Answers
When angle opposite to the unknown sides and other two sides are given then we use law of cosines
Law of cosine
[tex] c^2 = a^2 + b^2 - 2ab cos(c) [/tex]
From the given diagram
[tex] AB^2 = CB^2 + AC^2 - 2(CB)(AC) cos( c) [/tex]
CB = 108
AC= 55
Angle c= 59
[tex] AB^2 = 108^2 + 55^2 - 2(108)(55) cos( 59 ) [/tex]
[tex] AB^2 = 8570.34767 [/tex]
Take square root on both sides
AB = 92.6 m
To find out angle B we use sine law
[tex] \frac{sin(a)}{a} = \frac{sin b}{b} = \frac{sin c}{c} [/tex]
[tex] \frac{sin b}{b} = \frac{sin c}{c} [/tex]
From the figure
[tex] \frac{sin B}{AC} = \frac{sin C}{AB} [/tex]
[tex] \frac{sin B}{55} = \frac{sin 59}{92.6} [/tex]
sin(B) = 0.50916647
B = [tex] sin^{-1} [/tex](0.50916647)
Angle B= 30.61 degrees
Related Questions
Describe the composition of an atom.
Answers
Atom is made up of electrons,protrons and neutrons.
Nucleus is ,ade of protrons and neutrons which is located in centre of the atom and electrons revolve
around it in specific orbits.
Hope it helps.
The atom consists of a tiny nucleus surrounded by moving electrons. The nucleus contains protons, which have a positive charge equal in magnitude to the electron's negative charge.
Community center has an L shaped swimming pool that is 10 feet deep. What is the volume of the pool
1200
1040
640
880
Answers
In order to find this split the pool into two separate rectangular prisms.
The first one's measurements are 4ftx16ftx10ft
4*16*10 = 640
the next prism is 4ftx10ftx10ft
4*10*10 = 400
640+400= 1040 cubic feet
The total volume of pool is:
1040 cubic ft.
Step-by-step explanation:We know that the total volume of the pool is the sum of the volume of two rectangular prism.
one is a rectangular prism with dimensions 20ft.×10ft.×4ft.and the other rectangular prism has dimensions: 6ft.×4ft.×10ft.Hence, the volume of first rectangular prism is:
20×10×4=800 cubic ft.
Volume of second rectangular prism is:
6×4×10=240 cubic ft.
Hence, total volume of pool is:
800+240=1040 cubic ft.
A mobile phone carrier charges an extra fee if a customer uses more than 500 minutes each month. Tom has already used 230 minutes this month. Which inequality can be used to determine how many more minutes Tom can use this month without going over the 500-minute limit?
Answers
Answer:
x + 230 ≤ 500
Step-by-step explanation:
Given,
The time for which Tom used the phone = 230 minutes,
Let he further used the mobile for x minutes,
So, the total time for which he used the phone = ( x + 230 ) minutes,
According to the question,
For the extra minutes more than 500 minutes, the mobile phone carrier charges an extra fee,
Thus, if he wants to use the phone, without going over the 500-minute limit,
Then, the total time used by him ≤ 500 minutes,
⇒ x + 230 ≤ 500
Which is the required inequality.
find the circumference of a circle with an area of 530.93
Answers
r^2 = A/π
r^2 = 530.93 / 3.14
r^2 = 169.08
r = 13
C = 2 π r
C = 2 (3.14)(13)
C = 81.64
answer
81.64 m
puppys mass 4500 grams kittens is 450,000milligrams who has the greater mass
Answers
A town doubles its size every 22 years. If the population is currently 4,500, what will the population be in 88 years?
Answers
4,500×1.50^x=y
4,500 is the population that it starts with, while 1.50 is telling that it is increasing by 50%. X is the number of years.
We are trying to find it in 88 years, so we should replace x with 4. Here is the reason, it doubles every 22 years and we are looking 88 years.
4,500×1.50^4= 22,781.25
There can't be .25 of a person, so the answer would be 22,781.
Can someone help me with this question?
Answers
10 + n/28 > 14
10 + 112/28 > 14
10 + 4 > 14
14 > 14
This reads "fourteen is greater than fourteen," which is false.
n = 112 is NOT a solution to the inequality 10 + n/28 > 14.
So, 10+112/28=14
So 14 > 14
It's not true.
So it is NO.
Hoping this helps you!
Have a good day my friend!!:D
My pleasure :)
what is the product? (x-5)(2x+3x-1)
Answers
Multiply each term of the binomial by each term of the trinomial.
Then collect like terms.
[tex] (x - 5)(2x^2 + 3x - 1) = [/tex]
[tex] = x * 2x^2 + x * 3x + x * (-1) - 5 * 2x^2 - 5 * 3x - 5 * (-1) [/tex]
[tex] = 2x^3 + 3x^2 - x - 10x^2 - 15x + 5 [/tex]
[tex] = 2x^3 - 7x^2 - 16x + 5 [/tex]
Answer:
-18^x-45x on edge
Step-by-step explanation:
sorry if this is late just letting people know in the future
Jake bought the pizza shown above for lunch, which was cut into four equal slices. What percentage of the pizza did Jake eat if he had three slices?
A) 25%
B) 50%
C) 67%
D) 75%
the pic is below
Answers
Hope this helped☺☺
If he still has 3 slices left, he ate 25% and has 75% left
Hope I helped!
Let me know if you need anything else!
~ Zoe
Jerome made P points in the game . Harold made 11 fewer points than Jerome . How many points did Harold make in the games in terms of P!!!!!!!!!!!
Answers
This is the answer
Find the required annual interest rate to the tenth of a percent for $5200 to grow to $6500 if interest is compounded quarterly for five years
Answers
The compound interest formula is
A=p(1+(r/n))^(nt), where A is the total amount including interest earned, p is the principal invested, r is the rate, n is the number of times per year the interest is compounded, and t is the number of years.
With our information we have:
6500=5200(1+(r/4))^(4×5)
6500=5200(1+(r/4))^20
Cancel 5200 by dividing:
6500/5200 = [5200(1+(r/4))^20]/5200
1.25=(1+(r/4))^20
Using a calculator, take the 20th root of each side:
1.25^(1/20) = [(1+(r/4))^20]^(1/20)
1.011219651 = 1+(r/4)
Subtract 1 from each side:
1.011219651-1 = 1+(r/4)-1
0.011219651=r/4
Multiply each side by 4:
0.011219651×4 = (r/4)×4
0.0448786 = r
0.045 = r
Final answer:
After rearranging the formula and solving for the interest rate, the required rate is found to be approximately 4.7%.
Explanation:
The subject of this question is finding the required annual interest rate that will grow a principal amount of $5,200 to $6,500 when compounded quarterly over five years. To solve this, we shall use the compound interest formula:
A = P(1 + r/n)^(nt)
Where:A is the amount of money accumulated after n years, including interest.
P is the principal amount (the initial amount of money).
r is the annual interest rate (decimal).
n is the number of times that interest is compounded per year.
t is the time the money is invested for, in years.
We are given:
A = $6,500
P = $5,200
n = 4 (since interest is compounded quarterly)
t = 5 years
We need to solve for r. First, we rearrange the formula to isolate r:
(1 + r/n) = (A/P)[tex]^({1/(nt))}[/tex]
Then we can insert our known values and solve for r:
(1 + r/4) = ($6,500/$5,200)^(1/(4*5))
Calculate the right-hand side:
(1 + r/4) = (1.25)[tex]^({1/20)}[/tex]
Find the 20th root of 1.25:
(1 + r/4) ≈ 1.01168
Subtract 1 from both sides:
r/4 ≈ 0.01168
Multiply both sides by 4:
r ≈ 0.04672
Convert the decimal to a percentage:
r ≈ 4.672%
Round to the nearest tenth of a percent:
r ≈ 4.7%
Therefore, the required annual interest rate to the tenth of a percent for $5200 to grow to $6500 with interest compounded quarterly for five years is approximately 4.7%.
can someone please help me with this question
Answers
13.4 - 1.7 = 11.7 degrees warmer
I think the answer is C but I’m not sure. Plz help me out
Answers
two triangles are similar, and the ratio of the lengths of each pair of corresponding sides is 2:1. which statement regarding the two triangles is NOT True?
A- Their corresponding angles have a ratio of 2:!
B- Their areas have a ratio of 4:1
C- Their perimeters have a ratio of 2:!
D- Their altitudes have a ratio of 2:!
Answers
In the case of similar figures, we have the same basic shape however it is just make larger or smaller. Since this is the case, all of the angles will remain the same.
Imagine different sizes of stop signs. They are all similar and all the angles are the same. Only the lengths of the sides change.
All statements are true. Ratio of corresponding angles, areas, perimeters, and altitudes is 2:1. No false statement exists.
To determine which statement regarding the two triangles is NOT true, let's analyze each option step by step.
Given:
- Two triangles are similar.
- The ratio of the lengths of each pair of corresponding sides is 2:1.
Let's denote the lengths of corresponding sides in the first triangle as [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex], and in the second triangle as [tex]\( 2a \)[/tex], [tex]\( 2b \)[/tex], and [tex]\( 2c \),[/tex] respectively.
A. Their corresponding angles have a ratio of 2:1.
- This statement is true because corresponding angles in similar triangles are congruent, so their ratios would indeed be 2:1.
B. Their areas have a ratio of 4:1.
- The area of a triangle is proportional to the square of the length of its sides. So if the ratio of the lengths of corresponding sides is 2:1, the ratio of their areas would be [tex]\( (2:1)^2 = 4:1 \)[/tex]. Hence, this statement is also true.
C. Their perimeters have a ratio of 2:1.
- The perimeters of triangles are directly proportional to the lengths of their sides. Since the ratio of the lengths of corresponding sides is 2:1, the ratio of their perimeters would indeed be 2:1. So, this statement is also true.
D. Their altitudes have a ratio of 2:1.
- The ratio of the altitudes of two similar triangles is equal to the ratio of their corresponding sides. So, if the ratio of corresponding sides is 2:1, the ratio of their altitudes would also be 2:1. Therefore, this statement is true.
Since all the statements are true, the correct answer is NONE.
a rectangular deck has a area of 320 ft squared. the length of the desk is 4 feet longer than the width. find the dimensions of the desk. Solve by completing the square.
Answers
width • (width +4)= 320
Distribute the multiplication over addition and move all to the left side.
w^2 +4w-320=0
(w-16)•(w+20)=0 yet, The product of two things is 0 if one is 0 or both are 0 so
w-16=0 so w=16 and
w+20=0 so w= -20
Now the width or length could not be negative so we discard the solution w=-20.
Answer
width= 16 inches
length =16+4=20
Verify
w•l=320
16•20=320✔️
how many times larger is 9x10(9) than 3x10 (-4)
Answers
Step-by-step explanation: Well you see here 9x10 isnt 9 its 90 and 3x10 isnt -4 its 30
If a horses man grows 6/5 per month, how long will it take to grow 24/10 cm
Answers
Explanation :the horses mane grows 6/5 cm per month lets let x = number of monthsit is going to grow 24/10 in x months
so 6/5x (6/5 times the number of months) = 24/10divide both sides by 6/5, eliminating the 6/5 on the left side.so x = (24/10) / (6/5)...and when dividing fractions, u flip what u r dividing by, and multiply. 24/10 * 5/6 = 120/60 which reduces to 2 months. is the correct answer!
*20 Pts* What are two fractions with different denominators that each have the LCD of 36?
Answers
Hope this helps :)
At 3 p.m., the outside temperature was 4 degrees F. The temperature then fell steadily by 2 degrees F every hour for the next four hours. What was the temperature at 7 p.m.?
Answers
What is the slope of a line that is parallel to y=5x+3
Answers
[tex]y = 5x + 3[/tex]
the slope is equal to the slope of the line above. The slope of the line above is 5 (the number in front of the x represents the slope). Therefore the slope of a line that is parallel to the line above is 5.
Express 5/8 as a percent. 62.5% 40% 58% 62% Express as a percent.
62.5%
40%
58%
62%
Answers
hope i helped :D
divide 5 by 8 and you get 0.625. You will then move the decimal point two places to the right which will make it 62.5.
How to make a box and whisker plot for 21,21,22,20,13,13,27,24
Answers
The circumstance of a circle is 9pie cm. What is the diameter?
Answers
Circumference=pi*diameter
9 pi/pi=9
Hope this helped☺☺
ABC is congruent to FGH, AB=8.3, BC=10.4, and CA=4.2. What is the measure of segment GH?
Answers
For a better understanding of the explanation provided here please go through the diagram in the attachment given below.
As we can see from the diagram of the congruent triangles ABC and FGH, the vertices A,B,C of [tex] \Delta ABC [/tex] correspond to the vertices F,G,H of [tex] \Delta FGH [/tex], so the corresponding sides must correspond too. Thus, AB corresponds to FG, BC corresponds to GH and CA corresponds to GF.
Now, we know that BC=10.4. Therefore, it's corresponding side GH must be 10.4 too because they are corresponding sides of a congruent triangle.
Thus, GH=10.4 is the correct answer.
Please help me with this
Simplify this expression:
3 2/3x-4/5(x-3 3/4)
Answers
I don’t think you need the parentheses
Sally decided to look at new and used vans. Sally found a used van for $14000. A new van is $20000, so what percent of the price of a new van does Sally pay for a used van?
Answers
Final answer:
Sally pays 70% of the price of a new van for a used van, which is calculated by dividing the price of the used van by the price of the new van and multiplying by 100.
Explanation:
To determine what percent of the price of a new van Sally pays for a used van, we use the formula for percentage: (Part / Whole) × 100. In this case, the price of the used van ($14,000) is the part, and the price of the new van ($20,000) is the whole. Hence, the calculation will be ($14,000 / $20,000) × 100.
Performing the calculation, we get: (14,000 / 20,000) × 100 = 0.7 × 100 = 70%.Therefore, Sally pays 70% of the price of a new van for a used van.
What’s equivalent to 4/7 X 5/9? 5/9X4/7, 4/7 X 5/9, 4/9 X 5/7, 4/7 X 9/5 X=times
Answers
♡´･ᴗ･`♡вяαιиℓιєѕт ρℓєαѕє♡´･ᴗ･`♡
What is -2(3x+12y-5-17x-16y+4) simplified?
Answers
Answer:
B. 28x + 8y + 2
Step-by-step explanation:
The two-way table shows the number of students in a school who have rabbits and/or birds as pets:
Have Rabbits Do Not Have Rabbits Total
Have Birds 18 22 40
Do Not Have Birds 25 35 60
Total 43 57 100
How many more students have rabbits than birds?
3
7
22
25
Answers
Answer:
3
Step-by-step explanation:
There are a total of 18+22 = 40 people with birds. There are a total of 18+25 = 43 people with rabbits.
This is a difference of 43-40 = 3 people.
There are 3 more students have rabbits than birds
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Have Rabbits Do Not Have Rabbits Total
Have Birds 18 22 40
Do Not Have Birds 25 35 60
Total 43 57 100
There are a total of 18+22 = 40 people with birds.
So 40 people with birds.
There are a total of 18+25 = 43 people with rabbits.
So 43 people with rabbits.
This is a difference of 43-40 = 3 people.
Hence, there are 3 more students have rabbits than birds
To learn more on Statistics click:
https://brainly.com/question/30218856
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What the answer to simplifying( 6 to the power of negative 2) by (3 to the power of negative 3) and (3•6) to the power of 4