A quadratic function is defined by f ( x ) = x 2 − 8 x − 4 . which expression also defines f and best reveals the maximum or minimum of the function.

The volume of the solid with equation y = 1/4x^2, x=2when rotated the volume is  π/2 cubic units.

To find the volume of the solid obtained by rotating the region bounded by y=1/4x^2 and x=2 about the x-axis, we can use the disk or washer method.

First, let's sketch the region and the solid. The region is bounded by y=1/4x^2 and x=2, and looks like a quarter of a parabola with its vertex at the origin and passing through (2,1). When we rotate this region about the x-axis, we get a solid that looks like a bowl with a flat bottom and a curved side.

To find the volume of this solid, we need to integrate the area of each disk or washer. Since the region is bounded by x=2, we can set up our integral as follows:

V = ∫[0,2] π(1/4x^2)^2 dx

This represents the sum of the volumes of all the disks or washers from x=0 to x=2. Simplifying the integral, we get:

V = π/16 ∫[0,2] x^3 dx
V = π/16 * [x^4/4] from 0 to 2
V = π/16 * (2^4/4 - 0)
V = π/2

Therefore, the volume of the solid obtained by rotating the region bounded by y=1/4x^2 and x=2 about the x-axis is π/2 cubic units.

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Answer:

y=3x-13

Step-by-step explanation:

because it is perpendicular to y=-1/3x+5 the gradient is 3.

so, so far for the line you are working out you have y=3x+c

now substitute the points(1,-10) into this equation

so... -10=3 times 1 +c

which gives

-10=3+c

now solve to get c

so...-10-3=c

       -13=c

so the equation of the line is ...y=3x-13

Answer:

BD also equals to 13 cause the diagonals are equal

Step-by-step explanation:

hope this is what u want

hope it helped u

The coordinates of the vertices of the feasible region are

(B) (0, 0),(2, 0), (0, 4)

A region that satisfies a set of inequality rules is referred to as a viable region. The area complies with all requirements set forth by a linear programming scenario. The idea is an approach to optimization.

We have the Constraints

y≥0, x≥0, y≤ -2x + 4

We can observe the graph of the following Linear programming problem (LPP) to see which are the vertices of the feasible region.

We notice that a triangle is the most frequently possible solution to these criteria, hence it must have three vertices.

The viable region's triangle's vertices are as follows:

(0, 0),(2, 0), (0, 4)

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Im looking for the same answer did you get it?

Answer:

2.6 ,-1,1

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

so you have to use the equation

y2 - y1 / x2 - x1

to find the slope

now all you have to do is substitute

-10 - 5 / 9 - 14

-15/ -5

3

Answer:

\(m=3\)

Step-by-step explanation:

\(\mathrm{Slope\:between\:two\:points}:\quad \mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}\)

\(\left(x_1,\:y_1\right)=\left(9,\:-10\right),\:\left(x_2,\:y_2\right)=\left(14,\:5\right)\)

\(m=\frac{5-\left(-10\right)}{14-9}\)

\(\mathrm{Refine}\)

\(m=3\)

Answer:

    x              y

    5            20

    15           10

    45           5

Step-by-step explanation:

Pattern x:

Start with 5.

Multiply by 3: 5 * 3 = 15

Multiply by 3: 15 * 3 = 45

Pattern x:

Start with 20.

Multiply by 1/2: 20 * 1/2 = 10

Multiply by 1/2: 10 * 1/2 = 5

    x              y

    5            20

    15           10

    45           5

The radius of the pipe is approximately 8.13 cm.

To find the radius of the pipe, we can use the formula for the volume of a cylinder, which relates the depth of the water, the width of the surface, and the radius of the pipe.

The volume of a cylinder is given by the formula V = π\(r^2\)h, where V is the volume, r is the radius, and h is the height or depth.

In this case, we are given the depth of the water as 18 cm and the width of the surface as 48 cm.

Since the width of the surface is equal to the diameter of the pipe, we can use the formula for the diameter of a circle, which is twice the radius.

Therefore, the radius is half of the diameter, or r = 48/2 = 24 cm.

Using the formula for the volume of a cylinder, we can write the equation as V = π\((24)^2\)(18), where V is the volume.

We know that the volume is equal to the cross-sectional area of the pipe multiplied by the depth of the water.

The cross-sectional area is given by the formula A = π\(r^2\).

Now we can solve for the radius.

Rearranging the equation V = π\((24)^2\)(18), we get

\((24)^2\) = V/(π(18))

Solving for \((24)^2\), we find that the radius is approximately 8.13 cm.

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Answer:

both of the solution is B and C

Answer:

The value of x + y is   -16.

Step-by-step explanation:

If each term is calculated by multiplying the previous one times 5 and then subtracting 20 from that result, then we can use that information to relate the first term (x) and the second one (0).

Following the info above, the following equation applies:

0 = 5 x - 20

then we solve for x:

5x = 20

x = 20/5

x = 4

Now we do the same study relating the second term (0) and the third one (y):

y = 5 (0) - 20

y = -20

Now that we have the value for both unknowns, we can estimate what they ask you: The value of x + y:

x + y = 4 + (-20) = 4 - 20 = -16

Answer:

the answer is \(12^{4}\)

Step-by-step explanation:

basically how many there are, you just put that in the top right

Answer:

20,736

Step-by-step explanation:

12x12x12x12

= 12^4

=20,736

Boole. K-map stands for Karnaugh Map and is used to simplify and minimize the expression of logic in a similar form to algebra.

George Boole is the mathematician we honor for discovering ways to express and minimize logic through a new but similar form of algebra. The technique used to simplify and minimize these expressions is known as a Karnaugh Map, or K-map for short. A K-map is a visual representation of a Boolean expression using squares and circles to represent true or false variables in a table. By arranging the variables in the table, the same logic can be expressed in a simpler form with fewer variables. This allows for a simpler and more efficient form of logic expression. K-maps are used in many fields, such as digital logic design, where the efficiency of expression is important.

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Answer:

D. p = -6

Step-by-step explanation:

1. combine like terms

5/6 P + 7 = 7/6 P + 9

2. subtract 7/6 P from both sides

-2/6 P + 7 = 9

3. subtract 7 from both sides

-2/6 P = 2

4. multiply both sides by -6/2

Answer:

p = -6

Answer: D

Step-by-step explanation:

Answer:

8x + 12

Step-by-step explanation:

2x + 3 + 2x + 3 + 2x + 3 + 2x + 3

8x + 12

Answer:

8x + 12

Step-by-step explanation:

3+3+3+3=12

2+2+2+2=8

da x stays da same

Considering the vertex of the quadratic function at point (6,-2), it is found that:

a) The meaning is that the turning point of the function is at point (6,-2).

b) If the parabola is concave down, then the vertex is a maximum. If the parabola is concave up, then it is a minimum.

c) If the parabola is concave down, then f(2) = f(10) < f(6). If the parabola is concave up, then f(2) = f(10) > f(6).

d) f(2) = f(10).

A quadratic equation is defined by the rule presented as follows:

y = ax² + bx + c.

The vertex can represent either a maximum point or a minimum point, depending on the coefficient a, as follows:

The vertex is also the turning point of the graph of the parabola.

In this problem, the coordinates of the vertex are (6,-2), hence:

When two points are equidistant from the vertex, they have the same numeric value, hence:

f(2) = f(6).

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Answer: 250

Step-by-step explanation: :)

Answer: 250

Based on the given conditions, formulate:: 15 x 100 over 60

Simplify fraction(s): 5 x 50

Calculate the product or quotient: 250

(a) The recurrence relation for the number of ternary strings of length n that do not contain "22" as a substring is given by:

F(n) = 2F(n-1) + F(n-2), where F(n) represents the number of valid strings of length n.

(b) The recurrence relation for the number of ternary strings of length n that do not contain "20" or "22" as a substring is given by:

G(n) = F(n) - F(n-2), where G(n) represents the number of valid strings of length n.

(a) To derive the recurrence relation for part (a), we consider the possible endings of a valid string of length n. There are two cases:

If the last digit is either "0" or "1", then the remaining n-1 digits can be any valid string of length n-1. Thus, there are 2 * F(n-1) possibilities.

If the last digit is "2", then the second-to-last digit cannot be "2" because that would create the forbidden substring "22". Therefore, the second-to-last digit can be either "0" or "1", and the remaining n-2 digits can be any valid string of length n-2. Thus, there are F(n-2) possibilities.

Combining both cases, we obtain the recurrence relation: F(n) = 2F(n-1) + F(n-2).

(b) To derive the recurrence relation for part (b), we note that the valid strings without the substring "20" or "22" are a subset of the valid strings without just the substring "22". Thus, the number of valid strings without "20" or "22" is given by subtracting the number of valid strings without "22" (which is F(n)) by the number of valid strings ending in "20" (which is F(n-2)). Hence, we have the recurrence relation: G(n) = F(n) - F(n-2).

In summary, for part (a), the recurrence relation is F(n) = 2F(n-1) + F(n-2), and for part (b), the recurrence relation is G(n) = F(n) - F(n-2).

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Driving a personal car would be the most cost-effective mode of transportation for this commute, with a total daily cost of approximately $4.60 ($3.60 for gas + $1 for travel time).

Based on the given information, the most cost-effective mode of transportation for this commute would be to drive a personal car. Taking public transportation or carpooling may be more environmentally friendly options, but they may not save as much money as driving alone.

Assuming an average speed of 60 miles per hour on the highway, the commute would take approximately 20 minutes each way, or 40 minutes round-trip. This means the total cost of travel time for each workday would be $40 ($60/hour x 2/3 hour).

Using a cost calculator such as GasBuddy, we can estimate that the cost of driving 20 miles per day (round-trip) would be around $3.60 per day, assuming an average fuel efficiency of 25 miles per gallon and a gasoline price of $2.50 per gallon.

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The major thing that Ryan should be worried about is the C) high annual depreciation.

Normally, when we buy cars they have so much value but when the cars start being used more often, they tend to depreciate in value due to wear and tear and second value of the product. This tells us that when a car is driven for more miles in a year, it will depreciate greatly.

We are told that Ryan plans to drive about 40 miles to work and back everyday which means that in a year he would have driven thousands of miles. This will lead to a high depreciation.

Thus, we can conclude that the most important thing that Ryan should be worried about when purchasing this old hatchback is the high depreciation.

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Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.

Given Information :A study conducted several years ago reported that 21% of public accountants changed companies within 3 years.

The American Institute of CPAs would like to update the study.

They would like to estimate the population proportion of public accountants who changed companies within 3 years with a margin of error of 3% and a 95% level of confidence.

Required:a. To update this study, how many public accountants should be contacted? Solution: Given that: the percentage of public accountants changed companies within 3 years is 21%.The level of confidence is 95%.

The margin of error is 3%.We have to find out the sample size.To find the sample size we use the formula :n = [Z² x p x q ] / E²

Where, Z = Standard normal deviation corresponding to a 95% confidence level is 1.96.p = proportion = 21/100 = 0.21q = 1-p = 1-0.21 = 0.79E = margin of error = 3/100 = 0.03

Putting all the given values in the formula, we get:n = [1.96² x 0.21 x 0.79] / 0.03²On solving, we get,n = 2734.84 ≈ 2735Therefore, 2735 public accountants should be contacted to update the study with a margin of error of 3% and a 95% level of confidence. Answer: 2735.

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To obtain the residuals from the fit in 8.4a and plot them against y and x, as well as prepare a normal plot, we need the specific details of the fit and the data used.

WE know that residuals represent the differences between the observed values and the predicted values from a statistical model or regression analysis.

Since the residuals against y and x can help identify patterns or trends in the data that may indicate issues with the model's fit.

A normal plot, known as a Q-Q plot, compares the distribution of the residuals to a theoretical normal distribution. If the residuals closely follow a straight line in the normal plot, the residuals are normally distributed, which is an assumption of many statistical models.

Interpreting these plots involves examining the patterns and deviations from expected behavior. If the residuals exhibit a consistent pattern, it might indicate that the model does not capture all the relevant information in the data.

Thus if the residuals appear randomly scattered around zero with no discernible pattern, it suggests that the model adequately explains the data. Deviations in the normal plot may indicate departures from the assumption of normality in the residuals, which could impact the reliability of statistical inferences.

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Answer:

Rewrite in slope-intercept form.

y = 5/4x + 4

Using the slope-intercept form, the y-intercept is b=4

Step-by-step explanation:

Yes, Both the students are correct because both students calculate the area of a rectangular garden.

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

Roberto says they can use the expression;

⇒ 2(3)+2(3)

And, Jay says they can use the expression;

⇒ (4.9) 3

Now,

Since, The garden club plants a rectangular garden that.

And, It has been divided into six sections.

Here, The members want to find the area of the sections they planted with herbs.

Roberto says they can use the expression;

⇒ 2(3)+2(3)

Clearly, Robert find the area of garden as;

⇒ 2(3)+2(3) = 12 ft²

And, Jay find the area of garden as;

⇒ (4.9) 3 = 14.7 ft²

Thus, Both the students are correct because both students calculate the area of a rectangular garden.

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Answer:

I think the answer is 5 hours and 15 minutes or 5.25 hours. Sorry if I'm wrong

Step-by-step explanation:

Answer:

5.25 Hours

Step-by-step explanation:

To find the time, you would divide 4200 kilometers by 800 kilometers per hour because the kilometers would cancel each other out giving only hours which is 5.25 hours

Answer:

s=8

Step-by-step explanation:

The two angles are vertical angles and vertical angles are equal.

110 = 8s-2

Add 2 to each side.

110+2 = 8s-2+2

112 = 8s

Divide each side by 8

112/8=8s/8

14=s

There are no points on the graph of the function y = x + 12 where the tangent line is horizontal.

The given function is y = x + 12. We need to find the points on the graph where the tangent line is horizontal.

To find the points where the tangent line is horizontal, we need to determine the points where the derivative of the function is equal to zero. The derivative of the function y = x + 12 can be found by differentiating it with respect to x.
Derivative of y = x + 12:
dy/dx = 1

Setting the derivative equal to zero, we have:
1 = 0
Since 1 can never be equal to zero, there are no points on the graph where the tangent line is horizontal for the given function y = x + 12.
Therefore, there are no points on the graph at which the tangent line is horizontal for the given function y = x + 12.

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The measure of lengths of the legs are 7 and 24. Therefore, option C is the correct answer.

The Pythagoras theorem which is also referred to as the Pythagorean theorem explains the relationship between the three sides of a right-angled triangle. According to the Pythagoras theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides of a triangle.

Given that, the hypotenuse of a right triangle measures 25.

A) 3²+4²= Square of the hypotenuse

25=Square of the hypotenuse

Hypotenuse=5 units

B) 5²+5²= Square of the hypotenuse

50=Square of the hypotenuse

Hypotenuse=5√2 units

C) 7²+24²= Square of the hypotenuse

625=Square of the hypotenuse

Hypotenuse=25 units

D) 10²+15²= Square of the hypotenuse

325=Square of the hypotenuse

Hypotenuse=√325 units

Therefore, option C is the correct answer.

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Answer:

2

Step-by-step explanation:

2=3x-4

6=3x

x=2

Answer:

\(2\)

Step-by-step explanation:

Let \(x\) be that certain number.

Two is equal to 4 less than 3 times \(x\)

\(2=3x-4\)

\(2+4=3x\)

\(6=3x\)

\(6/3=3x/3\)

\(2=x\)

That certain number is \(2\).