There's one triangle satisfying angle BCA = 60 degrees, AB = 12 and AC = 10 shown below:
The only possible value of BC is a, as shown above. What is a?
Please don't round your answer. Keep it as a square root.
Answers
Answer:
see attached
Step-by-step explanation:
you need to create 2 right angle triangles
one on the left has 60° which makes it a special right angle triangle with the property of the following:
the side that's opposing the 30° angle will be 1/2 of the long side,
the side that's adjacent to the 30° angle will be √3/2 of the long side
once you know these, the rest is easy
Answer:
a = 5 + √69
Step-by-step explanation:
I am just providing another way of solving this. The answer provided by user elzny is absolutely correct and probably easier to understand. He has done a great job.
We can solve for a using the law of cosines which states that given, two sides of a triangle(say a and b) and an included angle (say C), the third side, c can be determined by the relation:
c² = a² + b² -2ab(cosC)
or
a² + b² -2ab(cosC) = c²
If we look at the triangle we see that angle C measures 60° and the two sides that include this angle are of lengths 10 and a. The third side is 12
Plugging in these values into the equation,
10² + a² - 2(10)(a)(cos 60) = 12²
100 + a² -20a(cos 60) = 144
cos 60 = 1/2
So
100 + a² - 20a (1/2) = 144
(100 - 144) + a² - 10a = 0
a² -10a -44 = 0
This is a quadratic equation which can be solved to get two values for a
The solution to this quadratic equation is done using the quadratic formula
[tex]x = \dfrac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }[/tex]
where
a = coefficient of x² = 1 in this problemb = coefficient of x = -10 in this problemc = constant = -44Plugging in these values,
[tex]x = \dfrac{ -(-10) \pm \sqrt{(-10)^2 - 4(1)(-44)}}{ 2(1) }\\\\x = \dfrac{ 10 \pm \sqrt{100 - (-176)}}{ 2 }\\\\x = \dfrac{10}{2} \pm \dfrac{\sqrt{276}}{2}}[/tex]
Factor 276 to get 276 = 4 x 69
[tex]\sqrt{276} = \sqrt{4 \cdot 69} = \sqrt{4} \cdot \sqrt{69} = 2 \sqrt{69}[/tex]
This results in
[tex]x = \dfrac{ 10 }{ 2 } \pm \dfrac{2\sqrt{69}\, }{ 2 }\\\\x = 5 \pm \sqrt{69}\\\\[/tex]
[tex]\sqrt{69}[/tex] is greater than 5 so we take only the positive component which is
[tex]5 + \sqrt{69}[/tex]
Which is the same answer as what elzny provided.
The pro of this methodology:
Direct implementation without splitting the triangle
The con:
You have to solve a quadratic equation which is not fun. But most scientific calculators can do this for you
Thanks!
Related Questions
Emily noticed that on halloween, her child got three basic types of candy: chocolate, gummy, and hard candy. She has 15 more hard candies that chocolate, and 5 less than twice the amount for gummy candy than chocolate. if she had a total of 178 pieces of candy, how many of each type did she get?
Answers
Answer: gotta scroll down sry
Step-by-step explanation:
First set up equations with variables that show the information you have:
c = chocolate // g = gummy // h = hard candy
178 = c + g + h
h = c + 15
g = 2c - 5
Then, solve all the equations for a number:
178 = c + g + h (leave as is)
15 = -c + h (subtract 'c' from the original equation's right side and switch the sides of the equation)
-5 = -2c + g (subtract '2c' from the original equation's right side and switch the side of the equation)
Then, line up all the variables and subtract the top equation by the lower two:
178 = c + g + h
15 = -c + 0g + h
-5 = -2c + g + 0h
---------------------------
168 = 4c + 0g + 0h >>>> 168 = 4c
Solve for 'c' and plug it into the other equations to find 'h' and 'g':
168/4 = 4c/4
42 = c
15 = -(42) + h -5 = -2(42) +g
57 = h 79 = g
Add all the numbers together to double-check:
42 + 57 + 79 = 178
chocolates = 42
gummies = 79
hard candies = 57
(a) Reflect the point (7,9) across the x-axis
(b) Reflect the point (7,9) across the y-axis
Answers
(b) When we reflect (7,9) across the y-axis, we would get (-7,9)
I got my answer by understanding the reflection graph rule:
When you reflect a point across the x-axis, the x-axis will stay the same; however for the y-axis, we have to change the sign to its opposite. The term “reflect x-axis” means that we go across the x-axis. Therefore the x-axis stays the same, while the y-axis sign changes.
When you reflect a point across the y-axis, the y-axis will stay the same; however for the x-axis, we have to change the sign to its opposite. The term “reflect y-axis” means that we go across the y-axis. Hence why the y-axis stays the same, while the x-axis sign changes.
Make word problems with the following equations:
1) 8 - ( - 3)
2) 2 - 8
3) Design your own problem, make it difficult with a number line visual and a word problem.
Answers
Dan and Clair both have 0.00$ in their bank accounts. Dan works 5 days a week with 10.00$ per hour and he works 10 hours. Dan brings home 500$ each week and puts 250$ in his bank account. He spends 200$ on a vacation and spends 42$ on food. Clair doesn’t work that much. She spends most of her days babysitting. She get 5$ per hour and is their once a week for three hours. She gets 15$ a week and puts it in her account and spend 18$ . What is the difference from Dans bank account money to Clair’s?
Hope it helps.
ANSWER BEFORE 2/6 PLS!!!!
At Washington Elementary School, the sixth grade teachers are giving a prize to each student who does all their homework for a week. Mr. Price is trying to figure out how many students are in sixth grade so that he knows how many : prizes to buy. There are 26 kids in Ms. Wright's class, 28 kids in Mrs. Lynn's class, 25 kids in Ms. Render's class, and 27 kids in Mr. Price's class. Mr. Price goes to the store and buys 13 bags. In each bag there are 11 prizes. In Ms. Wright's class, 1/2 of the students did all of their homework. In Mrs. Lynn's class, 3/4 of the students did all of their homework. In Ms. Render's class, 4/5 of the students did all of their homework. In Mr. Price's class, 7/9 of the students did all of their homework. Mr. Price takes the remaining prizes and gives half of them to the fifth grade teachers. How many prizes did Mr. Price give to fifth grade?
Answers
Answer:
89
Step-by-step explanation:
because yes
I need help please.
This work is fractions
Answers
Answer:
Step-by-step explanation:
help me with this please ASAP!!
Answers
Find and interpret the marginal frequencies. Cell Phone Company A B Data Plan Limited 78 94 Unlimited 175 135 people have a limited data plan. people have an unlimited data plan. people use Company A. people use Company B. people were surveyed. Skip to navigation
Answers
Answer:
78
Step-by-step explanation:
78
Reflect the point (-3,-8) across the y-axis
Reflect the point (-3,-8) across the x-axis
Answers
Step-by-step explanation:
When reflecting a point across an axis, that means the opposite coordinate will switch signs.
Reflecting a point across the YAXIS means that the X coordinate will switch signs
Reflecting a point across the XAXIS means that the Y coordinate will switch signs
Taking (-3, -8)....
Reflecting it across the y-axis, we will flip the sign of the X coordinate. It's -3, so we make that +3, giving us
(3, -8)
Reflecting across the x-axis, we will flip the sign of the Y coordinate. it's -8, so we make that +8, giving us
(-3, 8)
Just put 2 expressions and thats it
Answers
Answer: 20 minuse n
Step-by-step explanation:
the difference of 20 and n
HELP PLEASE Three cylinders have a height of 8 cm.... Find the volume of each cylinder. Round all answers to the nearest hundredth. Use 3.14 for pi.
Answers
Step-by-step explanation:
Just use the equation for volume of a cylinder
For cylinder 1
V=(3.14)r^2h
V=(3.14)1^2(8)
V=(3.14)(1)(8)
V=25.12 cm
For cylinder 2
V=(3.14)r^2(h)
V=(3.14)(2^2)(8)
V=(3.14)(4)(8)
V=100.48 cm
For cylinder 3
V=(3.14)r^2(h)
V=(3.14)(3^2)(8)
V=(3.14)(9)(8)
V=226.08cm
If your confused or have a question just ask
Hope this helped :)
Answer:
Step-by-step explanation:
The volume of the cylinder is calculated by multiplying the area of its base by its height. The height of the cylinder is 8 inches (the height of the cube through which it is being drilled). Therefore, its volume is πr2h = π * 3.752 * 12 = 168.75π in3.
i don't know how to do this onee please help
Answers
Answer:
A
w = 85
Step-by-step explanation:
To find out the number you can divided 102 by 1.2 and you get 85 meaning 85 is the answer.
Answer:
A;
Step-by-step explanation:
120% = 1.2 (decimal form)
Therefore: 1.2 x w = 102 or 102 = 1.2 x w
102 = 1.2 x w
Divide both sides by 1.2 to get:
100 = w
Please help me with this maths question
Answers
-, x=-3, y=-1
2
substitute X=-3, y=-1 -1 is the answer
In 9 hours Ali reads 63 chapters of a book. What is his rate in chapters per hour?
Answers
Answer: 7
Step-by-step explanation:
In 9 hours, Ali can read 63 chapters. To find how many chapters, on average, he can read per hour, we divide 63 by 9 to get 7.
This is how we put it as an equation:
[tex]9 hours = 63 chapters\\1 hour = \frac{63}{9} chapters \\1 hour = 7 chapters[/tex]
If you still have questions, please reply back, I will help you as much as I can :)
Suppose you have two bank accounts. In Account A you deposit $100. In Account B you deposit $300. Account A has a simple interest rate of 4.3%. Account B has a simple interest rate of 2.1%. One year later, you get a bank statement from each bank and one of the statements shows an incorrect amount of interest. The interest for Account A is $4.30. The interest for Account B is $630. Which account statement is incorrect? Find the bank's likely error.
Answers
The interest for Account B is likely incorrect.
The interest for Account A can be calculated as follows:
$100 * 4.3% = $4.30
The interest for Account B should be calculated as follows:
$300 * 2.1% = $6.30
Since the interest for Account B is much higher than it should be, the statement from that account is likely incorrect. The bank's likely error is overstating the interest earned on Account B.
75% of what number is 24? Show your work or explain how you arrived at your answer.
Answers
24=3x/4
24 x 4/3 = x
answer is 32!
A four-sided figure is resized to create a scaled copy. The proportional relationship between any given side length in the original figure, f, and the corresponding side length in the scaled copy, s, can be represented by the equation
s
=
1
6
f
s=
6
1
f. What is the scale factor from the original figure to the scaled copy?
Answers
Answer: 12:1
Step-by-step explanation:
A four-sided figure is resized to create a scaled copy. The proportional relationship between any given side length in the original figure, , and the corresponding side length in the scaled copy, , can be represented by the equation . What is the scale factor from the original figure to the scaled cop
Nick had some candy to give his three children He first took five pieces for himself and then evenly divided the rest among his children Each child received four pieces How many pieces did he start with?
Answers
Answer:
Step-by-step explanation:
5 + (x divided by 3) 3 times 4 is 12
12+5=17
P=(4)(3)+5
P=17
Proportional or not?
Equation=_____
Answers
Knowing this, we’re able to use the equation -
y = 3x
Hopefully this made sense! If you have any questions, please ask. Have a great day!
y = 3x
Jennifer sold 2 fewer than 3 times as many candy bars as Catherine sold. If the total number of candy bars that they sold was 30, how many candy bars did Jennifer sell?
Answers
Answer:
18
Step-by-step explanation:
10*3 = 30 - 2 = 18
Question 5(Multiple Choice Worth 2 points)
(Rotations MC)
Use the graph to answer the question.
graph of polygon ABCD with vertices at 0 comma 0, 5 comma 2, 5 comma negative 5, 0 comma negative 3
Determine the coordinates of polygon A′B′C′D′ if polygon ABCD is rotated 270° counterclockwise.
A′(0, 0), B′(−2, 5), C′(5, 5), D′(3, 0)
A′(0, 0), B′(2, −5), C′(−5, −5), D′(−3, 0)
A′(0, 0), B′(−5, −2), C′(5, −5), D′(3, 0)
A′(0, 0), B′(−5, −2), C′(−5, 5), D′(0, 3)
Answers
Answer:
23
############################
Answer: The answer the second option
Step-by-step explanation:Because since 270 degrees counterclockwise is equal to 90 clockwise you would use the 90 formula and swap the x and y and add a negative to the x and if you do that with each on the second d option should match you answer exactly.
P.S Also, I know this is absolutely correct because I took the test and got a 100, and I hope this helps you in the future to understand a question similar to this without any help, you got this and I hope you have a wonderful day or night :)
Brainliest:Cube A has a side length of 4 cm. Cube B has sides that are twice as long as Cube A. Find the volumes of Cube A and Cube B.
Answers
Answer:
Step-by-step explanation:
96 sq. cm. for cube a and cube b is 192sq cm
Answer:
Cube A: 64³ cm
Cube B: 512³ cm
Step-by-step explanation:
Since we know these figures are cubes, we only need to know the length of one side, 4. To find Cube A’s volume, we multiply 4 times 4 times 4 to get 64. Cube A has a volume of 64³ cm.
We know Cube B’s sides are twice as long as Cube A, so they have to be 8 cm. 8 times 8 times 8 is 512. Cube B has a volume of 512³ cm.
The Pythagorean Theorem and its Converse
1-5
Please answer all questions and solve step by step and please try to show/explain with the least words as possible and use mostly numbers to for explain there can still be some words tho.
Answers
The radius of the base of the cone is √189 ft.
What is the Pythagorean theorem?In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. The theorem can be used to determine how steep mountains or slopes are. To calculate the distance between an observer and a location on the ground when the observer is looking down from a tower or structure. It is mostly utilized in the construction industry.
For question 5 :
Given a right-angle triangle that has a hypotenuse of 14 and a base is 9 cm.
From the Pythagorean theorem:
Hypotaneuse² = base² + height²
14² = 9² + height²
height² = 196 - 81
height² = 115
height = √115
For question 4:
The distance from the top of the cone to the edge is 15 feet. The height of the cone is 6 feet.
The radius of the cone = base pf right angle triangle
From the Pythagorean theorem:
Hypotaneuse² = base² + height²
15² = base² + 6²
225 - 36 = base²
base = √189
For question 3:
The distance from the plane to the airport is = 3.35 * 10,000ft
for Question 2:
the height of the television will be 15.65 inches
Learn more about the Pythagorean theorem here:
https://brainly.com/question/10174253
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what do you think the deffinition of woman is ???
( Just something fun to see how people think of this. )
Answers
Answer:A woman is an adult female human. Prior to adulthood, a female human is referred to as a girl (a female child or adolescent). The plural women is sometimes used in certain phrases such as "women's rights" to denote female humans regardless of age.
Step-by-step explanation:
Answer:
An adult female human being.
Jayce is buying a used car. He plans to split the cost into monthly payments over the next 48 months. If each payment is $128.76, how much will Jayce pay for the car in all?
Answers
Answer: 6180.48
Step-by-step explanation:
Based on the given conditions, formulate: 48*128.76
Calculate the product or quotient: 6180.48
get the result: 6180.48
Answer: 6180.48
Don't forget to give a thanks:)
Answer:
6180.48
Step-by-step explanation:
Because 128.76 times 48 is $6180.48. So in all jayce will pay $6180.48
your are welcome.
Daniel volunteers on the weekend at the Central Library. As a school project, he decides to record how many people visit the library, and where they go. On Saturday, 457 people went to The Youth Wing, 468 people went to Social Issues, and 348 went to Fiction and Literature.
On Sunday, the library had 300 total visitors. Based on what Daniel had recorded on Saturday, about how many people should be expected to go to Social Issues? Round your answer to the nearest whole number.
Answers
Answer:the answer is 15000000000.
Step-by-step explanation: 457 turns to 500 because of 5.
468 turns to 500 because of 6.
348 turns to 200 because of 4.
300 turns to 300 because of 0.
500 x 200 x 500 x 300 = 15000000000
Apollo traveled 54 leagues in 3 days. Then he tripled his rate. How long would it take him to travel 594 leagues at this new speed?
Answers
Answer:
11 days
Step-by-step explanation:
First, you have to find the original rate. Then, multiply that by three. Lastly, take 594 and divide by the tripled number.
54 ÷ 3 = 18
18 x 3 = 54
594 ÷ 54 = 11
Simplify 2x + 5(- 7x - 8) - 10
Answers
……………………..,……..
You have 2 different savings accounts. For Account A, the simple interest earned after 9 months is $6.75. For Account B, the simple interest earned after 21 months is $19.25. If the interest rate is 3.6% for Account A and 2.2% for Account B, how much is the principal in each account? Which account earned you the most interest the first month? Explain your answer.
Answers
Answer:
Account A Principal: $250
Account B Principal : $500
Account B earned $0.17 more interest in the first month
Step-by-step explanation:
Let the principal in account A be PA and the principal in account B be PB
Simple interest I = Prt where P is principal, r is interest rate (in decimal) and t - time in years
Therefore, given interest I
P = I/rt
We will assume both interest rates are annual interest rates
For account A, interest = 3.6% per year
This works out to 0.036 per year
For account B, interest = 2.2% which works out to 2.2/100 per year = 0.022 per year
Account A
I = 6.75, r = 0.036 t = 9 months = 9/12 year = 3/4 year = 0.75 year
PA = 6.75/(0.036 x 0.75) = $ 250.00
Account B
I = 19,25, r = 0.022, t = 21/12 = 1.75 years
PB = 19.25/(0.022 x 1.75) = P = $ 500.00
Account A interest earned per month = 6.75/9 = $0.75
Account B interest earned per month = 19.25/21 = $0.92
Hence account B earned more interest in the first month
The amount of interest earned by account B over account A
= 0.92 = 0.75 = $0.17
Three out of 5 students at Maria's school participate in a school club or sport. There are 475 students at marias school how many of them can be expected to participate in a school club or sport
Answers
So, the expected number of participating students is:
475 * (3/5) = 285.
Therefore, we can expect 285 students out of 475 to participate in a school club or sport.
Find the missing angles measurements pt. 2
6-10
(I point for each question)
Please answer all questions and solve step by step and please try to show/explain with the least words as possible and use mostly numbers to for explain there can still be some words tho.
Answers
Answer:
Step-by-step explanation:
Angle 5: 55
Angle 6: 125
Angle 7: 55
Angle 8: 125
Hope this helps.
the value of the x and y for the given system of equations are 6, and -2 respectively.
What are Systems of equations?Simultaneous equations, a system of equations Two or more equations in algebra must be solved jointly (i.e., the solution must satisfy all the equations in the system). The number of equations must match the number of unknowns for a system to have a singular solution.
There are four methods for solving systems of equations: graphing, substitution, elimination, and matrices.
Given, a system of equations
2x + 5y = 2
2x - 5y = 22
Adding both equations:
4x = 24
x = 6
From equation 1
2 * 6 + 5y = 2
5y = -10
y = -2
Therefore, the value of the x and y for the given system of equations are 6, and -2 respectively.
Learn more about the System of equations here:
https://brainly.com/question/12628931
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