5) In the segment below, segment DC = 29,
lengths AB, BC, AC, rounded to the nearest tenth, and angle measures for
Answers
Applying the trigonometric ratios and the triangle sum theorem, the missing lengths and angles are:
AB = 27.2 units
BC = 33.5 units
AC = 50.4 units.
m∠A = 38°
m∠ABC = 112°
What are the Trigonometric Ratios?The trigonometric ratios, SOHCAHTOA, are used to find the sides or angles of a right triangle.
Find BD using TOA:
tan ∅ = opp/adj
tan 30 = BD/29
BD = tan 30 × 29
BD = 16.7 units
Find AD using TOA:
tan ∅ = opp/adj
tan 52 = AD/16.7
AD = (tan 52)(16.7)
AD = 21.4 units
Find AB using SOH:
sin 52 = 21.4/AB
AB = 21.4/sin 52
AB = 27.2 units
Find BC using CAH:
cos 30 = 29/BC
BC = 29/cos 30
BC = 33.5 units
Find AC:
AC = AD + DC
AC = 21.4 + 29
AC = 50.4 units.
m∠A = 180 - 52 - 90 = 38° (triangle sum theorem)
m∠ABC = 180 - m∠A - m∠C (triangle sum theorem)
m∠ABC = 180 - 38 - 30
m∠ABC = 112°
Learn more about the trigonometric ratio on:
https://brainly.com/question/10417664
#SPJ1
Related Questions
In an arithmetic sequence, the sum of the second and eighth terms is $5$, and the product of the fourth and fifth terms is also $5$. What is the $20$th term of this sequence?
Answers
Answer:
10
Step-by-step explanation:
Let $a_n$ be the $n$th term of this sequence. We know $a_2 + a_8 = 5$, and that forces $a_5 = \dfrac 5 2$, the average of these terms.
Then $a_4a_5 = 5$ gives us $a_4 = 2$.
The common difference is $\dfrac 1 2$, and in general, $a_n = \dfrac n 2$.
Therefore the $20$th term is $\dfrac{20}{2} = \boxed{10}$.
The 20th term of the arithmetic sequence will be equal to [tex]T_{20}=10[/tex]
What is arthematic sequence?Arthematic sequence is the type of the number series in which the difference between the first and the second term is always constant in the whole series.
Let [tex]$a_n$[/tex] be the nth term of this sequence.
We know
[tex]$a_2 + a_8 = 5$[/tex], and that forces [tex]$a_5 = \dfrac 5 2$[/tex], the average of these terms.
Then [tex]$a_4a_5 = 5$[/tex] gives us [tex]a_4 = 2$.[/tex]
The common difference is [tex]\dfrac 1 2$,[/tex]and in general, [tex]$a_n = \dfrac n 2$[/tex].
Therefore the 20th term is
[tex]T_{20}=$\dfrac{20}{2} = \boxed{10}$.[/tex]
Hence the 20th term of the arithmetic sequence will be equal to [tex]T_{20}=10[/tex]
To know more about arthematic sequence follow
https://brainly.com/question/6561461
#SPJ1
Which data set does this stem-and-leaf plot represent?
7, 0, 6, 2, 8
77, 7, 0, 6, 6, 0, 0, 2, 8
17, 27, 40, 46, 56, 60, 82, 88
40, 88, 82, 46, 56, 60, 17, 60, 27, 17
Answers
Answer:
it's 40, 88, 82, 46, 56, 60, 17, 60, 27, 17
You’ll earn points just answer.. I know the answer already I’m just giving points
Answers
Answer:
10 inches
Step-by-step explanation:
2+2.25+2.25+2.25+2.5+2.75+2.75+3.25=10!!!!!!!!!
Answer:
thank youuu
Step-by-step explanation:
How to solve the square root of x - 1.
Answers
Answer:
I know i'm late but I think this might be right, I don't know, I used a website-
Step-by-step explanation:
When
√x-1
STEP
1
:
Isolate the square root on the left hand side
Radical already isolated
√x-1 = 0
STEP
2
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(√x-1)2 = ()2
After squaring
x-1 =
STEP
3
:
Solve the linear equation
Rearranged equation
x -1 = 0
Add 1 to both sides
x = 1
A possible solution is :
x = 1
STEP
4
:
Check that the solution is correct
Original equation
√x-1 =
Plug in 1 for x
√(1)-1 =
Simplify
√0 = 0
Solution checks !!
Solution is:
x = 1
also, want to talk and be friends?
~Dreamer1331~
If
x
=
−
9
and
y
=
2
, evaluate the following expression:
2
(
y
−
3
x
y
)
Answers
Explanation: x=-9 y=2
2(y-3xy)
=2(2-3(-9)(2))
=4-2(3(-18))
=4-108
=-104
Hope it helped
A. 0.31
B 0.52
C 0.56
D 0.26
Answers
Answer:
0.56
Step-by-step explanation:
16 km
12 km
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
С
kilometers
Answers
Step-by-Step Explanation:
Javier uses 1/8 teaspoon of nutmeg for each loaf of banana bread he makes. How many loaves f banana bread can Javier with 4 teaspoons of nutmeg?
Answers
PLEASE HELP ME I NEED HELP
Answers
Answer:
5x + 7y = 37
Step-by-step explanation:
I hope it is the answer
find the speed and direction of a plane with a velocity of 〈5,-12〉.
Answers
Answer:
Below in bold.
Step-by-step explanation:
Speed = √(5^2 + (-12)^2)
= √169
= 13,
Direction = arctan (5/-12)
= -22.61 degrees ( its in the 4th quadrant)
So we can write the direction as 90 + 22.61
= 112.61 degrees.
Pa help po salamat,
Answers
Answer:
- a frequency table is how much a number occurs, for example there are 4 10's in data list given so the frequency is 4
- the prompt asked for a width of 6 so 1 - 6, there was no numbers of 1, 2, 3, 4, 5, 6 in the list making the frequency 0
I need help on this question and please explain what I got wrong so I understand and what I'm supposed to do.
Answers
Answer:
A. 64
Step-by-step explanation:
In this problem, you're trying to find out what b is.
With the information that you have, you know that the answer will be 16, and your denominator (what you'll be dividing by) is 4. What you got wrong in this was thinking of it as "what times 4 equals 16", to which you got the answer 4 because 4*4=16. But, that's not exactly what you're supposed to be doing.
If we looked at it like that in this problem, you'd have b=4, making the equation then look like 4/4=16. This isn't true because 4/4=1.
Instead, to get the correct answer, you'll be multiplying 4, the denominator, by 16, our solution. With this, you'll get the answer A. 64.
If you have any more questions, feel free to reach out for help.
Answer:
We are given an equation of [tex]\frac{b}{4} = 16[/tex] and we need to determine what b is. The way that we would do this is what you did and we would multiply both sides by 4 which would get rid of the 4 in the fraction and this would end up multiplying 16 by 4 giving us [tex]b=64[/tex]. This would best match with option A which is 64.
Hope this helps! Let me know if you have any questions
In a cafe, there are 5 women, 4 men, and 2 employees. Write the following reports:
a) between women and men
b) between men and employees
c) between customers and employees
d) between women and the total number of people in the cafe
e) between men, employees and women
Answers
Max is creating a playlist and can have at most 180 minutes of music. He currently has 45 minutes. How many more minutes of music could Max include in the playlist?
Answers
Answer:
max could still add 135 minutes of music into his playlist
Step-by-step explanation:
180 - 45 = 135
Answer:
So we know that Max's playlist can have at most 180 minutes of music meaning that our amount of music cannot exceed that number. We are also given that Max already has 45 minutes of music on there so we need to subtract that from 180 minutes to see how much we have left.
[tex]180\ minutes - 45\ minutes[/tex]
[tex]135\ minutes[/tex]
Max still has 135 minutes left on his playlist that he can fill up.
Hope this helps! Let me know if you have any questions
Why is 1/2 the same as 0.5
Answers
Answer:
it’s because 0.50 is half of 100 and 1/2 is a reduced fraction of 50/100.
Step-by-step explanation:
There are 24 pictures on a roll of film. Adelle had 84 pictures from her trip home. She said that 12 other pictures were spoiled. How many rolls of film did Adelle use?
Answers
Answer:
Total pictures = 84+12 = 96
roll of films = 96 / 24 = 4
she used 4 rolls
Which of these numbers are relatively prime to 51? Select all that apply. da) 84 Ob) 70 Oc) 62 0d) 30
Answers
Answer:
b) 70
c) 62
Step-by-step explanation:
Numbers are relatively prime when they have no factors in common.
__
The factors of 51 are ...
51 = 3×17
The factors of the other numbers are ...
84 = 2²×3×7 . . . . . has a factor of 3 in common with 51
70 = 2×5×7 . . . . . . no factors in common
62 = 2×31 . . . . . . . no factors in common
30 = 2×3×5 . . . . . has a factor of 3 in common with 51
The numbers 70 and 62 are relatively prime to 51.
The length of a rectangle is 3 times the
width. Find the dimensions of the
rectangle if its perimeter is 16 cm.
Answers
Step-by-step explanation:
length = 3×width
2×length + 2×width = 16
length + width = 8
we can use the first equation in the second :
3×width + width = 8
4×width = 8
width = 2 cm
therefore,
length = 3×width = 3×2 = 6 cm
A rectangle has sides measuring (12x - 2) units and (x + 8) units.
Part A: What is the expression that represents the area of the rectangle? Show your work. (5 points)
Part B: What is the expression that represents the perimeter of the rectangle? Show your work. (5 points)
Part C: What are the degree and classification of the expression obtained in Part A? (3 points)
Answers
The area equation is:
A = (12x - 2)*(x + 8)
Which is a polynomial of degree 2, and the perimeter is:
P = 26x + 12
How to write the area of the rectangle?
Remember that for a rectangle of length L and width W, the area is written as:
A = L*W
Here we know that:
L = (12x - 2)
W = (x + 8)
Then the equation for the area is:
A = (12x - 2)*(x + 8).
How to write the perimeter?For a rectangle of length L and width W, the perimeter is:
P = 2*(L + W).
Replacing what we know, we get:
P = 2*(12x - 2 + x + 8) = 2*(13x + 6) = 26x + 12
What are the degree and classification of the area equation?The area equation is:
A = (12x - 2)*(x + 8).
Notice that this is a polynomial that is made of the product of two polynomials of degree 1, so this is a polynomial of degree 2.
If you want to learn more about polynomials:
https://brainly.com/question/4142886
#SPJ1
can someone answer this question- I will give brainily if it is correct.
Answers
Answer:
A
Step-by-step explanation:
since decimals are 10ths and 100ths places, you can translate such into fractions
hope this helps:)
The price of a certain computer stock t days after it is issued for sale is p ( t ) = 100 + 20t − 3t^2 dollars. The price of the stock initially rises, but eventually begins to fall. During what period of time does the stock price rise? 0 ≤ t ≤ If you owned the stock, after how many days would you sell it? days
Answers
The period of time does the stock price rise is 0 ≤ t ≤ 10/3.
It would sell in 3.34 days.
What is differentiation?It is the process of finding the derivative, or rate of change, of a function.
The price of a certain computer stock after t days is
p(t) = 100 + 20t - 3t²
Now, take the derivative of the given function and equate it to zero to find the critical points,
p'(t) = 20 - 6t = 0
t = 20/6
t = 10/3 days
Thus, there are two intervals in which the given function is defined
(0, 10/3) and (10/3, ∞)
For the interval (0,10/3 ),
p'(1) = 20 - 6(1) =14
For the interval (10/3, ∞),
p'(2) = 20 - 6(2) = 8
Since p'(t) in the interval (0, 10/3) indicates that the function is increasing.
0 < t <10/3
Since at the point t = 3.34 days it would sell.
Learn more about this concept here:
https://brainly.com/question/23857227
#SPJ1
1,000 km = 1 mm
True or False
Answers
Answer: Heavily false. False by a long shot.
Step-by-step explanation: 1,000 kilometers is equivalent to 1e+9 millimeters. This is nine zeros after 1. So, this can be simplified as 1,000,000,000 milimeters, or rather, 1 billion millimeters. You can calculate this yourself by multiplying 1000 by 1,000,000 (1km = 1,000,000 mm.)
Which of the following are always congruent?
Answers
Answer:
B. Vertical angles
Step-by-step explanation:
Warren's Scores
Absolute Deviation from Mean Score
mean - individual score
0
25
15
10
20
30
10
15
5
25
20
15
20
5
Answers
50 dollars is on Emma's way
Step-by-step explanation:
Not math is free okay but only mathematics is free
A random sample of 87 eighth grade students’ scores on a national mathematics assessment
test has a mean score of 283. The test results prompts a state school administrator to declare
that the mean score for the eighth graders on the exam is more than 280. Assume the
population deviation is 37. At α = 0.14, is there enough evidence to support the administrator’s
claim?
Answers
There is not enough evidence to support the administrator’s claim and the true mean is not significantly greater than 280.
What is a statistical hypothesis?A hypothesis to test the given parameters requires that we determine if the mean score of the eighth graders is more than 283, thus:
The null hypothesis:
[tex]\mathbf{H_o \leq 283}[/tex]
The alternative hypothesis:
[tex]\mathbf{H_i > 283}[/tex]
From the population deviation, the Z test for the true mean can be computed as:
[tex]\mathbf{Z = \dfrac{\hat X - \mu _o}{\dfrac{\sigma}{\sqrt{n}}}}[/tex]
[tex]\mathbf{Z = \dfrac{283 -280}{\dfrac{37}{\sqrt{87}}}}[/tex]
Z = 0.756
Note that, since we are carrying out a right-tailed test, the p-value for the test statistics is expressed as follows:
P(z > 0.756)
P = 0.225
Since the P-value is greater than the significance level at α = 0.14, we can conclude that there is not enough evidence to support the administrator’s claim and the true mean is not significantly greater than 280.
Learn more about hypothesis testing here:
https://brainly.com/question/16251072
#SPJ1
Rita reads 48 chapters of a book in 6 hours.
What is her rate in chapters per hour?
Answers
Answer:
To find Rita's rate per hour, all you have to do is divide 48/6 which 8. This means that Rita reads 8 books per hour
Step-by-step explanation:
(53 +9r²s) (12rs²-g³) + (-7r²s +7rs²)
Answers
Answer:
(negatively proximity is (31 + 1r¼)car bite
Step-by-step explanation:
Hope it helps
Michiko is selling raffle tickets to raise money for the school band. The odds against winning a prize in the raffle are 13:1. What is the probability of winning a prize? Express your answer as a decimal. If necessary, round your answer to the nearest thousandth.
0.929
14
0.071
0.077
Answers
The probability of winning a prize is 0.929 if Michiko is selling raffle tickets to raise money for the school band. The odds against winning a prize in the raffle are 13:1 option first is correct.
What is probability?It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.
We have:
The odds against winning a prize in the raffle are 13:1
This means 13 to 1 odds for winning:
The probability of winning a prize:
Winning = 13/(13+1) = 0.929 or
=92.8571%
Losing = 1 - 0.9286 = (0.0714) or
=7.14%
Thus, the probability of winning a prize is 0.929 if Michiko is selling raffle tickets to raise money for the school band. The odds against winning a prize in the raffle are 13:1 option first is correct.
Learn more about the probability here:
brainly.com/question/11234923
#SPJ1
Answer:
0.071
Step-by-step explanation:
If the odds against winning a prize are 13:1, then the odds in favor of winning a prize are 1:13.
Pleas help ppppppp pls
Answers
Step-by-step explanation:
option A is correct answer
Obisa has a radio which uses 18-volt batteries. Each battery has 1.5 volts. How many batteries does he need to use his radio?
Answers
Answer:
I believe he would need 12 batteries