Which of the following are among the basic postulates of Euclidean Geometry?
Check all that apply.
A) Any straight line segment can be extended indefinitely.
B) All right triangles are equal.
C) A straight line segment can be drawn between any two points.
D) All right angles are equal.

Answer:  1.166666... the 6s go on forever

When rounded to say four decimal places, then we'd get 1.1667

We can write that as  \(1.166666\ldots = 1.1\overline{6}\)

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Explanation:

The quick way to get the answer is to type 7/6 into your calculator, or 7÷6, and you should get 1.1667 approximately. The reality is that the "6"s go on forever. But at some point, we have to round.

When writing \(1.166666\ldots = 1.1\overline{6}\) the horizontal bar tells us which digit goes on forever.

If you want to do this by long division, then check out the work shown below.

EXPLANATION

Since the initial amount of money was of $29,820, and the account earns interest rate by a reason of 7% per year, we can use the simple interest rate equation as shown as follows:

Where P=Principal= 29,820, r=rate in decimal form=7/100=0.07 , t=time in years=4,

Plugging in the numbers into the expression:

Multiplying numbers:

Adding the Interest to the Initial Capital: 29,820+8,349 = 38,169

In conclusion, Colin will have $38,169 after 4 years

Step-by-step explanation:

the surface areas are always the sum of the areas of the individual sides and base area.

so, all we need to do here is calculating the areas of triangles, rectangles (actually squares) and a hexagon.

the area of a triangle is

baseline × height / 2

or with Heron's formula when we have all sides

s = (a+b+c)/2

area = sqrt(s×(s-a)×(s-b)×(s-c))

the area of a rectangle is

length × width

for a square that is then

side × side = side²

and the area of a regular hexagon can be created again as sum of multiple sub-shapes. but ultimately it is

3 × sqrt(3) × side² / 2

1.

square base area : 10×10 = 100 cm²

lateral areas :

one triangle is 10×13/2 = 65 cm²

4 triangles are then 4×65 = 260 cm²

total surface area :

100 + 260 = 360 cm²

2a.

3 lateral triangles :

3 × 8×10/2 = 120 units²

base area (Heron's, as all 3 sides are 8 units) :

s = 3×8/2 = 12

area = sqrt(12×4×4×4) = sqrt(3×4×4×4×4) = 16×sqrt(3)

total surface area :

120 + 16×sqrt(3) = 147.7128129... units²

2b.

4 lateral triangles :

4 × 8×10/2 = 160 units²

base area : 8×8 = 64 units²

total surface area :

160 + 64 = 224 units²

2c.

6 lateral triangles :

6 × 8×20/2 = 480 units²

base area :

3×sqrt(3)×8²/2 = 96×sqrt(3)

total surface area :

480 + 96×sqrt(3) = 646.2768775... units²

2d.

base area : 16² = 256 units²

4 lateral triangles. but we need to get their height first.

Pythagoras :

(16/2)² + 24² = height²

8² + 24² = height²

64 + 576 = height²

height² = 640

height = sqrt(640) = sqrt(64×10) = 8×sqrt(10)

4 triangles are

4 × 16×8×sqrt(10)/2 = 256×sqrt(10) units²

total surface area :

256 + 256×sqrt(10) = 256×(1 + sqrt(10) = 1,065.543081... units²

Answer:

Step-by-step explanation:

If two triangles are congruent, then the corresponding sides and angles are congruent with each other.

Given:

The following are congruent parts:

Note Pay attention to order of vertices when comparing the congruent parts

\(\\ \sf\longmapsto <E\cong <U\)

\(\\ \sf\longmapsto \overline{RE}=\overline{SU}\)

\(\\ \sf\longmapsto ∆DRE=∆SUN\)

\(\\ \sf\longmapsto <R\cong <S\)

Hope it helps

Answer:

x + 1.5y = 25

Step-by-step explanation:

Given that Mr. Guy spends a total of $25, we can set the equation equal to 25. Since x is used to represent the number of pencils, we put 1x into the left side of the equation. We also know that it cost $1.50 for each y pens, therefore 1.5y. If we put together what we have, the equation will be x + 1.5y = 25.

Answer:

You are 11.5  feet off the floor are you in 5 minutes

You are 23  feet off the floor are you in 10 minutes

it will take 13.91 minutes to reach the ground

Step-by-step explanation:

If   you are top , height will keep decreasing as you move downward.

Given

top height 32 feet

Descending speed = -2.3 feet /minute

Here negative sign implies that height is decreasing.

concept used

distance = speed * time

How many feet off the floor are you in 5 minutes?

time = 5 minutes

distance descended = -2.3 feet /minute*5 minutes = - 11.5 feet

Hence ,

I would have moved 11.5 feet from the top.

Distance from ground will be = Top height - distance descended

Distance from ground will be = 32 - 11.5 = 20.5 feet

____________________________________________

How many feet off the floor are you in 10 minutes

distance descended = -2.3 feet /minute*10 minutes = - 23 feet

Hence ,

I would have moved 23 feet from the top.

Distance from ground will be = Top height - distance descended

Distance from ground will be = 32 - 23= 9 feet

______________________________________________

When you reach the ground distance descended will be 32 feet.

Since its a descend distance off the floor has to be taken as negative value

Thus, distance descend in this case will be -32 feet

-32 feet= -2.3 feet /minute*Time

Time = -32/-2.3 = 13. 91 minutes.

Thus, it will take 13.91 minutes to reach the ground.

The most conservative cutover method when converting to a new system is the Phased Cutover.

This method allows for the implementation of the new system in multiple stages, thereby reducing risk. First, the new system is installed and tested. Next, a small portion of data is moved to the new system.

After data is moved, the new system is tested again. This process is repeated until all data has been moved and tested, and the new system is running smoothly.

Once the new system is running successfully, the old system is discontinued.

The phased cutover method ensures that the new system is functioning correctly, and gives time for system users to get used to the new system, before the old system is turned off.

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To solve the compound inequality we need to solve each inequality, then we have:

Now we need to remember that the word OR means the union of the solution sets for each inequality then the solution is:

if the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph., then the visitor  would run 14 .45 miles  before swimming to minimize the time it takes to reach the island .

we are given that an island is 1 mi due north of its closest point along a straight shoreline., where the visitor is staying at a cabin on the shore that is 15 mi west of that point, in some point the visitor runs at a rate of 6 mph and swims at a rate of 2.5 mph. Considering x be the distance the visitor runs. so the total time will be :

Time (T)= x/6 + √((15-x)²+1²)/2.5

Differntiating both sides respect to  x , we get

dT/dx = 1/6 -(15-x)/√(15-x)²+1)/2.5

=>1/6 = (15-x)/√(15-x)²+1)/2.5

=>6(15-x) = 2.5√(15-x)²+1)

Now considering   15 - x = y, we get  

=>6y = 2.5√(y²+1)

=>36y² = 6.25y² + 6.25

=>29.75y² = 6.25

y = √(25/119),  therefore ,x = 15 - √(25/119) = 14 .45

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Given the equation:

Answer:

a. 35 degrees

b. 145 degrees

Step-by-step explanation:

a. Since the two base angles of this triangle are congruent, we can conclude that the triangle is isosceles, which means that the two base angles and sides are congruent.

Now, knowing that information, we can subtract 110 from 180 (the sum of all interior angles in a triangle) and we get 70. But this isn't our answer. This is the sum of both base angles. Since the base angles are congruent, we can divide the 70 by 2 to get the measure of ONE base angle, which is 35 degrees.

b. There are two approaches to solve this problem. I have worked both out.

1) We can use the Exterior Angle Theorem, which states that the sum of the interior angles is equal to the exterior angle. We can add 110 to 35, so we get 145 degrees as the measure of <1.

2) The second approach is supplementary angles. Since we see that one of the base angles and <1 is on the same line, we can subtract 35 from 180 to find the measure of <1 to get 145 degrees.

Either way you use, you get the correct answer. Hope this helped!

Answer:

Step-by-step explanation:

f(x) = 2x

When x = 2

Substitute the value of x into f(x)

That's

f(2) = 2(2)

= 4

Hope this helps you

Answer:

f(2)= 4

Step-by-step explanation:

To find f(2) we will use y=2x since f(x)=y

●y=2*2= 4 wich is f(2)

The wide-area search method employs the use of markers such as knots at regular intervals along the search line.

Given the method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line.

In order to locate, relieve distress, and preserve the life of a person who has been reported missing or is believed to be lost, stranded, or is considered a high-risk missing person, wide area search and rescue refers to activities occurring within large geographic areas. It also refers to the removal of any survivors to a safe location.

Hence, the wide-area search method employs the use of markers such as knots at regular intervals along the search line to indicate distance from the beginning of the search line

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Answer: 138.598 grams per minute

Step-by-step explanation:

You have 440 pounds. Convert this to grams so that it is easier.

There are roughly 199581 grams in 440 pounds (453.592 grams in 1 pound).

Now that you have the number of grams it eats in a day. You now have to convert days to minutes.

There are 24 hours in a day so divide 199581 grams by 24 hours to get the number of grams eaten in 1 hour.

199581/24 = 8315.875

Now you have the number of grams eaten in 1 hour.

There is 60 minutes in 1 hour so divide 8315.875 by 60 to get the number of grams every minute.

8315.875 / 60 = 138.598

So the number of grams every minute the elephant eats is roughly 138.598 grams.

Answer:

6 4/7

Step-by-step explanation:

I personally break it down like this:

Is 2 greater than 7? No so that means the whole number would stay 5.

Same for the other number. Then add the whole numbers attached to the fraction. Which is 6. Then go to the fraction. 2/7 + 2/7 is 4/7. This cannot be simplified anyfurther.

Answer: \(6\frac{4}{7}\)

Step-by-step explanation:

\(5\frac{2}{7}+1\frac{2}{7}\)

Add the whole numbers 5 and 1

\(5+1=6\)

Add the fractions (Don't forget you only add the numerators, not the denominators. You leave the denominators the same.)

\(\frac{2}{7}+\frac{2}{7}=\frac{4}{7}\)

Combine the answers

\(6+\frac{4}{7}\\\\=6\frac{4}{7}\)

\(5\frac{2}{7}+1\frac{2}{7}\)  as a mixed number in the simplest form is \(6\frac{4}{7}\)

50%

since 98/2 = 49

Thats it

Answer:

AC=AB+BC

x=1+9/3

x =4

Ac = 3(4)+1 + 9

Ac = 12+1+9

Ac= 22

Answer: the diagonals of a trapezoid do not bisect each other.

Step-by-step explanation:

We're going to prove that the diagonals of a trapezoid do not bisect each other. But instead of just straight up telling you the proof, we're going to do it using something called an indirect proof. This means we're going to assume that the diagonals do bisect each other and then show that this leads to a contradiction.

So, let's assume that the diagonals of our trapezoid, call them d1 and d2, do bisect each other. That means that they cut each other in half. Now, since a trapezoid has exactly one pair of parallel sides, we know that the midpoint of d1 and d2 must also be the midpoint of the parallel sides.

But here's the catch: the midpoint of a line segment is the same distance from both ends of the segment. So, if the midpoint of d1 is the same as the midpoint of d2, that means that d1 and d2 are the same length! And that's a contradiction, because we know that the diagonals of a trapezoid are not the same length.

So, by assuming that the diagonals of a trapezoid bisect each other, we've shown that it leads to a contradiction. And that means that our assumption was wrong, which means that the diagonals of a trapezoid do not bisect each other.

Answer:

The weight of the contents in the container is;

Explanation:

Given that the shipping container is in the shape of a right rectangular prism with a length of 12 feet, a width of 13.5 feet, and a height of 15 feet.

Recall that the volume of a right rectangular prism can be calculated using the formula;

substituting the given values;

from the question,the container is completely filled with contents that weigh an average, 0.47 pound per cubic foot.

The weight of the content would be;

substituting the density and volume of contents, we have;

Therefore, the weight of the contents in the container is;

Nonnormative influences are irregular and do not follow a predictable timetable.

Nonnormative influences are events or circumstances that are irregular and do not follow a predictable timetable. They include unique experiences that are not shared by most individuals or that occur at unusual times in an individual's life.

These events can have a significant impact on an individual's development, but they are not necessarily predictable or systematic. Examples of nonnormative influences include winning the lottery, experiencing a natural disaster, or developing a serious illness.

Nonnormative influences are important to study because they highlight the uniqueness of each individual's developmental path. By examining nonnormative influences, developmental psychologists can gain insight into the factors that shape individuals' lives and the ways in which individuals cope with adversity and change. However, because nonnormative influences are by definition irregular and unpredictable, they are more difficult to study than normative influences, and researchers must be creative in their approaches to understanding these events and circumstances.

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0.3654 is the probability that the accident involved someone 45 or older given that the accident involved a driver with BAC over 0.08.

A probability is a number that expresses the possibility or likelihood that a specific event will take place. In addition to being represented as percentages ranging from 0% to 100%, probabilities can also be expressed as proportions between 0 and 1.

The probability is a measure of how likely an event is to occur. It gauges the event's degree of certainty. P(E) = Number of Favorable Outcomes/Number of All Outcomes is the formula for probability.

Given that,

one of these 500 accidents was chosen at random.

the accident involved someone 45 or older

Thus, P ( 45 and over | driver with BAC over 0.08) = P (A | B)

P (A | B) = P (A∩B) / P(B)

or, P (A | B) = P ( 45 and over ∩ driver with BAC over 0.08) / P (driver with BAC over 0.08)

or, P (A | B) = 38 / 104

or, P (A | B) =  0.3654

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The complete question is as follows:

The difference between her best time and her worst time is equal to 0.26 seconds.

What is algebra ?

Algebra is a branch of mathematics that deals with various symbols and the arithmetic operations such as division , multiplication , etc.

Jodie has to swim for 100 meters. The four of her times to cover this distance are 22.98 seconds, 23.09 seconds, 23.06 seconds, 22.83 seconds.

Let's find the time per sec to swim at each instances.

So ,

100 meters in 22.98 seconds meant :

= 100 / 22.98

= 4.35 m/sec

Similarly ,

100 meters in 23.09 seconds meant :

= 4.33 m/sec

100 meters in 23.06 seconds meant :

= 4.34 m/sec

100 meters in 22.83 seconds meant :

= 100 / 22.83

= 4.38 m/sec

So , we can find out that Jodie swims distance of 100 meters fastest on speed of 4.38 m/sec in 22.83 seconds and slowest on speed of 4.33 m/sec in 23.09 seconds.

The difference between her best time and her worst time is :

= 23.09 - 22.83

= 0.26 seconds

Therefore , the difference between her best time and her worst time is equal to 0.26 seconds.

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Answer:

23.5% of $8200=23.5/100 ×8200

=$1927

Hence, the increase in dollars is $1927

The total amount of money in her account at the end of last year=8200+1927

=$10,127

It will take 8 minutes for the cold water faucet to fill the tub by itself.

Let x be the time in minutes that the hot water faucet would take to fill the tub by itself. Then the cold water faucet would take 2x minutes to fill the tub by itself. We can then set up an equation in terms of x:1/x + 1/2x = 1/6Multiplying both sides by 6x gives:6 + 3 = xSimplifying gives:x = 9So the hot water faucet would take 9 minutes to fill the tub by itself. Therefore, the cold water faucet would take twice as long, or 2(9) = 18 minutes to fill the tub by itself.

The problem states that a bathtub can be filled by the cold water faucet twice as long as the hot water faucet. Let's say it takes the hot water faucet "x" amount of time to fill the tub by itself. The cold water faucet would take twice as long, which is "2x".If we add both times together, we get the total time to fill the tub. In this problem, it takes 6 minutes to fill the tub when both faucets are open. Therefore, we can create an equation with this information. We know that the equation for the rate is:rate × time = workWe can also state that the work (filling the tub) is 1, and therefore the equation becomes:1/x + 1/2x = 1/6Multiplying both sides by 6x, we get:6 + 3 = xSimplifying the equation gives us:x = 9Therefore, the hot water faucet takes 9 minutes to fill the tub by itself. We know that the cold water faucet takes twice as long, or 2(9) = 18 minutes to fill the tub by itself.

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Answer:

King repeated the phase, “100 years later” 4 times How many times did Dr. King repeat the phrase “Now is the time

Step-by-step explanation:

Answer:

42 65 76 84 32

Step-by-step explanation:

xdr tfycyvyv

Answer:

all you need to do is multiply length times width times height.

Step-by-step explanation:

5 1/2 x 3= 16.5

16.5 x 2 1/4= 453.75

now just add both answers :)

I really hope this helps! <3 Good luck!

Answer:

x^2-4-8

Step-by-step explanation:

x^2-4(x+2)

x^2-4x-8

Answer:

The athlete's tangential velocity is 0.88 m/s.

Step-by-step explanation:

We have that the athlete completes 4 laps around a track with a radius of 25 meters in 12 minutes:

\( \omega = \frac{\theta}{t} \)

Where:

ω: is the angular speed

θ: is the angular displacement

t: is the time = 12 min = 720 s

The angular displacement is:

\( \theta = 4 rev*\frac{2\pi rad}{1 rev} = 25.13 rad \)

Now, the angular speed is:

\( \omega = \frac{\theta}{t} = \frac{25.13 rad}{720 s} = 0.035 rad/s \)

Finally, the athlete's tangential velocity is:

\( v = \omega r = 0.035 rad/s*25 m = 0.88 m/s \)

Therefore, the athlete's tangential velocity is 0.88 m/s.

I hope it helps you!