A kite is flying 85 ft off the ground, and its string is pulled taut. The angle of elevation of the kite is 58 . Find the length of the string. Round your answer to the nearest tenth.

The ladder reaches approximately 26.11 feet up the wall.

What is trigonometric equations ?

Trigonometric equations are equations that involve trigonometric functions of one or more variables. The most common trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.

We can use trigonometry to solve this problem. The ladder, the wall, and the ground form a right triangle, where the ladder is the hypotenuse, the distance we want to find is one leg, and the angle between the ground and the ladder is the angle opposite the leg we want to find. We can use the sine function to solve for the height h:

sin(65) = h/30

Multiplying both sides by 30, we get:

h = 30 * sin(65)

Using a calculator, we find:

h ≈ 26.11

Therefore, the ladder reaches approximately 26.11 feet up the wall.

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(i)   −10

(ii)   6

(i)The average rate of change for the function f(t) = −3t2+2t−4 between t=2 and t=5 is −10.

(ii)The average rate of change for the function f(t) = −3t2+2t−4 between t=−1 and t=3 is 10.An average rate of change is the ratio of the change in a function to the change in the input. The average rate of change for the function f(t) = −3t2+2t−4 between t = 2 and t = 5 can be calculated as follows:-f(5) − f(2) / 5 − 2= -95 - (-20) / 5 - 2 = -75 / 3 = -25So, the average rate of change for the function f(t) = −3t2+2t−4 between t = 2 and t = 5 is −25.The average rate of change for the function f(t) = −3t2+2t−4 between t = −1 and t = 3 can be calculated as follows:-f(3) − f(-1) / 3 - (-1) = -25 - 1 / 3 + 1 = -24 / 4 = -6So, the average rate of change for the function f(t) = −3t2+2t−4 between t = −1 and t = 3 is 6.

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If Allison needs 13 inches of cloth for sewing project, then Allison will need to buy 33.02 centimeter of cloth.

The length of cloth that Allison needs to buy is =  13 inches ,

The conversion factor is ⇒ 1inch = 2.54 centimeter,

Allison needs 13 inches of cloth, and we know that 1 inch is the same as 2.54 centimeters.

So, to convert 13 inches to centimeters we multiply it by the conversion factor of 2.54 centimeters per inch,

Which is written as;

⇒ (13 inches) × (2.54 centimeters per inch)

⇒ 33.02 centimeters

Therefore, Allison needs to buy 33.02 centimeters of cloth for her sewing project.

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The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

a) The probability that in any given hour zero new visitors will arrive at the website is given by;P(X = 0) = (e^-λ λ^0)/0!Where λ = 2.3Thus;P(X = 0) = (e^-2.3 2.3^0)/0!P(X = 0) = (0.1003)/1P(X = 0) = 0.1003b) The probability that in any given hour exactly one new visitor will arrive at the website is given by;P(X = 1) = (e^-λ λ^1)/1!Where λ = 2.3Thus;P(X = 1) = (e^-2.3 2.3^1)/1!P(X = 1) = (0.2303)/1P(X = 1) = 0.2303c) The probability that in any given hour two or more new visitors will arrive at the website is given by;P(X ≥ 2) = 1 - P(X = 0) - P(X = 1)Thus;P(X ≥ 2) = 1 - 0.1003 - 0.2303P(X ≥ 2) = 0.6694d) The probability that in any given hour fewer than three new visitors will arrive at the website is given by;P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)Thus;P(X < 3) = 0.1003 + 0.2303 + 0.2642P(X < 3) = 0.5948Therefore,The probability that in any given hour zero new visitors will arrive at the website is 0.1003.The probability that in any given hour exactly one new visitor will arrive at the website is 0.2303.The probability that in any given hour two or more new visitors will arrive at the website is 0.6694.The probability that in any given hour fewer than three new visitors will arrive at the website is 0.5948.

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"Yes, there is." The coordinates of point P are either (11/4, 63) or (73/52, 36), depending on the chosen value of x.

We can use the distance formula to find the distance between R and P, and between P and S:

Distance formula:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Plugging in the values, we get:

RP = √((x - (-3))² + (y - 1)²)

SP = √((x - 4)² + (y - 3)²)

Now, we can set up an equation based on the given ratio of RP to SP:

RP/SP = 5/4

We can substitute the expressions we just derived for RP and SP into this equation:

√((x - (-3))² + (y - 1)²) / √((x - 4)² + (y - 3)²) = 5/4

Squaring both sides of the equation to eliminate the square roots, we get:

((x - (-3))² + (y - 1)²) / ((x - 4)² + (y - 3)²) = 25/16

Expanding the squares and simplifying, we get:

41x² - 146x - 191y² + 1210y + 2900 = 0

For simplicity, let's solve for y:

y = (73x + 2900)/191

Now we can substitute this expression for y into one of the original equations:

RP = √((x - (-3))² + ((73x + 2900)/191 - 1)²)

Simplifying this expression, we get:

RP = √(1049x² - 12212x + 36010)/191

We want RP to be 5x units long, so we can set up the equation:

√(1049x² - 12212x + 36010)/191 = 5x

Squaring both sides, we get:

Expanding the square and simplifying, we get:

1044x² - 12212x + 36010 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / 2a

where a = 1044, b = -12212, and c = 36010. Plugging in these values, we get:

x = (-(-12212) ± √((-12212)² - 4(1044)(36010))) / 2(1044) x = (12212 ± √(5924688)) / 2088 x = (12212 ± 3864) / 2088

This gives us two possible values for x:

x = 11/4 or x = 73/52

Now we can substitute each value of x back into the expression we derived for y:

y = (73x + 2900)/191

For x = 11/4, we get:

y = (73(11/4) + 2900)/191 = 63

So one possible set of coordinates for P is (11/4, 63).

For x = 73/52, we get:

y = (73(73/52) + 2900)/191 = 36

So another possible set of coordinates for P is (73/52, 36).

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The you can also add filters and create calculated fields as per your requirement.Download, Market, capitalizations

To download and connect to the raw data Market Caps of S_P500 Companies 2008-2015.xls on Canvas>Files> Tableau Data Files using Tableau, you need to follow the steps given below:Step 1: Open Tableau and click on the Connect to Data option.Step 2: In the Connect Pane, choose Microsoft Excel as the file type and then browse the Excel file named Market Caps of S_P500 Companies 2008-2015.xls from the location where it is saved on your computer.Step 3: Once you have selected the file, click on the Open option.Step 4: After selecting the file, the Excel file window will open. Here, you can see the tabs containing different sheets. Choose the sheet you want to connect to.Step 5: After choosing the sheet, you can see a preview of the data. Click on the Sheet1 tab to open it.Step 6: Now, you can create a visualization of the data by dragging the fields to the Columns and Rows shelves. You can also add filters and create calculated fields as per your requirement.Download, Market, capitalizations

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Mrs. kenimer had a chocolate bar that weighed 1/2 lb. At recess she ate some of her chocolate bar, now her bar weights 1/4 of a pound. Mrs. kenimer ate 3/8 lb of the chocolate bar.

The British imperial and American cοnventiοnal methοds οf measurement bοth use the pοund as a unit οf mass. The internatiοnal avοirdupοis pοund, which is fοrmally defined as precisely 0.45359237 kilοgrammes and is split intο 16 avοirdupοis οunces, is the term that is currently mοst frequently used. The avοirdupοis pοund's wοrldwide standard sign is lb.

Given,

Mrs.kenimer had a chocolate bar that weighed 1/2 lb or 0.5lb

At recess she ate some of her chocolate bar, now her bar weights 1/4 of a pound or 0.25 of a pound.

Remaining weight of the chocolate bar= ½* ¼ = 1/8 lb

She ate= (1- ¼)= ¾ or 0.75 of a pound

So she ate= ½ * ¾ = 3/8 lb of the chocolate.

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There is gain of $1,000 on the sale. The solution has been obtained by using the arithmetic operations.

What are arithmetic operations?

All real numbers are believed to be able to be described by the four fundamental operations, often known as "arithmetic operations". Quotient, product, sum, and difference are the next four mathematical operations after division, multiplication, addition, and subtraction.

We are given that an equipment costing $135,000 has a book value of $124,000 and it is sold for $125,000.

Since, the sale value is higher than the book value, therefore there is a gain.

Using arithmetic operations, we get

Gain on sale = $125,000 - $124,000

Gain on sale = $1,000

Hence, there is gain of $1,000 on the sale.

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The second part of the question i.e. how is it recorded for this transaction is related to the subject accountancy and not mathematics.

(a) the events A and B are disjoint.

(b) the probability that A or B occurs is 0.6.

What is Probability?

In mathematical terms, probability is defined as the ratio of the number of favorable outcomes to the total number of possible outcomes in a given event or experiment. The probability of an event is represented by a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.

(a) If the knowledge that an event A has occurred implies that a second event B cannot occur, then the events A and B are said to be disjoint. This means that A and B have no outcomes in common and cannot happen simultaneously.

(b) If event A and event B are disjoint and event A has probability 0.5 and event B has probability 0.1, then the probability that A or B occurs is the sum of their probabilities:

P(A or B) = P(A) + P(B) = 0.5 + 0.1 = 0.6

Note that since A and B are disjoint, the probability of both events happening simultaneously is 0. Therefore, P(A and B) = 0.

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If you are traveling at 60 mph, you are also traveling at 96.56 kph.

To convert 60 miles per hour (mph) into kilometers per hour (kph), we need to use a conversion factor. A conversion factor is a ratio that relates two different units of measurement. In this case, we can use the fact that 1 mile is equal to 1.60934 kilometers. To convert mph to kph, we need to multiply the given value by this conversion factor.

So, to convert 60 mph to kph, we can set up the following equation:

60 mph x (1.60934 km/1 mile) = 96.56 kph

This means that 60 mph is equivalent to 96.56 kph. Therefore, if you are traveling at 60 mph, you are also traveling at 96.56 kph.

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The x in the equation 326 = x + 8.50(36) represents the B. The delivery fee at the second store.

An equation is an algebraic statement that two or more mathematical expressions are equal or equivalent.

Equations are depicted using the equation symbol (=) to show the equality of algebraic expressions, which are the combination of values, constants, numbers, and variables using the mathematical operands.

The number of potted plants ordered for sponsors = 36

The charge per plant = $8.50

Delivery fee = $20

Equation: 326 = x +8.50(36)

Thus, in the equation, 326 = x + 8.50(36), x represents Option B, which is a fixed charge.

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Answer:

2

Step-by-step explanation:

gradient = slope = Δy/Δx = (4 - 2) / (-2 --3) = 2/1 = 2

20 grams are formed in 20 minutes, the limiting amount (in grams) of C after a long time is 40 grams and 0 grams of A and 30 grams if B chemicals remain after a long time.

The reaction can be represented by the following equation:

2A + B -> C

Initially, there are 40 grams of A and 50 grams of B. After 10 minutes, 10 grams of C is formed. This means that 5 grams of B and 10 grams of A were used up in the reaction.

After 10 minutes, there are 30 grams of A and 45 grams of B remaining. The reaction will continue until one of the reactants is used up. In this case, A is the limiting reactant because there are less grams of A remaining than B.

After 20 minutes, 20 grams of C will be formed because the reaction rate is constant. This means that 10 grams of B and 20 grams of A will be used up in the reaction.

After 20 minutes, there will be 10 grams of A and 35 grams of B remaining. The reaction will continue until all of the A is used up.

After a long time, the limiting amount of C will be 40 grams because all of the A will be used up in the reaction. This means that 20 grams of B will be used up in the reaction.

After a long time, there will be 0 grams of A and 30 grams of B remaining.

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Answer:

250.56

Step-by-step explanation:

we know each dress is 8.70 , and when we buy 40 dresses or more we get 10 percent off the total.

let us first multiply 8.70 x 42 , giving us the total cost as 278.4
there is a 10 percent discount , so 27.84 should be reduced from original price

Final price = 250.56

Answer: To find the x and y intercepts of the line 2x + 5y = -6, we can substitute 0 for x to find the y-intercept and 0 for y to find the x-intercept.

y-intercept:

To find the y-intercept, we set x = 0 and solve for y:

2x + 5y = -6

2(0) + 5y = -6

5y = -6

y = -6/5

Therefore, the y-intercept is (-0,6/5)

x-intercept:

To find the x-intercept, we set y = 0 and solve for x:

2x + 5y = -6

2x + 5(0) = -6

2x = -6

x = -3

Therefore, the x-intercept is (-3,0).

Hence, the intercepts of the line 2x + 5y = -6 are (-3, 0) for the x-intercept and (0, -6/5) for the y-intercept.

Step-by-step explanation:

Answer:

pepperoni slices : 72

cheese slices: 55

Step-by-step explanation:

p is the number of pepperoni slices

c is the number of cheese slices

so p + c = 127 => c = 127 - p

3p + 2c = 326

3p + 2(127 - p) = 326

3p + 254 - 2p = 326

p = 326 - 254 = 72

c = 127 - 72 = 55

Therefore, the point on the line y = 3x + 4 that is closest to the origin is: (x, y) = (3/5, -2/5).

An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.

Here,

To find the point on the line y=3x + 4 that is closest to the origin, we can use the distance formula between a point and a line. The point on the line that is closest to the origin will lie on the perpendicular line that passes through the origin and intersects the given line.

First, let's find the slope of the perpendicular line. Since the given line has a slope of 3, the perpendicular line will have a slope of -1/3 (the negative reciprocal of 3). Therefore, the equation of the perpendicular line is:

y = (-1/3)x + b

where b is the y-intercept.

Next, we need to find the point where the perpendicular line intersects the given line y=3x + 4. To do this, we can set the two equations equal to each other and solve for x and y:

(-1/3)x + b = 3x + 4

Multiplying both sides by 3 gives:

-x + 3b = 9x + 12

Rearranging gives:

10x = 3b - 12

x = (3/10)b - 6/5

Substituting this expression for x into either equation gives the corresponding value of y:

y = 3((3/10)b - 6/5) + 4 = (9/10)b - 14/5

Now, we need to find the value of b that makes the point (x, y) on the line y = 3x + 4 closest to the origin. The distance between the origin (0, 0) and any point (x, y) on the line y = (-1/3)x + b is given by the distance formula:

distance = √(x² + y²)

Substituting the expressions for x and y in terms of b gives:

distance = √((3/10)b - 6/5)² + ((9/10)b - 14/5)²)

To minimize the distance, we can take the derivative of the distance formula with respect to b and set it equal to zero:

d(distance)/db = (3/5)b - 12/5 = 0

Solving for b gives:

b = 4

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From the given concentrations of the solution, She needs to add 32.83 pounds of water to get 32.83 pounds of syrup.

Concentration is equal to [ (mass of sugar)/(mass of solution) ] × 100

1) 20% concentration

sugar mass equals 0.5 pounds

concentration = 0.5 lbs × 100 / mass of solution = mass of sugar * 100

The solution weighs 2.5 pounds.

Sugar and solution combined equal 2.5 pounds, hence 2.5 pounds minus 0.5 pounds equals 2.0 pounds of water.

She needs to add 2.0 pounds of water to get 2.5 pounds of syrup.

2) 25% concentration

adhere to the same process.

Solution mass = 0.5 lbs × 100 / 25 =

Solution weight is 2.0 lbs.

water weighs 2.0 lbs minus 0.5 lbs, or 1.5 lbs.

She needs to add 1.5 pounds of water to get 2.0 pounds of syrup.

3) Repeat the process

Concentration = 0.5 lbs × 100 / 1.5, where mass of solution = mass of sugar × 100

solution weight is 33.33 pounds.

water's mass is 32.83 pounds after subtracting 0.5 pounds.

She needs to add 32.83 pounds of water to get 32.83 pounds of syrup.

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Complete question -

Ella has 0.5 lbs of sugar. How much water should she add to make the following concentrations? Tell Ella how much syrup she will have in each case. 20%, 25% and 1.5% syrup?

The length of ⌢ WX ⌢ expressed as a fraction times π is:6÷π

What is Circle ?

In geometry, a circle is a two-dimensional shape consisting of all the points that are equidistant from a given point, called the center. The distance from the center to any point on the circle is called the radius of the circle.

From the given information, we know that V, W, and X are points on a circle with center V, and that VW = WX = 3. We also know that ∠WVX = 90°.

Since WX is a diameter of the circle, it has length equal to twice the radius of the circle. Let r be the radius of the circle, then we have:

VW + WX = 2r

3 + 3 = 2r

r = 3

So the radius of the circle is 3. Since WX is a diameter, its length is 2r = 6. Therefore, the length of ⌢ WX ⌢ expressed as a fraction times π is:6÷π

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Answer:

65.1

Step-by-step explanation:

cos(37)=[tex]\frac{52}{x}[/tex]

[tex]x=\frac{52}{cos(37)}[/tex]

[tex]x=65.111....\\x=65.1[/tex]

The prοduct οf 5 and 10√72 is 300√2    

The square rοοt οf a number is a value that, when multiplied by itself, gives the οriginal number. It is denοted by the symbοl √, and the number under the symbοl is called the radicand.

Fοr example, the square rοοt οf 25 is 5, because 5 multiplied by itself equals 25. This can be written as √25 = 5

Here we have

5 and 10√72    

As we knοw 72 = 36 × 2

10√72 = 10 [ √(36 × 2) ]

= 10 [√(6 × 6 × 2) ]

= 10 (6) √2

= 60 √2

Hence, the prοduct οf 5 and 10√72 can be calculated as fοllοws

=>  5 × 60√2 = 300√2  

Therefοre,

The prοduct οf 5 and 10√72 is 300√2    

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32 is the incorrect answer

Answer: infinite solution

If u continue to solve it will be equal in both sides therefore it is infinite solution

The evidence from the text suggests that the zombie trick helped the main character feel mentally prepared for the "Zombie 5K" event.

The main character initially expresses doubts about her ability to complete the race. She says, "I was worried that I wouldn't be able to finish the Zombie 5K. I wasn't very confident in my running abilities, and I was afraid I would get too scared by the zombies." This shows that she lacked confidence and had fears about the event.

However, after her friends played the zombie trick on her, the character's mindset changed. She says, "After the zombie trick, I felt more prepared to face the real zombies during the race. I knew it was just a trick, but it helped me overcome my fears and feel more confident." This suggests that the zombie trick had a positive impact on her mental preparation for the race.

Furthermore, the character's behavior during the race supports this idea. She describes how she used strategies to avoid the zombies and successfully completed the race. She says, "I made sure to stay aware of my surroundings and avoid the zombies as best as I could.

I kept reminding myself that they were just people in costumes, and that helped me stay focused on finishing the race." This shows that the character was mentally prepared for the race and able to perform well despite the challenges.

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According to the given table and graph:

a) The number of customers a restaurant employee can serve is 5.

b) The number of customers a grocery store clerk can serve is 12 for him.

c) The customer's food price per employee is 7 higher than the restaurant's price.

Line charts use data point "markers" connected by straight lines. These data points connected by straight lines are useful for visualization. Line charts are used in different fields for different purposes, but they are especially useful when you need to graphically represent changes in values ​​over time.

Line charts are widely used in finance to create visual representations of values ​​over time, such as changes in security prices, company earnings lists, and the history of major stock indices. It is also useful for comparing different stocks. In the field of investing, especially technical analysis, line charts are used by investors to visualize trends, which greatly aids analysis.

Given a graph of restaurants and a table of grocery stores, it shows the relationship between number of employees per customer. You have to solve the subtasks of the given task.

The price at the store is 12 ÷ 2 or 6 customers per employee.

According to the question;

A diagram of a restaurant and a grocery store table are shown.

a) at a restaurant;

For 2 employees, no. Customers = 10

For 4 employees, no. Customers = 20

so

If he increases the number of employees by two, no. We have 10 more customers.

⇒ The number of customers a restaurant employee can serve;

= 10 ÷ 2

= 5 customers

b) At the grocery store.

For 2 employees, no. Customers = 24

For 4 employees, no. Customers = 48

So when the number of employees increases by 2.

⇒ How many customers can a grocery store clerk serve;

= 24 ÷ 2

= 12 customers

c) so

Restaurant rate of customers per employee = 5 customers/employee

Grocery store customer rate per employee = 12 customers/employee

Also, food prices per customer per employee are higher than restaurant prices.

= 12 - 5

= 7  

Thus , the answers will be ;

a) No. of customers , one employee can help at restaurant is 5.

b) No. of customers , one employee can help at grocery store is 12.

c) The grocery rate of customer per employee is 7 more than restaurant's rate.

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The complete question is as follows:

Answer:

[tex]11x^2 - 5x + 5[/tex] (Option 2)

Step-by-step explanation:

Equation:

[tex](3x^2 - 4x -1) +(8x^2 - x + 6)[/tex]

We can drop the parenthesis since there is nothing to distribute

[tex]3x^2 - 4x -1 +8x^2 - x + 6[/tex]

Combine like terms

[tex]3x^2 + 8x^2 -4x -x -1 +6\\\\11x^2 - 5x + 5[/tex]

Using the trend line equation, we can find that the record was set in the year 2005.

Data is shown visually in a scatter plot.

The coordinate axes are used in a straightforward scatter plot to plot the points according to their values.

Now in the given question,

The scatter plot equation is:

y = - 0.14x + 12.5

Now we know that y = 11.8 seconds.

So,

11.8 = -0.14x + 12.5

⇒ 0.14x = 12.5 - 11.8

⇒ x = 0.7/0.14

⇒ x = 5

Therefore, the year when the record was set is 2000+5 = 2005.

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The area of triangle JKL is given as follows:

D. 24 units².

The area of a triangle of base b and height h is given by half the multiplication of these two dimensions, according to the equation presented as follows:

A = 0.5bh.

Considering segment JK as the base, it's length is given as follows:

b = 2 - (-2) = 4 units.

The midpoint of the base has the coordinates given as follows:

The height is the distance between the midpoint of the base and the remaining vertex, hence between (0,4) and (0, -2), thus:

h = 4 - (-2) = 6 units.

Then the area of the triangle is obtained as follows:

A = 4 x 6

A = 24 units².

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The surface area of the rectangular prism is 208 [tex]cm^2\\[/tex]

Since there are two of these faces, their combined area is as follows:

2 x [tex]48 cm^2[/tex] =[tex]96 cm^2[/tex]

We must add together the areas of all six faces to determine the total surface area:

[tex]48 cm^2 + 64 cm^2 + 96 cm^2 = 208 cm^2[/tex]

Hence, the rectangular prism has a surface area of 208 [tex]cm^2\\[/tex]

The region enclosed by an object's shape is referred to as the area. The area of the shape is the area that the figure or any other two-dimensional geometric shape occupies in a plane. Each shape's area is determined by its dimensions and characteristics. The regions of various shapes vary. The square's area is distinct from a kite's area.

If two items are similar in shape, the area they cover need not be equal unless and until the dimensions of the two shapes are likewise equivalent. Let's say there are two rectangle boxes, each measuring L1 and L2 in length and B1 and B2 in width.

From the question:

A rectangular prism is the name of the 3D shape depicted in the image.

We must first determine the area of each face of a rectangular prism in order to find its surface area.

The image's rectangular prism is 4 cm x 6 cm x 8 cm.

The top and bottom faces' combined surface area is equal to the surface area of a rectangle, which is:

4 x 6 = 24[tex]cm^2\\[/tex]

Given that there are two of these faces, the top and bottom faces' combined area is:

2 x 24[tex]cm^2\\[/tex]= 48 [tex]cm^2\\[/tex]

The front and rear faces' combined surface area is equal to the surface area of a rectangle, which is:

4 x 8 = 32[tex]cm^2\\[/tex]

As there are two of these faces, their combined surface area is as follows:

64 square cm = 2 x 32 [tex]cm^2\\[/tex]

The area of a rectangle is equal to the area of the left and right faces, which is:

6 x 8 = 48 [tex]cm^2\\[/tex]

Since there are two of these faces, their combined area is as follows:

2 squares of 48 [tex]cm^2\\[/tex] each equal 96 [tex]cm^2\\[/tex].

We must add together the areas of all six faces to determine the total surface area:

[tex]48 cm^2 + 64 cm^2 +96 cm^2 = 208 cm2.[/tex]

Hence, the rectangular prism has a surface area of 208 [tex]cm^2.[/tex]

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complete question:

What do we call the 3D shape below and what is its SURFACE AREA? Explain how you determined your answer and show your work!!!!

Answer:

  f(x) = -3(x -(-1))² +7

Step-by-step explanation:

You want the equation of the quadratic function that matches the given table.

The first step in solving the problem is to look at the given information. To use the given equation, you need to know the vertex of the function, and its vertical scale factor.

A quadratic function is symmetrical about the line through its vertex. That means we can locate the vertex by looking for x-values where the y-value is the same. The x-value of the vertex is halfway between those x-values.

Here, f(x) = 4 for both x=-2 and x=0. That means the x-value of the vertex is ...

  (-2 +0)/2 = -1

This value of x is in the table, and f(-1) is given as 7. This means the vertex is (-1, 7) and these are the values that go in the two rightmost boxes.

  f(x) = ( )(x -(-1))² + 7

The scale factor in the first box can be found by considering the difference between the f(x) value at the vertex, and the f(x) value at a point that is 1 unit either side:

  ( ) = f(-2) -f(-1) = 4 -7 = -3

The scale factor is -3, so the equation is ...

  f(x) = -3(x -(-1))² +7