The diameter of a circle is 3 miles. What is the area?

The equation of a line perpendicular to the x-axis is x = 3

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

The equations

By definition, the equation of a line perpendicular to the x-axis is represented as

x = k

Where

k is a real value

Using the above as a guide, we have the following:

x = 3

Hence, the equation is x = 3

Read more about linear relation at

https://brainly.com/question/30318449

#SPJ1

The completed table is as follows:

x | y

8 | 0

9 | 3

36 | 6

8 | 2√2

8 | -2√2

To solve the equation x = y², we can substitute the values of x and find the corresponding values of y in the table.

Let's fill in the missing entries one by one:

For x = 9, we need to find y. Since x = y², we take the square root of both sides to solve for y. So, y = √9 = 3. Therefore, the corresponding value for y is 3.

For x = 36, again, we apply the square root operation to both sides, giving y = √36 = 6. Hence, the corresponding value for y is 6.

For y = 2√2, we need to find x. Squaring both sides of the equation, we have [tex]x = (2\sqrt2)^2 = 4 \times 2 = 8[/tex]. Therefore, the corresponding value for x is 8.

For y = -2√2, we follow the same process as in step 3. Squaring both sides, we get [tex]x = (-2\sqrt2)^2 = 4 \times 2 = 8[/tex]. So, the corresponding value for x is 8.

After filling in the missing entries, the completed table is as follows:

x | y

8 | 0

9 | 3

36 | 6

8 | 2√2

8 | -2√2

Please note that there can be multiple valid solutions for this equation, but this table provides one possible solution.

For more such questions on table

https://brainly.com/question/12151322

#SPJ8

Answer:

C

Step-by-step explanation:

the common ratio r of a geometric sequence is

r = [tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{-\frac{4}{15} }{\frac{2}{5} }[/tex] = - [tex]\frac{4}{15}[/tex] × [tex]\frac{5}{2}[/tex] = - [tex]\frac{2}{3}[/tex]

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

learn more about word problem from

https://brainly.com/question/21405634

#SPJ1

The amount of net income on the income statement for the year is $26,200.

To determine the net income, we need to calculate the total revenue and subtract the total expenses.

Total Revenue = Service Revenue = $50,400

Total Expenses = Wages Expense + Advertising Expense + Rent Expense = $8,400 + $5,400 + $10,400 = $24,200

Net Income = Total Revenue - Total Expenses = $50,400 - $24,200 = $26,200

Therefore, the amount of net income on the income statement for the year is $26,200.

To calculate the net income, we consider the revenue and expenses recorded in the company's financial records.

Revenue represents the inflow of money from the company's primary operations. In this case, the revenue is listed as "Service Revenue" with a value of $50,400.

Expenses represent the outflow of money incurred by the company in conducting its operations. The expenses mentioned in the records are "Wages Expense" ($8,400), "Advertising Expense" ($5,400), and "Rent Expense" ($10,400).

To calculate the net income, we subtract the total expenses from the total revenue:

Net Income = Total Revenue - Total Expenses

Total Revenue = $50,400

Total Expenses = $8,400 + $5,400 + $10,400 = $24,200

Net Income = $50,400 - $24,200 = $26,200

Learn more about compound interest here:

https://brainly.com/question/24274034

#SPJ8

Answer:

number (a) = 4

Step-by-step explanation:

We have proven trigonometric  equation a² + b² = p² + q², using the given equations a sin θ + b cos θ = p --- (1) and a cos θ - b sin θ = q --- (2).

To prove that a² + b² = p² + q², we need to manipulate the given equations and show their equivalence.

Given equations:

a sin θ + b cos θ = p --- (1)

a cos θ - b sin θ = q --- (2)

Square equation (1):

(a sin θ + b cos θ)² = p²

Expanding and simplifying:

a² sin² θ + 2ab sin θ cos θ + b² cos² θ = p² --- (3)

Square equation (2):

(a cos θ - b sin θ)² = q²

Expanding and simplifying:

a² cos² θ - 2ab sin θ cos θ + b² sin² θ = q² --- (4)

Now, adding equations (3) and (4):

a² sin² θ + a² cos² θ + b² sin² θ + b² cos² θ + 2ab sin θ cos θ - 2ab sin θ cos θ = p² + q²

Using the trigonometric identity: sin² θ + cos² θ = 1, we simplify:

a² + b² = p² + q²

We have proven that a² + b² = p² + q², using the given equations (1) and (2).

For more such questions on trigonometric  equation

https://brainly.com/question/24349828

#SPJ8

The robot's locations for each time t are P(14, 27) when t = 14, and P(0.7, 0.4) when t = 0.7.

To find the robot's location, P, for each time t, we can use the equation of a straight line.

Given points A(0, -1) and B(1, 1), we can calculate the slope (m) of the line using the formula:

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

m = (1 - (-1)) / (1 - 0) = 2/1 = 2

Now that we have the slope, we can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

For point A(0, -1):

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

y + 1 = 2x

Simplifying the equation, we get:

y = 2x - 1

Now we can substitute the values of t into the equation to find the corresponding locations of the robot, P.

For t = 14:

y = 2(14) - 1

y = 28 - 1

y = 27

So, when t = 14, the robot's location is P(14, 27).

For t = 0.7:

y = 2(0.7) - 1

y = 1.4 - 1

y = 0.4

So, when t = 0.7, the robot's location is P(0.7, 0.4).

for such more question on straight line

https://brainly.com/question/10118420

#SPJ8

Answer:

Step-by-step explanation:

[tex]\frac{sin(x)}{1-cos(x)} -cot(x)=csc(x)\\[/tex]

[tex]\frac{sin(x)}{1-cos(x)} -\frac{cos(x)}{sin(x)} =csc(x)[/tex]

[tex]\frac{sin^{2}(x)-cos(x)+cos^{2}(x) }{(1-cos(x))sin(x)} =csc(x)\\\\\frac{1-cos(x)}{(1-cos(x))sin(x)} =csc(x)\\[/tex]

[tex]\frac{1}{sin(x)} =csc(x)\\csc(x)=csc(x)[/tex]

QED

Answer:

See below for proof.

Step-by-step explanation:

Use the cotangent identity to rewrite cot(x) as cos(x) / sin(x):

[tex]\dfrac{\sin(x)}{1-\cos(x)}-\cot(x)=\dfrac{\sin(x)}{1-\cos(x)}-\dfrac{\cos (x)}{\sin(x)}[/tex]

Make the denominators of both fractions the same:

                              [tex]=\dfrac{\sin(x)}{1-\cos(x)}\cdot{\dfrac{\sin(x)}{\sin(x)}-\dfrac{\cos (x)}{\sin(x)}\cdot{\dfrac{1-\cos(x)}{1-\cos(x)}[/tex]

                              [tex]=\dfrac{\sin^2(x)}{\sin(x)(1-\cos(x))}-\dfrac{\cos (x)(1-\cos(x))}{\sin(x)(1-\cos(x))}[/tex]

Expand the numerator of the second fraction:

                              [tex]=\dfrac{\sin^2(x)}{\sin(x)(1-\cos(x))}-\dfrac{\cos (x)-\cos^2(x)}{\sin(x)(1-\cos(x))}[/tex]

[tex]\textsf{Apply the fraction rule} \quad \dfrac{a}{c}-\dfrac{b}{c}=\dfrac{a-b}{c}:[/tex]

                              [tex]=\dfrac{\sin^2(x)-(\cos (x)-\cos^2(x))}{\sin(x)(1-\cos(x))}[/tex]

                              [tex]=\dfrac{\sin^2(x)-\cos (x)+\cos^2(x)}{\sin(x)(1-\cos(x))}[/tex]

                              [tex]=\dfrac{\sin^2(x)+\cos^2(x)-\cos (x)}{\sin(x)(1-\cos(x))}[/tex]

Apply the trigonometric identity, sin²θ + cos²θ = 1, to the numerator:

                              [tex]=\dfrac{1-\cos (x)}{\sin(x)(1-\cos(x))}[/tex]

Factor out the common term (1 - cos(x)) from the numerator and denominator:

                              [tex]=\dfrac{1}{\sin(x)}[/tex]

Finally, use the cosecant identity, csc(x) = 1 / sin(x):

                              [tex]=\csc(x)[/tex]

Hence we have verified that the left side of the equation equals the right side.

The applied overhead cost for job 201 is $36,000 and total cost for job 201 under direct materials cost as allocation base is $86,000.

Allocation base is a technique utilized in accounting to designate the cost of something to its use or product to recognize the price of the finished product.

Example provides the total overhead cost at $120,000 for the period, the base data of $100,000 direct material cost and 500 direct labor hours. The base data are used to calculate the predetermined factory overhead rate, which is used to apply overhead costs to work in progress.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the base data. The predetermined factory overhead rate is multiplied by the actual activity in the allocation base to obtain the applied overhead cost.

Direct materials cost as allocation base $30,000 is the actual direct material cost used in job 201. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct material cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $30,000*120% = $36,000.

Total cost for job 201 under direct materials cost as allocation base is $30,000+$20,000+$36,000 = $86,000.

-Direct labor cost as allocation base:

The actual direct labor cost used in job 201 is $20,000. The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor cost, which is $120,000/$100,000=120%.

The applied overhead cost for job 201 is $20,000*120% = $24,000.

Total cost for job 201 under direct labor cost as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Direct labor hours as allocation base:

The actual direct labor hours used in job 201 is 400 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the direct labor hours, which is $120,000/500 hours = $240 per hour.The applied overhead cost for job 201 is $240*400 hours = $96,000.

Total cost for job 201 under direct labor hours as allocation base is $30,000+$20,000+$96,000 = $146,000.

-Physical output as allocation base: The actual output in units completed for job 201 is 2,000 shirts.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the output in units, which is $120,000/10,000 units = $12 per unit.

The applied overhead cost for job 201 is $12*2,000 units = $24,000.Total cost for job 201 under physical output as allocation base is $30,000+$20,000+$24,000 = $74,000.

-Machine hours as allocation base: The actual machine hours used in job 201 is 240 hours.

The predetermined factory overhead rate is calculated by dividing the total overhead cost for the period by the machine hours, which is $120,000/5,000 hours = $24 per hour.

The applied overhead cost for job 201 is $24*240 hours = $5,760.

Total cost for job 201 under machine hours as allocation base is $30,000+$20,000+$5,760 = $55,760.

For more such questions on cost visit:

https://brainly.com/question/31479672

#SPJ8

In this case we have a translation of 8 units to the left and 11 units upwards.

To find the translation, we just need to compare the two known vertices before and after the translation.

If we have a translation of a units in the x-axis and b units in the y-axis, we will get:

T(a, b)L ---> L'

We know that L = (7, -3) and L' = (-1, 8)

Then we can write:

(7 + a, -3 + b) = (-1, 8)

Then we have two equations:

7 + a = -1 ---> a = -1 - 7 = -8

-3 + b = 8 ---> b = 8 + 3 = 11

Then we have a translation of 8 units to the left and 11 units up-.

Learn more about translations at:

https://brainly.com/question/1046778

#SPJ1

Complete question:

"Right triangle LMN has vertices L(7, –3), M(7, –8), and

N(10, –8). The triangle is translated on the coordinate plane so the coordinates of L’ are (–1, 8).

Find the translation done"

The mean for the given frequency tables is:

(a) Grade Frequency: 48.7

(b) Daily Low Temperature Frequency: 54.5

(c) Points per Game Frequency: 54.5

To find the mean for the given frequency tables, we need to calculate the weighted average. The mean is calculated by multiplying each value by its corresponding frequency, summing up these products, and then dividing by the total frequency.

(a) Grade Frequency:

To find the mean for the grade frequency table, we need to multiply the midpoints of each class interval by their respective frequencies and then divide by the total frequency.

The midpoints are:

54.5, 64.5, 74.5, 84.5, 94.5

The frequencies are:

2, 3, 6, 11, 5

Calculating the weighted sum: (54.52) + (64.53) + (74.56) + (84.511) + (94.5*5) = 1315

Calculating the total frequency: 2 + 3 + 6 + 11 + 5 = 27

Mean = 1315 / 27 ≈ 48.7

(b) Daily Low Temperature Frequency:

Since the frequency for the 49.5–59.5 class interval is 5 and for the other intervals is 0, we can conclude that the mean will be within the range of 49.5–59.5. The mean will be the midpoint of this class interval.

Mean = (49.5 + 59.5) / 2 = 54.5

(c) Points per Game Frequency:

Similarly to part (b), since the frequency for the 49.5–59.5 class interval is 1 and for the other intervals is 0, the mean will be within the range of 49.5–59.5.

Mean = (49.5 + 59.5) / 2 = 54.5

For more such questions on mean

https://brainly.com/question/1136789

#SPJ8

To estimate the minimum sample size required to estimate the population mean with a 95% confidence level and a desired margin of error, we can use the formula:

n = (Z * σ / E)²

Where:

n = sample size

Z = Z-score corresponding to the desired confidence level

σ = population standard deviation

E = desired margin of error

In this case, the desired confidence level is 95%, so the corresponding Z-score is the critical value associated with a 95% confidence level. From standard normal distribution tables, the Z-score for a 95% confidence level is approximately 1.96.

Given that the population standard deviation is 1.6 hours and the desired margin of error is 25 hours, we can plug in these values into the formula:

n = (1.96 * 1.6 / 25)²

Simplifying the equation:

n = (0.3136 / 25)²

n = 0.0125²

n ≈ 0.00015625

To find the minimum sample size, we need to round up to the nearest whole number since the sample size must be a whole number:

n ≈ 1

Therefore, the minimum sample size required to estimate the population mean with 95% confidence and a margin of error of 25 hours is approximately 1.

It is important to note that a sample size of 1 is not practically feasible or reliable for making statistical inferences. This result suggests that there may be other factors or considerations that need to be taken into account to determine a suitable sample size for this particular study.

For more such questions on sample size

https://brainly.com/question/30509642

#SPJ8

The code represented by the word "AFGAN" would be "02034."

To find the code represented by the word "AFGAN," we need to refer to the given code representation of the word "AFGANISTAN," which is "02034560."

From the given code, we can determine that the letters "AFGAN" correspond to the first five digits of the code.

Therefore, the code represented by the word "AFGAN" would be "02034."

Learn more about code at https://brainly.com/question/25781514

#SPJ1

Answer:

9 squares

Step-by-step explanation:

Anne bought a piece of ribbon = 7 over 9 m long = 63 m²

she used = 3 over 18 m = 54 m²

left = 9 m²

maximum number of squares she could form of 1 m = 9

When a technician is faced with such issue, the following options can be considered:

Apply pressure to the back of the rivet with a screwdriver or other blunt object. This will help to keep the rivet from spinning and will also help to break the seal between the rivet and the sheet metal.

Use a carbide drill bit. Carbide drill bits are more durable than standard drill bits and are less likely to break when drilling through rivets.

Use a lubricant: Lubricants can help to prevent the drill bit from grabbing the rivet and can also help to cool the drill bit.

Therefore, any of the mentioned options could be taken in such situation .

Learn more on rivets :https://brainly.com/question/12967824

#SPJ1

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

For more such questions on distance

https://brainly.com/question/26550516

#SPJ8

Answer:

Step-by-step explanation:

The measure of the interior angle of a triangle is 180 degrees

therefore 3x + 2x + 90 = 180

5x + 90 = 180

5x = 90

x = 18

3x = 3(18)  = 54 degrees

2x = 2(18) = 36 degrees

To check:

54 + 36 + 90 = 180

Answer:

Step-by-step ex-plane

The zeros of a polynomial function can be used to determine how the graph behaves at those points. The multiplicity of a zero also plays an important role in shaping the graph of a polynomial function.

The graph of the seventh degree polynomial function with zeros 1, 2 (multiplicity of 3), 4, and 6 (multiplicity of 2) will cross the x-axis at 1 only. This is because the zero at 1 has a multiplicity of 1.

The graph will only touch (be tangent to) the x-axis at 2. This is because the zero at 2 has a multiplicity of 3.

At the zero of 2, the graph of the function will flatten out against the x-axis.

Therefore, the correct answers are:

- The graph of the function will cross through the x-axis at 1 only.

- The graph will only touch (be tangent to) the x-axis at 2.

- At the zero of 2, the graph of the function will flatten out against the x-axis.

Answer:

28,45,53 is a Pythagorean Triple

Step-by-step explanation:

To determine whether 28, 45, and 53 form a Pythagorean triple, we need to check whether they satisfy the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

So, we need to check whether:

28^2 + 45^2 = 53^2

Evaluating the left-hand side of the equation, we get:

784 + 2025 = 2809

And evaluating the right-hand side of the equation, we get:

2809 = 2809

Since both sides are equal, we can conclude that 28, 45, and 53 form a Pythagorean triple, because they satisfy the Pythagorean theorem. Therefore, 28^2 + 45^2 = 53^2 is a true statement, and we can say that the lengths 28, 45, and 53 can form the sides of a right triangle.

"UX = sup X," means that the union of the set X, denoted by UX, is equal to the supremum of X. In other words, if X is a nonempty set of ordinal numbers, then the union of those ordinals, UX, is itself an ordinal number, and it is equal to the supremum of X.

In set theory, the symbol "∪" denotes the union of sets. So, when we say "∪X," it represents the union of all the elements in the set X.

On the other hand, "sup X" stands for the supremum (or least upper bound) of the set X. The supremum of a set is the smallest ordinal number that is greater than or equal to all the elements in the set.

Therefore, when it is stated that "UX = sup X," it means that the union of the set X, denoted by UX, is equal to the supremum of X. In other words, if X is a nonempty set of ordinal numbers, then the union of those ordinals, UX, is itself an ordinal number, and it is equal to the supremum of X.

Learn more about set notation here:

https://brainly.com/question/24614358

#SPJ1

Answer:

$828.53

Step-by-step explanation:

The formula is: A = P(1 + r/k)^(kt)

A = 750(1 + 0.02/12)^(12*5)

A = 750(1 + 0.00166667)^60

A = 750(1.00166667)^60

A = 750(1.104713)

A = $828.53 (rounded to the nearest cent)

So, the accumulated amount after 5 years with a 2% interest rate compounded monthly is $828.53.

The best definition of phi is:

golden ratio, also known as the golden section, golden mean, or divine proportion, in mathematics, the irrational number (1 + Square root of√5)/2, often denoted by the Greek letter ϕ or, which is approximately equal to 1.618.

Phi = 1/phi Phi = 1 + phi The latter facts together give the definition of the golden ratio: x = 1/x + 1 This equation (equivalent to x^2 - x - 1 = 0) is satisfied by both Phi and -phi, which therefore can be called the _golden ratios_.

Hence, Phi is the value of the golden ratio which is the best definition of phi.

Learn more about the Golden Ratio at:

https://brainly.com/question/30746225

The given statement presents a contradiction in the assumption by assuming the existence of a well-ordered set and an increasing function, and shows that the function's value is always less than the input element in the set.

The given statement is a part of a proof demonstrating a property of an increasing function on a well-ordered set. Here's an explanation in 150 words:

The statement assumes that we have a well-ordered set W, equipped with a strict total order "<." Additionally, we have a function f defined on the set of all elements of W to W itself. The function f is said to be increasing, meaning that for any x and y in W, if x < y, then f(x) < f(y).

The proof aims to show that for every element x in W, f(x) is always less than x. To do this, it considers the set X, which contains all elements x in W such that f(x) < x. The assumption is made that X is nonempty and let z be the least element of X.

Then, the proof considers the element w = f(z), and it aims to reach a contradiction. It assumes that w is greater than f(z), i.e., f(w) < w. This leads to a contradiction because it contradicts the definition of X, where x should be in X if f(x) < x.

For more such questions on function

https://brainly.com/question/11624077

#SPJ8

6. Mr. Chao's students measured the length of different markers in inches. The data

collected is below.

Data set: 4, 5.5, 4.25, 5, 6.25, 6, 5.5, 5.25, 6.25, 4, 6.25, 5, 4.75

Answer:

5x + 3y = 13 parallel.

6x - 10y = 7 perpendicular.

Step-by-step explanation:Two lines with slopes  and  are parallel when  and are perpendicular when

Now determine the slope of all the lines

The line jk passes through the points

(-5,5) and (1,-5) so its slope is

To determine the slope of the lines in the blue rectangles, isolate y from each one and the coefficient of x is the slope

5x-3y = 8 ------> y = (5/3)x + 8/3 ------> slope 5/3

Neither parallel nor perpendicular.

6x+10y = 11 ------> y = (-6/10)x + 11/10 = (-3/5)x + 11/10 ------> slope -3/5

Neither parallel nor perpendicular.

5x + 3y = 13 ------> y = (-5/3)x + 13/3 ------> slope -5/3

This line is parallel

6x - 10y = 7 ------> y = (6/10)x - 7/10 = (3/5)x -7/10 ------> slope 3/5

Since (-5/3)(3/5) = -1 this line is perpendicular.

Answer:

To find the angles of intersection between the curves f(x) = x^2 and g(x) = |x|, we need to find the points where the two curves intersect.

Substituting g(x) into f(x), we get:

x^2 = |x|

To solve this equation, we need to consider two cases:

Case 1: x ≥ 0

In this case, the equation simplifies to:

x^2 = x

Solving for x, we get:

x(x - 1) = 0

So x = 0 or x = 1.

Case 2: x < 0

In this case, the equation simplifies to:

x^2 = -x

Solving for x, we get:

x(x + 1) = 0

So x = 0 or x = -1.

Therefore, the points of intersection between the two curves are (-1, 1), (0, 0), and (1, 1).

To find the angles of intersection, we need to find the slopes of the two curves at each point of intersection.

At (0, 0), the slopes of both curves are 0.

At (-1, 1) and (1, 1), the slope of f(x) = x^2 is 2x, and the slope of g(x) = |x| changes direction at x = 0, so we need to consider the left and right limits separately:

At x = -1, the slope of g(x) = -1, and at x = 1, the slope of g(x) = 1.

Therefore, the angles of intersection between the two curves are:

- At (0, 0), the two curves are tangent and intersect at a right angle.

- At (-1, 1) and (1, 1), the two curves intersect at acute angles.

Answer:

XYZThe name of angle below is XYZ

Answer:

(A) - [tex]f(g(x))=-18x^2+27x-19[/tex]

(B) - Quadratic

(C) - x=3/4

Step-by-step explanation:

Given:

[tex]f(x)=-2x^2+x-9\\\\g(x)=3x-2[/tex]

Find:

(A) -[tex]f(g(x))= \ ??[/tex]

(B) - Determine if f(g(x)) is linear or quadratic

(C) - Identify the slope or axis of symmetry

[tex]\hrulefill[/tex]

Part (A) -

Simply plug the function g(x) into f(x) to find f(g(x)):

[tex]f(g(x))=-2(3x-2)^2+(3x-2)-9[/tex]

Simplifying:

[tex]\therefore \boxed{f(g(x))=-18x^2+27x-19}[/tex]

Thus, part (A) is solved.

Part (B) -

To determine if a function is linear or quadratic, you need to examine its form and characteristics. Here are some key differences between linear and quadratic functions:

Linear Function:

Quadratic Function:

Using the information above we can determine f(g(x)) is quadratic.

Part (C) -

The axis of symmetry of a quadratic function can be found by using the formula x = -b / (2a), where a and b are the coefficients of the quadratic function in standard form. The resulting x-coordinate represents the vertical line that divides the parabola into two equal halves.

[tex]\text{In our case}: \ a=-18 \ \text{and} \ b=27\\\\\\\Longrightarrow x=\dfrac{-27}{2(-18)} \\\\\\\therefore \boxed{x=\frac{3}{4} }[/tex]

Thus, part (C) is solved.