Find the equation of a line perpendicular to another line

The Answer to this problem is BN=3.8 Units.

The statement △FEB≅△CNB indicates that triangle FEB is congruent to triangle CNB, meaning their corresponding sides and angles are equal. However, without additional information, such as the length of a congruent side in △FEB, we cannot determine the exact length of BN.

The given statement, △FEB≅△CNB indicates that triangle FEB is congruent to triangle CNB. In congruent triangles, corresponding sides and angles are equal.

However, to determine the exact length of BN, more information is needed. Examples of useful additional information would include the length of a corresponding side in △FEB, or the lengths of other sides in △CNB in relation to the length of BN, if these are also congruent sides.

Given the information provided in the question, it's not possible to provide an exact numeric value for the length of BN at this time. Please confirm if there are any additional details in your question or your course materials that could further clarify this issue.

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Using a system of equations, it is found that for the room's dimensions:

The perimeter of a rectangle of length l and width w is given by:

[tex]P = 2(l + w)[/tex]

The length of a rectangular room is 2 feet longer than twice the width, hence:

[tex]l = 2w + 2[/tex]

The room's perimeter is 196 feet, hence:

[tex]2l + 2w = 196[/tex]

From the second equation:

[tex]2(2w + 2) + 2w = 196[/tex]

[tex]6w = 194[/tex]

[tex]w = \frac{194}{6}[/tex]

[tex]w = 32.33[/tex]

Then:

[tex]l = 2w + 2 = 2(32.333) + 2 = 66.67[/tex]

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The dimensions of the room are 32 feet by 66 feet, with a total area of 2112 square feet, which can be calculated for carpet replacement based on the room's perimeter.

To find the dimensions of a rectangular room where the length is 2 feet longer than twice the width and the perimeter is 196 feet, we first need to establish equations based on the given information. Let the width of the room be represented by w and the length be represented by l. From the problem, we have that l = 2w + 2. The perimeter P of a rectangle is given by P = 2l + 2w. Plugging in what we know, we can set up the equation:

196 = 2(2w + 2) + 2w

Solving this, we get:

Now, we use the width to find the length:

So, the dimensions of the room are 32 feet by 66 feet. Since the student wants to determine the square footage for carpet replacement, we can calculate the area by multiplying the length and width:

Area = 32 feet × 66 feet = 2112 square feet

Based on the daily consumption calculated from the given data, Lee's cat eats approximately 91.25 pounds of cat food in a year.

The question is asking for the estimated number of pounds of food that Lee's cat eats in one year. Lee's cat consumes a five-pound bag of food in 20 days. So, let's first determine how much he eats in 1 day. If 5 pounds is consumed in 20 days, then in 1 day, the cat eats 5/20, or 0.25 pounds.

Since there are approximately 365 days in a year, we multiply this daily consumption by 365. So, 0.25 pounds/day * 365 days/year = 91.25 pounds/year.

So, the best estimate for the amount of cat food that Lee's cat eats in one year would be approximately 91.25 pounds.

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The required inequality is -6<x<8

An inequality is an inequation separated by <,>≥,≤. In Mathematics, the relationship between two values that are not equal is defined by inequalities. Inequality means not equal. Generally, if two values are not equal, we use “not equal symbol (≠)”. But to compare the values, whether it is less than or greater than, different inequalities are used.

Given here: A number x is more than -6 and at most 8.

Clearly we can infer that the number lies between the interval (-6,8)

Thus we can construct the inequality for x as

-6<x<8 or x has 11 integral values

Hence, The required inequality is -6<x<8

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The two names for the​ segment are AC and CA that has endpoints A and C the answer would be AC and CA.

A segment bisector is a line, ray, line segment, or point that divides a line segment into two equal halves at its center.

It is given that:

A segment has endpoints A and C.

As we know, the line segment is the line that goes to the endpoints on both sides.

The line segment can be represented as AC and CA

Or

The bar(AC) and bar(CA)

Thus, the two names for the​ segment are AC and CA that has endpoints A and C the answer would be AC and CA.

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I believe that aside from the bar graph, the line graph would actually best suits to convey this information. Because just like the bar graph, we can actually see the peaks of the grades. And through the peaks, we can easily compare the grades one by one.

Answer:

line graph

Answer:

0

Step-by-step explanation:

The mode of the data is 2 which occurs more frequently during these two weeks.

Mode is the number that appears most frequently in the given set of data. The Median represents the middle value of the given data when arranged in a particular order.

The daily rainfall during two week period in april weeks given as;

1, 0.5, 0.3, 0, 0,0, 1.2, 3, 0, 1.1, 0.7, 2, 1.3, 2 inches.

Calculation of the mode:

First, we Rearrange the data from the lowest to the highest value.

0, 0, 0, 0, 0.3, 0.5, 0.7, 1, 1.1, 1.2, 1.3, 2, 2, 3

Since there is an even number of data, find the mode in the middle;

0, 0, 0, 0, 0.3, 0.5, 0.7, 1, 1.1, 1.2, 1.3, 2, 2, 3

Therefore, the mode of the data is 2 which occurs more frequently during this two-week peroid.

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Answer:

(3a,a)

Step-by-step explanation:

Yes, the function y=8x is a linear function because it has the form y = a + bx, where a is the y-intercept and b is the multiplicative slope factor, both of which are present in this equation with a=0 (implied) and b=8.

The question whether y=8x is a linear function can be answered by examining the form of the equation. A linear equation can generally be expressed as y = a + bx, where a is the y-intercept and b is the slope of the line. Since the equation y=8x fits this form, with a slope of 8 and a y-intercept of 0 (implied), it is indeed a linear function. A graph representing this equation would display a straight line with a slope of 8, confirming its linear nature. The equation y=xb is nonlinear when b is a power rather than a multiplicative parameter, demonstrating the contrast between linear and nonlinear functions. However, in our case, 8 is simply a multiplicative factor, which is characteristic of a linear function.

Final answer:

The expected value for the game is $4, which means on average a player would expect to gain $4 before the entry fee. However, after subtracting the cost to play ($15), the net expected value is -$11, indicating a loss on average for each play.

Explanation:

To determine the expected value of the game mentioned, we first identify the possible outcomes and their corresponding probabilities. Next, we multiply each outcome value by its probability, and sum up these products. Finally, we deduct the cost of the game ($15) from the sum to find the expected net gain or loss.

Probability of picking a $5 bill = 4/10

The expected value (EV) calculation would be:

EV = (1/10 * $100) + (2/10 * $20) + (3/10 * $10) + (4/10 * $5) - $15

EV = ($10) + ($4) + ($3) + ($2) - $15

EV = $19 - $15

EV = $4

Therefore, the expected value for the game is $4. This means on average you would expect to gain $4 per game before considering the entry fee. Since you pay $15 to play, you need to subtract this from the $4 gain to obtain the net expected value, which would be -$11, indicating a loss in the long run.