Answers
Answer: P≈15.5 units.
Step-by-step explanation:
The perimeter of a triangle is equal to the sum of all its sides:
P = a + b + c,
where P is the perimeter and a, b, c are the sides of the triangle.
The segment length formula makes it possible to calculate the distance between two arbitrary points in the plane, provided that the coordinates of these points are known:
\(\boxed {d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} }\)
1) (1,6) (3,1) ⇒ x₁=1 x₂=3 y₁=6 y₂=1
\(a=\sqrt{(1-3)^2+(6-1)^2} \\\\a=\sqrt{(-2)^2+5^2} \\\\a=\sqrt{4+25} \\\\a=\sqrt{29} \approx5.4\ units\\\)
2) (1,6) (6,1) ⇒ x₁=1 x₂=6 y₁=6 y₂=1
\(b=\sqrt{(1-6)^2+(6-1)^2} \\\\b=\sqrt{(-5)^2+5^2} \\\\b=\sqrt{25+25} \\\\b=\sqrt{50} \approx7.1\ units\\\)
3) (3,1) (6,1) ⇒ x₁=3 x₂=6 y₁=1 y₂=1
\(c=\sqrt{(3-6)^2+(1-1)^2} \\\\c=\sqrt{(-3)^2+0^2} \\\\a=\sqrt{9+0} \\\\a=\sqrt{9} =3\ units\\\)
4) P=a+b+c
P≈5.4+7.1+3
P≈15.5 units.
Related Questions
A FALLING APPLE WITH A TOTAL POTENCIAL ENERGY OF 10 JOULES AND A KINECTIC ENERGY OF 5 JOULES IS ABOUT TO REACH THE GROUND. WHAT IS THE APPLE'S TOTAL MECHANICAL ENERGY?
Answers
Therefore , the solution of the given problem of unitary method comes out to be has 15 Joules of mechanical energy in total shortly before it touches the ground.
Definition of a unitary method.This well-known simplicity, already-existing variables, and any necessary elements from the initial Diocesan customised query can all be used to finish the work. As a response, you can be given another chance to use the item. Otherwise, important effects on algorithmic knowledge will vanish.
Here,
An object's kinetic energy and potential energy are added to determine its overall mechanical energy. In this instance, the falling apple has a total mechanical energy of 10 Joules because of its potential energy and 5 Joules because of its kinetic energy.
=> Potential energy + kinetic energy = total mechanical energy.
=> The mechanical energy = 10 + 5 joules.
=> 15 Joules are the total mechanical energy.
The apple has 15 Joules of mechanical energy in total shortly before it touches the ground.
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what is the measure of angle 1 in degrees?
Answers
Answer:
39°
Step-by-step explanation:
angles are alternate exterior angles making them congruent
for example:
What is formed when a sodium atom and chlorine atom react chemically
Answers
Answer:
Step-by-step explanation:
When sodium and chlorine atoms come together to form sodium chloride (NaCl), they transfer an electron. The sodium (Na) atom transfers one electron to the chlorine (Cl) atom, so that they both have full outer shells.
help I'm not that smart!!!!!!!
Answers
Answer:
arc CDE = 172°
Step-by-step explanation:
arc CAE = 103° + 50° + 35° = 188°
arc CDE = 360° - arc CAE
360° - 188° = 172°
Problem 1.3-9 (a) Show that P(Ai) = 3!
4! for each i. b) Show that P(Ai ∩ Aj) = 2!
4! , i = j.(c) Show that P(Ai ∩ Aj ∩ Ak) = 1!
4! , i = j, i = k, j = k.
Answers
Problem 1.3-9(a): To show that P(Ai) = 3!/4! for each i, we start by observing that there are 4 friends, each of whom can be seated at the table in one of four seats. Therefore, there are 4! ways to seat the four friends.
Now, let's suppose that Ai represents the event that friend i is seated in the first chair. There are 3! ways to seat the remaining three friends in the remaining three chairs once friend i is seated in the first chair. Therefore, P(Ai) = 3!/4! for each i. We can also write this as P(Ai) = 1/4 for each i.
Problem 1.3-9(b): We want to show that P(Ai ∩ Aj) = 2!/4! for i = j. Let's start with the observation that there are 4! ways to seat the four friends. If i = j, then there are 3! ways to seat the other two friends, but there are only two chairs available for the other two friends. Therefore, P(Ai ∩ Aj) = 2!/(4-1)! = 2!/3! = 1/6 for i = j.
Problem 1.3-9(c): We want to show that P(Ai ∩ Aj ∩ Ak) = 1!/4! for i = j = k. Let's start with the observation that there are 4! ways to seat the four friends. If i = j = k, then there are 2! ways to seat the other friend, but there is only one chair available for the other friend. Therefore, P(Ai ∩ Aj ∩ Ak) = 1!/4! = 1/24 for i = j = k.
Answer: P(Ai) = 3!/4! for each i. P(Ai ∩ Aj) = 2!/4! for i = j. P(Ai ∩ Aj ∩ Ak) = 1!/4! for i = j = k.
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Can you use a right triangle to represent the distance between any two points on the coordinate plane?.
Answers
Yes. A leg of a right triangle can indicate the distance that separates two vertical or horizontal points, and the hypotenuse can represent the distance between two non-vertical or non-horizontal points.
We can use this theorem to calculate the distances between two locations on a coordinate grid. Consider the following example using the points:
( 3, 4 ) and ( − 2, 1 )
We can see how to make a right triangle with the hypotenuse as that of the line connecting these two spots. A right angle is formed at the coordinates ( 3, 1), where the vertical line from ( 3, 4 ) and the horizontal line from ( 2, 1 ) intersect.
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Need help please !!!!!!!!
Answers
A car travels 40 kph for 20 kilometers, 50 kph for 25 kilometers, 60 kph for 45 minutes and 48 kph for 15 minutes. What is the average speed of the car, in kph
Answers
The average speed of the car is 51 kph. The result is obtained by dividing the total distance by the total time taken.
What is average speed?Average speed is the overall speed of a moving object during a given amount of time. It can be expressed as
Avg speed = Total distance covered / Total time taken
The speed itself can be found by the following formula.
s = d/t
Where
s = speedd = distancet = timeA car can travel at the following speeds.
First lap with s₁ = 40 kph and d₁ = 20 km.Second lap with s₂ = 50 kph and d₂ = 25 km.Third lap with s₃ = 60 kph and t₃ = 45 minutes.Fourth lap with s₄ = 48 kph and t₄ = 15 minutes.Find the average speed!
We should convert the unit of time from minutes to hour.
t₃ = 45 minutes = ¾ h
t₄ = 15 minutes = ¼ h
We count the time and distance in each travels.
t₁ = d₁/s₁ = 20/40 = ½ h
t₂ = d₂/s₂ = 25/50 = ½ h
d₃ = s₃×t₃ = 60 × ¾ = 45 km
d₄ = s₄×t₄ = 48 × ¼ = 12 km
Avg speed = (s₁ + s₂ + s₃ + s₄)/(t₁ + t₂ + t₃ + t₄)
Avg speed = (40 + 50 + 60 + 48)/(½ + ½ + ¾ + ¼)
Avg speed = 102/2
Avg speed = 51 kph
Hence, the car has the average speed of 51 kph.
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Find the standard deviation ofthe given data rounded to thenearest hundredth.12, 53, 141, 219, 500
Answers
1) Let's find the standard deviation for this data set:
\(12,53,141,219,500\)2) So, let's apply the formula for standard deviation:
\(\begin{gathered} S\left(X\right)=\sqrt{\frac{\sum_{i=1}^n\left(x_i-\bar{x}\right)^2}{n}} \\ \end{gathered}\)3) Let's find the mean and compute the variance:
\(\bar{x}=\sum_{i=1}^na_i=\frac{12+53+141+219+500}{5}=\frac{925}{5}=185\)The sum of all entries is divided by the number of data points.
Now, for the variance:
\(\begin{gathered} \sum_{i=1}^n\left(x_i-\bar{x}\right)^2=\frac{\left(12-185\right)^2+\left(53-185\right)^2+\left(141-185\right)^2+\left(219-185\right)^2+\left(500-185\right)^2}{5} \\ \frac{149670}{5}=29934 \end{gathered}\)Finally, we can take the square root of that variance to get the standard deviation:
\(\sigma\left(X\right)=\sqrt{\sum_{i=1}^n\frac{\left(x_i-\bar{x}\right)^2}{n}}=\sqrt{29934}=173.014\)a certain phone company charges $4.50 for the first five minutes of an international phone call. additional time is charged at $.50 per minute. how much would a customer be charged for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day?
Answers
A customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day.
Charge for first 5 charged = $ 4.50
Charge for additional time = $ 0.50 per minute
Starting time = 9:35 p.m.
End time = 11:15 p.m.
Total minutes = 100 minutes
Total charge = 4.50 + (95 x 0.50)
= 4.50 + 47.50
= 52.00
Hence, a customer would be charged $ 52 for an international phone call that started at 9:35 p.m. and ended at 11:15 p.m. the same day i.e. for 100 minutes.
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Each of the following sets of dimensions represents the dimensions of a right rectangular prism. All of them have the same volume except length: ; width: 10; height: 3 length: 1; width: 5; height: 7 length: 2; width: 5; height: 3 length: 4; width: 2 ; height: 3
Answers
The first and third rectangular prisms have the same volume of 30 cubic units.
The second rectangular prism has a volume of 350 cubic units, and the fourth rectangular prism has a volume of 24 cubic units.
How do we calculate?The volume of each of the rectangular prisms can be calculated as follows:
1. length: 1; width: 10; height: 3
volume = 1 x 10 x 3 = 30
2. length: 5; width: 10; height: 7
volume = 5 x 10 x 7 = 350
3. length: 2; width: 5; height: 3
volume = 2 x 5 x 3 = 30
4. length: 4; width: 2; height: 3
volume = 4 x 2 x 3 = 24
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what is the purpose of using prefixes in the metric system
Answers
The purpose of using prefix in the metric system is to properly sale the basis of the unit so large numeric values can be used effectively.
If the metric system is not properly prefixed it can lead to various inconsistencies in the the numeric values. for example if you go to a computer store and you do not know the scale like (kb, mb, gb, tb) you will get quite confused about what is the sales representative saying
Consider you went to a store to get sugar and you do not know the metric system say(gram, kg, mg) you would not know how much sugar you need directly by taking it in your hands.
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Solve the equation t=r+7kw attempted this problem 4 times. all recorded score is 0%. unlimited attempts remaining
Answers
Answer:
Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.
If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.
To improve your chances of solving the equation successfully, consider the following steps:
Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.
Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.
Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.
Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.
Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.
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Answer:
Solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles.
If you attempted the problem four times and all recorded scores were 0%, it suggests that your attempts did not yield the correct solution. To solve the equation t = r + 7kw, we need to have specific values or information about the variables involved. Without any additional details, it is not possible to provide a numerical solution.
To improve your chances of solving the equation successfully, consider the following steps:
Review the equation: Make sure you understand the structure and the relationship between the variables. In this case, t is equal to the sum of r and 7 times the product of k and w.
Check for errors: Review your calculations and ensure there are no mistakes in your algebraic manipulations. Double-check your arithmetic operations and signs.
Seek assistance: If you're having difficulty solving the equation, consider reaching out for help. Consult a teacher, tutor, or someone knowledgeable in the subject matter. They can guide you through the problem-solving process and clarify any misunderstandings.
Practice and persistence: Continue practicing similar equations to improve your problem-solving skills. Persistence and practice are key to mastering mathematical concepts.
Remember, solving equations requires a systematic approach, attention to detail, and understanding of the underlying principles. Keep practicing and seeking assistance, and you will improve your problem-solving abilities over time.
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There are 30 giraffe and 6 penguin at the zoo. Which tatement correctly compare the two quantitie?
Answers
To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.
To compare the two quantities, you need to divide the number of giraffes by the number of penguins.
30 giraffes / 6 penguins = 5
This means that there are 5 times as many giraffes as penguins at the zoo.
There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.
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4. A large pizza with 12 slices cost $9.00.How
much is each slice
Answers
Answer:
1.33
Step-by-step explanation:
12÷9 =1.33
each pizza slice costs $1.33
⚠️HELP PLS AND THANK U!! Will give brainliest if you give a good explanation! Have a good weekend! ⚠️The population of fish in a local bay is modeled by the equation P(t) = 2,500(1.025)', where t represents the
number of years since 2,500 fish were first measured. Based on this equation, which of the following
represents the percent the population will grow in a decade?
(1) 2.5%
(3) 28%
(2) 25%
(4) 32%
Answers
Answer:
Its 25%
Step-by-step explanation:
The percent population that will grow in a decade is 28% option (3) 28% is correct.
What is an exponential function?It is defined as the function that rapidly increases and the value of the exponential function is always positive. It denotes with exponent y = a^x
where a is a constant and a>1
We have:
\(\rm P(t) = 2,500(1.025)^t\)
Plug t = 10
\(\rm P(10) = 2,500(1.025)^{10}\)
P(10) = 3200
Percent grow = [(3200 - 2500)/2500]×100
Percent grow = 28%
Thus, the percent population that will grow in a decade is 28% option (3) 28% is correct.
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how to solve number 16
Answers
Answer:
T < -19
Step-by-step explanation:
-6 > t + 13 ( neg & neg = positive)
- 6 - 13 > t
-19 > t
help me pls..........
Answers
Answer:
1000x or 1000 thousand times greater
Step-by-step explanation:
every decimal to the left is 10x greater than the one right of it.
a furlong is a distance of 180 yards. a fortnight is a time period of two weeks. a race horse is running at a speed of 7 yards per second. what is his speed in furlongs per fortnight?
Answers
The race horse's speed is approximately 256 furlongs per fortnight.
To determine the race horse's speed in furlongs per fortnight, we need to convert both the distance and time units to their respective values.
1 furlong is equal to 180 yards, so the horse's speed in yards per second (7 yards/second) can be converted to furlongs per second:
Speed in furlongs per second = (7 yards/second) / (180 yards/furlong) = 7/180 furlongs/second
Next, we need to convert the time from seconds to fortnights. Since a fortnight is a time period of two weeks, and there are 7 days in a week, a fortnight consists of 14 days:
Time in seconds per fortnight = (14 days/fortnight) * (24 hours/day) * (60 minutes/hour) * (60 seconds/minute) = 1,209,600 seconds/fortnight
Finally, we can calculate the horse's speed in furlongs per fortnight by multiplying the speed in furlongs per second by the time in seconds per fortnight:
Speed in furlongs per fortnight = (7/180 furlongs/second) * (1,209,600 seconds/fortnight) = 46,080/180 furlongs/fortnight ≈ 256 furlongs/fortnight
The race horse's speed is approximately 256 furlongs per fortnight.
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Find the average rate of change for the function f(x) =x^2 -6x+2 on the closed side interval (-5,2)
Answers
Answer:
- 9
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
\(\frac{f(b)-f(a)}{b-a}\)
Here [a, b ] = [ - 5, 2 ], thus
f(b) = f(2) = 2² - 6(2) + 2 = 4 - 12 + 2 = - 6
f(a) = f(- 5) = (- 5)² - 6(- 5) + 2 = 25 + 30 + 2 = 57 , thus
average rate of change = \(\frac{-6-57}{2-(-5)}\) = \(\frac{-63}{7}\) = - 9
a normal distribution has a mean of µ = 70 with σ = 12. if one score is randomly selected from this distribution, what is the probability that the score will be less than x = 76?
Answers
The probability that a randomly selected score from this normal distribution is less than x = 76 is 0.6915
To find the probability that a randomly selected score from a normal distribution with mean µ = 70 and standard deviation σ = 12 is less than x = 76,
we need to use the standard normal distribution and calculate the z-score corresponding to x = 76, and then look up the corresponding area under the standard normal curve using a standard normal distribution table.
The z-score is calculated as:
z = (x - µ) / σ
z = (76 - 70) / 12
z = 0.5
By using a standard normal distribution table, we can find the area under the curve to the left of z = 0.5, which is 0.6915.
Therefore, the probability that a randomly selected score from this normal distribution is less than x = 76 is 0.6915 or approximately 69.15%.
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PLS HELP ASAP ILL GIVE BRAINLKEST PLS THANKS PLS
Answers
Answer:
I believe number 9 is the middle answer
Step-by-step explanation:
please correct me if I'm wrong
Mark wants to fence 4 rectangular gardens, each with a length of 9 1/4 feet and a width of 4 1/2feet. What is the length of fencing mark needs to surround all 4 gardens
Answers
Answer:
110 ft
Step-by-step explanation:
The length of fencing is four times the perimeter of one garden.
The formula for the perimeter of a rectangle is
P = 2l + 2w
The total perimeter for all four rectangles is
P = 4× (2l + 2w) = 8l + 8w
Data:
l = 9¼ ft
w = 4½ ft
Calculation:
P = 8l + 8w = 8×9¼ + 8×4½ = 72⁸/₄ + 32⁸/₂ =(72 + 2) + (32 + 4) = 74 + 36 = 110 ft
The total length of fencing is 110 ft.
can some one give me a hand here???????
Answers
At the sewing store, Natalie bought a bag of mixed buttons. The bag included 15 buttons, of which 40% were large. How many large buttons did Natalie get?
Answers
Answer:
6
Step-by-step explanation:
The bag included 15 buttons, of which 40% were large means 40% of 15
40% = 40/100 = 2/5 = 0.4
Of = multiply
40% of 15 = 0.4 * 15
0.4 * 15 = 6
The answer is 6 large buttons
Hope this helps :)
Have an awesome day!
Identify the transformation from c to d. A) 360 rotation,B) 270 Clockwise Rotation,C) 90 Clockwise rotation,D) 180 rotation?
Answers
Answer:
A) 360 rotation
Step-by-step explanation:
Answer:
360
Step-by-step explanation:
PLEASE HELP QUICKLY!!! Use the following image to answer the questions below:
Answers
2000 restaurants will grow about 3% every year, what is the equation that represents it. Y = restaurants and t = years
Answers
Answer:
Y= PV*(1 + g)^t
Step-by-step explanation:
Giving the following information:
Number of Restaurants (PV)= 2,000
Growth rate (g)= 3%
To calculate the number of restaurants after t years, we need to use the following formula:
Y= PV*(1 + g)^t
For example, for 10 years:
Y= 2,000*(1.03^10)
Y= 2,688
Find the inverse Laplace transform 5s +2 L-1 (s² + 6s +13) 1-5e-3t cos 2t - 12e-3t sin 2t Option 1 3-5e-3t cos 2t - 6 e³t sin 2t Option 3 13 2-e³t cos 2t - ¹2e-3t sin 2t Option 2 4-5e-3t cos 2t + 6 e³t sin 2t
Answers
3) the inverse Laplace transform is 13 - 2e^(-3t) cos 2t - (1/2) e^(-3t) sin 2t.
Given:
L-1(5s + 2/(s² + 6s + 13))
= (1-5e^(-3t) cos 2t - 12e^(-3t) sin 2t)
We can find the inverse Laplace transform as follows:
L-1(5s + 2/(s² + 6s + 13))
= L-1(5s/(s² + 6s + 13) + 2/(s² + 6s + 13))
L-1(5s/(s² + 6s + 13)) + L-1(2/(s² + 6s + 13))
Applying partial fractions for L-1(5s/(s² + 6s + 13)):
5s/(s² + 6s + 13)
= A(s + 3)/(s² + 6s + 13) + B(s + 3)/(s² + 6s + 13)A
= (-2 - 9i)/10 and B = (-2 + 9i)/10
Therefore,
L-1(5s/(s² + 6s + 13))
= (-2 - 9i)/10 L-1((s + 3)/(s² + 6s + 13)) + (-2 + 9i)/10 L-1((s + 3)/(s² + 6s + 13))
= (-2 - 9i)/10 L-1((s + 3)/(s² + 6s + 13)) + (-2 + 9i)/10 L-1((s + 3)/(s² + 6s + 13))
= (1-5e^(-3t) cos 2t - 12e^(-3t) sin 2t)L-1((s + 3)/(s² + 6s + 13))
= L-1(1/(s² + 6s + 13)) - 5 L-1(e^(-3t) cos 2t) - 12 L-1(e^(-3t) sin 2t)
Applying the inverse Laplace transform for 1/(s² + 6s + 13),
we get:
L-1(1/(s² + 6s + 13)) = (1/3) e^(-3t) sin 2t
The inverse Laplace transform of e^(-3t) cos 2t and e^(-3t) sin 2t are given by:
(L-1(e^(-3t) cos 2t))
= (s + 3)/((s + 3)² + 4²) and (L-1(e^(-3t) sin 2t))
= 4/((s + 3)² + 4²)
Substituting all the values in L-1((s + 3)/(s² + 6s + 13))
= L-1(1/(s² + 6s + 13)) - 5 L-1(e^(-3t) cos 2t) - 12 L-1(e^(-3t) sin 2t)
We get,
L-1((s + 3)/(s² + 6s + 13))
= (1/3) e^(-3t) sin 2t - 5(s + 3)/((s + 3)² + 4²) - (24/((s + 3)² + 4²))
Therefore,
L-1(5s + 2/(s² + 6s + 13))
= (-2 - 9i)/10 ((1/3) e^(-3t) sin 2t - 5(s + 3)/((s + 3)² + 4²) - (24/((s + 3)² + 4²)))
Option 3 is correct: 13 - 2e^(-3t) cos 2t - (1/2) e^(-3t) sin 2t.
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Asia has 3 days to complete all 6 of her over due math assessments. Each day one more assessment is added on. How many assignments will Asia have to do per day to be done with her overdue assignments?
Answers
Answer:
3 a day.
Step-by-step explanation: