Using isosceles triangle theorems solve for x and y
To solve for x and y in a right triangle, use the Pythagorean Theorem (x² + y² = h²) and trigonometric relationships (x = hcosΘ and y = hsinΘ). The Isosceles Triangle Theorem, which states the base angles of an isosceles triangle are equal, isn't directly used to solve for x and y.
Explanation:In solving for x and y using isosceles triangle theorems, we often utilize the Pythagorean Theorem and trigonometric relationships. Since this involves a right triangle, where x is the adjacent side, y is the opposite side, and h is the hypotenuse, we can use the formula for the Pythagorean Theorem, x² + y² = h².
To find x, we rearrange the trigonometric definition of cosine (cosΘ= x/h) to get x = hcosΘ. Similarly, we can find y using the definition of sine (sinΘ = y/h) and get y = hsinΘ. These solutions use trigonometry.
Keep in mind, the Isosceles Triangle Theorem states that the base angles of an isosceles triangle (a triangle with at least two equal sides) are equal. However, this theorem isn't directly involved in solving for x and y. Instead, the trigonometric relationships and Pythagorean Theorem solves for these values within a right triangle.
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15 points!
Solve. 1/3r + 1 = −2/3r − 2 Drag and drop the answer into the box.
a. -3
b. -1/3
c. 2/3
d. 18
r = ???
Please help and thanks!
Answer: a -3
Step-by-step explanation:
Tristan bought an orange that weighs 1/5 pound. He cut the orange into 8 slices. How much does each orange slice weigh?
Answer:
1/40 pound
Step-by-step explanation:
The graph shows the number of laps that Jan runs as her coach times her.
What is the slope of the line and what does it mean in this situation?
Select from the drop-down menus to correctly complete each statement.
The slope of the line is_ .
This means that Jan runs _ laps every_minutes .
Answer:
Jan run 2 laps every minute
Step-by-step explanation:
A laboratory culture contains 150 bacteria. After twenty minutes, the culture contains 300 bacteria. After one hour, the culture contains 1200 bacteria. Make a conjecture about the rate at which the bacteria increases
The bacteria in your culture appear to be experiencing exponential growth, doubling in population size every 20 minutes. This is common in organisms that reproduce by binary fission like bacteria, but the growth rate can be influenced by various environmental factors.
Explanation:Based on your data, the number of bacteria in your culture seems to double every 20 minutes. This type of growth pattern is known as exponential growth, which is common in prokaryotes and other organisms that reproduce by binary fission.
For example, if you were to start with 1000 bacteria in a nutrient-rich environment, after one hour (or three 20-minute intervals), each bacterial cell would've divided several times, increasing the total population size from 1000 to 8000. This is based on the principle that in exponential growth, the number of new organisms added to the population in each round of division (or generation) increases as the population size increases. This results in a 'J-shaped' growth curve when plotted over time, illustrating the increasing rate of population growth.
However, please note that in reality, bacterial growth is influenced by several factors including nutrient availability and environmental conditions and the growth rate may not remain constant over time. For a more accurate analysis, you could take readings at more frequent intervals and plot a graph of population size versus time to observe the growth pattern.
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I need help I don't understand this!!
How to convert 14520 millimeters to liters?Report to the nearest hundredth of a liter.
What is the greatest number of points of intersection that can occur when 2 different circles and 2 different straight lines are drawn on the same piece of paper.
Answer:
11
Step-by-step explanation:
Make a diagram. Two geometric figures intersect if they have one or more points in common. Draw two circles which intersect in points. Draw a line which intersects the two circles in points. Draw another line which intersects the two circles in points and also intersects the first line. There are 11 points of intersection.
What was the biggest decrease in time from the 1st leg to the 2nd leg?? Relay scores
the high school marching band rehearses with either 6 or 10 members in every line.What is the smallest number of people who can be in the marching band?
Answer:
The smallest number of people who can be in the marching band are 30.
Step-by-step explanation:
The high school marching band rehearses with either 6 or 10 members in every line.
To get the smallest number of people who can be in the marching band, we will find the LCM of 6 and 10.
6 = 2 x 3
10 = 2 x 5
The LCM is 2 x 3 x 5 = 30.
Hence, the smallest number of people who can be in the marching band are 30.
If the students are 6 in each line, then there will be 5 lines in total.
If the students are 10 in each line, there will be 3 lines in total.
Tim mixed 2 parts vinegar and 5 parts water to make a cleaning liquid. How many parts of vinegar did Tim mix with each part of water?
one over ten
one over five
two over seven
two over five
Answer:
2/5
Step-by-step explanation:
What is the missing term in the factorization?
12x^2-75=3(2x+?)(2x-5)
Can anybody help me asap please?
Thank you
One day, a king left his castle with a bag of silver coins to wander his kingdom. to the first peasant he met, he gave one-half of the coins plus two more. A little later, he met another peasant to whom he also gave one-half of his coins plus two more. Walking on, he met a third peasant and again gave half his coins plus two more. FInally, the king went home with two coins left in his bag. How many coins did he have to begin with? Create an algebraic equation. Please explain why.
Answer:
The king left his castle with 44 silver coins.
Step-by-step explanation:
A king left his castle with a bag of silver coins and he gave his coins to 3 peasants in an order. Finally he went home with two coins left.
To solve this question we calculate it in reverse order.
Finally the king has in his bag = 2 coins
Before it he met third peasant king had =
= (2+2) × 2
= 4×2 = 8
Before the king met third peasant, he had 8 coins.
Before he met Second peasant king had :
= (8+2) × 2
= 10 × 2 = 20
Before he met second peasant king had 20 coins.
Before he met first peasant he had :
= (20+ 2) × 2
= 22 × 2 = 44
Before King met first peasant he had 44 silver coins.
Alec is trying to find the surface area of a shoe box. What unit will he use?
A) cubic feet
B) square feet
C) cubic inches
D) square inches
There were 58 adults who completed the 16-mile charity bike ride. There were 65 (1 pt) children who completed the 10-mile charity bike ride. What is the total number of miles ridden by all the adults and children in the bike
can someone help me with these 3
Figure ABCD is a parallelogram with point C (3, −2). Figure ABCD is rotated 90° counterclockwise to form figure A′B′C′D′. What coordinate would be the output for point C'?
The floor of the commons room at King Middle School is in the shape of a square with side lengths of x^2 y^3 feet. New tile is going to be put on the floor of the room. Find the area of the floor.
(0,0), (1,5), (2,20), (3,45), (4,80) what's the rule?
Which doubles fact can help you solve 4+5=?
The question seeks an applicable double fact to help solve 4+5, however, no exact double fact would provide the precise result because they pertain only to pairs of the same number. The closest double fact is 4+4, and though this is not an exact match, it helps to get a ballpark figure.
Explanation:The question asks: Which doubles fact can help you solve 4+5=? In this case, you might think of using the double fact of 4+4. Although it's not exactly the same as 4+5, it's close and can give you a good guess. However, no exact double fact would help you to get the exact answer to 4+5 because these are two different numbers. The sum of 4+5 equals to 9. The purpose of double facts is to aid in mental mathematics by recalling the results of certain simple additions, but only pairs of the same number are used;
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Evaluate the following expression using the values given:
Find 4x − y − 2z if x = −2, y = 3, and z = −2
−15
15
−7
7
Write a real world situation that could be modeles by the equation 8+2x=6x.Then solve the problem
A real-world situation that could be modeled by the equation 8+2x=6x is a scenario where you have a certain amount of money and you are earning a fixed amount of money per hour. By solving the equation, you can determine how many hours it will take for your earned money to equal the given amount of money. To solve the problem, isolate the variable x by subtracting 2x from both sides and dividing both sides by 4.
Explanation:A real-world situation that could be modeled by the equation 8+2x=6x is a scenario where you have a certain amount of money and you are earning a fixed amount of money per hour. Let's say you have $8 and you are earning $2 per hour. On the other side, you have $6 and you are earning $6 per hour. By solving the equation, you can determine how many hours it will take for your earned money to equal the given amount of money.
To solve the problem, you need to isolate the variable x. Start by subtracting 2x from both sides to get 8 = 4x. Then, divide both sides by 4 to get x = 2. Therefore, it will take 2 hours for your earned money to equal $6.
Grade 9 mathematics please help asap. Thank you so much!!!
Taylor buys 6 bus tickets. He pays for the tickets with a $20 bill. Let c represent the cost of each ticket. Which expression shows how much change Taylor will receive?
Answer:
(20 - 6c)
Step-by-step explanation:
Taylor buys bus tickets = 6
Let the cost of the one ticket = c
Cost of 6 tickets = $6c
If Taylor has paid $20 for these 6 tickets then the change he will receive = $20 - $6c
Therefore, the expression to calculate the change Taylor will receive will be
(20 - 6c)
angles x and y are supplementary.angle x is 3 times the measure of angle y what is the measure of angle x
What is the change in temperature from -8°F to 14°F?
In a 50-question test, the highest score in the class is three times the lowest score minus four. The difference between the highest score and the lowest score is 30. What is the highest score?
The highest score on the test is 47, found by setting up and solving a system of equations based on the information given in the question.
Explanation:The problem described in the question can be solved using algebra. Let's denote the highest score as H and the lowest score as L. According to the question, we have two equations:
H = 3L - 4 H - L = 30.
We can solve this system of equations step by step. Since both equations have H, they can be set equal to each other: 3L - 4 = 30 + L. If you simplify this equation by subtracting L from both sides, you get 2L - 4 = 30. Then add 4 to both sides to isolate 2L on one side: 2L = 34. Divide both sides by 2, to solve for L: L = 17. Then substitute L into one of your original equations (H = 3L - 4), so H = 3*17 - 4 = 51 - 4 = 47. So, the highest test score is 47.
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Math help please!! ^o^
Answer: I say c too. I trust you with that answer.
Step-by-step explanation:
Is this the correct answer? Am I missing anything? Do I need to delete anything?
It should be congruent angles, for "congruent angles" are angles that have the same measures
vertical angles measurements are also equal, however, you want to be as broad as possible
hope this helps
Female elk can weigh up to six hundred pounds. In standard form, how many non-zero digits does this weight contain