two cyclists leave towns kilometers apart at the same time and travel toward each other. one cyclist travels slower than the other. if they meet in hours, what is the rate of each cyclist?

Answer:

number one ×=30-4y/7

second one x=-4y/3+2

those are the answers I got hope it helps

Answer:

The answer for your question is C. 22°, 22°, and 136°.

Explanation:

A right triangle will always have one angle that is 90°.

All of the other options have a 90° angle, so your answer is C.

Hope this helps!

Answer:

The slope of a linear model can be calculated using the formula:

m = Δy / Δx

where:

Δy = change in y (the dependent variable, in this case, total cost)

Δx = change in x (the independent variable, in this case, number of candy bars)

This is essentially the "rise over run" concept from geometry, applied to data points on a graph.

In this case, we can take two points from the table (for instance, the first and last) and calculate the slope.

Let's take the first point (3 candy bars, $6.65) and the last point (25 candy bars, $48.45).

Δy = $48.45 - $6.65 = $41.8

Δx = 25 - 3 = 22

So the slope m would be:

m = Δy / Δx = $41.8 / 22 = $1.9 per candy bar

This suggests that the cost of each candy bar is $1.9 according to this linear model.

Please note that this assumes the relationship between the number of candy bars and the total cost is perfectly linear, which might not be the case in reality.

Answer:

b

Step-by-step explanation:

Answer:

If 250 per 600

Step-by-step explanation:

600 x 3 is 1800, so 250 x 3 is 750.

So you're answer would be 750

Answer:

A, 1,2

Step-by-step explanation:

we translate it first into language of math

we use n for the number

n² = 3n - 2

then, do some algebra things

n² - 3n + 2 = 0

then factorize it

(n - 2)(n - 1) = 0

first n

n - 2 = 0

n = 2

2nd n

n - 1 = 0

n = 1

so n can be 1 or 2

the fraction that lies will be one 1 half

Step-by-step explanation:

yes

Answer:

I believe its 17/24

Step-by-step explanation:

hope this helps

The factored form of the polynomial P(x) = x³ + 2x² + 4x + 8 is P(x) = (x + 1)(x² + x + 7). The quadratic factor x^2 + x + 7 cannot be further factored into linear factors with real coefficients.

To factor the polynomial P(x) = x³ + 2x² + 4x + 8, we can look for potential roots by applying synthetic division or by using synthetic substitution. In this case, we can start by trying small integer values as possible roots, such as ±1, ±2, ±4, and ±8, using the Rational Root Theorem.

By synthetic substitution, we find that -1 is a root of the polynomial. Dividing P(x) by (x + 1) using long division or synthetic division, we get:

P(x) = (x + 1)(x² + x + 7)

Now, we need to factor the quadratic expression x² + x + 7. However, upon factoring this quadratic expression, we find that it cannot be factored further into linear factors with real coefficients. Therefore, the factored form of P(x) is:

P(x) = (x + 1)(x² + x + 7)

Please note that the quadratic factor x² + x + 7 does not have any real roots. Therefore, the complete factored form of P(x) is as given above.

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The opposite side of the right triangle (x) is approximately 6.888 inches long.

To solve this problem, we can use the trigonometric ratio for the sine function, which is opposite/hypotenuse. We have the hypotenuse as 12 inches and the opposite angle as 35 degrees, so we can set up the equation:

sin(35) = opposite/12

To solve for the opposite, we can multiply both sides by 12:

opposite = 12 * sin(35)

sin(35) as approximately 0.574:

opposite = 12 * 0.574

opposite ≈ 6.888

Therefore, the opposite side of the right triangle (x) is approximately 6.888 inches long.

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x+5y=8... equ 1

-x+2y=-1 ..... equ2

Add equ 1 to equ 2

0x+7y=7

7y=7

Y=1

Subsitute the value of y in equ 1 or equ 2

By subsituting In equ 1

X+5(1)=8

X=3

Answer:

The 11th check

Step-by-step explanation:

Answer:

$0.78

Step-by-step explanation:

You divide the $7.80 by 10 to get the cost of one tulip.

Answer:In this item, I take it that we are to get  the cube root of the given expression, -64x6y9. First, we look into the numerical coefficient, this is the product when -4 is multiplied to itself three times as shown below.

   -64 = (-4)(-4)(-4)

Then,

  x6 = x2 (x2) (x2)

and,

   y9 = (y3)(y3)(y3)

If we take the cube root, we consider only one item per product. Thus, the answer is,

   -4x²y³

Step-by-step explanation:

Answer:

5 groups

Step-by-step explanation:

10/2=5

Graphing is a way to visually represent data or information in a clear and concise manner. It can help to identify trends, patterns, and relationships between variables.

Graphs come in many different types, including bar graphs, line graphs, scatter plots, and pie charts.

The type of graph used will depend on the nature of the data and what you want to communicate.

Graphing can be useful in a variety of fields, including science, economics, finance, and business.

For example, a line graph can be used to show changes in stock prices over time, while a scatter plot can be used to identify correlations between two variables, such as age and income.

Graphing requires careful attention to detail and accuracy in order to produce clear and meaningful visual representations of data. It is an important tool for anyone who wants to better understand and communicate information.

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To increase usability in a spreadsheet, you can use comments, descriptive labels, and data validation.

To increase usability in a spreadsheet, you can utilize the following techniques:

1. Comments: Comments allow you to add explanatory notes or instructions within cells. They can provide additional context or clarify the purpose of certain data or formulas. Users can view comments by hovering over the respective cell, making it helpful for collaboration and documentation.

2. Descriptive Labels: Instead of relying solely on cell references or generic labels, use descriptive labels that clearly indicate the purpose of each column, row, or range of cells. This approach enhances readability and makes it easier for users to understand the data and navigate through the spreadsheet.

3. Data Validation: Implement data validation rules to ensure the accuracy and integrity of the data entered into the spreadsheet. Data validation allows you to define constraints or conditions for input, such as numeric ranges, predefined lists, or specific text formats. It helps prevent errors and assists users in entering valid data.

4. Formatting: Properly formatting the cells, columns, and rows can greatly enhance usability. Use consistent formatting for similar types of data, apply color schemes or conditional formatting to highlight important information or trends, and adjust the column widths and row heights to optimize readability.

5. Sheet Organization: Organize the spreadsheet by using multiple sheets if needed. Group related information on separate sheets, and provide clear sheet names that reflect the content or purpose of each sheet. This helps users locate and navigate to specific sections or data within the spreadsheet.

6. Clear Instructions or Documentation: Provide clear instructions or documentation either within the spreadsheet or as separate documentation. Explain the purpose of the spreadsheet, any specific procedures or workflows, and how to interpret the data or use any embedded formulas or macros. This helps users understand the spreadsheet's functionality and ensures consistent usage.

7. Error Handling: Implement error handling mechanisms to provide informative error messages or alerts when users input incorrect or incompatible data. Clear error messages guide users in correcting their input and reduce frustration when dealing with potential errors.

By incorporating comments, descriptive labels, data validation, formatting, sheet organization, clear instructions/documentation, and error handling, you can significantly enhance the usability of your spreadsheet and make it more user-friendly for both yourself and others who interact with it.

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The first step is converting both the velocity and the wind in vector form, as follows:

Then the true speed of the plane is given by the addition of these two vectors, as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{|v_1|^2 + |v_2|^2 + 2 \cdot |v_1| \cdot |v_2| \cdot \cos(\theta)}\)

The magnitudes of each vector are given as follows:

The angle between these two vectors is given as follows:

\(\theta = 100^\circ - 42^\circ = 58^\circ\)

Thus the resulting speed is obtained as follows:

\(\vec{v_1} + \vec{v_2} = \sqrt{180^2 + 30^2 + 2 \cdot 180 \cdot 30 \cdot \cos(58^\circ)} = 197.54\)

The resulting angle of the plane is then obtained as follows:

\(\angle = \arctan\left(\frac{|v_1| \cdot \sin(\theta) + |v_2| \cdot \sin(\theta_2)}{|v_1| \cdot \cos(\theta) + |v_2| \cdot \cos(\theta_2)}\right)\)

Hence:

\(\angle = \arctan\left(\frac{180 \cdot \sin(58^\circ) + 30 \cdot \sin(42^\circ)}{180 \cdot \cos(58^\circ) + 30 \cdot \cos(42^\circ)}\right)\)

\(\angle = 59.87^\circ\)

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Answer:

  197.5 km/h

Step-by-step explanation:

You want the resultant speed with an airplane at a speed of 180 km/h at 100° is acted upon by a wind at a speed of 30 km/h at 42°. Angles are bearings CW from north.

A vector calculator makes short work of this. The resultant speed is ...

  197.5 km/h at 92.6°

The law of cosines can be used to find the side opposite the known angle in the triangle with sides 30 km/h and 180 km/h. The known angle is ...

  180° -(100° -42°) = 122°

So, the resultant speed is ...

  c = √(a²+b²-2ab·cos(C))

  = √(30² +180² -2(30)(180)·cos(122°)) ≈ √39023.13

  c ≈ 197.543

The true speed of the plane is about 197.5 km/h.

__

Additional comment

You will notice that we used bearing angles directly in the calculator computation. As long as angles are consistently measured, it doesn't matter how they're measured.

When plotting the vectors on the Cartesian plane, we need to subtract the bearing angles from 90° to make them correspond to the vectors plotted on a map with north at the top.

We know that Juan should consider hiring a professional installer to ensure that the carpet is installed correctly and looks great in the room.

Based on the floor plan shown, Juan will need to measure the dimensions of the bedroom to determine the amount of carpet he will need.

He should measure the length and width of the room, including any alcoves or closets. It's also important to consider the quality and type of carpet he wants to install.

Once he has these measurements, he can calculate the square footage of the room and determine how much carpet he will need to purchase. It's important to factor in extra carpet for trimming and fitting purposes.

Additionally, Juan should consider hiring a professional installer to ensure that the carpet is installed correctly and looks great in the room.

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Answer:

\(\sf m=\dfrac{1}{3}\)

Step-by-step explanation:

The slope of a line can be found using the following formula:

\(\sf m=\dfrac{y_2-y_1}{x_2-x_1}\)

Given the points (1, 5) and (4, 6):

where:

x₁ = 1, x₂ = 4

y₁ = 5, y₂ = 6

Substitute these values into the formula:

\(\sf \sf m=\dfrac{y_2-y_1}{x_2-x_1}\\\\m=\dfrac{6-5}{4-1}\\\\m=\dfrac{1}{3}\)

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Answer:

b 1/3.5

Step-by-step explanation:

Answer:

Daniel's time: 3 minutes 45 seconds

Brandon's time: 3 minutes 27 seconds

Step-by-step explanation:

Well, 5 feet per every second so side A would be 327.6 / 3 = 109.2

then 489 / 5 = 97.8 add them two you get 207 seconds which is 3 minutes and 45 seconds for  Daniel.

For Brandon you have to find the hypotenuse of the triangle which in short is 588.6 / 3 = 196.2

This was my first answer on this so though Its problebly not the best I hope I did something to help. ;-;

The Binomial Distribution applet will calculate the probability of the basketball player making 2 or less shots, and it turns out to be equal to 0.8425.

Using the Binomial Distribution Applet, we can find the probability that the basketball player makes 2 shots or less by inputting the given information into the applet. The number of trials is 3, the probability of success is 0.54, and the number of successes we are looking for is 2 or less.

Here are the steps to finding the probability using the Binomial Distribution Applet: Input the number of trials as 3, Input the probability of success as 0.54, Input the number of successes as 2, Click the "Calculate" button

The applet will then calculate the probability of the basketball player making 2 or less shots, which is 0.8425. Therefore, the answer to the question is 0.8425.

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Step-by-step explanation:

opposite/hypotenuse = sin x

Answer:

It's a guess.

1 known

2 cancelled.

Hope this helps!

And I am sorry if it doesn't

Only two positive integers, 2 and 8, fit the description.

2 = 10 (base 2) = 2 (base 3)

8 = 1000 (base 2) = 22 (base 3)

Their sum is 10.

Based on the given data, it is advisable for management at Kelsh to eliminate the North Division in order to avoid the traceable fixed expenses associated with it, while keeping the total common corporate expenses unaffected.

When considering the elimination of a division, it is crucial to analyze the impact on expenses and overall profitability. In this case, the information states that if the North Division is eliminated, its traceable fixed expenses can be avoided. Traceable fixed expenses refer to the costs that are directly associated with a specific division or segment of a company. By eliminating the North Division, Kelsh can avoid incurring these interests, potentially improving the company's financial performance.

Furthermore, the data states that the total common corporate expenses would be unaffected by the elimination of the North Division. Common corporate expenses are costs incurred at the corporate level that are not directly attributable to any specific division or segment.

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Answer:

D) infinitely many solutions

Step-by-step explanation:

5 ( x-3 ) - 3x = 8x - 15 - 6x

5x - 3x - 15 = 8x - 6x - 15

2x - 15 = 2x - 15

2x = 2x

Since, equations of both lines are same. Therefore, there are infinitely many solutions.

Answer:

D

Step-by-step explanation:

Given

5(x - 3) - 3x = 8x - 15 - 6x

5x - 15 - 3x = 2x - 15

2x - 15 = 2x - 15

Since both sides are the same then any real value of x will be a solution.

That is there are infinitely many solutions

Answer:

24.75FT

Step-by-step explanation:

The triangles in the picture are similar meaning that 36/8=4.5

66inches into ft = 3.5

3.5x4.5=24.75

Answer: C. 24.75 ft

Step-by-step explanation:

• Set up the proportion.

• Cross multiply.

• Complete the multiplication on the left side.

• Divide both sides by 100.

• Complete the divisions on both sides.

Answer:

1/8 of the pizza

Step-by-step explanation:

whole pizza=1

5/8 is gone so 1-5/8=8/8-5/8=3/8

3/8-1/4 = 3/8-2/8=1/8

hope this helps