the ratio is equal to 20g.

To find the amount of each part of the ratio, we can multiply the value of one part by the corresponding number in the ratio.

The amounts are:

5 parts: 5 × 20g = 100g

4 parts: 4 × 20g = 80g

3 parts: 3 × 20g = 60g

Therefore, to divide 240g in the ratio 5:4:3, we need 100g, 80g, and 60g for each part of the ratio, respectively.

Answer

100g , 80g , 60g

Step-by-step explanation:

      Ratio = 5 : 4 : 3

Let the unit share be 'x'.

So, three shares are 5x, 4x and 3x.

Total weight = 240 g

Total shares = 5x + 4x + 3x =  12x

Sum of all the shares equal to the total weight.

          12x = 240g

             x = 240 ÷ 12 = 20

The value of unit share is 20 g. From this we can find the weight of each share.

5x = 5 * 20 = 100g

4x = 4 * 20 = 80 g

3x = 3 * 20 = 60 g

Answer:

a)220 4 leaf clovers, 780 3 leaf clovers b)440 four leaf clovers, 1560 3 leaf clovers

Step-by-step explanation:

100:1000=1:10 22:x=1:10 x=220

220x2=440

1000-220=780

780x2=1560

Answer: False, False, True, True, True.

Step-by-step explanation:

Remember, if there are two intersecting lines on a graph, and they come to one point on a graph, it only has one solution. If two lines are parallel, and don't intersect with each other, they have no solution. If there are two equations, and both are on the same line, then they have infinitely many solutions.

y - 3x = -2, and y = 3x - 2, are equal, since they are one line.

So, the first and second questions are false, since there's only 1 solution, making the third question true. The point (-1, -5), is a true answer, since the x would be -1, and the y would be -5. (Example below.)

y = 3x - 2

y = 3(-1) - 2

y = -3 - 2

y = -5

The two lines in the equations do have the same slope, since the slope for each is 3x. Or think about slope-intercept form, (y = mx + b)

y - 3x = -2, and y = 3x - 2

y - 3x = -2

y = 3x - 2 is equal to y = 3x - 2, which makes this answer true.

Hope this helps, (and can you give brainliest, please?)

The open circle at 3 indicates that 3 is not included in the solution set. This inequality can be read as "X is less than 5" or "X is strictly less than 5."

In mathematics, an expression is a combination of numbers, symbols, and operators that represents a value. Expressions can be as simple as a single number or variable, or they can be complex combinations of mathematical operations. For example, 2 + 3 is a simple expression that represents the value 5, while (2 + 3) x 4 - 1 is a more complex expression that represents the value 19. Expressions can be evaluated or simplified using the rules of arithmetic and algebra.

Here,

1. Simplify:

3(4x-2)+ 7X (2-1) + 4 (6+4)+(-8)

Multiplying inside the parentheses first:

12x - 6 + 7x + 4 + 40 - 8

Combining like terms:

19x + 30

Final answer: 19x + 30

2. Graph:

3 > X

This is a simple inequality in one variable (X). To graph it on a number line, we first draw a dot at 3 (since the inequality is strict), and then shade all values less than 3:

<=========o---

The open circle at 3 indicates that 3 is not included in the solution set.

3. Write the inequality:

X < 5

This is a simple inequality in one variable (X). The inequality sign is "less than," and the number on the right-hand side is 5. This inequality can be read as "X is less than 5" or "X is strictly less than 5."

4. Solve for x:

3x - 7 = 42

Adding 7 to both sides to isolate the variable:

3x = 49

Dividing both sides by 3 to solve for x:

x = 16.33 (rounded to two decimal places)

Final answer: x = 16.3

5. Find 32% of $542.50:

To find 32% of $542.50, we can use the formula:

percent * amount = part

where "percent" is the percentage expressed as a decimal, "amount" is the whole amount, and "part" is the result we're looking for.In this case, we have:

0.32 * $542.50 = part

Multiplying:

$173.60 = part

Final answer: $173.60

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For the standard normal curve, the area to the left of 0.1 is the same as the area to the right of 0.9 is true . So, the correct answer is D.

The standard normal curve is a normal distribution with a mean of 0 and a standard deviation of 1. This curve is often used in statistics to model natural phenomena, and it has many important properties.

Option A is incorrect because the area under the standard normal curve between 0 and 2 is not twice the area between 0 and 1. The area under the curve increases as we move away from the mean, so the area between 0 and 2 will be greater than the area between 0 and 1.

Option B is also incorrect because the area under the standard normal curve between 0 and 2 is not half the area between -2 and 2. The area between -2 and 2 covers more of the curve than the area between 0 and 2, so the area between 0 and 2 will be smaller than half the area between -2 and 2.

Option C is incorrect because the standard normal curve does not have a fixed IQR (interquartile range). The IQR depends on the quartiles of the distribution, which can vary depending on the sample size and the distribution's shape.

Option D is the correct answer because the standard normal curve is symmetric around the mean of 0. This means that the area to the left of any point on the curve is the same as the area to the right of its negative counterpart. Therefore, the area to the left of 0.1 is equal to the area to the right of 0.9.

Therefore, Correct option is D.

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The triangle ABC with the given dimensions:AB = 10, BC = 6, CA = 90 are constructed.

The dimension of the triangle ABC are:

AB = 10

BC = 6

CA = 90

Thus, the triangle with the given dimensions are constructed.

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A) Values of y will be 1, 0, -1, 0, 1

B) and C) plot the values as shown in below figure.

Trigonometric functions are a set of mathematical functions that relate the angles and sides of right triangles.

A) for f(x) = cos x; the values of x-y chart are:

  x                   y = f(x)

  0                      1

  [tex]\frac{\pi }{2}[/tex]                      0

  [tex]\pi[/tex]                      -1

  [tex]\frac{3\pi }{2}[/tex]                     0

  [tex]2\pi[/tex]                     1

B) the points are plotted as given figure below.

C) Connects the dots to show the graph of y = cos x; sown in figure below please check it.

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Answer:

f(x) = (x^2 - 25) / (x - 5)

Step-by-step explanation:

Note that this function is undefined at x=5, which satisfies condition (a). Also, the function is defined for all other real numbers, which satisfies the domain and range requirement of (a).

For condition (b), note that the function is defined for all positive numbers greater than 1, including 1, since the denominator (x-5) will be positive for these values of x.

For condition (c), note that the function is undefined at x=1, since the denominator (x-5) will be negative for x slightly less than 1. Therefore, the function is defined for all positive numbers greater than 1, but not including 1.

Answer:

Step-by-step explanation:

To find the current price index number using the 1975 price of 56.7 cents as the reference value, we can use the formula:

Price Index = (Current Price / Base Price) x 100

Where "Current Price" is the current cost of gasoline, and "Base Price" is the 1975 price of 56.7 cents.

Substituting the values given in the problem, we get:

Price Index = ($2.93 / $0.567) x 100

Price Index = 516.899

Therefore, the current price index number, using the 1975 price of 56.7 cents as the reference value, is 516.899.

On solving the question we can say that so the other side of triangle is [tex]B = \sqrt324[/tex], therefore the angle will be [tex]cos^{-1} (0.38)[/tex].

A triangle is a closed two-dimensional geometric object consisting of three line segments, called edges, that intersect at three places called vertices. Triangles are distinguished by their sides and angles. A triangle can be equilateral (all sides equal), isosceles, or odd, depending on the sides. Triangles are classified as acute (any angle less than 90 degrees), right (angles equal to 90 degrees), or obtuse (any angle greater than 90 degrees). The area of ​​a triangle can be calculated using the formula A =​​ (1/2)bh. where A is the area, b is the base of the triangle, and h is the height of the triangle.  

here two sides of the triangle are given that are 19.5 and 7.5

so by

[tex]A^2 = B^2 + C^2\\B^2 = 19.5^2 - 7.5^2\\B^2 = 380.25 - 56.25\\B^2 = 324\\B = \sqrt324[/tex]

so the other side is [tex]B = \sqrt324[/tex], therefore the angle will be [tex]cos^{-1} (0.38)[/tex].

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Answer:

Step-by-step explanation:

To find the zeros of the function, we set y to zero and solve for x:

y = (x+1)(x-2)(x-6) = 0

Setting each factor equal to zero and solving for x gives us the zeros:

x+1 = 0 or x-2 = 0 or x-6 = 0

x = -1, x = 2, x = 6

So the zeros of the function are -1, 2, and 6.

To graph the function, we can use the zeros and the leading coefficient to sketch a rough graph. The leading coefficient is positive, so the graph will open upward. The zeros are -1, 2, and 6, so the graph will intersect the x-axis at those points. We can also find the y-intercept by plugging in x = 0:

y = (0+1)(0-2)(0-6) = 12

So the y-intercept is (0, 12).

Using this information, we can sketch the graph:

The relative maximum of the function is (0, 4), and the relative minimum is (6, -152).

To find the relative extrema of the function f(x) = x^4 - 8x^3 + 4, we first take the derivative of the function:

f'(x) = 4x^3 - 24x^2

Then we set f'(x) = 0 to find the critical points:

4x^3 - 24x^2 = 0

4x^2(x - 6) = 0

This gives us two critical points: x = 0 and x = 6.

Next, we find the second derivative of f(x):

f''(x) = 12x^2 - 48x

We can use the Second-Derivative Test to determine the nature of the critical points.

For x = 0, we have:

f''(0) = 0 - 0 = 0

This tells us that the Second-Derivative Test is inconclusive at x = 0.

For x = 6, we have:

f''(6) = 12(6)^2 - 48(6) = 0

Since the second derivative is zero at x = 6, we cannot use the Second-Derivative Test to determine the nature of the critical point at x = 6.

To determine whether the critical points are relative maxima or minima, we can use the first derivative test or examine the behavior of the function around the critical points.

For x < 0, f'(x) < 0, so the function is decreasing.

For 0 < x < 6, f'(x) > 0, so the function is increasing.

For x > 6, f'(x) < 0, so the function is decreasing.

Therefore, we can conclude that the critical point at x = 0 is a relative maximum and the critical point at x = 6 is a relative minimum.

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Using the two points you have plotted, draw the parabola. It should look like a downward-facing curve opening at the vertex (0, 7).

What is parabola?

A parabola is a symmetrical, U-shaped curve that is formed by the graph of a quadratic function.

Assuming you meant [tex]f(x) = -x^2 + 7[/tex], here's how you can graph the parabola using the parabola tool:

Find the vertex

The vertex of the parabola is located at the point (-b/2a, f(-b/2a)), where a is the coefficient of the [tex]x^2[/tex] term and b is the coefficient of the x term. In this case, a = -1 and b = 0, so the vertex is located at the point (0, 7).

Plot the vertex

Using the parabola tool, plot the vertex at the point (0, 7).

Plot a second point

To plot a second point, you can choose any x value and find the corresponding y value using the quadratic function. For example, if you choose x = 2, then [tex]f(2) = -2^2 + 7 = 3[/tex]. So the second point is located at (2, 3).

Therefore, Using the two points you have plotted, draw the parabola. It should look like a downward-facing curve opening at the vertex (0, 7).

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Complete Question:

Use the parabola tool to graph the quadratic function.

f(x) = -√² +7

Graph the parabola by first plotting its vertex and then plotting a second point on the parabola.

Answer:

Step-by-step explanation:

[tex]\{A\cup B \}=\{1,2,3,7,10,11,12,14,16,17,18,19 \}\\\\\{A \cap B \}=\{ 1,7,10,14\}[/tex]

A∪B: Any element which is in either or both sets.

A∩B: Only elements that are in both A and B.

V is 5.92 centimetres above the pyramid's base at its highest point.

A pyramid is a 3D pοlyhedrοn with the base οf a pοlygοn alοng with three οr mοre triangle-shaped faces that meet at a pοint abοve the base. The triangular sides are called faces and the pοint abοve the base is called the apex. A pyramid is made by cοnnecting the base tο the apex. Sοmetimes, the triangular sides are alsο called lateral faces tο distinguish them frοm the base. In a pyramid, each edge οf the base is cοnnected tο the apex that fοrms the triangular face.

Give the altitude the letter h. Next, we have:

tan(60) = h/2

Simplifying, we get:

h = 2 tan(60) = 2 √(3)

The Pythagorean theorem yields the following:

[tex]$\begin{align}{{V O^{2}+O F^{2}=V F^{2}}}\\ {{V O^{2}+1^{2}=6^{2}}}\\ {{V O^{2}=35}}\end{align}$[/tex]

Taking the square root of both sides, we get:

VO ≈ 5.92 cm

Rounding to three significant figures, we get:

VO ≈ 5.92 cm

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Continuous numerical values make up the data type for the variable "Age of a tennis player selected at random in the Wimbledon tennis tournament."

Discrete numerical, continuous numerical, and categorical data are the three basic types that can be identified.

- Non-numerical categorical variables, such as gender or eye colour, represent categories or groups.

- Discrete numerical data, such as the number of siblings or pets, are numerical data that can only take on specified values.

Continuous numerical data, like age or weight, are numerical data that can have any value within a range.

Because age can have any value within a range, the data for the variable "Age of a randomly chosen tennis player in the Wimbledon tennis competition" is continuous numerical (for example, a player could be 18.5 years old or 25.2 years old). Hence, continuous numerical data is the right response.

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Using graphs, we can see that the point (4,2) can be a coordinate where y will represent x.

The graph is simply a structured representation of the data. The numerical information gathered through observation is referred to as data.

If there is just one value of y (output) for every value of x, the relationship between x and y is said to be a function (input).

In other words, there can only be one value of y for each value of x.

Determine each plotted point's coordinates first:

(-4,4)

(-2,3)

(0,1)

(2, -1)

(3,0)

The following point cannot have any of the x-coordinates of the displayed points, which are -4, -2, 0, 2, and 3.

Options include:

A (0,1) →The relationship cannot be regarded as a function at this stage as the x-coordinate zero already has a corresponding value of y.

B (2,2) →Although there is already a value of y for the location x=2, the relationship cannot be regarded as a function at this point.

C (3,4) →Although there is already a value of y for the location x=3, the relationship cannot be regarded as a function at this point.

D (4,2) → The relationship will still be regarded as a function even though there are no points on the graph with the coordinates x=4 displayed.

Therefore, option D (4,2) is the point where y will represent x.

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The complete question:

Please see attached question

When g be continuous on [1,6], where g(1) = 18 and g(6): = 11. Does a value 1 < c < 6 exist such that g(c) = 12

The intermediate value theorem is a fundamental theorem in calculus that states that if a continuous function f(x) is defined on a closed interval [a, b], and if there exists a number y between f(a) and f(b), then there exists at least one point c in the interval [a, b] such that f(c) = y.

According to the intermediate value theorem,

since g(x) is a continuous function on the closed interval [1, 6]

since g(1) = 18 is greater than 12, and

g(6) = 11 is less than 12,

there must be at least one value c between 1 and 6 where g(c) = 12.

Therefore, we can conclude that a value of c does exist such that g(c) = 12.

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