Explain how you would solve a triangles given two sides and the included angle?
To solve a triangle given two sides and included angle, use the law of cosines. This law is expressed as a² = b² + c² - 2bc cos(A), where a, b, c are the lengths of the sides, and A is the included angle.
Explanation:To solve a triangle given two sides and the included angle, you would use the Law of Cosines. This law is used when you're given two sides and the included angle in a triangle (often abbreviated as SAS). The law states,
a² = b² + c² - 2bc cos(A)
where a, b, and c are the lengths of the sides of the triangle, and A is the included angle. So, in this case, if you're given sides b and c and included angle A, you would substitute these values into the formula to find side a.
For instance, if side b is 3 units, side c is 4 units, and angle A is 60 degrees, we would substitute these values into our formula like so: a² = 3² + 4² - 2(3)(4) cos(60).
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The correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.
Solving triangles using the sine and cosine ruleFor angle placed in between two sides of a triangle, we can use the cosine rule to determine the unknown angle
According to the cosine formula, we will have:
[tex]a^2=b^2+c^2-2bc \ cos\theta[/tex]
where a, and c are the sides of the triangle and theta is the central angle.
Also, the remaining angles can be determined using the law of cosines as shown:
a/sinA = b/sinB = c/sinC
Hence the correct way to solve a triangles given two sides and the included angle is by the sine and cosine rule.
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Four family members compared their ages. Terell is 3 years younger than Danny. Danny is 1 year younger that Pablo. Pablo's age is 1/3 Shaniqua age. How old is Terell if shaniqua is 36 years old?
Suppose 6000 is placed in an account that pays 3% interest compounded each year. Assumed that no withdrawals are made from the account .
Find the amount at the end of one year ?
Find the amount in the account at the end of two year .
Final answer:
With a principal amount of $6000 and a 3% annual interest rate compounded yearly, the account balance at the end of one year will be $6180, and at the end of two years, it will be $6365.40.
Explanation:
To calculate the amount of money in an account with compounded interest, we can use the formula [tex]A = P(1 + r/n)^{(nt)[/tex], where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate (decimal), n is the number of times the interest is compounded per year, and t is the time the money is invested for in years.
For the student's case, with $6000 placed in an account at 3% interest compounded each year with no withdrawals:
To find the amount at the end of one year, we calculate it as [tex]A = 6000(1 + 0.03/1)^{(1\times 1)[/tex], which equals $6000 × 1.03 = $6180.To find the amount at the end of two years, [tex]A = 6000(1 + 0.03/1)^{(1\times 2)[/tex], giving us $6000 × 1.03² = $6365.40.As such, after one year, the student would have $6180, and after two years, the balance would be $6365.40.
10 POINTS
Solve the combined inequality:
6 -2x < 12 or 7 + 2x < -11
Javier's family bought 3 juices at Bagel Mania. Which of these could NOT be the amount of money Javier's family spent of juices
Juices ___ small $0.75
Large $1.25
A. $2.25
B. $2.75
C. $3.25
D $3.50
Is Sylvia buys 5 shirts for $75 a unit rate?
I believe you are finding the total cost of 5 shirts given the unit rate. To compute for the total cost, you have to multiply the unit rate to the number of shirts bought:
5 shirts x $75 unit rate = $375
Therefore, Sylvia will spend $375 to buy 5 shirts.
The minimum size of a photo book ordered through a website is 6 pages. The website charges $1.70 per page for the first 6 pages. Any additional pages increase the cost of the photo book by $0.90 per page. If x represents the number of additional pages in a photo book order, which equation can be used to find the total cost, in dollars, of a photo book ordered through the website?
A vehicle travels a distance of 5t4 − 10t2 + 6 miles in t + 2 minutes.
The vehicle's speed is __________miles/minute.
Answer:
Speed of the vehicle=[tex]\frac{5t^{4}-10t^{2}+6}{t+2}miles/min[/tex]
Step-by-step explanation:
Given that,
Distance traveled by the vehicle = 5t⁴ - 10t² + 6 miles
time = t + 2 minutes
We need to find the speed of vehicle. Use the formula of speed is:
[tex]Speed=\frac{Dstance}{Tme}[/tex]
[tex]Speed=\frac{5t^{4}-10t^{2}+6}{t+2}[/tex]
So, speed of the vehicle=[tex]\frac{5t^{4}-10t^{2}+6}{t+2}[/tex]
That's the final answer.
Answer:
The speed is 5t^3 - 10t^2 + 10t - 20 + 46/(t+2) miles per minute.
In the diagram, what is the value of x?
What is the correct expression of 34,000 x 96,000 using scientific notation?
For this case we have the following product:
[tex] 34000 * 96000
[/tex]
We can rewrite both numbers using scientific notation.
We have then:
[tex] (3,4 * 10 ^ 4) * (9,6 * 10 ^ 4)
[/tex]
Then, we can rewrite the expression as follows:
[tex] (3,4 * 9,6) * (10 ^ 4 * 10 ^ 4)
[/tex]
Same basis, the exponents are added:
[tex] (3,4 * 9,6) * 10 ^ 8
[/tex]
Multiplying the expression within the parenthesis we have:
[tex] (32.64) * 10 ^ 8
[/tex]
Rewriting the left term as scientific notation we have:
[tex] (3,264 * 10 ^ 1) * 10 ^ 8
[/tex]
Finally we have:
[tex] 3,264 * 10 ^ 9 [/tex]
Answer:
the correct expression of 34,000 x 96,000 using scientific notation is:
[tex] 3,264 * 10 ^ 9 [/tex]
Use technology or a z-score table to answer the question.
The number of huckleberries picked during a huckleberry contest are normally distributed with a mean of 300 and a standard deviation of 53. Jill picked 276 huckleberries in the contest.
What percent of huckleberry pickers picked less than Jill?
Round your answer to the nearest whole number.
Answer:
33%
Step-by-step explanation:
33%
What is the volume of this rectangular prism? Rectangular prism with height labeled 3 centimeters, width labeled 5 centimeters, and length labeled 6 centimeters. cm³
With 128,134,140,146,152,whats the next number If the pattern continues?
Find the value of x so that this quadrilateral is a parrallelogram
Find the median to the base of an isosceles triangle if the length of its base is 15 in and its area is 75 in2
What is 1/4 written as a percent
Which of the following describes the graph of the transformed function compared with the parent function? Select all that apply.
Answer: a,c,d
Step-by-step explanation: got it right on edge :)
Johan takes out a 20-year mortgage at 4% to buy a house. When he looks at investing in 20-year, fixed-rate Treasuries, which of the following rates is most likely closest to the coupons on the Treasuries? Select the best answer from the choices provided. 2.2% 7.8% 3.9% 9.2%
Answer:
3.9%
Step-by-step explanation:
Investing in treasuries is often seeing as a risk free investment since it is sure that they will pay, but the rates are too low, when banks and other finnance corporations set up their mortages and other kinds of large loans interests rates they set them up higher than the fixed rate treasuries since otherwise it´d just be a better deal to put that money on treasuries than lending it to people.
Jeremy 7 years older than Esmeralda in 3 years the sum of their ages will be 57 how old is Jeremy now
solve the system of equations by substitution. 3/8 x + 1/3 y =17/24 and
x + 7y = 8
Answer:
1,1
Step-by-step explanation:
Correct:)
Ratio Question solving with algebra need help must finish soon
I need help please ASAP and I will mark branlist
A science teacher needs up to 15 female and male students for a competition. The science teacher needs at least 6 male volunteers. Let x represent the number of male volunteers and y represent the number of female volunteers. Which inequalities model the situation? Select each correct answer.
a. x+y≤15
b. y≥0
c. x+y<15
d. x>6
e. x≥6
5n + 3 = 2(n + 2) + 3n
N= ???
-Show All Work!-
What is the diameter of a circle with a circumference of 176 feet use for 22 over for pie
Find the cosine and the tangent of 60 degrees
Answer:
D!!!
Step-by-step explanation:
Colleen has a bank account balance of $16.43. Toby has a bank account balance of –$10.21. Yosef has a bank account balance of $8.98. Which of the following statements are true?
Select all that apply.
A.
Colleen has the most money in her bank account.
B.
Toby has more money than Colleen.
C.
Yosef has less money than Toby.
D.
Toby's balance is further from zero dollars than Yosef's balance.
E.
Colleen's balance is further from zero dollars than Toby's balance.
Option A and option E are true, Colleen has the most money in her bank account and Colleen's balance is further from zero dollars than Toby's balance.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
Given that Colleen has a bank account balance of $16.43.
Toby has a bank account balance of –$10.21.
Yosef has a bank account balance of $8.98.
Colleen has the most money in her bank account is true because $16.43 is greater than $8.98.
So the statement in A is true.
Colleen's balance is further from zero dollars than Toby's balance is also true.
Toby has more money than Colleen is false.
Yosef has less money than Toby is uncertain.
Hence, Option A and option E are true, Colleen has the most money in her bank account and Colleen's balance is further from zero dollars than Toby's balance.
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PLEASE HELP WILL GIVE BRAINLIEST ******* Lucy made tables of values to approximate the solution to a system of equations.
Answer:(1.6,1.3)
Step-by-step explanation:
What is the volume of the pyramid?
Yi and Sue play a game. They start with the number $42000$. Yi divides by a prime number, then passes the quotient to Sue. Then Sue divides this quotient by a prime number and passes the result back to Yi, and they continue taking turns in this way.
For example, Yi could start by dividing $42000$ by $3$. In this case, he would pass Sue the number $14000$. Then Sue could divide by $7$ and pass Yi the number $2000$, and so on.
The players are not allowed to produce a quotient that isn't an integer. Eventually, someone is forced to produce a quotient of $1$, and that player loses. For example, if a player receives the number $3$, then the only prime number (s)he can possibly divide by is $3$, and this forces that player to lose.
Who must win this game, and why? Explain your reasoning in complete sentences. (Don't just show one example of how the game could go. Instead, explain why the same player must always win, no matter what strategy either player tries to use!)