To solve triangle ABC, we use the Law of Cosines to find angle C and the Law of Sines to find angles A and B. Plugging in the given values, we find that angle C is approximately 103.39 degrees, angle A is approximately 25.70 degrees, and angle B is approximately 50.91 degrees.
Explanation:Given that c = 82, b = 2, and a = 12, we can use the Law of Cosines to solve for the missing angles.
Using the Law of Cosines, we have:
c^2 = a^2 + b^2 - 2ab*cos(C)
Plugging in the values, we get:
82^2 = 12^2 + 2^2 - 2(12)(2)*cos(C)
6724 = 144 + 4 - 48cos(C)
660 = -48cos(C)
cos(C) = -660/48
C = acos(-660/48)
Using a calculator, we find that C ≈ 103.39 degrees.
To find angle A, we can use the Law of Sines:
a/sin(A) = c/sin(C)
Plugging in the values, we get:
12/sin(A) = 82/sin(103.39)
Solving for sin(A), we get:
sin(A) = (12*sin(103.39))/82
A = asin((12*sin(103.39))/82)
Using a calculator, we find that A ≈ 25.70 degrees.
Finally, we can find angle B using the fact that the sum of the angles in a triangle is 180 degrees:
B = 180 - A - C
Plugging in the values, we get:
B = 180 - 25.70 - 103.39
Using a calculator, we find that B ≈ 50.91 degrees.
A ≈ 25.70 degrees
B ≈ 50.91 degrees
C ≈ 103.39 degrees
To solve the triangle ABC, we can use the Law of Sines. The Law of Sines states. the correct answer is:option b. A≈9.59°, B≈88.41°, c≈12.17°
To solve the triangle ABC, we can use the Law of Sines. The Law of Sines states:
sinA/a = sinB/b=sinC/c
Given that C=82°, b=2, and a=12, we want to find angles A and B and side
Let's find angle A using the Law of Sines:
sinA/12=sin82°/2
Now, solve for angle A:
sinA=12⋅ sin82°/2
A=sin −1(12⋅ sin82°/2)
A≈9.59°
Now that we have angle A, we can find angle B using the fact that the sum of angles in a triangle is 180°:
B=180°−A−C
B=180°−9.59°−82°
B≈88.41°
Now, we can find side c using the Law of Sines:
sinA/a= sinC/c
sin9.59°/12= sin82°/c
Now, solve for c:
c=12⋅sin82°/ sin9.59°
c≈12.17
So, the correct answer is:
A≈9.59°,
B≈88.41°,
c≈12.17°
completed question
Given that C=82°, b=2 , and a=12 , solve triangle ABC. Round the answer to the nearest hundredth.
A. A=9.59°, B=88.41°, c=11.89
B. A=9.59°, B=88.41°, c=12.17
C. A=88.41°, B=9.59°, c=11.89
D. A=88.41°, B=9.59°, c=12.17
he table shows the number of calories in different numbers of apples. Number of Apples 3 5 8 Number of Calories 195 325 520 How many calories are in 9 apples? Enter your answer in the box.
Answer:
The answer is 585
Step-by-step explanation:
I took the k12 test the answer above is correct
A zookeeper predicted that the weight of a newborn lion would be 2.8 pounds. when the zoo's lion gave birth, the newborn weighed 3.5 pounds. what is the zookeepers's percent error?
Answer:
20%
Step-by-step explanation:2.8-3.5 then divide that by 3.5 and multiple the answer by 100 to get the percent
Answer: 20%
Step-by-step explanation:
According to the zookeeper ,
The predicted weight of the newborn lion = 2.8 pounds
The actual weight of the newborn lion = 3.5 pounds
Now , the zookeepers's percent error = [tex]\dfrac{|Predicted-actual|}{actual}\times100[/tex]
[tex]=\dfrac{|2.8-3.5|}{3.5}\times100\%\\\\=\dfrac{|-0.7|}{3.5}\times100\%\\\\=\dfrac{0.7}{3.5}\times100\%\\\\=\dfrac{100}{5}\%=20\%[/tex]
Hence, the zookeepers's percent error = 20%.
can i get help for b please? URGENT
Answer:
195 cm
Step-by-step explanation:
Total the number of players and their total heigh
number of players = 2 + 6 + 3 + 1 + 1 = 13
total height = (2 × 200) + (6 × 201) + (3 × 202) + 203 + 204
= 400 + 1206 + 606 + 203 + 204 = 2619 cm
let x be the height of the new player, then
[tex]\frac{2619+x}{14}[/tex] = 201 ( multiply both sides by 14 )
2619 + x = 14 × 201 = 2814 ( subtract 2619 from both sides )
x = 2814 - 2619 = 195
height of new player is 195 cm
Please help out with this if you can.
Answer:
3/7 and 4/17
Step-by-step explanation:
a) given that Shen is playing a game and the probability of unlocking the treasure test is 3/10.
To find the odds in favour of his character unlocking the treasure chest.
Since probability = 3/10 we have favourable and total are in the ratio 3:10
i.e. favourable:Favourable+unfavourable= 3:3+7
Hene odds= favourable:unfavourable =3/7
Answer is 3/7
b) Given that odds against choosing a blue block are 13/4
This means there are 4 blue blocks and 13 other colour blocks.
Total blocks= 13+4 =17
No of blue blocks = 4
Probability of selecting blue block=4/17
1. Which percent is indicated by the shaded area of the grid below?
A. 40%
B. 41%
C. 49%
D. 59%
2. Write 15% as a decimal.
A. 1.5
B. 0.15
C. 0.015
D. 0.0015
Write 5.6 as a percent.
A. 56%
B. 5.6%
C. 560%
D. 0.56%
Answer: 1) A. 41% (2)B. 0.15
(3) C. 560%
Step-by-step explanation:
In question 1, all you need to do is to count the number of shaded box, and tho total boxes are 100, so number of shaded box/100
=41/100 = 41%
In question (2)
15/100,whenever you shift a decimal to the left hand side the zero will go away, so shiftingit twice to the left handside,the two zeros will go away, so you will have 0.15
In question3
5.6 to percentage,
Simply multiply by 100/100
5.6 ×100/100 = 560/100 =560%
suppose that many large samples were taken from population A, which is normally distributed, and population c, which is not normally distributed. The means of the samples of which of the following populations would approximate a normal distribution?
a. both population a and population c
b. neither
c. population c
d. population a
Answer:
Both populations -Apex
Step-by-step explanation:
Solve the inequality.
x/8>4 ??
Answer:
x > 32
Step-by-step explanation:
x/8 > 4 Multiply both sides by 8
x > 32
A diagonal shortcut across a rectangular lot is a 100 feet the lot is 60 feet wide what is the length of the lot
A. 40 feet
B. 60 feet
C.80 feet
D.90 feet
Da answer should be A. 40 feet hope it's da right answer
#20 please help me with this Austin’s and an explanation please
Answer:
10 2/15 hours
Step-by-step explanation:
If we have a candle that is 11 2/5 inches tall
It burns 1 1/8 inches per hour. We need to divide to see how long the candle will last
11 2/5 ÷ 1 1/8
I will convert the mixed numbers to improper fractions
11 2/5 = (5*11+2)/5 = 57/5
1 1/8 = (8*1+1)/8 = 9/8
57/5 ÷ 9/8
Copy dot flip
57/5 * 8/9
456/45
Now we change it back to a mixed number
45 goes into 456 10 times with 6 left over
10 6/45
This simplifies to 10 2/15
If x is a rational number and y is the opposite of x, why do x and y have the same absolute value
Answer:
Absolute value is the distance away from zero, so if x is a rational number and y is opposite, they would both be the same distance away from zero, regardless of their sign.
Step-by-step explanation:
Absolute value is the distance of a number away from zero. For example, if x is equal to the rational number -2, the absolute value of -2 is just 2, given that both 2 and -2 are only a distance of 2 away from the number zero. Think of it as your walk or drive to school. If you live 4 miles from school, you drive a distance of 4 miles there and 4 miles back. That distance is not calculated as a positive 4 miles there and a negative 4 miles back, but rather just 4 miles there and 4 miles back, for a total distance of 8 miles. So, if x=4 and y=(-4), the absolute value of both would be 4.
how would i graph y=-x-6
Answer:
Step-by-step explanation:
-6 is your (y) while -x is your (x), for -x turn that to (-1/1) which is down 1 and right 1. That's your answer
Write a linear function for the line represented by the point-slope equation y - 4 = 3 (x - 4)
MUST SHOW WORK TO GET CREDIT. PLEASE HAVE LEGIT AND IN DETAIL ANSWERS.
Answer:
Y = 3 X + (-8)
Step-by-step explanation:
The given equation is in the slope intercept form
Equation is
Y - 4 = 3 (X - 4)
In a linear function → it takes number X as a input and gives mX + b as output.
m and b are constant.
mX → it is called scaling by factor m.
+b → it is called a shift by an amount b.
Then we can say that linear function looks like this
f(X) = mX + b
Let Y = f(X)
Hence,
Y = mX + b
From the given equation
Y - 4 = 3 (X - 4)
Y - 4 = 3 X - 12
Y = 3 X + (-8) (m = 3 , b = - 8)
It is the linear form of the given equation
The complement of an angle is 35 degrees what is the measure of the angle?
A. 35 degrees
B. 70 degrees
C. 45 degrees
D. 55 degrees
Complementary angles add up to 90 degrees.
The complement angle to 35 is:
90 - 35 = 55 degrees.
The answer is D.
April
has 3 pounds of trail mix she puts equal amounts in each of 8 bags how mush trail mix is in each bag
To solve this, simply divide 8 into 3
8/3=2 2/3
Each person gets 2 2/3 pounds of trail mix.
Answer: 3/8 or 0.375 trail mix is in each bag.
Step-by-step explanation: April has 3 pounds of trail mix. If there are 8 bags, we can divide 3 by 8 to give us how much trail mix is in each bag.
A circle has a circumference of 28.26 units. What is the diameter of the circle?
Answer:
The diameter of the circle is 9.
Step-by-step explanation:
Because circumference is equal to [tex]\pi[/tex] * d, we can backtrack and use this equation to find diameter. Let's say [tex]\pi[/tex] is equal to 3.14.
28.26 = 3.14d
Divide both sides by 3.14.
9 = d
The diameter of the circle is 9.
To find the diameter of a circle with a circumference of 28.26 units, the formula D = C / π is used, yielding a diameter of approximately 9 units.
Explanation:The student's question pertains to finding the diameter of a circle when the circumference is given. The circumference (C) of a circle is related to the diameter (D) by the formula C = πD, where π (pi) is approximately 3.14159. Given that the circumference of the circle is 28.26 units, we can solve for the diameter by rearranging the formula to D = C / π.
Substituting the given circumference into the formula gives us:
D = 28.26 units / 3.14159
When we do this calculation, we find that the diameter is approximately 9 units. Therefore, the diameter of the circle is approximately 9 units.
Which is the following sum in simplest form? sqrt 8+ 3 sqrt2 +sqrt 32
Answer:
Exact Form:
9√2
Decimal Form:
12.72792206
Step-by-step explanation:
Simplify expression
Answer:
[tex]9\sqrt{2}[/tex]
Step-by-step explanation:
sqrt 8+ 3 sqrt2 +sqrt 32
[tex]\sqrt{8} +3\sqrt{2} +\sqrt{32}[/tex]
Simplify each square root
[tex]\sqrt{8}=\sqrt{2*2*2}=2\sqrt{2}[/tex]
[tex]\sqrt{32}=\sqrt{4*4*2}=4\sqrt{2}[/tex]
Given expression becomes
[tex]2\sqrt{2} +3\sqrt{2} +4\sqrt{2}[/tex]
All are like terms so we add it
[tex]9\sqrt{2}[/tex]
The value of a car decreases about 7% percent each year after it is manufactured.The 2017 Honda Civic costs $19,540
Answer: a) , where 'A' is the value of car after 't' years.
b) $12446.784
Step-by-step explanation:
Given: A new car that sells for $21,000 depreciates (decreases in value) 16% each year.
Then a function that models the value of the car will be
, where 'P' is the selling price of car, 'r' is the rate of depreciation in decimal, 't' is the time in years and 'A' is the value of car after 't' years.
Thus after substituting given value, the function becomes
To find the value after 3 years, substitute t=3 in the above function.
Hence the value of car after 3 years=$12446.784
The value of a car such as the 2017 Honda Civic decreases approximately 7% per year after manufacture. This is an example of exponential decay. After the first year, the car's value would be close to $18,172.
Explanation:The value of a car declining annually after its manufacture is an example of exponential decay in mathematics. In the case of the 2017 Honda Civic costing $19,540, the value decreases by approximately 7% each year. To calculate this, we can use the formula for exponential decay which is A = P(1 - r), where A is the final amount, P is the initial amount (price of the car), r is the rate of decrease (in decimal form), and n is the number of time periods (years in this case).
Now, if you want the value of the car after its first year, replace P with $19,540, r with 0.07, and n with 1. When calculating this, you should get a value close to $18,172, which is the approximate value of the car one year after it was manufactured.
Learn more about Exponential decay here:https://brainly.com/question/2193799
#SPJ12
A student earns a 98 on a test for answering 1 question incorrectly and earns a 94 for answering three questions incorrectly.
What is the slope
Hint: Its negative
Answer:
I believe it is -2
Step-by-step explanation:
6.19 round to whole number
Answer:
6 is the closest whole number
Step-by-step explanation:
Answer: 6
Step-by-step explanation: If the first digit in 6.19 is less than 5 then we simply remove the decimal after the whole number (0.19 in this case) to get the answer. If the first digit in 6.19 is 5 or above, then we add 1 to the whole number (6 in this case) and remove the decimal after the whole number (0.19 in this case) to get the answer.
I hope that helped! Good luck, fam! :D
- Une
What is the value of x?
Answer:
They are all 180 degrees
70+30=100
180-100=
Ans:80 Degrees
Step-by-step explanation:
Angeline bought s yards of satin fabric priced at $8.09 per yard, and c yards of cotton fabric priced at $3.79 per yard. What expression could you use to determine the total cost of the fabric? If she bought 5 yards of satin fabric and 8 yards of cotton fabric, how much did Angeline spend in all?
Answer:
70.77
Step-by-step explanation:
Hope this helps
5 times larger than the sum 2 and 8
Answer:
50
Step-by-step explanation:
The sum of 2 and 8 is 10. 10 times 5 is 50
Answer:
50
Step-by-step explanation:
10 times 5 is 50
A regular triangle has a perimeter of 51 m. How long is each side?
Please help me
A regular or equilateral triangle has all sides of equal length. The length of each side can be found by dividing the total perimeter by the number of sides. Hence, each side of the triangle is 17 meters long.
Explanation:The question is asking about the sides of a regular triangle, which is another name for an equilateral triangle. In an equilateral triangle, all sides are of equal length. The perimeter of a triangle (or any polygon) is just the sum of the lengths of all its sides. So, if the perimeter of the regular triangle is 51m, that means the total length of all three sides is 51m. Since all three sides are of equal length, we can find the length of each individual side by dividing the total perimeter by the number of sides. In this case, 51m divided by 3 sides equals 17m. Therefore, each side of the regular triangle is 17 meters long.
Learn more about Triangle Side Length here:https://brainly.com/question/24273594
#SPJ3
For a certain experiment, if we expect to get an apple 8 times in 200 trials, what is the theoretical probability of getting an apple?
Answers:
A) 1/50
B) 1/30
C) 1/25
D) 1/100
Can I have some help finding this answer please
Answer:
The hypotenuse of this is 6
Step-by-step explanation:
Answer:
hypotenuse = 6
Step-by-step explanation:
For a right triangle, we know that sin (theta) = opposite / hypotenuse
sin 45 = 3 sqrt(2)/ hypotenuse
Multiply both side by hypotenuse
hypotenuse * sin 45 = 3 sqrt(2)
Divide by sin 45 on both sides
hypotenuse * sin 45/ sin 45 = 3 sqrt(2)/sin 45
hypotenuse = 3 sqrt(2)/sin 45
hypotenuse = 6
Find the x-intercept and y-intercept of -x+2y=8
y-intercept: (0,4)
x-intercept: (8,0)
Y-intercept:
I made x=0
[tex]0+2y=8\\[/tex]
divide by 2 on both sides
[tex]y=4[/tex]
x-intercept
I made y=0
[tex]x+2(0)=8\\x=8[/tex]
Help will mark brainiest!
Answer:
Sry Im guessing. You divide the actual length of pole by the shadow then multiply it to shadow of the tower...
Step-by-step explanation:
Hope it helps
Help with this please
Answer: The question is saying to write an equation in slope form: y=mx+b
M=1/4 and b=-3/4
It is the first answer: y=1/4x-3/4
Janet’s gross pay is $750, from which $31is deducted for OASDI, $10 for Medicare, and $14 for income tax. What is her net pay?
Answer:
Net pay = $695
Step-by-step explanation:
To find her net pay, we take the gross pay and minus the deductions
Net pay = 750 - 31 - 10 - 14
Net pay = 695
What is the equation of the line graphed below?
A. y=mx
B. y=m(x+1)
C. y=mx+b
D. y=m/x+1