Find the value of each variable using sine and cosine. Round your answers to the nearest tenth.
Answers
Answer:
r = 19.0
s = 17.7
Step-by-step explanation:
In the given right triangle ABC,
Measure of Hypotenuse (AC) = 26
m(∠CAB) = 43°
By applying sine rule in the given triangle,
sin(43)° = [tex]\frac{\text{Opposite side}}{Hypotenuse}= \frac{BC}{AC}[/tex]
sin(43)° = [tex]\frac{s}{26}[/tex]
s = 26[sin(43)°]
s = 17.73
s ≈ 17.7
Similarly, by applying cosine rule in the given triangle,
cos(43)° = [tex]\frac{\text{Opposite side}}{Hypotenuse}= \frac{AB}{AC}[/tex]
= [tex]\frac{r}{26}[/tex]
r = 26[cos(43)°]
r = 19.02
r ≈`19.0
Related Questions
Would it be possible to draw a triangle with the following side lengths?
7 feet, 9 feet, 13 feet
Answers
Answer:
it is not possible
Step-by-step explanation:
Verify the following identity and show steps
(Cos2 θ)/(1+sin2 θ)= (cot θ-1)/(cot θ+1)
Answers
Answer:
Verified below
Step-by-step explanation:
We want to show that (Cos2θ)/(1 + sin2θ) = (cot θ - 1)/(cot θ + 1)
In trigonometric identities;
Cot θ = cos θ/sin θ
Thus;
(cot θ - 1)/(cot θ + 1) gives;
((cos θ/sin θ) - 1)/((cos θ/sin θ) + 1)
Simplifying numerator and denominator gives;
((cos θ - sin θ)/sin θ)/((cos θ + sin θ)/sin θ)
This reduces to;
>> (cos θ - sin θ)/(cos θ + sin θ)
Multiply top and bottom by ((cos θ + sin θ) to get;
>> (cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ)
In trigonometric identities, we know that;
cos 2θ = (cos² θ - sin²θ)
cos²θ + sin²θ = 1
sin 2θ = 2sinθcosθ
Thus;
(cos² θ - sin²θ)/(cos²θ + sin²θ + 2sinθcosθ) gives us:
>> cos 2θ/(1 + sin 2θ)
This is equal to the left hand side.
Thus, it is verified.
The weight of 8 science books is 28 pounds. What is the weight of 11 science books?
The weight of 11 science books is
pounds.
Answers
Answer:
11 books = 33 Pounds
Step-by-step explanation:
24 divided by 8 = 3 pounds per book.
3 x 11 = 33 pounds
Hope this helps
Answer:
38.5
Step-by-step explanation:
28÷8=3.5
3.5×11=38.5
A dog ran along a fence 10 times. The fence is 5 feet 3 inches long. How far did the dog travel? (12 inches = 1 foot
Answers
5 feet and 3 inches, 1 foot=12 inches, 12×5=60+3=63×5=315. so your answer is 315
in the graph, the vector terminating at A represents the complex number z. the vector terminating at B represents the product of z and -2. which graph correctly represents the product?y
Answers
Answer: The first one in the picture.
Step-by-step explanation: I got this right on Edmentum.
*There’s a picture below
sketch the graphs using 3 points that belong to it y = -3x +2
Answers
Answer:
Step-by-step explanation:
Answer:
0,2
1,-1
2,-4
Step-by-step explanation:
CAN SOMEONE PLZZZ HELP ME? THIS IS DUE IN LIKE 5 MINUTES
Answers
Answer:
I think E im not sure which other one.
Step-by-step explanation:
Answer:
A and E
Step-by-step explanation:
hope this helps and hope you get a good score on your assignment/test/quiz
1. Determine the area under the standard normal curve to the left of z=2.10.
Answers
In your calculator you need to go to 2nd distr and then normalcdf. Then enter the lower bound as -99, the upper bound as 2.1, mean as 0 and standard deviation as 1. Then press enter and you should get 0.982 as your answer :)
What is the measure of angle XYZ?
Answers
Answer:
63degrees
Step-by-step explanation:
Using the theorem which states that the measure of angle at the vertex is half the angle of its intercepted arc.
Given
angle of its intercepted arc = 126 degree
Required
angle at the vertex = x =<XYZ
According to the theorem;
x = 1/2(126)
x = 126/2
x = 63
Hence the measure of <XYZ is 63degrees
Kim is evaluating the expression 20 - 3p + 1 when p=4. Which expression can Kim use to evaluate the expression correctly?
Answers
Answer:
20-3(4)+1
Step-by-step explanation:
Which One Doesn't Belong (WODB)
Indicate which multiplication problem you believe does NOT belong in the group.
Explain Why!
Answers
Answer:
I think A does not belong to the multiplication problems, because A's outcome is 2 digit while the others are 1 digit.
Step-by-step explanation:
⚠️ANSWER ASAP⚠️ 4x−(2x−9)−12x How many terms
Answers
Answer:
4
Step-by-step explanation:
I need the answer for this question
Answers
Answer:
6,912 i think that's the answer I'm not sure though
Step-by-step explanation:
Answer:
[tex]8,400in^2[/tex]
Step-by-step explanation:
Area of Trapezoid: [tex]A=h(\frac{b1+b2}{2} )[/tex]
Given: B1, B2 and h
B1 = 18 in
B2 = 24
h = 16 in
Substitute variables for the give numbers:
[tex]A=16(\frac{18+24}{2} )\\A = 336 in^2[/tex]
The 336 in is for one desk, and they want you to find 25 desks. So multiply 336 and 25.
[tex]x = 25(336)\\x = 8,400in^2[/tex]
why wont u let me see the awner when it says "u have 12 awsners left"
Answers
Answer:
do you have an android if you do download the app its free no monthly payments like the web browser im using the app
Myrna is buying a new rug for her living room. What is the area of the rug, in square feet?
8 ft
12 ft
Ο Α. 40 ft2
O
B. 48 ft?
o
C. 80 ft2
D 96 ft2
Answers
Answer:
The answer is 96 square feet because if you look at the first rectangle (the one on the top left), you should multiply 5 times 6 which equals 30.
Answer:
(D), 96 square feet
Step-by-step explanation:
The formula for area is:
Length * Width = Area
Let's plug in the values:
8 * 12 = 96 square feet
Therefore, the answer is (D), 96 square feet. Hope this helps!
Smooth transitions in an informative essay_____
two paragraphs seamlessly.
A.connect
B.Separate
C.Divide
D.Classify
Answers
hope your day is good !!
please can someone help me quickly? i will give brainliest (please no links)
Answers
Which of the following is not a term in the expression
Answers
answer and show work and ill give brainliest
Answers
9514 1404 393
Answer:
(d)
Step-by-step explanation:
The area of the semicircle is ...
A = (1/2)πr²
A = (1/2)(3.14)(4 m)² = 25.12 m²
The area of the triangle is ...
A = 1/2bh
A = 1/2(12 m)(8 m) = 48 m²
Then the total area of the composite figure is ...
total area = semicircle area + triangle area
= 25.12 m² + 48 m² = 73.12 m²
_____
Additional comment
The areas of choices A-C are too small. Choice A represents the area of the full circle. Choice B represents the area of the triangle only. Choice C is completely irrelevant. Choice D is the sum of the first two choices, inappropriately using the full circle area.
You should talk to your teacher about this question. None of the offered choices is correct.
Country A has an exponential growth rate of 4.6% per year. The population is currently 5,849,000, and the land area of Country A is 38,000,000,000 square yards. Assuming this growth rate continues and is exponential, after how long will there be one person for every square yard of land?
Answers
In other words, we need to know when the population of the country will be 27,000,000,000.
We know that the population grows exponentially, so we use the exponential growth formula:
Where:
P is the population as a function of time
is the initial population
r is the annual growth rate
t is time in year.
The information we have allows us to conclude that:
So the exponential growth equation is:
We want to know when P = 27, 000,000,000.
So:
Now we solve for t, and as soon as we answer for t, the answer will be 189.66 years. Hope this helps! Mark brainly please!
Answer:
195.205998 years
Step-by-step explanation:
P=P0(1.046)^t P=future population P0=initial population t=years passed
38,000,000,000 = 5,849,000(1.046)^t
1.046^t = 38,000,000,000/5,849,000
1.046^t = 38,000,000/5,849
plug in log on both sides
log 1.046^t = log (38,000,000/5,849)
t[log 1.046] = log (38,000,000/5,849)
t = In (38,000,000/5,849)/ In 1.046
t ≈ 195.205998 (hope this helps)
In August 2003, 56% of employed adults in the United States reported that basic mathematical skills were critical or very important to their job. The supervisor of the job placement office at a 4-year college thinks this percentage has increased due to increased use of technology in the workplace. He takes a random sample of 30 employed adults and finds that 21 of them feel that basic mathematical skills are critical or very important to their job.
Required:
Is there sufficient evidence to conclude that the percentage of employed adults who feel basic mathematical skills are critical or very important to their job has increased at the a = 0.05 level of significance?
Answers
Answer:
Yes
Step-by-step explanation:
First, suppose that nothing has changed, and possibility p is still 0.56. It's our null hypothesis. Now, we've got Bernoulli distribution, but 30 is big enough to consider Gaussian distribution instead.
It has mean μ= np = 30×0.56=16.8
standard deviation s = √npq
sqrt(30×0.56×(1-0.56)) = 2.71
So 21 is (21-16.8)/2.71 = 1.5494 standard deviations above the mean. So the level increased with a ˜ 0.005 level of significance, and there is sufficient evidence.
A bag contains one red pen, four black pens, and three blue pens. Two pens are randomly chosen from the bag and are not replaced.
What is the probability that a blue pen is chosen first and then a red pen is chosen?
A. 1/7
B. 3/8
C. 3/56
D. 3/14
Answers
3 1/7 x 10 answer plz
Answers
Answer:
31.43
Step-by-step explanation:
3 1/7 = 3.14285714285
3 1/7 x 10 = 31.4285714286 which is about 31.43
Answer:
31 [tex]\frac{3}{7}[/tex]
Step-by-step explanation:
[tex]\frac{22}{7}[/tex]×[tex]\frac{10}{1}[/tex]
[tex]\frac{220}{7}[/tex]
31 [tex]\frac{3}{7}[/tex]
What is the approximate value of 12−−√ ?
3.5
2
6
4.5
Answers
Please help!!! Solve for the m
Answers
Answer:
36°
Step-by-step explanation:
[tex]m\angle C =sin^{-1}\frac{17}{29}\\m\angle C =35.888297553\degree\\m\angle C =36\degree[/tex]
Given the following information: P(A) = 0.62 P(B) = 0.25 P(A and B) = 0.12 P(B given A) = 0.19 What is the probability of A or B? Round your answer to the nearest hundredth as needed. P(A or B) =|
Answers
Answer:
P(A or B) = 0.75
Step-by-step explanation:
Venn probabilities:
Supposing that we have two events A and B, the probability P(A or B) is given by:
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B)[/tex]
In this question, we have that:
[tex]P(A) = 0.62, P(B) = 0.25, P(A \cap B) = 0.12[/tex]
So
[tex]P(A \cup B) = P(A) + P(B) - P(A \cap B) = 0.62 + 0.25 - 0.12 = 0.62 + 0.13 = 0.75[/tex]
Then
P(A or B) = 0.75
HELP ME PLEASE......
Answers
Answer:
reflective.
Step-by-step explanation:
this has a somewhat meaningful undertone, meaning it is not sarcastic or scholarly. It also is not arguementative because it is not agrueing anything.
The heights, in inches, of several seventh-grade students at Evan Mills Middle School are
listed below.
56, 50, 47, 55, 50, 51, 55, 45, 55, 49, 45, 44
Which box plot best displays these data?
AHHH
40 42 44 46 48 50 52 54 56 58 60
T
B
A+++
40 42 44 46 48 50 52 54 56 58 60
40 42 44 46 48 50 52 54 56 58 60
40 42 44 46 48 50 52 54 56 58 60
Answers
question in screenshot
Answers
Explanation: When you simply that’s the answer.
During week 3, Frank rode his bike about the same amount of time as week 1 and 2 combined. About how many hours did he ride his bike during week 3?
A 4 hours
B 4 hours
C 6 hours
D 7 hours
Answers
Answer:
6 hours
Step-by-step explanation:
3 1/4
+ 2 5/6 =
72/12 = 6