Solve each triangle. Round your answers to the nearest tenth.
show work If possible
Answers
∠ABC = 76°
BC = 20.1
CA = 28.0
Step-by-step explanation:Solving the triangle means finding all unknown angles and sides of the triangle.
(i) Two of the angles (∠BCA = 60° and ∠CAB = 44°) are given. To find the third angle (∠ABC), use one of the theorems stating that the sum of angles of a triangle is equal to 180°.
Therefore, the sum of angles of the triangle ABC is 180°. i.e
∠ABC + ∠BCA + ∠CAB = 180°
=> ∠ABC + 60° + 44° = 180°
=> ∠ABC + 104° = 180°
=> ∠ABC = 180° - 104°
=> ∠ABC = 76°
(ii) One side (BA) of the triangle is given. To get the other sides, we use the sine rule as follows;
=> [tex]\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}[/tex]
=> [tex]\frac{sinBCA}{BA} = \frac{sinCAB}{BC} = \frac{sinABC}{CA}[/tex]
Substitute the necessary values
[tex]\frac{sin60}{25} = \frac{sin44}{BC} = \frac{sin76}{CA}[/tex] ---------------------(ii)
(a) To get side BC, use the first two terms of equation (ii)
[tex]\frac{sin60}{25} = \frac{sin44}{BC}[/tex]
Cross multiply
BC x sin 60 = 25 x sin 44
BC x 0.8660 = 25 x 0.6947
0.8660 x BC = 17.3675
BC = [tex]\frac{17.3675}{0.8660}[/tex]
BC = 20.05
=> BC = 20.1 to the nearest tenth
(b) To get CA, use any two terms of equation (ii). Using the first and third terms, we have;
[tex]\frac{sin60}{25} = \frac{sin76}{CA}[/tex]
Cross multiply
CA x sin 60 = 25 x sin 76
CA x 0.8660 = 25 x 0.9703
0.8660 x CA = 24.2575
CA = [tex]\frac{24.2575}{0.8660}[/tex]
CA = 28.01
=> CA = 28.0 to the nearest tenth
Related Questions
Lauren is tutoring students at the library on Saturday. If she is at the library for a total of 6 hours and she helps each
student, one at a time, for 7 of an hour, how many students does she tutor?
3
Answers
Answer:
Lauren tutors 42 students in total
Step-by-step explanation:
She tutors for 6 hours and she teaches 7 students an hour , so we just have to multiply 7 by 6 which is 42
Hope it helps:)
In a survey, 15 high school students said they could drive and 15 said they could not. Out of 60 college students surveyed, 30 said they could drive. Micah concluded that knowing that a person is in college means they are more likely to drive. Is Micah’s conclusion correct? Explain.
Answers
Answer:
No.
Step-by-step explanation:
#1, the sample size is not indicative of a proper high school population, unless of all there is a small amount of students in the high school (or even only 30 students in it). On a individual basis, it can vary widely, and so data analysis such as this is not correct. The data size is skewed as well for the college, especially as college campuses typically house more students then usual. To only ask 60 college students also skew the data gotten. Another sample error may be locational error, in which the location of the schools may warrant the need for a driver license, or if it is not needed, as well as the distance of the student's house and/or where needed facilities are to accommodate a student's needs and desires.
If we were to set all these problems aside and focus more on the question, 15 high school students said they could drive, and 15 said they could not, which makes the sample size of 30 high school students in all. 15 say they can drive, therefore:
15/30 = 1/2, or there is a 50% chance of obtaining a student that can drive.
On the other hand, out of 60 college students surveyed, 30 said they can drive, therefore:
30/60 = 1/2, or there is a 50% chance of obtaining a student that can drive.
∴ Micah's prediction is incorrect in obtaining a college student that can drive more easily then obtaining one that can drive in a high school.
However, remember that too small of a data size can lead to a heavy skew, and it will not represent reality as well.
~
Answer:
Sample Response: No, Micah is not correct. Since there are equal numbers in the group that drive and the group that doesn’t drive, the relative frequency for each is 50%. Because the relative frequencies are the same, there is no association between the variables.
Step-by-step explanation:
Got this from Edg 2021
Please Help I'll give brainliest
Answers
Answer:
259.8
Step-by-step explanation:
You are taking a survey on your experience at Taco Bell. For the first three questions you can
answer Below Average, Average, or Above Average for each question. The last five questions
you can respond with either Agree or Disagree. How many total outcomes are there for this
survey? *
Answers
9 for the first 3 questions
10 for the last 5 questions
Hope this helps ;)
The total outcomes for this survey are 864.
What are the outcomes of the set?An elementary event is one with only one possible consequence. The sample space of an experiment is the event that contains all feasible results. A single consequence may appear in a variety of circumstances.
Given, You are responding to a poll about Taco Bell. You can select Below Average, Average, or Above Average for each of the first three questions. You may choose to agree or disagree with the past five questions.
Here, we utilize the combinations formula to determine how many outcomes there are in this survey.
Three questions have three options, while five questions have two.
Hence,
total outcomes = 3³ * 2⁵ = 27 * 32 = 864
Therefore, There are 864 total responses to this survey.
Learn more about the outcomes of the set here:
https://brainly.com/question/28353187
#SPJ2
The value of a car is deprecting at the rate of 12% Find the correct value of car when cost of car was rs 350000 last year
Answers
Answer:
The cost of the car is $ RS 308,000.
Step-by-step explanation:
Given that the value of a car is deprecting at the rate of 12%, to find the correct value of car when cost of car was $ RS350,000 last year, the following mathematical calculation must be performed:
100 - 12 = 88
88/100 = 0.88
350,000 x 0.88 = X
308,000 = X
Therefore, the cost of the car is $ RS 308,000.
Tomato juice comes in three different sized cans. The red can contains 6 cups, the blue can contains 2 pints, and the yellow can contains 32 fluid ounces. Part A Which can holds the most tomato juice? Enter red, blue, or yellow in the answer box.
Answers
Answer:
Red can
Step-by-step explanation:
Tonato juice come in different sizes
The red can contains 6 cups
The blue can contains 2 pints
The yellow can contains 32 fluid ounces
Therefore the can that holds the highest juice is the red can with 6 cups if tomato juice
an article cost $1424 it may be purchased by depositing $560 and making monthly payment of 48 how many monthly are required to complete payment?
Answers
Answer:
18 monthly payments are required to complete payment
Step-by-step explanation:
We start with our $1,424.
Then subtract $560 from the original number above.
Leaving us with $864.
We then divide the $864 by $48 and we end up with 18.
So our answer is 18 monthly payments are required to complete payment.
Find the equation in terms of x of the line through the points (-4,-6) and (1,9)
Answers
Answer:
y = 3x + 6
Step-by-step explanation:
y2 - y1 / x2 - x1
9 - (-6) / 1 - (-4)
15/5
= 3
y = 3x + b
9 = 3(1) + b
9 = 3 + b
6 = b
What is the equation of the line that passes through point (3, −1) and has a slope of 2?
Answers
Answer:
equation y = 3x + b.
Step-by-step explanation:
To come up with the equation of a line in slope intercept form, we need the slope and the y-intercept. First, substitute the given slope in for m. We get the equation y = 3x + b.
There are 5 red marbles, 15 blue marbles,
reach in and randomly draw two marbles without replacing the first, what is the
probability that both will be blue?
Answers
Answer:
Probability is 0.552, or about 55%
Step-by-step explanation:
first there are 20 marbles in total: odds are 15/20 = 3/4
Then, there are 19 marbles in total : odds are 14/19
So the odds of both of them being blue are: 3/4 * 14/19 = 0.552 (rounded to the thousandths place)
Please give brainliest thanks!
plzzzzzzzzz guysssss im failinggggg
Answers
Step-by-step explanation:
a) Given,
Total marks in English = 90
Marks scored by James = 60
Therefore,
Percentage of marks scored
[tex] = \frac{60}{90} \times 100[/tex]
= 66.67% (approx. )
Then,
Total marks in Science = 150
Marks scored by James = 78
Therefore,
Percentage of marks scored
[tex] = \frac{78}{150} \times 100[/tex]
= 52%
At last,
Total marks in Maths = 120
Marks scored by James = 75
Therefore,
Percentage of marks scored
[tex] = \frac{75}{120} \times 100[/tex]
= 62.50%
b) In English test James scored highest percentage.
I need help for this math question ASAP
A line segment joins points P(–1, –7) and Q(7, 3). Determine the length of PQ to 1 decimal place.
Answers
if the needle below is spun twice and the letters are recorded both times , which of the following would be the probability it would land on letters A and C (in either order)?
(1) 1/3
(2)2/3
(3)2/9
(4)5/6|
Answers
Which is NOT a way to state the meaning of the expression c+5?
Answers
the sixth graders rasied money to fund a feild trip. the five classes raised $42, $51, $38, $49, and $40. what is the median on the ammount of money raised?
a. $36
b. $42
c. $40
d. $13
Answers
Explanation: it is the number between 51 and 49
Answer:
The median is $42, or B.
Step-by-step explanation:
Our numbers are :
42, 51, 38, 49, and 40.
The first step to finding the median is ordering the numbers from least to greatest.
38, 40, 42, 49, 51.
Now we find the number perfectly in the middle - that's 42, between 49 and 40. The median is $42, or B.
Please mark brainliest!
Rectangle, Square, or Rhombus?
Answers
Answer:
maybe rhombus
Step-by-step explanation:
don't take my word for it
Answer:
I think Rhombus. I am not so sure.
Step-by-step explanation:
Have a nice day! :-)
Find the value of x in the isosceles triangle shown below
Answers
Answer:
x²+4² =8²
x²+16 =64
x² =64-16.
x² =48
x. =√48
answer is option D
Answer:
D
Step-by-step explanation:
The segment x is a perpendicular bisector and divides the triangle into 2 right triangles.
Using Pythagoras' identity in either of the 2 right triangles, then
x² + 4² = 8²
x² + 16 = 64 ( subtract 16 from both sides )
x² = 48 ( take the square root of both sides )
x = [tex]\sqrt{48}[/tex] → D
1. In the diagram below, segment AB is tangent to circle C at point D and
AC LBC. If m
Answers
Answer:
∠ DCB = 28°
Step-by-step explanation:
∠ ACD = 180° - (90 + 28)° = 180° - 118° = 62° , then
∠ DCB = 90° - 62° = 28°
Can someone help I’m confused
Answers
Answer:
D and E
Step-by-step explanation:
Let's double check:
D. 9 ÷ 3 = 3
E. 4 × 9 = 36
---------------------------------------------------------------------------------------------------------------
Have a great summer :)
Answer:
the answers would be A, D, and E
Step-by-step explanation:
just replace the Cs with the number 9 and solve from there.
for example c/3=3 would say 9/3=3
Suzie bought 17.75 lbs of flour. If the price for 1lb is $19.68, calculate the total amount she paid to the shopkeeper
Answers
( excluding the .75)
17 x 19.68 = $334.56
.75 = 3/4
19.68 / 4 = $4.92
($4.92 for every quarter of a pound)
4.92 x 3 = $14.76 ( .75 = 3/4)
334.56 + 14.76 = $349.32
CHECK
17.75 x 4 = 71 ( Figure out how many fourths make 17.75)
71 x 4.92 = $349.32
She paid the shopkeeper $349.32
Find x round your answer to the nearest tenth of a degree PLZ HELP ASAP BRAINLIEST!!!!!!!
Answers
Answer:
45.9˚
Step-by-step explanation:
use trig formulas
23 and 16 correspond to the hyp and adj sides to angle x.
adj/hyp is cos so use the cos formula.
cos x = 16/23
arccos --> inverse cos
x = arccos(16/23)
put it in a calculatior and round to nearest 10th.
45.92079....
= 45.9˚
Answer:
Step-by-step explanation:
Two containers, A and B begin with equal volumes of liquid.
120 ml is then poured from A to B.
А
B
Container B now contains 4 times as much liquid as A.
Find the volume of liquid left in container A at the end.
A
A
B.
B
Volume left in container A=
20
ml
Answers
Answer:
volume left in A is 80ml
Step-by-step explanation:
let original volume in both be x ml
after pouring from A to B
vol in A = x - 120
vol in B = x + 120
now it is given that
vol in B = 4 times vol in A
implies
[tex]x + 120 = 4 \times (x - 120) \\ x + 120 = 4x - 480 \\ 3x = 600 \\ x = 200[/tex]
hence original volume in A is 200ml. after pouring in B it is 200-120 = 80 ml
what do you think the soultion is to the queation. I need help???
Answers
Answer:
w = 16, x = 11, y = 6, z = 7.5
Step-by-step explanation:
The scale factor is the ratio of corresponding sides, image to original.
scale factor = [tex]\frac{6}{8}[/tex] = [tex]\frac{3}{4}[/tex]
Then by proportion
[tex]\frac{12}{w}[/tex] = [tex]\frac{3}{4}[/tex] ( cross- multiply )
3w = 48 ( divide both sides by 3 )
w = 16
----------------
[tex]\frac{x}{12}[/tex] = [tex]\frac{3}{4}[/tex]
4x = 36
x = 9
-------------------
[tex]\frac{4.5}{y}[/tex] = [tex]\frac{3}{4}[/tex]
3y = 18
y = 6
----------------------------
[tex]\frac{z}{10}[/tex] = [tex]\frac{3}{4}[/tex]
4z = 30
z = 7.5
How many times does
1/8 go into 1/4
Answers
Answer:
One eighth is one part of eight equal sections. Two eighths is one quarter and four eighths is a half. It's easy to split an object, like a cake, into eighths if you make them into quarters and then divide each quarter in half
find the percent increase is admission to the amusement park is raised from $70 to $80.
Answers
Answer:
14.286% increase
Step-by-step explanation:
Since the admission to the amusement park increased by $10 we need to find what percentage of $70 equals $10.
We can find this percentage by multiplying 10 (the difference in money) by 100 (a hundred percent), and dividing that by 70 (the initial cost)
[tex]10*100/70=14.286[/tex]
can someone PLEASE help me with this!?! its due tonight
explaining your answer = brainliest
what is the perimeter of the square?
Answers
Answer:
24
Step-by-step explanation:
6*4
HELP ME NEED HELP NOW
Answers
Answer:
the product X Y is constant so the relationship is not an inverse variation.
Step-by-step explanation:
Any help is appreciated!!!!!!
Answers
Answer:
d
Step-by-step explanation:
ddddddddddddddddddddddddddfffffdff
I think the answer Is B but i am not sure
5.0×10
1
1.50×10
5
= ?
help please last day of school
Answers
Answer:
5.0x10=50
1.50x10=15
Step-by-step explanation:
calculator
2+2+2+2-2×2-2+2=? . (16-14-12-24)
Answers
Answer:
12 I think
I'm not sure
Byeee