Find the image of the following points under the rotation through +90° about the centre origin. (a) A(4, 5) (b) B(-2, 3) (c) C(-3, -5) (d) D(4, -1)​

A system of equations to determine the number of home versions and professional versions of the software the company sold is given by:

20h + 45p = 38,075

h + p = 1000

The number of home versions sold is 277 and the number of professional versions sold is 723.

In order to write a linear equation to describe this situation, we would assign variables to the number of home versions sold and the number of professional versions sold respectively, and then translate the word problem into a linear equation as follows:

Since a home version of their photo editor cost $20, and a professional version, cost $45, a linear equation that models the situation is given by:

20h + 45p = 38,075

Additionally, the company sold 1000 copies of the photo editing software;

h + p = 1000

Solving the equations simultaneously, we have:

20h + 45(1000 - h) = 38,075

20h + 45,000 - 45h = 38,075

25h = 6,925

h = 277 home versions.

p = 1000 - h

p = 1000 - 277

p = 723 professional versions.

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Answer:

y= 1/cosx+7/tanx

dy/dx = 1secxtanx-cosec^2x

x ≈ 17.8 cm (rοunded tο 1 decimal place).

The trigοnοmetric functiοns in mathematics are real functiοns that relate the angle οf a right-angled triangle tο the ratiοs οf its twο side lengths. They are alsο knοwn as circular functiοns, angle functiοns, οr gοniοmetric functiοns.

All geοsciences, including navigatiοn, sοlid mechanics, celestial mechanics, geοdesy, and many οthers, use them extensively. They are sοme οf the mοst straightfοrward periοdic functiοns, and as a result, Fοurier analysis is frequently used tο study periοdic phenοmena.

Tο sοlve fοr x, we can use the trigοnοmetric functiοn cοsine since we have the adjacent side and the hypοtenuse.

cοs(θ) = adjacent/hypοtenuse

cοs(38°) = x/hypοtenuse

We knοw that the perpendicular is y = 11 cm, sο we can use the Pythagοrean theοrem tο find the hypοtenuse:

[tex]\rm hypotenuse^2 = perpendicular^2 + base^2[/tex]

[tex]x^2 = y^2 + (adjacent)^2[/tex]

[tex]x^2 = 11^2 + (x cos(38^\circ))^2[/tex]

[tex]x^2 = 121 + (x 0.7880107536)^2[/tex]

[tex]x^2 = 121 + 0.6201117996x^2[/tex]

[tex]0.3798882004x^2 = 121[/tex]

[tex]x^2 = 318.5022183[/tex]

x ≈ 17.84 cm (rounded to 1 decimal place)

Therefore, x ≈ 17.8 cm (rounded to 1 decimal place).

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The quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres. The total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.

To determine the quantity of fuel utilized by the water tanker in March 2022, we need to first calculate the total distance that the water tanker has covered in March 2022.

The total distance covered can be calculated using the formula:

distance = rate × time

From Annexure A, we can see that the water tanker was supplied to the construction site on the following dates in March 2022:

March 1, 2, 3, 6, 7, 8, 9, 10, 13, 14, 15, 16, 17, 20, 21, 22, 23, 24, 27, 28, 29, 30, and 31

Counting the number of days, we get a total of 23 days. Since the water tanker was supplied every day, we can assume that it covered the same distance every day.

The rate of fuel consumption of the Mercedes water tanker averages 5 km/l, which means that it can travel 5 km for every litre of fuel it consumes. Therefore, the distance covered by the water tanker on a full tank of fuel is:

distance = rate × fuel capacity

= 5 km/l × 460 litres

= 2300 km

So, the total distance covered by the water tanker in March 2022 is:

distance = 23 days × 2300 km/day

= 52,900 km

Next, we can determine the quantity of fuel utilized by the water tanker in March 2022 using the formula:

quantity of fuel = distance ÷ rate

Using the values we have calculated, we get:

quantity of fuel = 52,900 km ÷ 5 km/l

= 10,580 litres

Therefore, the quantity of fuel utilized by the water tanker in March 2022 is 10,580 litres.

To determine the total amount of money that was utilized on fuel for the water tanker in March 2022, we can multiply the quantity of fuel utilized by the fuel price in March 2022:

total cost = quantity of fuel × fuel price

From the problem statement, the fuel price in March 2022 was R19.55 per litre. Substituting the values we have calculated, we get:

total cost = 10,580 litres × R19.55/litre

= R206,929.00

Therefore, the total amount of money that was utilized on fuel for the water tanker in March 2022 is R206,929.00.

Complete question:

Records of the number of water tankers that were supplied to the construction site appear in the calendar on ANNEXURE A. The water tanker has a fuel capacity of 460 litres. The rate of fuel consumption of the Mercedes water tanker averages 5 km/l. The prices of fuel per litre in March and June 2022 appear below. MARCH 2022 FUEL PRICES DIESEL 50 ppm (a 4. 1) (b ) COST R19,55 JUNE 2022 FUEL PRICES DIESEL 50 ppm Source: COST R24,14 Calculate the total distance that the water tanker has covered in March 2022. Hence, determine the quantity of fuel that was utilized by the water tanker in March 2022. Determine the total amount of money that was utilized on fuel for the water tanker in March 2022​. Quantity of fuel utilized by water tanker March 2022

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The final result of the expression (6e−3f−4)⋅2 is e3f−8.

The calculation is as follows: (6e−3f−4)⋅2 = (6e-3f-4)*2. In order to calculate this expression, it is necessary to use the Order of Operations. The Order of Operations is a set of rules that determine the order in which operations should be performed when evaluating an expression. First, any parentheses need to be evaluated. In this expression, there are parentheses surrounding 6e−3f−4. This means that any operations within the parentheses should be done first. Inside the parentheses, there is an exponent, e−3f, and a subtraction, 4. Exponents should be done first, so e−3f should be evaluated first. This is equivalent to e multiplied by e multiplied by e, multiplied by f, which is equal to e3f. Then, 4 should be subtracted from e3f, which is equal to e3f−4. After the parentheses have been evaluated, the remaining multiplication should be done. This is equivalent to (e3f−4)*2, which is equal to e3f−8.

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Based on the sample of 37 sandwich cookies, it can be concluded that the average weight of a sandwich cookie is close to 11.3 grams, as the manufacturer claimed. This conclusion is supported by the mean, standard deviation, and range of the sample.

Standard deviation is a measure of how spread out a set of numbers is. It gives us an idea of how much variation there is from the average or expected value. It is calculated by taking the square root of the variance, which is the average of the squared differences from the mean.

The manufacturer of a sandwich cookie claims that the average weight of a sandwich cookie is 11.3 grams. To test this claim, a statistics class randomly selected 37 sandwich cookies and weighed them. The sample of 37 sandwich cookies had a mean of 11.2 grams, standard deviation of 0.5 grams, and range of 10.1 to 12.5 grams.

The mean of 11.2 grams is very close to the manufacturer’s claim of 11.3 grams. The standard deviation of 0.5 grams indicates that the sample of sandwich cookies had a very small amount of variance. The range of 10.1 to 12.5 grams indicates that the sample had sandwich cookies with weights that were close to the mean, which further supports the conclusion that the mean is close to 11.3 grams.

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This means that the Mt. Rinjani eruption was approximately 20 times larger and more powerful than the Mt. Pinatubo eruption.

An exponent is a mathematical operation that involves raising a base number to a certain power. The exponent tells how many times the base number should be multiplied by itself. For example, in the expression 2³, 2 is the base number and 3 is the exponent, and it means that 2 should be multiplied by itself three times: 2 x 2 x 2 = 8. Exponents are commonly used in algebra, calculus, and other branches of mathematics.

Here,

The Volcanic Explosivity Index (VEI) is a logarithmic scale used to measure the relative size and power of volcanic eruptions. Each increase of 1 on the VEI scale represents a tenfold increase in the eruption's size and power.

The difference in VEI between the Mt. Rinjani eruption and the Mt. Pinatubo eruption is 7.3 - 6.0 = 1.3.

To calculate the difference in size and power, we need to raise 10 to the power of 1.3:

10¹.³ = 19.95

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From the given data, the probability that the pedestrian was not intoxicated or the driver was not intoxicated is 99.7%.

To find the probability that the pedestrian was not intoxicated or the driver was not intoxicated, we can add the probabilities of the two mutually exclusive events:

Pedestrian not intoxicated and driver intoxicated

Pedestrian intoxicated and driver not intoxicated

From the table, we can see that there were 603 pedestrian deaths where the driver was not intoxicated and 54 pedestrian deaths where the driver was intoxicated, for a total of 657 deaths where the driver was not intoxicated. Similarly, there were 246 pedestrian deaths where the pedestrian was not intoxicated and 83 pedestrian deaths where the pedestrian was intoxicated, for a total of 329 deaths where the pedestrian was not intoxicated.

Therefore, probability that pedestrian was not intoxicated or driver was not intoxicated is:

P = (657 + 329) / 986

= 0.9969

Converting to percentage and rounding to one decimal place,

P = 99.7%

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Answer:

yes, a triangle with the side lengths 12, 5, and 12 does exist.

Step-by-step explanation:

side a = 12

side b = 5

side c = 12

area = 29.34In

Answer:

3, 9

Step-by-step explanation:

Surface A = 2(wl + hl + hw)

Where in the red prism, l is 12, w is 6, h is 9 and in the red prism l is 4, w is 2, h is 3

Lenght 12/4 =3

Width 6/2 =3

Height 9/3 =3

Calculate surface are of red prism

SA = 2( 6x12 + 9x12 + 9x6)

SA = 2( 72 +108+54)

SA = 2(234) = 468 m²

Calculate surface area of blue prism

SA = 2(2x4 + 3x4 + 3x2)

SA = 2(8 +12+6)

SA = 2(26)

SA =52

Area of red /area of blue = 468/52

Ans =9

Answer:

B. Make a table of equal ratios to find how long it takes each printer to print 120 photos and find the difference would be an appropriate process to determine how much longer it will take Khalil's printer to print 120 photos than Alex's.

Step-by-step explanation:

To use this process, we can set up a table showing the ratio of photos printed to time taken for each printer. Then we can use these ratios to find how long it would take each printer to print 120 photos, and find the difference between the two times to determine how much longer it would take Khalil's printer.

The Construction of line MN and perpendicular at point N as well as angle MNP = 60°such that NP would be 6.3 cm is given below as image.

In Euclidean geometry, an angle is a shape made up of two rays that share a terminal and are referred to as the angle's sides and vertices, respectively. Angles can be formed in the plane where two rays are positioned. Moreover, when two planes overlap, angles are created. Dihedral angles are what they are called.

In geometry, two lines are considered to be perpendicular if they meet or intersect at right angles of 90°. The Latin term "perpendicularis," which denotes a plumb line, is where the word "perpendicular" originally made its appearance.

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The width of Averi's area model is 4 units.

The area model for factoring 4x²+20x-16 is shown above. The width of Averi's area model is 4 units. To factor the given expression, Averi used an area model.

In this model, the width represents the greatest common factor of the given expression while the length represents the remaining factors of the expression. Averi determined that the greatest common factor of 4x²+20x-16 was 4.

Therefore, she created a rectangle with a width of 4 and a length of (x²+5x-4). The dimensions of the rectangle are determined by the factors of the given expression.

The area of the rectangle represents the original expression. Therefore, the area of the rectangle can be calculated by multiplying the width and length of the rectangle. The area of the rectangle is equal to: Area of rectangle = width x length Area of rectangle = 4(x²+5x-4)Area of rectangle = 4x²+20x-16

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The number of students are 110 students offer Biology but not Mathematics.

Let's use a Venn diagram to solve this problem. We know that 125 students offer Biology and 110 offer Mathematics, and we want to find out how many offer Biology but not Mathematics.

First, we can fill in the number of students who offer both Biology and Mathematics, which is the overlap between the two circles. We can do this by subtracting the total number of students who offer both from the total number of students who offer either:

220 (total) - (125 + 110) = 220 - 235 = -15

Wait a minute! A negative number of students doesn't make sense in this context. What this tells us is that there must be some double-counting going on - in other words, some students are being counted twice, once in each of the Biology and Mathematics categories.

To correct for this, we need to add back in the number of students who are counted twice, which is the overlap between the two circles. We can calculate this by adding the number of students who offer Biology and Mathematics together:

125 + 110 = 235

Now we can redo the calculation:

220 (total) - 235 (double-counted) = -15

This tells us that there are 15 students who are being counted twice. To find the number of students who offer Biology but not Mathematics, we need to subtract this number from the number of students who offer Biology:

125 - 15 = 110

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Answer: if im correct i think its 95

On replacing the incandescent light bulb with a fluorescent light bulb (a) the energy saved in one day is 0.22 kWh, (b) the energy saved in one year is 80.3 kWh. and (c) the cost savings in one year is $8.03.

a. The energy saved in one day by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:

Energy saved in one day = Energy consumed by incandescent bulb - Energy consumed by fluorescent bulb

Energy saved in one day = (75 watts x 4 hours) - (20 watts x 4 hours)

Energy saved in one day = 300 watt-hours - 80 watt-hours

Energy saved in one day = 220 watt-hours

To convert watt-hours to kilowatt-hours (kWh), we divide the watt-hours by 1000:

Energy saved in one day = 220 watt-hours / 1000

Energy saved in one day = 0.22 kWh

b. The energy saved in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:

Energy saved in one year = Energy saved in one day x Number of days in one year

Energy saved in one year = 0.22 kWh/day x 365 days/year

Energy saved in one year = 80.3 kWh

c. The cost savings in one year by using the fluorescent light bulb instead of the incandescent light bulb can be calculated as follows:

Cost savings in one year = Energy saved in one year x Cost per kWh

Cost savings in one year = 80.3 kWh x $0.10/kWh

Cost savings in one year = $8.03

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Answer:

1:3 is your rate for dollars per soda

Step-by-step explanation:

The three points that are solutions to the linear inequality y < 0.5x + 2 are (-3, -2), (-1, -2), and (1, -2)

To check which points are solutions to the linear inequality y < 0.5x + 2, we can substitute the coordinates of each point into the inequality and check whether the inequality is true or false.

For the point (-3, -2):

y < 0.5x + 2

-2 < 0.5(-3) + 2

-2 < -0.5

This inequality is true, so (-3, -2) is a solution.

For the point (-2, 1):

y < 0.5x + 2

1 < 0.5(-2) + 2

1 < 1

This inequality is false, so (-2, 1) is not a solution.

For the point (-1, -2):

y < 0.5x + 2

-2 < 0.5(-1) + 2

-2 < 1.5

This inequality is true, so (-1, -2) is a solution.

For the point (-1, 2):

y < 0.5x + 2

2 < 0.5(-1) + 2

2 < 1.5

This inequality is false, so (-1, 2) is not a solution.

For the point (1, -2):

y < 0.5x + 2

-2 < 0.5(1) + 2

-2 < 2.5

This inequality is true, so (1, -2) is a solution.

Therefore, the three points that are solutions are (-3, -2), (-1, -2), and (1, -2).

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The given question is incomplete, the complete question is:

Which points are solutions to the linear inequality y < 0. 5x +2? Select three options. (-3,-2) (-2,1) (-1,-2) (-1, 2) (1,-2)

Answer:

Step-by-step explanation:

B and E

6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true. The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.

We must find x in order to determine what value of x results in the equation 23x + 5 = 11 being true.

Initially, we must remove 5 from both sides of the equation to isolate the variable x:

23x + 5 - 5 = 11 - 5

When we combine the left and right sides, we obtain:

23x = 6

Then, by multiplying both sides of the equation by 23, we must find x:

23x/23 = 6/23

When we combine the left and right sides, we obtain:

x = 6/23

As a result, 6/23 is the value of x that ensures that the equation 23x + 5 = 11 holds true.

The solution to this problem cannot be found in the available selections since none of the answer possibilities match this value.

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Therefore , the solution of the given problem of coordinates comes out to be the coordinates of the reflection of G(3, -2) across the y-axis (-3, -2).

By utilising one or even more variables or coordinates, a coordinate system is able to precisely locate points or other mathematical items on such a room, including Euclidean space. Coordinates, which seem to be pairs of integers, are used to locate a point or object on a double plane. The y and x vectors are used to represent the position of a point on a two-dimensional surface. a group of figures used to designate particular places.

Here,

G(3, -2) will have the following coordinates after being reflected across the y-axis:

=> (-3, -2).

A point's x-coordinate changes sign when it is reflected across the y-axis, but its y-coordinate stays the same.

Consequently, the coordinates of the reflection of G(3, -2) across the y-axis (-3, -2).

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The coordinates of the resulting point after the reflection across the y - axis will be G'(3, 2) and The coordinates of the resulting point after the reflection across the x - axis will be G'(3, 2).

A reflection on the coordinate     plane (x , y ) is a type of transformation. It takes a geometric figure such as a line,    segment, point or shape and transforms it into a congruent   geometric figure called the image.

a. It is given that a point (-3, 2) reflected   across the y - axis.

Now, when any given coordinate    is reflected across the y - axis then, the sign of the x - coordinate is inverted and the y - coordinate remains same.

Therefore, the coordinates of the resulting    point after the reflection across the y - axis    will be G'(3, 2)

b. It is given that a point (3, -2) reflected   across the x - axis.

Now, when any given coordinate    is reflected across the x - axis then, the sign of the y - coordinate is inverted and the x - coordinate remains same.

Therefore, the coordinates of the resulting    point after the reflection across the x - axis    will be G'(3, 2).

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(a) The probability that Thomas is selected for the position given that the company's revenue did not improve is 4/7.

(b) To find the probability, p, that the company's revenue will generally improve, we can calculate the probability that at least one of Rachel, Sam, or Thomas is selected for the position.

This can be done by calculating the sum of the probabilities of each of them being hired, which is 1/7 + 2/7 + 4/7 = 7/7 = 1. Therefore, the probability that the company's revenue will generally improve is 1.

(c) To find an inequality that must be satisfied by x, we must take into account the probabilities that each of Rachel, Sam, and Thomas is hired for the role.

For example, if x = 1/2, then the probability that Rachel is hired is 1/2, Sam is hired is 1, and Thomas is hired is 2. Therefore, the inequality that must be satisfied by x is 0 < x ≤ 1/2.

For further information on (a) The probability that Thomas is selected for the position given that the company's revenue did not improve is 4/7.

(b) To find the probability, p, that the company's revenue will generally improve, we can calculate the probability that at least one of Rachel, Sam, or Thomas is selected for the position. This can be done by calculating the sum of the probabilities of each of them being hired, which is 1/7 + 2/7 + 4/7 = 7/7 = 1. Therefore, the probability that the company's revenue will generally improve is 1.

(c) To find an inequality that must be satisfied by x, we must take into account the probabilities that each of Rachel, Sam, and Thomas is hired for the role. For example, if x = 1/2, then the probability that Rachel is hired is 1/2, Sam is hired is 1, and Thomas is hired is 2. Therefore, the inequality that must be satisfied by x is 0 < x ≤ 1/2.

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In our proof, as the trapezium are congruent and the rest of the sides are equal ∴AC = BD. Hence, the cyclic trapezium is isosceles and its diagonals are equal.

Step 1:

The diagonals are AC and BD, and the line CE is parallel to AD.

We know that a parallelogram's opposite angles are equal.

∠D = ∠AEC......(1)

We also know that the sum of a cyclic quadrilateral's opposite angles is 180 degrees.

∠D + ∠ABC = 180..........(2)

We can deduce from (1) and (2) that

AEC + ABC = 180....... (3)

AEC and CEB are now a linear pair.

AEC + CEB = 180................. (4)

We can conclude from (3) and (4) that,

CEB = ABC

The sides opposite the equal angles are also equal, as we know.

CEB = ABC

CE = CB ... (5)

However, because AECD is a parallelogram, opposite sides must be equal.

∴CE = AD ... .(6)

From equation (5) and (6), we can conclude that

AD = CB ......(7)

As a result, the cyclic trapezium ABCD is isosceles.

Step 2:

Establishing that its diagonals are equal.

We have AC and BD as diagonals.

In triangle DBA and CBA,AD = CB from (7)⇒AB = AB (common side).

ADB + ACB (angles in the same segment of a circle are equal). As a result of the SAS rule, ABD and ABC are congruent.

Because they are congruent and the other sides are equal, AC = BD. As a result, a cyclic trapezium is isosceles and has equal diagonals.

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The unit rate is 8.4 miles per hοur.

Distance and displacement are twο quantities that seem tο mean the same but are distinctly different with different meanings and definitiοns. Distance is the measure οf “hοw much grοund an οbject has cοvered during its mοtiοn” while displacement refers tο the measure οf “hοw far οut οf place is an οbject.”

Tο find the unit rate in miles per hοur, we need tο divide the distance by the time.

The distance is 1 2 2 1  miles and the time is 1 4 4 1  hοurs.

Sο, the unit rate in miles per hοur is:

(1 2 2 1  miles) / (1 4 4 1  hοurs) = 8.4 miles per hοur (rοunded tο οne decimal place)

Therefοre, the unit rate is 8.4 miles per hοur.

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The volume of the given solid above which is a triangular prism would be = 510 ft³.

To calculate the volume of the given prism the formula should be used such as;

Volume = 1/2 × base× height × length

Where base = 10ft

height = 6 ft

length = 17ft

Volume = 1/2 × 10×6×17

= 5×6×17

= 510 ft³

Therefore the volume of the given shape above would be = 510 ft³ when the formula for triangular prism is used.

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37.70/12

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h(2) + j(−7) = −7(1 + j)

Suppose that f(x) = h^−1(x) and that both j and h are defined for all values of x. Let h(11) = 2 and f(12) = −7. We need to evaluate the following. h(2) + j(−7)For finding the value of h(2), we can use f(x) = h^−1(x) where x = h(2)f(h(2)) = 2h(2) = f^−1(2)We need to find h(2). Therefore, we need to find f^−1(2). We know f(12) = −7f(h(2)) = 2⟹ h(2) = −7Substitute h(2) = −7 in h(11) = 2h(11) = h(2 + 9) = h(2) + 9 = 2 + 9 = 11Therefore, h(2) = −7 and h(11) = 2.h(2) + j(−7) = −7 + j(−7) = −7(1 + j)Therefore, h(2) + j(−7) = −7(1 + j).

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Answer: distributive property

Step-by-step explanation:1 2 times 95 can indeed be rewritten as 12(100-5) and we can use the distributive property IN OUR HEADS, so we get 1200 - 60 = 1140.

Answer:

96π cubic feet

Step-by-step explanation:

Surface area of a cylinder
A = 2πr(h+r)

where r = radius, h = height

Here

r = diameter/w = 8/2 = 4 feet

h = 8 feet

A = 2π · 4 (8 + 4)

= 8π (12)

= 96π cubic feet

Answer:

g(x) was shifted 9 units to the left and 5 units down

Step-by-step explanation:

Horizontal shifts take place when the x value is changed within the parentheses, or in this case, absolute value.

The graph is shifted 9 units left because of the + 9.

Vertical shifts happen when the entire equation is added or subtracted to.

The graph is shifted 5 units down because of the - 5.

See the graph for a visualization.