Compare and contrast the direct write-off method and the allowance method for bad debts.

Answer:

The unit rate is 25$

Step-by-step explanation:

The unit rate gives the amount by which the money in the his account increases per month. It measures the rate of increase in the account.Which in this case the unit rate is 25$

The distance between the points (-3, 2) and (2, -2) is approximately sqrt(41), which is an irrational number.

To find the distance between two points (-3, 2) and (2, -2), we can use the Pythagorean theorem and consider the points as the vertices of a right triangle.

The base of the triangle is the horizontal distance between the x-values of the two points.

In this case, it is given by:

Base = 2 - (-3) = 2 + 3 = 5

Next, we need to find the height of the triangle, which is the vertical distance between the y-values of the two points. It is given by:

Height = -2 - 2 = -4

Now, we have the base and the height of the triangle.

To find the distance between the two points, we can use the Pythagorean theorem, which states that the square of the hypotenuse (distance) is equal to the sum of the squares of the other two sides (base and height).

Using the Pythagorean theorem:

Distance^2 = Base^2 + Height^2

Distance^2 [tex]= 5^2 + (-4)^2[/tex]

Distance^2 = 25 + 16

Distance^2 = 41

To find the distance, we take the square root of both sides:

Distance = sqrt(41).

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The functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

a) To find two functions f and g such that (fog)(x) = 1/(x + 2), we need to determine how the composition of the two functions f and g produces the given expression.

Let's start by assuming g(x) = x + a, where a is a constant. This means that g(x) adds the constant a to the input x.

Next, let's determine the function f(x) such that (fog)(x) results in the desired expression. We have:

(fog)(x) = f(g(x)) = f(x + a)

b) To simplify the expression 1/(x + 2) and make it match f(g(x)), we can consider f(x) = 1/x.

Substituting the expressions for f(x) and g(x) into (fog)(x), we have:

(fog)(x) = f(g(x)) = f(x + a) = 1/(x + a)

Comparing this with the desired expression 1/(x + 2), we see that a = 2. Therefore, the functions f and g are:

a. f(x) = 1/x

b. g(x) = x + 2

Using these functions, we can verify the composition (fog)(x):

(fog)(x) = f(g(x)) = f(x + 2) = 1/(x + 2)

Thus, (fog)(x) = 1/(x + 2), which matches the desired expression.

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The interval between neighboring x value is 1

the ratio between neighboring y-values 1

To find interval between neighboring x value, we subtract as follows

interval = 2 - 1 = 3 - 2 = 4 - 3 = 5 - 4 = 1

To find the ratio between neighboring y-values, we divide

ratio = 4 / 1 = 16/4 = 256 / 16 = 1024 / 256 = 4

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complete question

The table below represents an exponential function.

x

1

2

3

4

5

y

1

4

16

256

1,024

What is the interval between neighboring

X-values shown in the table?

What is the ratio between neighboring y-values?

[tex]{\huge{\blue{\bold{\mathfrak{Step\:by\:step\: solution}}}}}[/tex]

To divide 80,000,000 by 200, we can follow these steps:

1. Write out the division problem: 80,000,000 ÷ 200

2. Divide the first digit of the dividend (8) by the divisor (2), which gives us 4.

3. Write 4 above the second digit of the dividend (0), which gives us 40.

4. Subtract 40 from 80, which gives us 40.

5. Bring down the next digit of the dividend (0), which gives us 400.

6. Divide 400 by 200, which gives us 2.

7. Write 2 above the 0 in the dividend, which gives us 4000.

8. Subtract 4000 from 4000, which gives us 0.

So the answer is 400,000. To write it in standard form, we move the decimal point 5 places to the left, which gives us:

[tex]\purple{4 \times {10}^{5}} [/tex]

The answer is:

400,000

Work/explanation:

Divide:

80 000 000 ÷ 200

[tex]\sf{400,000}[/tex]

The answer is already in standard form.

The values for x and y derived using trigonometric ratios are:

3). x = 3 and y = 3+ √3

4). x = 6 and y = 12

The trigonometric ratios is concerned with the relationship of an angle of a right-angled triangle to ratios of two side lengths.

The basic trigonometric ratios includes;

sine, cosine and tangent.

3). Considering right triangle ADB:

sin45 = x/3√2 {opposite/hypotenuse}

√2/2 = x/3√2

x = (3√2 × √2)/2 {cross multiplication}

x = 3

cos45 = BD/3√2

√2/2 = BD/3√2

BD = 3

Considering that triangle ADC:

tan60 = 3/DC

√3 = 3/DC

DC = √3

y = BD + DC = 3 + √3

y = 15 × tan23 {cross multiplication}

y = 6.3671

cos23 = 15/x {adjacent/hypotenuse}

x = 15/cos23

x = 16.2954

4). Considering right triangle ADB:

sin60 = 3√3/x

√3/2 = 3√3/x

x = 6

cos60 = BD/6

1/2 = BD/6

BD = 3

considering right triangle ADC:

tan30 = 3√3/DC

√3/3 = 3√3/DC

DC = 9

y = 3 + 9 = 12

Therefore, the values for x and y derived using trigonometric ratios are:

3). x = 3 and y = 3+ √3

4). x = 6 and y = 12

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There exists two solutions to the absolute value function |0.5x + 1| = 5.

The absolute value function in this problem is defined as follows:

|0.5x + 1| = 5.

The first solution is obtained as follows:

0.5x + 1 = -5

0.5x = -6

x = -6/0.5

x = -12.

The second solution is obtained as follows:

0.5x + 1 = 5

0.5x = 4

x = 4/0.5

x = 8.

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The values of `a, b,` and `c` correctly complete the division of [tex]$$\frac{1}{5}\div \frac{5}{6}[/tex] = [tex]\frac{6}{25}$$[/tex] is `a-1, b-5, c-8`. The correct option is $\boxed{\textbf{(C)}\ a-1,b-5,c-8}$.

To complete the division in the correct manner, the value of `x, b, and c` is to be calculated.

The given fraction is:

[tex]\frac{1}{5}\div \frac{5}{6}[/tex]

= [tex]\frac{1}{5}\cdot \frac{6}{5}[/tex]

= [tex]\frac{6}{25}$$[/tex]

Therefore, the value of `x` is `6`.

Now, we have the equation `5/6 = 6/bc` that is to be solved for `b` and `c`.

Multiplying both sides of the above equation with `bc`,

we get:

[tex]\frac{5bc}{6} = 6$$[/tex]

Multiplying both sides of the equation by `6/5`, we get:

[tex]bc = \frac{36}{5}$$[/tex]

Therefore, the values of `a, b,` and `c` correctly complete the division of [tex]$$\frac{1}{5}\div \frac{5}{6}[/tex] = [tex]\frac{6}{25}$$[/tex] is `a-1, b-5, c-8`.

Hence, the correct option is $\boxed{\textbf{(C)}\ a-1,b-5,c-8}$.

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The values of a, b and c in the expression are a = 1, b = 1 and c = 6

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

1/5 * 5/6 = a * b/c

From the above, we have

1/5 * 5/6 = a * b/c

Evaluate the products

1/6 = a * b/c

Rewrite the expression as

1 * 1/6 = a * b/c

By comparison, we have

a = 1, b = 1 and c = 6

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The price that should be charged to maximize profits:  $80.5 (option a).

To determine the price that should be charged to maximize profits, we need to find the quantity that maximizes the firm's profit function. The profit function can be calculated by subtracting the total costs from the total revenue.

First, let's find the total revenue function. The demand equation given is P = 78 − 15Q, where Q = Q1 + Q2. We can rearrange this equation to express Q in terms of P: Q = (78 - P) / 15.

The total revenue function is calculated by multiplying the price (P) by the quantity (Q): TR = P * Q. Substituting Q, we get TR = P * [(78 - P) / 15].

Next, we need to find the total cost function. The marginal costs associated with producing in the two plants are MC1 = 3Q1 and MC2 = 2Q2. The total cost is the sum of the costs in both plants: TC = MC1 + MC2. Substituting the respective marginal cost equations, we get TC = 3Q1 + 2Q2.

Finally, we can calculate the profit function by subtracting the total cost from the total revenue: Profit = TR - TC.

Now, to find the price that maximizes profits, we need to differentiate the profit function with respect to price (P) and set it equal to zero. By solving this equation, we can find the value of P that maximizes profits.

Taking the derivative of the profit function with respect to P and setting it equal to zero, we get d(Profit)/dP = 0. Solving this equation will give us the value of P that maximizes profits.

After solving the equation, we find that P = $80.5 maximizes profits. Therefore, the price that should be charged to maximize profits is A) $80.5.

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The difference in elevations is 14,212 feet.

The action or fact of raising or being raised to a higher or more important level, state, or position. Elevation is distance above sea level. Elevations are usually measured in meters or feet. They can be shown on maps by contour lines, which connect points with the same elevation; by bands of color; or by numbers giving the exact elevations of particular points on the Earths surface.

Given:

The highest point in California is Mount Whitney at 14,494 feet above sea level. The lowest point is the Death Valley at 282 feet below sea level

The positive 14,494 minus 282 feet would be a difference of 14,212 feet.

So, the difference is 14,212 feet.

Therefore, the difference in elevations is 14,212 feet.

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Amount received by B can be calculated by solving the equation, Amount received by B = $2750So, the amount B gets is $2750.

The correct option for the given question is B. 2750.Divide $5000 along A, B and C so that A may receive 1/4th much as B and C together and B gets 1/3rd of what A and C received together.

The amount that B gets.

Let's suppose the amount B gets is x.

Now, we can proceed as given below:

Given that the total amount = $5000

Amount received by A = (1/4) * (Amount received by B and C)

Amount received by B = (1/3) * (Amount received by A and C)

Amount received by C = (Amount received by B and A) - (Amount received by B)

Now, we have,Amount received by B + Amount received by C = 3 * Amount received by B/3 + Amount received by A/3

Amount received by A = (1/4) * [Amount received by B + Amount received by C]

Amount received by B = (1/3) * [Amount received by A + Amount received by C]

Amount received by C = [Amount received by B + Amount received by A] - [Amount received by B]

Let's solve this problem in detail: Amount received by A = (1/4) * (Amount received by B + Amount received by C)

Now, Amount received by A = (1/4) * ($5000 - Amount received by A)

By solving the above equation,

Amount received by A = $1000Amount received by B = (1/3) * (Amount received by A + Amount received by C)

Also, Amount received by B + Amount received by C = 3 * Amount received by B/3 + Amount received by A/3

Again, $5000 - Amount received by A = 2 * (Amount received by B + Amount received by C)

By substituting the value of Amount received by A in the above equation,Amount received by B + Amount received by C = $3000

Amount received by B = (1/3) * [Amount received by A + Amount received by C]

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Answer:

Vertical Stretch

Step-by-step explanation:

The parent function [tex]f(x)=|x|[/tex] when multiplied by 2.5 is a vertical stretch of the absolute value equation. I've attached a graph so you can see the difference between the two functions.

The correct expression for the maximum number of cars that can be parked in the parking lot is 4c + 15. Option C

Given that there are 4 main rows with an equal number of parking spots in each row, and each row can accommodate c cars, the total number of parking spots in the main rows is 4c.

Additionally, there are 15 parking spots specifically allocated for store employees.

To find the maximum number of cars that can be parked in the parking lot, we need to add the number of parking spots in the main rows and the number of parking spots for employees.

Expression:

Total number of cars = Number of cars in main rows + Number of cars in employee spots

Number of cars in main rows = 4c

Number of cars in employee spots = 15

Therefore, the maximum number of cars that can be parked in the parking lot is:

Total number of cars = 4c + 15

This expression represents the sum of cars parked in the main rows and the cars parked in the employee spots, giving us the maximum capacity of the parking lot. Option C.

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Step-by-step explanation:

Remember that

[tex](a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} [/tex]

So

[tex](2x) {}^{2} = 4 {x}^{2} [/tex]

So the first blank is 4

[tex]2ab = 2(2x)(3) = 12x[/tex]

So the second blank is 12

And finally

[tex]3 {}^{2} = 9[/tex]

So the final blank is 9.

Slope = 4

y-intercept = -1

Slope-intercept form is one of the most common ways to write a linear equation when graphing.

Slope-intercept Form

Slope-intercept form is written as y = mx + b. In this equation, m is the slope. Slope represents the rate of change of the equation. The slope can also be described as the change in y over the change in x.

Additionally, the b represents the y-intercept. The y-intercept is the y-value where the graph intersects with the y-axis.

Finding Slope and Y-intercept

The equation we are given is y = 4x - 1. This means that the slope is 4. So, the rate of change for the equation is 4 units up per 1 unit right. Additionally, the y-intercept is -1. This means that the function will intersect the y-axis when y = -1. Using this information, we could graph the function if we wanted.

The cruise ship's resultant velocity is approximately 22.67 mph, and its direction is approximately 10.2 degrees south of east.

To find the resultant direction, we can use vector addition. Let's represent the southward velocity of the cruise ship as vector A and the eastward velocity of the Gulf Stream as vector B.

Given:

Magnitude of vector A (southward velocity of the cruise ship) = 22 mph

Magnitude of vector B (eastward velocity of the Gulf Stream) = 4 mph

To find the resultant velocity, we add the two vectors together. Since the vectors are perpendicular to each other, we can use the Pythagorean theorem to find the magnitude of the resultant vector:

Resultant velocity = √(A^2 + B^2) = √(22^2 + 4^2) ≈ 22.67 mph

Now, to find the direction of the resultant vector, we can use trigonometry. The angle between the resultant vector and the south direction can be calculated as:

θ = arctan(B / A) = arctan(4 / 22) ≈ 10.17 degrees

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The situation that has a straight line and passes through the origin is when "All of the choices" are true.

A straight line equation in slope-intercept form is given by; y = mx + b, where m is the slope and b is the y-intercept.However, when the straight line passes through the origin, then the value of b becomes zero, which means the equation becomes; y = mx.

Therefore, among the given situations, the one that has a straight line and passes through the origin is "All of the choices."

Since all the given situations have a proportional relationship, which means as one variable increases, the other variable increases, then they all form a straight line that passes through the origin.

Therefore, all the given situations have a straight line and passes through the origin.

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The inequality 5m - 7 > 16 holds true for the values m = 6, 7, 8, 9, and 10, in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.

To determine the values for which the inequality 5m - 7 > 16 holds true, we can solve it algebraically and then check if each value in the given set satisfies the inequality.

Let's solve the inequality:

5m - 7 > 16

Adding 7 to both sides, we have:

5m > 23

Dividing both sides by 5, we get:

m > 23/5

Now we need to check if each number in the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} satisfies the inequality m > 23/5.

For m = 1:

1 is not greater than 23/5, so the inequality does not hold true.

For m = 2:

2 is not greater than 23/5, so the inequality does not hold true.

For m = 3:

3 is not greater than 23/5, so the inequality does not hold true.

For m = 4:

4 is not greater than 23/5, so the inequality does not hold true.

For m = 5:

5 is not greater than 23/5, so the inequality does not hold true.

For m = 6:

6 is greater than 23/5, so the inequality holds true.

For m = 7, 8, 9, and 10:

All these values are also greater than 23/5, so the inequality holds true for them as well.visit

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Answer:

Here are some recommended books on partial differential equations (PDEs) from beginner to advanced level:

1. "Partial Differential Equations: An Introduction" by Walter A. Strauss: This is a great introductory book on PDEs that covers the basics of first-order equations, second-order equations, and higher-order equations.

2. "Partial Differential Equations" by Lawrence C. Evans: This is a more advanced textbook that covers a wide range of topics in PDEs, including elliptic equations, parabolic equations, hyperbolic equations, and conservation laws.

3. "Nonlinear Partial Differential Equations" by Peter J. Olver: This is an advanced book that covers the theory and applications of nonlinear PDEs, including Hamiltonian systems, solitons, and integrable systems.

4. "Introduction to the Theory of Nonlinear Elliptic Equations" by V. G. Maz'ya and S. Poborchi: This is an advanced book that provides a comprehensive introduction to the theory of nonlinear elliptic equations.

5. "Geometric Partial Differential Equations and Image Analysis" by Guillermo Sapiro: This is an advanced book that covers the application of PDEs to image analysis, including topics such as denoising, segmentation, and registration.

These books provide a good foundation for understanding PDEs and their applications, and can be useful for students and researchers at various levels of expertise.

Answer:

  (d)  x² -2x +3

Step-by-step explanation:

You want the quotient (x³ - 3x² + 5x - 3) ÷ (x - 1).

The constant in a product will be the product of the constants in the factors. That is if (x² +bx +c) is a factor of the cubic, we must have ...

  -1·c = -3 . . . . . . . where the other factor is (x -1), having constant -1

  c = 3

Only one answer choice matches: x²-2x+3.

Using synthetic division to find the entire quotient can be almost as fast.

The tableau is shown in the attachment. It tells you the quotient is ...

  x² -2x +3

__

Additional comment

"The entry in the left part of the table" is the zero of the binomial divisor. The divisor (x-1) is zero when x=1, so that entry is 1.

<95141404393>

The statements that are true about the rational equations are options A and C.

[tex]\frac{4}{x + 6} + \frac{1}{x^{2} } = \frac{x+10}{x^{3} +6x^{2} }[/tex]

Note that x ≠ 0, and x ≠ -6

The left side of the equation is equal to

[tex]\frac{4}{x + 6} + \frac{1}{x^{2} } = \frac{4*x^{2} + (x+6)}{(x+6)x^{2} } = \frac{4x^{2} + x + 6 }{x^{3} + 6x^{2} }[/tex]

Since the left side of the equation have the same denominators, their numerators are equal. Hence

4x² + x + 6 = x + 10

then

4x² = 10-6
4x² = 4
x² = 1,

x₁ = 1, and x₂ = -1

Thus, both numbers are the solution of the given problem.

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Full Question:

Although part of your question is missing, you might be referring to this full question:

Which of the following statements are true about the given rational equation?

4/x+6 +1/x²=x+10/x³+6x²

Check all of the boxes that apply.

A. x = 1 is a solution.

B. x = 0 is an extraneous solution.=

C. x = –1 is a solution.

D. x = –6 is an extraneous solution.

Answer:

a) 13

b) B

Step-by-step explanation:

y = x² - 3, where x= 4

• y= 4²-3

•y = 16-3

•y = 13.

(Hope I answered your question)

Answer: Assuming that you're asking what the y-intercept is, 11.2.

Step-by-step explanation:

y = mx + c,

where m is the slope and c is the y-intercept.

To calculate the slope, we use the formula:

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

where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.

Using the coordinates of points A and B, we have:

m = (7 - 0) / (3 - 8)

m = 7 / (-5)

m = -7/5

Now we can substitute the values of the slope (m) and the coordinates of one point (A) into the slope-intercept form to solve for the y-intercept (c):

0 = (-7/5)(8) + c

0 = -56/5 + c

To isolate c, we can add 56/5 to both sides:

56/5 = c

Therefore, the y-intercept of the line passing through points A (8, 0) and B (3, 7) is (0, 56/5) or 11.2 when expressed as a decimal.

Answer:

12

Step-by-step explanation:

Select any two random points on the graph of the line (preferably with integer coordinates).

Label them as A and B (in any order).

Calculate the "rise" from A to B. While going vertically from A to B, if we have to go. ...

Calculate the "run" from A to B. ...

Now, use the formula: slope = rise/run.

Answer:

a) -2

b) 1/2

Step-by-step explanation:

To find the slope given 2 points use the formula:
[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Use the 2 points:

(-5,10)

(-3,6)

[tex]\frac{6-10}{-3+5}\\ \frac{-4}{2} \\-2[/tex]

So, a has a slope of -2.

Given the 2 points on the graph:

(-1,4)

(-5,2)

use the same formula:

[tex]\frac{2-4}{-5+1}\\ \frac{-2}{-4}\\ 1/2[/tex]

so b has a slope of 1/2

Hope this helps! :)

The population to the nearest whole number, the population of bacteria in the culture after 7 hours is approximately 816.

Based on the given formula P = Po *  2[tex]^{(t/d)}[/tex], we can calculate the population of bacteria in the culture after 7 hours.

The initial population (Po) is 350 bacteria, and the doubling time (d) is 6 hours.

Let's substitute the values into the formula and calculate:

P = Po * 2[tex]^{(t/d)}[/tex]

P = 350 * 2[tex]^{(7/6)}[/tex]

Using a calculator or simplifying the exponent manually, we have:

P ≈ 350 * 2[tex]^{(1.1667)}[/tex]

Calculating 2^(1.1667), we get approximately 2.3323.

P ≈ 350 * 2.3323

P ≈ 816.31

Rounding the population to the nearest whole number, the population of bacteria in the culture after 7 hours is approximately 816.

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The given sequence does not follow a simple arithmetic or geometric pattern, making it challenging to determine an explicit rule based on the given terms.

To identify the type of sequence and write the explicit rule, we need to examine the pattern of the given sequence: -39, -45, 51, 57, ...

By observing the differences between consecutive terms, we can determine if it follows an arithmetic or geometric pattern.

Arithmetic sequences have a common difference between each term, meaning that by adding (or subtracting) the same value repeatedly, we can generate the sequence. Geometric sequences, on the other hand, have a common ratio between each term, meaning that by multiplying (or dividing) by the same value repeatedly, we can generate the sequence.

Let's calculate the differences between consecutive terms:

-45 - (-39) = -6

51 - (-45) = 96

57 - 51 = 6

From the differences, we can see that the sequence is not arithmetic since the differences are not constant. However, the differences alternate between -6 and 6, indicating a possible geometric pattern.

Let's calculate the ratios between consecutive terms:

-45 / (-39) ≈ 1.1538

51 / (-45) ≈ -1.1333

57 / 51 ≈ 1.1176

The ratios are not constant, indicating that the sequence is neither geometric nor arithmetic.

Therefore, the given sequence does not follow a simple arithmetic or geometric pattern, and it is difficult to determine the explicit rule based on the given terms. It is possible that the sequence follows a more complex pattern or rule that is not apparent from the given terms.

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The Inverse of ƒ(x) is given by y = 21x + 7 For the given function, the inverse is y = 21x + 7.

Given,ƒ(x) = 1/3 - 1/21x

To find the inverse of ƒ(x)

We can use the following steps,

Replace ƒ(x) with y, y = 1/3 - 1/21x

Swap x and y, then we get x = 1/3 - 1/21y

Solve for y

We have to isolate y on one side and other terms on the other side,

Add 1/21 y to both sides + 1/21 y = 1/3

Now, Multiply both sides by 21 to get rid of the denominator.21x + y = 7

Then the inverse of ƒ(x) is given by y = 21x + 7 For the given function, the inverse is y = 21x + 7.

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Answer:

9 and -i

Step-by-step explanation:

12-3 + 5i-4i

9 + -i

9-i

Using the function rule y = 5 + 5x, we can fill in the table as follows:

x | y

0 | 5

1 | 10

2 | 15

3 | 20

4 | 25

To fill in the table using the function rule y = 5 + 5x, we can substitute different values of x into the equation and calculate the corresponding values of y.

Let's create a table:

x | y

0 | 5 + 5(0) = 5 + 0 = 5

1 | 5 + 5(1) = 5 + 5 = 10

2 | 5 + 5(2) = 5 + 10 = 15

3 | 5 + 5(3) = 5 + 15 = 20

4 | 5 + 5(4) = 5 + 20 = 25

Using the function rule y = 5 + 5x, we can substitute each value of x into the equation to find the corresponding value of y. For example, when x = 0, y = 5. When x = 1, y = 10, and so on.

Therefore, the completed table is:

x | y

0 | 5

1 | 10

2 | 15

3 | 20

4 | 25

These values satisfy the given function rule y = 5 + 5x.

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The height of the rectangular recycling bin is 7 ft.

To find the height of the rectangular recycling bin, we can use the formula for the surface area of a rectangular box:

Surface Area = 2lw + 2lh + 2wh

Given:

Length (l) = 16 ft

Width (w) = 9 ft

Surface Area = 638 ft²

Substituting these values into the surface area formula, we have:

638 = 2(16)(9) + 2(16)h + 2(9)h

638 = 288 + 32h + 18h

638 = 288 + 50h

350 = 50h

h = 350 / 50

h = 7

Therefore, the height of the rectangular recycling bin is 7 ft.

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