suppose you are in charge of a company that rents moving vans to customers. Each van costs $18,000, and you spend an average of $35 per rental day on maintenance costs. You rent the van for $59.99 per day. How could you set up a system of equations to find where your company "breaks even?" On average, how many days must one van be rented before the company makes any profit

To optimise the volume while maintaining the total dimensions at 7 inches, the camera's dimensions should be roughly 3.01 inches besides 3.311 inches besides 0.679 inches.

What 3 dimensions do we have?

The homes we reside in and the items we use on a daily basis all have three dimensions: length, weigth, and breadth.

Let's start by assigning variables to the dimensions. Let x be the height of the camera, then the length must be 1.1 times the height, which gives us a length of 1.1x.

The width is not explicitly given, but we can express it in terms of x and 1.1x. Since the sum of the dimensions is 7 inches, we have:

x + 1.1x + w = 7

where w is the width of the camera. Simplifying this equation, we get:

2.1x + w = 7

w = 7 - 2.1x

Now we can express the volume of the camera in terms of x:

V = x(1.1x)(7 - 2.1x)

Simplifying this expression, we get:

V = 8.235x³ - 15.365x² + 7x

To find the maximum volume, we need to find the value of x that maximizes V. We can do this by taking the derivative of V with respect to x, and setting it equal to zero:

dV/dx = 24.705x² - 30.73x + 7 = 0

Using the quadratic formula, we can answer this quadratic equation:

x = (-b ± √(b² - 4ac)) / 2a

where a = 24.705, b = -30.73, and c = 7. Plugging in these values, we get:

x = 0.735 inches or x = 3.01 inches

Since x represents the height of the camera, we discard the smaller root and take x = 3.01 inches.

Then the length is 1.1 times the height, which gives us a length of 3.311 inches.

The width can be found using the equation w = 7 - 2.1x, which gives us w = 0.679 inches.

Therefore, the dimensions of the camera should be approximately 3.01 inches by 3.311 inches by 0.679 inches to maximize the volume while keeping the sum of the dimensions at 7 inches.

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Answer:

One possible expression that meets the given requirements is:

(2x)/(x+1) = (2x/[(x-2)(x-3)]) / ([(x+1)/(x-2)(x-3)])

This expression simplifies to 2x/(x+1) when x is not equal to -1, 0, 2, or 3, as required.

Explanation: We can rewrite 2x/(x+1) as (2x/(x-2)(x-3)) * ((x-2)(x-3)/(x+1)). The first term in this expression is a division of two rational expressions, while the second term is a multiplication of two rational expressions. Then, we can simplify the first term by cancelling the (x-2)(x-3) terms in the numerator and denominator, which gives 2x/[(x-2)(x-3)]. We can also simplify the second term by expanding the denominator, which gives (x-2)(x-3)/(x-2)(x-3)(x+1) = 1/[(x-2)(x-3)] * 1/(x+1). Then, we can combine the two simplified terms to get the expression given above.

Step-by-step explanation:

Your speed is 60 miles per hour, when your friends average speed is 50 miles.

A rational function, which is a function that can be represented as the ratio of two polynomials, is a function that may be used in a rational model, which is a mathematical model. Rates of change, growth or decay, and proportions are only a few examples of the many various kinds of real-world events that may be represented using rational models. In order to describe complicated systems or processes, they are frequently employed in disciplines like economics, physics, and engineering. To determine the values of the variables that make the equation true, rational models can be solved using algebraic techniques including factoring, simplification, and cross-multiplication.

Given that, average speed is 10 miles per hour faster than other person.

Then, your speed is = s + 10.

For 180 miles, and 150 miles for friend the equation can be set as:

180/(s+10) = 150/s

We can cross-multiply to simplify:

180s = 150(s+10)

180s = 150s + 1500

30s = 1500

s = 50

Substituting the value in s + 10 = 50 + 10 = 60.

Hence. your speed is 60 miles per hour.

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The equation of the regression  line for predicting height based on shoulder girth is:y = 103.82 + 0.607x, which  mean that for every one-unit increase in shoulder girth, the predicted height increase by 0.607 units.

Since the equation of the regression line for  predicting height based on shoulder girth can be written as: y = a + bx, where y is the predicted height, x is the shoulder girth, a is the y-intercept, and b is the slope of the regression line.

To find  the values of a and b, we need to use the following formulas:

b = r(Sy/Sx)

a = ybar - b(xbar), where r is the correlation coefficient between height and shoulder girth, Sy is the standard deviation of height, Sx is the standard deviation of shoulder girth, ybar is the mean height, and x bar is the mean shoulder girth. now substituting the values we get :

b = 0.67(9.41/10.37) ≈ 0.607

a = 171.14 - 0.607(107.20) ≈ 103.82

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The quadrants in which the points A = (2,-3) B = (-4,1) as required to be determined are fourth and second quadrant respectively.

As evident from the task content; the quadrant in which the given points are located are to be determined.

On the Cartesian plane; given a pair of coordinates (x, y).

In the first quadrant; x is positive and y is positive.

In the second quadrant; x is negative and y is positive.

In the third quadrant; x is negative and y is negative.

In the fourth quadrant; x is positive and y is negative.

Ultimately, the point A = (2, -3) is located in the fourth quadrant and the point B = (-4, 1) is located in the second quadrant.

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Answer:

Step-by-step explanation:

nancy: 22

jay: 11 cause nancy has twice as many apples as jay.

ava has 8 apples cause jay has 3 more apples than ava :)

The length of the second lawn that Sid mows is 60 feet. We simply calculated the area of lawn here.

The area of the first lawn is given by:

A1 = 60 x 50 = 3000 square feet

Let L2 be the length of the second lawn. Since the width of the second lawn is the same as the first lawn, the area of the second lawn can be expressed as:

A2 = L2 x 150

Since the area of the second lawn is 3 times as big as the first lawn, we have:

A2 = 3A1

Substituting A1 and simplifying, we get:

L2 x 150 = 3 x 3000

L2 x 150 = 9000

L2 = 60 feet

Therefore, the length of the second lawn is 60 feet.

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The total number of people with flyers after 3 days of copying and distributing them is 343, which can be calculated using the formula P = 7^n, where P is the total number of people with flyers and n is the number of times the flyers are copied and distributed.

The formula for this problem is P = 7^n where P is the total number of people with flyers and n is the number of times the flyers are copied and distributed.

In this problem, n = 3 as the flyers were distributed on three separate days.

Therefore, P = 7^3 = 343

The calculation can be shown as follows:

1st day: 7 people receive the flyer

2nd day: 7 x 7 = 49 people receive the flyer

3rd day: 49 x 7 = 343 people receive the flyer

Therefore, the total number of people with flyers after 3 days is 343.

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The value of sides a and b from the triangle. A = 50 degrees, B = 50 degrees, c = 12 meters is 9.341 metres and angle C is 80 dgree.

From the Law of Sines states that the follow proportions must be true which is

sin (A)/a = sin (B)/b= sin (C)/c

Where A = 50 degrees

B = 50 degrees

c = 12 meters

Angle C = (180-100=80   ( angle in the triangle is 180 degree)

sin (50)/a = sin (50)/b= sin (80)/12

0.766/a = 0.766/b= 0.985/12

0.766/a = 0.766/b=0.082

0.766/a =0.082

a =0.766/0.082 = 9.341

0.766/b=0.082

b=0.766/0.082= 9.341

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complete questions

Solve the given triangle. A = 50 degrees, B = 50 degrees, c = 12 meters

Round your answers to the nearest integer.

C = ? degrees

b = ? meters

c = ? meters

The mean of 5x3+8 is 23 and the standard deviation of 5x3+8 is 5.65, rounded down to 2 decimal places.

Consider the following experiment: Throw two fair dice sequentially and define a random variable X as the sum of the numbers of the two dice. We are to compute the mean and standard deviation of 5x3+8. Mean of 5x3+8 is 23 and standard deviation of 5x3+8 is 5.65. Thus, option 1 and option 2 are the correct answers.What is the expected value of a discrete random variable?In probability theory and statistics, the expected value of a random variable is the measure of the center of the probability distribution. It represents the long-run mean of occurrences, for example, the average value in a long sequence of trials.The standard deviation of a random variable is the measure of the spread or variability of a probability distribution, similar to variance. It is the square root of variance, denoted as σ.Here, the sum of the numbers of two dice follows a uniform distribution, where each event is equally likely, and the probability of each event is 1/36. Therefore, the random variable X is discrete with probability mass function:f(x) = 1/36, for x = 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.Using this distribution, we can find the mean and standard deviation of the random variable X.Mean of 5x3+8=5(3)+8=23σ2=∑(x−μ)2P(X=x)where,μ = E(X) = ∑xf(x) = 7σ = √σ2=√ ∑(x−μ)2P(X=x)= √(2-7)2 (1/36)+ (3-7)2 (2/36)+ (4-7)2 (3/36)+ (5-7)2 (4/36)+ (6-7)2 (5/36)+ (7-7)2 (6/36)+ (8-7)2 (5/36)+ (9-7)2 (4/36)+ (10-7)2 (3/36)+ (11-7)2 (2/36)+ (12-7)2 (1/36)≈ 5.65Therefore, the mean of 5x3+8 is 23 and the standard deviation of 5x3+8 is 5.65, rounded down to 2 decimal places.

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Answer:

(-1,0) and (0, 4)

Step-by-step explanation:

The x and y intercept of a function (say the x intercept), is when y = 0 and vice versa.

The x intercept in this function is when y = 0

Thus,

4x-0=-4

4x = -4

x = -1.

So the x- intercept point = (-1, 0)

Similarly,

4(0)-y= -4

(x is equated to 0 to find the y - intercept)

-y = -4

∴ y = 4

y- intercept point = (0, 4)

Hope this helps! :)

The function f(x) = (x+4)/x is defined for all real numbers except x = 0, since division by zero is undefined. Therefore, the domain of the function is all real numbers except x = 0.

In interval notation, we can write the domain of the function as: (-∞, 0) U (0, ∞). This means that the function is defined for all values of x that are less than zero or greater than zero, but it is not defined at x = 0. The domain of a function is the set of all possible input values (also called independent variables) for which the function is defined. In other words, it is the set of values for which the function yields a valid output (also called dependent variable). In the case of the function f(x) = (x+4)/x, the domain is restricted by the fact that division by zero is undefined. Therefore, we cannot include x = 0 in the domain of the function. To find the domain of a function, we need to look for any values of the input variable that would make the function undefined or result in an error. These include situations such as division by zero, taking the square root of a negative number, or taking the logarithm of a non-positive number. In general, the domain of a function can be described using interval notation or set-builder notation, depending on the specific circumstances of the function. It is important to identify the domain.

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P(Z > -0.475) ≈ 0.68

(a) The probability of having at least 9 events can be calculated as follows:ppois(8, 10, lower.tail = FALSE)This gives the probability of having less than or equal to 8 events, so we subtract it from 1 to get the probability of having at least 9 events. Hence, the probability of having at least 9 events is:1 - ppois(8, 10, lower.tail = FALSE) = 0.3446(b) For a Poisson distribution with λ=10, the mean is μ=10 and the variance is σ²=10. Hence, the standard deviation is σ=√10 ≈ 3.162.To approximate this using a normal distribution, we need to standardize the Poisson random variable. That is,(X-μ)/σ ~ N(0,1)where X is a Poisson random variable with λ=10. We want to find P(X ≥ 9), which can be written as P(X > 8.5) using the continuity correction. Hence,P(X > 8.5) = P(Z > (8.5-10)/3.162) = P(Z > -0.475)Using a standard normal table or calculator, we find that P(Z > -0.475) ≈ 0.68. Therefore, the approximate probability of having at least 9 events is 0.68.

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Answer:

6t + 12

Step-by-step explanation:

6(t+2)

= 6t + 12

So, the answer is 6t + 12

We found that he can only use approximately 7.39 units of fencing for the fourth side. The possible locations for point H are (4.5, 12.39) and (4.5, -2.39).

To determine where Alex could place point H, we need to first calculate the length of the three sides of the fenced area that he has already plotted. We can do this using the distance formula:

Distance [tex]= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

From point E to point F:

Distance = [tex]\sqrt{(6-3)^2 + (5-5)^2}[/tex]

               = 3 units

From point F to point G:

distance = [tex]\sqrt{(9-6)^2 + (1-5)^2)}[/tex]

              = [tex]\sqrt{(9 + 16)}[/tex]

              = 5 units

From point G to point E:

Distance = [tex]\sqrt{(3-9)^2 + (5-1)^2}[/tex]

                = [tex]\sqrt{(36 + 16)}[/tex]

                = [tex]\sqrt{(52)[/tex]

                = [tex]2 \sqrt{(13)}[/tex] units

Therefore, the total length of fencing that Alex has already plotted is 3 + 5 + 2√13 = approximately 14.61 units.

To find the possible x-coordinate(s) of point H, we can use the formula for the distance between two points on the coordinate plane:

distance = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex]

For point H to be 7.39 units away from the midpoint of side EF (4.5, 5), we have:

[tex]\sqrt{(x - 4.5)^2 + (y - 5)^2}[/tex]

= 7.39

Squaring both sides and simplifying gives:

(x - 4.5)² + (y - 5)²= 7.39²

Since we know that x=4.5, we can substitute this value into the equation and solve for y:

(4.5 - 4.5)²+ (y - 5)² = 7.39²

(y - 5)² = 7.39²

y - 5 = ±7.39

y = 5 ± 7.39

So the possible locations for point H are (4.5, 5+7.39) and (4.5, 5-7.39), which correspond to the points (4.5, 12.39)

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The factors of 9 are 1 and 9.. To determine this, one can use the formula to find the factors of a number, which is n = a × b.

A counter example to the conditional statement "If an odd number is greater than 1 and less than 10, then it has no other factors than 1 and its self" would be the number 9. 9 is an odd number that is greater than 1 and less than 10, but it has other factors than 1 and itself. The factors of 9 are 1, 3, and 9. To determine this, one can use the formula to find the factors of a number, which is n = a × b, where n is the number, a is the first factor, and b is the second factor. In this case, n = 9, a = 1, and b = 9. Therefore, the factors of 9 are 1 and 9.

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The factored form of the function y = -8x(x + 6) is f(x) = -8(x + 3)(x - 3). The values of a, r, and s are -8, -3, and 3, respectively.

To put the function y = -8x(x + 6) in factored form f(x) = a(x - r)(x - s), the values of a, r, and s have to be identified. The step-by-step explanation is given below.Step 1: The given function is y = -8x(x + 6).Step 2: To write it in the factored form f(x) = a(x - r)(x - s), let us first multiply -8 by 6, which gives -48.Step 3: We now have y = -8x(x + 6) = -8x² - 48x.Step 4: Rearranging it, we get y = -8x² - 48x.Step 5: Factoring out -8 from both the terms, we get y = -8(x² + 6x).Step 6: Next, add (6/2)² = 9 to both the sides to make the expression a perfect square. y + 72 = -8(x² + 6x + 9).Step 7: The right side of the equation is now a perfect square. It can be written as y + 72 = -8(x + 3)².  (x + 3)² = x² + 6x + 9Step 8: Simplifying, we get y = -8(x + 3)² - 72.Step 9: The function y in factored form is f(x) = -8(x + 3)² - 72. Here, a = -8 and r = -3. Since the function is in the form f(x) = a(x - r)(x - s), we can find s by dividing -72 by -8 and adding r to the quotient. That is, s = (-72/-8) - 3 = 6 - 3 = 3. Therefore, the factored form of the function y = -8x(x + 6) is f(x) = -8(x + 3)(x - 3). The values of a, r, and s are -8, -3, and 3, respectively.

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The measure of angle ABC is: 20°

Consider quadrilateral ABCO. The sum of all of the measures of all interior angles in the quadrilateral ABCO is equal to 360°.

The Lines given as BA and BC are seen to be tangent to the circle, and then this means that the radii OC and OA are perpendicular to the tangent lines BC and BA. Therefore,

m∠BCO=90°;

m∠BAO=90°.

The measure of the angle AOC is 160° (because the measure of arc AC is 140°). So,

m∠ABC + m∠BCO + m∠BAO + m∠AOC = 360°,

m∠ABC = 360° - (m∠BCO + m∠BAO + m∠AOC)

= 360° - (90° + 90° + 160°)

= 20°

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Answer:

-15, 5, 17, 21, 25

Step-by-step explanation:

See attached worksheet.

Calculate each of the values of x on the table by using the number in place of the x in the equation.

h(x) = 4x + 5

h(-5) = 4*(-5) + 5

h(-5) = -15

===

h(3) = 4*(3)+5

h(3) = 12 + 5 or 17

==

Do the other values of x in the same manner to produce the attached table.

Answer:

Step-by-step explanation:

Simplify 10−7 to 3

3,13.−4−7

simplify 13.- 4 13. - 4

3,13.−11

The probability of selecting exactly 4 red balls from an urn with 20 red balls and 30 green balls is given by the formula P(X=4) = (20C4)(30C6) / (50C10) where X is the number of red balls chosen. This simplifies to P(X=4) = 0.2032.

The equation y = (-2/3)x + 6 represents a line that starts at the point (0, 6) on the y-axis and slopes downwards from left to right at a rate of 2 units down for every 3 units to the right.

Coordinate geometry is a branch of mathematics that deals with the study of geometry using the principles of algebra. It involves using algebraic equations and geometric concepts to analyze shapes and figures in a plane or in higher dimensions.

In this equation, -2/3 is the slope of the line, which tells us how steep the line is and in what direction it's heading. Specifically, a slope of -2/3 means that for every increase of 3 units in the x-direction, the y-value decreases by 2 units. So the line slopes downwards from left to right.

The 6 in the equation is the y-intercept of the line, which tells us where the line intersects the y-axis. Specifically, the y-intercept is the point (0, 6) on the line. This means that when x = 0, y = 6, so the line starts at the point (0, 6) on the y-axis.

Therefore, the equation y = (-2/3)x + 6 represents a line that starts at the point (0, 6) on the y-axis and slopes downwards from left to right at a rate of 2 units down for every 3 units to the right.

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The tοtal area οf the plywοοd after cutting οut the nοtch and hοle is 16ft²

Area is the measure οf a regiοn's size οn a surface. The area οf a plane regiοn οr plane area refers tο the area οf a shape οr planar lamina, while surface area refers tο the area οf an οpen surface οr the bοundary οf a three-dimensiοnal οbject.

Area can be understοοd as the amοunt οf material with a given thickness that wοuld be necessary tο fashiοn a mοdel οf the shape, οr the amοunt οf paint necessary tο cοver the surface with a single cοat

Area is a measure οf the amοunt οf space inside a 2-dimensiοnal shape οr regiοn, typically expressed in square units such as square inches, square feet, οr square meters.

Tο find the tοtal area οf the plywοοd after cutting οut the nοtch and hοle, we need tο subtract their areas frοm the οriginal area:

Tοtal area = 20ft² - 0.75ft² + 3.25ft²

Tοtal area = 16ft²

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The probability that no face card has been revealed is 1/3.

The expected number of face cards he has revealed is 12.

Probability is the branch of mathematics that deals with uncertainty. When a fair die is rolled, there are 6 possible outcomes. A deck of 52 cards has 13 ranks of four suits each. These suits are spades, clubs, hearts, and diamonds. A standard deck of cards contains 26 red cards and 26 black cards.

There are four aces in a deck of 52 cards. The probability of obtaining an ace on the first attempt is

4/52 ⇒ 1/13 ⇒ 0.0769.

The probability of not getting an ace on the first try is

48/52 ⇒ 12/13 ⇒ 0.9231.

The second attempt at drawing an ace is conditional on the first attempt.

If the first attempt results in not getting an ace, the probability of getting an ace on the second attempt are 4/51.

If the first attempt is unsuccessful, the probability of not getting an ace on the second attempt is 47/51.

The probability of getting an ace on the third attempt, after the first two attempts have failed, is 4/50.

The probability of not getting an ace on the third attempt is 46/50. And so on...

The probability of not revealing any face card is 16/48 = 1/3 because there are 16 non-face cards in the deck.

The expected number of face cards he has revealed is 12, and the expected number of non-face cards he has revealed is 40.

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There are several statements that are true when it comes to a smooth function in a neighborhood around a point and the forward and backward finite differences.

The true statements are:

1) The forward finite difference is the difference between the function value at a point and the function value at the next point.

2) The backward finite difference is the difference between the function value at a point and the function value at the previous point.

3) The forward and backward finite differences can be used to approximate the derivative of a function at a point.

4) The forward and backward finite differences are both equal to the slope of the tangent line to the function at the point.

5) The forward and backward finite differences are both equal to the derivative of the function at the point.

Therefore, the true statements are "The forward finite difference is the difference between the function value at a point and the function value at the next point.", "The backward finite difference is the difference between the function value at a point and the function value at the previous point.",

"The forward and backward finite differences can be used to approximate the derivative of a function at a point.", "The forward and backward finite differences are both equal to the slope of the tangent line to the function at the point.", and "The forward and backward finite differences are both equal to the derivative of the function at the point."

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Answer:

(0,-2)

Step-by-step explanation:

The vendor's revenue at a price of R1.80 per rose is R9.72

Let's assume that the vendor sells x roses at a price of p per rose.

According to the given condition, if he sells roses at R1.20 per rose, he can sell 350 roses. Hence, we can write:

350 = x - 3((p - 1.20)/0.20)

Simplifying the above equation, we get:

x = 3(p - 0.60) + 350

Now, if the price is increased to R1.80 per rose, the vendor's revenue will be:

Revenue = number of roses sold * price per rose

= (x - 3((1.80 - 1.20)/0.20)) * 1.80

= (x - 15) * 1.80

Substituting the value of x from the first equation, we get:

Revenue = (3(p - 0.60) + 350 - 15) * 1.80

= (3p - 0.30) * 1.80

Simplifying the above equation, we get:

Revenue = 5.4p - 0.54

Therefore, the vendor's revenue at a price of R1.80 per rose is given by the equation 5.4p - 0.54, where p is the price per rose in rands.

To find the vendor's revenue to the nearest cent, we need to substitute p = 1.80 in the above equation:

Revenue = 5.4(1.80) - 0.54

= R9.72 (approx.)

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a) Note that the Angle of Elevation from R to T is 63.4°

b) The angle fact tells you that the answer to part a) is also the angle of depression from T to R is "the Alternate Angle Postulate"

The principle used in below is SOH CAH TOA.

a) Tanθ = Opp/Adjacent

Tanθ = 340/165
Tanθ = 2.0606060606
θ = Tan⁻¹ 2.0606060606
θ = 63.4349

θ [tex]\approx[/tex] 63.4

b) The principle of alternate angles is a theorem in geometry that states that when a straight line intersects two other lines, the angles formed on opposite sides of the intersection and on opposite sides of the transversal are equal. This principle is based on the fact that parallel lines cut by a transversal create corresponding angles that are congruent.

Thus the angle fact tells you that the answer to part a) is also the angle of depression from T to R is "the Alternate Angle Postulate"

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For the rectangle, the answers will be a. Perimeter=52 inches, b. Perimeter=770 inches and c. Perimeter will be multiplied by 35 also.

What exactly is a rectangle?

A rectangle is a four-sided flat shape with opposite sides that are parallel and equal in length. It is a type of quadrilateral, a polygon with four sides.

Now,

(a) The perimeter of the drawing is the sum of the lengths of all sides of the rectangular garden plus the lengths of the two bricks on the top and bottom and the lengths of the two bricks on the left and right.

The length of the garden in the drawing is 7 inches, and the width is 4 inches. Thus, the perimeter of the garden in the drawing is:

P = 2(7 inches) + 2(4 inches) = 14 inches + 8 inches = 22 inches

Since the garden is surrounded by bricks, we need to add the lengths of the two bricks on the top and bottom and the lengths of the two bricks on the left and right. Each brick has a length of 1 inch, so the total length of the bricks is:

2(1 inch + 7 inches + 1 inch) + 2(1 inch + 4 inches + 1 inch) = 2(9 inches) + 2(6 inches) = 18 inches + 12 inches = 30 inches

Therefore, the perimeter of the drawing is:

22 inches + 30 inches = 52 inches

(b) The actual garden is 35 times larger than the drawing, so its length is 35 × 7 inches = 245 inches, and its width is 35 × 4 inches = 140 inches. Thus, the perimeter of the actual garden is:

P = 2(245 inches) + 2(140 inches) = 490 inches + 280 inches = 770 inches

(c) When the dimensions of the garden are multiplied by 35, the perimeter of the garden is also multiplied by 35. This is because the perimeter is a linear function of the length and width of the garden. Therefore, the effect on the perimeter of the garden is to increase it by a factor of 35.

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