CON
Enter a range of values for x.
a
a
3x-9⁰ 93°
27
26
[?] Enter

Answer:

  3° < x < 32.538°

Step-by-step explanation:

The possible values of the angle marked with an x-expression may not be as obvious as they first seem. There is a somewhat complicated interaction between the angle value and the length of the side(s) marked 'a'.

__

We can label the vertices of the figure A through D, clockwise from the bottom.

The minimum value of angle ACB (marked 3x-9°) is 0°. That will be its measure when AB +BC = AC, or B lies on line AC. In this case, the value of x is ...

  3x -9° = 0°

  3x = 9° . . . . add 9°

  x = 3° . . . . . divide by 3

value of 'a'

The maximum value of angle ACB will be found where both triangles are isosceles: AC ≅ BC ≅ DC. The length of 'a' can be found for that case using the Law of Sines:

  27/sin(93°) = a/sin(43.5°) . . . where (180° -93°)/2 = 43.5° is the base angle

  a = 27×sin(43.5°)/sin(93°) ≈ 18.611

value of 3x -9°

Angle ACB will obey the same Law of Sines requirement. If z represents the base angle in isosceles triangle ABC, then we have ...

  sin(z)/18.611 = sin(180-2z)/26

Recognizing that sin(180-2z) = sin(2z) and using the double-angle formula, we find ...

  sin(z)/18.611 = 2sin(z)cos(z)/26

  sin(z)(1/18.611 -cos(z)/13) = 0 . . . . . subtract the right side, factor

This has solutions that make the factors zero:

  sin(z) = 0   ⇒   z = 0 . . . . . . an extraneous solution in this case

  cos(z) = 13/18.611 ≈ 45.6925°

Then the value of x can be found from ...

  3x -9° = 180° -2z ≈ 88.615°

  x ≈ 3° +(88.615°/3) = 32.538°

_____

Additional comment

In the above, we have shown numerical values for the side lengths and angles in the maximum-x case. The various expressions can be combined to give ...

  3(x -3°) = 180° -2(arccos(13/27×sin(93°)/sin(43.5°)))

  x = 63° -2/3·arccos(13/27·sin(93°)/sin(43.5°))

Calculate the volume of the figure below.

A rice field in the shape of a parallelogram is 300 m long. The perpendicular distance between the base and its opposite side is 7. What is asked for in the problem? 120 m. What is its area? 8. What facts are given? 9. What is the formula to solve the problem? 10. What is the complete answer?​

Cube Root Values
What two whole numbers does 81 lie between

-7-3 log₂ (-n + 10) = -16

Drag numbers to the table so it shows a proportional relationship between x and y.

PLEASE HELP

A point is plotted on the number line at 4 3/5 . A second point is plotted at −3 3/4 .

What is the length of a line segment joining these points?

Enter your answer as a simplified mixed number in the box.

[tex]x \6 - 1 = x \4 + 1 \2[/tex]
answer. the question pls pls pls pls​

one lap around a dirt track is 1 /3 of a mile. It takes Bryce 1/9 of an hour to ride one lap.

How do I look at the recently posted questions? i'm lost and I want to answer some questions but I forgot how to go to the section. Send help please.

Which is the equation of a trend line that passes through the points (7, 450) and (14, 401)? y = negative 7 x 499 y = negative startfraction 1 over 7 endfraction x 451 y = startfraction 1 over 7 endfraction x 449 y = 7 x 401

Which of the following can represent the three angles in an obtuse, scalene triangle?
-50, 30, 100
-40, 50, 90
-30, 30, 120
-50, 50, 80

Which expression is equivalent to -15-(-8)

is 2.06532 rational or irrational?

In the figure below, \overline{AC}
AC
start overline, A, C, end overline and \overline{BD}
BD
start overline, B, D, end overline are diameters of circle PPP.
What is the arc measure of minor arc \stackrel{\large{\frown}}{BC}
BC
⌢
B, C, start superscript, \frown, end superscript in degrees?

Trigonometric ratio
adjacent= 12 cm
angle= 22°
find the opposite side by using tan.​

help help help help help

Question 13 of 17
Which values of x would make a polynomial equal to zero if
the factors of the polynomial were (x+4) and (x+8)?

Please awnser last question if correct we can do thisss

2. f(x)=4x+1 and ​g(x)=x2−4x−5​, find ​(g◦​f)(4​).

You collect a random sample of size n from a population and calculate a 95% confidence
with an increased margin of error?
O Use a 98% confidence level.
O Use a 90% confidence level.
O increase the sample size.
O Use the same confidence level, but compute the interval n times. Approximately 5% 0
© Nothing can guarantee that you will obtain a larger margin of error. You can only say



In a recent telephone survey, 5,000 randomly selected teenagers were asked to cite their primary social network site. Six of 10 teenagers said they use Mybook as
their primary social network site. A 95% confidence interval to estimate the true proportion of teenagers who use Mybook as their primary social network site is found to
be (0.2964, 0.9036). Which of the following is a correct interpretation of the confidence level?
O Ninety-five percent of all samples of this size would yield a confidence interval of (0.2964, 0.9036).
O There is a 95% chance that the true proportion of teenagers who use Mybook as their primary social network site is in the interval (0.2964, 0.9036).
O Ninety-five percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who use Mybook as their primary
social network site
O Ninety-five percent of all the samples of size 5,000 lie in the confidence interval (0.2964, 0.9036).
O There is a 95% chance that randomly selected teenagers will be part of the 60% who use Mybook as their primary social network site.



(05.04 MC)
Leon wants to estimate the proportion of the seniors at his high school who like to watch football. He interviews a simple random sample of 50 of the 200 seniors on
campus. He finds that 32 like to watch football. Is the random condition for finding confidence intervals met? Explain.
O Yes, the random condition for finding confidence intervals is met because np = 32 and n(1 - P) = 18, both of which are greater than 10
O Yes, the random condition for finding confidence intervals is met because the sample size is greater than 30.
O No, the random condition for finding confidence intervals is not met because np = 32 and n(1 - p) = 18, both of which are less than 100
O No, the random condition for finding confidence intervals is not met because the sample is not at least 50% of the population
O Yes, the random condition for finding confidence intervals is met because the sample is a simple random sample.




Cilantro tastes like soap to some people. This soap taste is inherited through the olfactory receptor gene OR6A2. About 14% of the population has this gene. You wa
to estimate the proportion of Americans who have this gene. How large a sample must you test, with a 3% margin of error and 95% confidence, to estimate the
proportion of people who carry the OR6A2 gene?
O 514 people
O 134 people
O 17.689 people
O 35 people
01.028 people



The faculty members at McAdenville High School want to determine whether there are enough students to have a Winter Formal. Sixty-three of the 150 students
surveyed said they would attend the Winter Formal. Construct and interpret a 99% confidence interval for p.
O The 99% confidence interval is (0.3162, 0.5238). We are 99% confident the true proportion of students attending the Winter Formal is between 31 62% and
52.38%.
© The 99% confidence interval is (0.3162, 0.5238). There is a 99% chance that a randomly selected student who will attend the Winter Formal lies between
31.62% and 52.38%
O The 99% confidence interval is (0.3162, 0.5238). Ninety-nine percent of all samples of this size will yield a confidence interval of (0.3162, 0.5238).
O The 99% confidence interval is (0.4762, 0.6838). We are 99% confident that the true proportion of students attending the Winter Formal is between 47 62%
and 68.38%
O The 99% confidence interval is (0. 4762, 0.6838). Ninety-nine percent of all samples of this size will yield a confidence interval of (0.4762, 0.6838)

PLEASE HELP ASAP, please don’t waste my time if you don’t know what your talking about THANK YOU GUYSSS

This diagram shows the plan for a wooden deck. The scale dimensions of the deck are shown.
If the scale used in the diagram is 1/4 = 1ft.
what is the perimeter of the actual deck?

36 ft

48 ft

12 ft

3 ft

1
Select the correct answer.
Which function defines (f + g)(),
f(t) = ln(2x) – 15
g(x) = 3 sin(I) – 7
=
OA. (f + 9) () = ln(2x) + 3 sin(x) + 22
3a )
OB
B. (f + g)() = ln(2x) + sin(o) – 66
OC. (f + 3)(0) = ln(2x) + 3 sin(a) – 22
(
In
D. ( + g)(x) = ln(2x) – 3 sin(x) = 8
Reset
Next

The function[tex]f(x)=-11sin (\frac{7}{3}x+\frac{1}{6}) - 2[/tex] models the average rate of change in temperature of a substance monitored in an experiment. In the function, x represents the number of minutes since the commencement of the experiment and the temperature of the substance is measured in degrees Fahrenheit.

Over what range of temperatures does the average rate of change in temperature fall?

Guests at a wedding have an appetizer
choice of soup or a salad, an entrée choice
of chicken, steak, or vegetarian, then a
dessert choice of vanilla or chocolate cake.
How many different meals are possible?

Hank has 6 black pens, 4 red pens, and 14 pencils in his desk drawer.
If he reaches into his desk drawer and randomly selects something to write with, what is the probability that he will grab a pen?

suppose that there is a circular race track. Joseph takes 25 minutes to finish it and Owuor takes 35 minutes
to finish it. If both of them start running from the same point at the same time in the same direction, after
how many minutes will they meet for the first time on the starting point?

The probability of spinning am even number is 40%. What is the probability of not spinning an even number, written as a decimal

4. At a local print shop, 25 copies cost $1.50. At this rate, how much would 60 copies cost?

96x 3+(9*8) ÷ 126,980 =?

help me pleeeeeeease