I really need help solving this practice from my prep guide in trigonometryI don’t know why but I have a hard time solving it completely
Answers
Given:
\(\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\sec (-\pi)\)First
Recall
\(\sec (\pi)=\frac{1}{\cos (\pi)}\)This implies
\(\sec (-\pi)=\frac{1}{\cos (-\pi)}\)Hence, the given expression becomes
\(\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\frac{1}{\cos (-\pi)}\)Using calculator
\(\cos (-\pi)=-1\)Hence,
\(\begin{gathered} \frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\frac{1}{\cos (-\pi)} \\ =\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}-\frac{1}{-1} \\ =\frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}+1 \end{gathered}\)Also,
\(\sin (\frac{7\pi}{4})=-\frac{1}{\sqrt[]{2}}\)This gives
\(\begin{gathered} \frac{\tan(-\frac{2\pi}{3})}{\sin(\frac{7\pi}{4})}+1 \\ =\frac{\tan(-\frac{2\pi}{3})}{-\frac{1}{\sqrt[]{2}}}+1 \end{gathered}\)Simplifying the expression gives
\(\begin{gathered} \frac{\tan(-\frac{2\pi}{3})}{-\frac{1}{\sqrt[]{2}}}+1 \\ =\tan (-\frac{2\pi}{3})\div-\frac{1}{\sqrt[]{2}}+1 \\ =\tan (-\frac{2\pi}{3})\times-\sqrt[]{2}+1 \\ =-\sqrt[]{2}\tan (-\frac{2\pi}{3})+1 \end{gathered}\)Using the following property
\(\tan (-x)=-\tan (x)\)It follows
\(\tan (-\frac{2\pi}{3})=-\tan (\frac{2\pi}{3})\)Hence the expression becomes
\(\begin{gathered} -\sqrt[]{2}\tan (-\frac{2\pi}{3})+1 \\ =-\sqrt[]{2}(-\tan (\frac{2\pi}{3}))+1 \\ =\sqrt[]{2}\tan (\frac{2\pi}{3})+1 \end{gathered}\)And
\(\tan (\frac{2\pi}{3})=-\sqrt[]{3}\)This gives
\(\begin{gathered} \sqrt[]{2}\tan (-\frac{2\pi}{3})+1 \\ =\sqrt[]{2}(-\sqrt[]{3)}+1 \end{gathered}\)Simplifying the expression gives
\(\begin{gathered} \sqrt[]{2}(-\sqrt[]{3)}+1 \\ =-\sqrt[]{6}+1 \end{gathered}\)Therefore, the answer is
\(-\sqrt[]{6}+1\)Related Questions
Problem 3: In the game “Sorry!” players draw a card and move around the board to get to their home.
The modern game has 45 cards in a deck - 5 ones and 4 each of 2, 3, 4, 5, 7, 8, 10, 11, 12, and SORRY. A
player can leave their start square if they draw a 1 or a 2. They can also leave their start square if they
draw a SORRY, but only if another player is on the board (the SORRY card allows you to leave your start
square by sending another player home). Assume there are four players in the game.
1. What is the probability that the first player gets out on the first card? (They draw a one or a
two)?
2. What is the probability that, if the first player is already out, the second player gets out? (They
draw a 1 or a 2 or a SORRY)
3. What is the probability that all four players get out on their first try?
4. What is the probability that none of the players get out on their first try?
5. What is the probability that at least one of the players gets out on their first try?
Answers
P(getting out on first try) = 5/45 = 1/9, P(getting out on second try) = (5 + 1)/40 = 3/20, P(all players getting out on first try) = (1/9) * (3/20) * (3/19) * (3/18) = 1/3690, P(none getting out on first try) = 1 - P(at least one getting out on first try), P(at least one getting out on first try) = 1 - P(none getting out on first try).
What does the first probability law state?According to the First Law of Probability, the outcomes of one chance event have no bearing on those of succeeding chances occurrences.
1. The odds of drawing a 1 or a 2 are added to determine the likelihood that the first player exits the game after the first card. There are 45 cards in all, 5 of which have a 1 or a 2, hence the probability of getting out on the first try is P(getting out on first try) = 5/45 = 1/9.
2. There are still 40 cards in the deck if the first player is already out, and the second player can exit the game by drawing a 1, a 2, or a SORRY. The probability of getting out on the second try is P(getting out on second try) = (5 + 1)/40 = 3/20 since there are 5 cards with a 1 or a 2, plus 1 SORRY card.
3. The first player must draw a 1 or a 2, the second player must draw a 1, the third player must draw a 2, the fourth player must draw a SORRY, and so on. The likelihood that this will occur is P (all players successfully exiting the game on their first attempt) = (1/9) * (3/20) * (3/19) * (3/18) = 1/3690.
4. The complement of the likelihood that at least one player goes out on their first try is the probability that none of the players get out on their first try. So, if we compute the likelihood that at least one player will be eliminated after their first attempt and deduct it from 1, we obtain: P (none succeeding on the first attempt) = 1 - P (at least one getting out on first try).
5. The chance that no players get out on their first try, which we computed in part 4, may be used to calculate the probability that at least one player gets out on their first try: P(at least one getting out on first try) = 1 - P. (none getting out on first try).
To know more about Probability visit:
https://brainly.com/question/30700591
#SPJ1
Which ordered pairs do not belong to a linear function in the form below?
y= kx+ b
A. (0, 1); (1, 0); (2, -1)
B. (0, 1); (1, 2); (2,5)
C. (-2,5); (-1, 2); (0, -1)
D. (-2, 1); (-1, 1); (0, 1)
Answers
Answer:
B. (0, 1); (1, 2); (2,5)
Step-by-step explanation:
All of the given answer choices have x-values that are sequential. A linear function will have y-values that are also evenly spaced.
A: 0-1 = -1, -1-0 = -1 . . . . differences are the same
B: 2-1 = 1, 5-2 - 3 . . . . . differences are not the same, not a linear function
C: 2-5 = -3, -1-2 = -3 . . . . differences are the same
D: 1-1 = 0, 1-1 = 0 . . . . differences are the same
The domain of this emath equation is
Answers
Answer:
x ≥ 5
Step-by-step explanation:
You want the domain of the equation y = √(x -5) -1.
DomainThe domain of the function is the set of x-values for which it is defined. The square root is not defined for negative values, so the domain is ...
x -5 ≥ 0
x ≥ 5 . . . . . . the domain of this function
__
Additional comment
The range is the set of y-values the function may produce. Here, that set of values is y ≥ -1.
<95141404393>
11. Martin's suitcase has a volume of 1,080 cubic inches. Lily's suitcase measures 9 inches wide, 13 inches long, and 21 inches high. What is the combined volume of the two suitcases?
Answers
Answer: 3,348 cubic inches
Step-by-step explanation:
1. Since we know that volume= length x width x height, then we can plug our values into this equation.
2. So, we would do volume= 9 x 12 x 21.
3. 9 x 12 = 108, and 108 x 21 =2,268.
4. Now that we have both of the volumes, we have to add them together.
5. 1,080 + 2,268 = 3,348
6. The combined volume is 3,348 cubic inches.
The figure below shows three small circles, each
with a diameter of 6 centimeters, inside a larger
circle.
Answers
X is less than 7 and greater than -7
Answers
Answer:
False
Step-by-step explanation:
& is greater that 7 because you are going back to the nmber like in the negatives
How do you solve this??
21 a(little 6) b(little 5)
————————————
7 a(little 3) b
Answers
\((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)
To solve this problemWe can use the rules of exponents and simplify the terms with the same base.
Dividing the coefficients: 21 / 7 = 3.
For the variables, you subtract the exponents: \(a^6 / a^3 = a^(^6^-^3^) = a^3.\)
Similarly,\(b^5 / b = b^(5-1) = b^4\).
Putting it all together, the simplified expression is:
\(3a^3b^4.\)
Therefore, \((21a^6b^5) / (7a^3b)\) simplifies to \(3a^3b^4.\)
Learn more about rules of exponents here : brainly.com/question/11975096
#SPJ1
Question 3 (1 point)
(07.07)
Find the product of (x + 5)2. (1 point)
O a
x2 - 10x + 25
Ob
x² – 25
Oc
x2 + 25
Od
x2 + 10x + 25
Answers
(a+b)2 =a2+2ab+b2
Someone please help! What is the domain and range of the relation?
Answers
Answer:
The domain is the set of all first elements of ordered pairs (x-coordinates).
The range is the set of all second elements of ordered pairs (y-coordinates).
Only the elements "used" by the relation or function constitute the range.
A polygon with an area of 10 square inches is dilated by a scale factor of 4, what is the new area?
Answers
The new area would be 40 square inches. When a scale factor dilates a polygon, the area is multiplied by the square of the scale factor. If the original area is 10 square inches and the scale factor is 4, the new area would be 10 x 4^2 = 10 x 16 = 40 square inches.
e) Over a season a football team won, drew and lost matches in the ratio 2:1:5.
The team lost 12 more matches than they won.
Workout how many matches the team drew.
HELP PLS!!! EXPLANATION COULD BE USEFUL TOO!!
Answers
Answer: 4 ties or draws
8 wins, 4 ties, 20 losses
===========================================================
Explanation:
The ratio 2:1:5 is of the format wins:ties:losses where getting a draw is the same as getting a tie.
So one possibility is that they won 2 matches, tied once, and lost 5 matches. The only problem is that it doesn't fit with the statement that "The team lost 12 more matches than they won."
We could guess-and-check our way to the answer, but I think using algebra is the most efficient route.
----------
Let x = number of ties
2x = number of wins and 5x = number of losses
Note the ratio 2x:x:5x reduces to 2:1:5 after dividing everything by x.
Since the team lost 12 more matches than they won, this means,
loss count = (win count) + 12
5x = (2x) + 12
5x-2x = 12
3x = 12
x = 12/3
x = 4
The team tied 4 times and has 2x = 2*4 = 8 wins and 5x = 5*4 = 20 losses.
The ratio 8:4:20 reduces to 2:1:5 when you divide all parts by the GCF 4.
Also, the gap between 8 wins and 20 losses is 20-8 = 12 to help fully confirm we have the correct answer.
Find the range of f(-5)=-2|x-5|+8 please with explination.
Answers
Answer:
Domain: set of possible input values (x-values)
Range: set of output values (y-values)
The range for the function \(f(x)=-2|x-5|+8\) is:
\(f(x)\leq 8\)
(5, 8) is the vertex of the line
Because |x - 5| is absolute (so always positive) and it is multiplied by -2,
-2|x - 5| will always be negative unless x = 5 (when it will be zero). Therefore, the max y-value is 8.
However, your question actually asked what the function is when x = -5:
\(f(-5)=-2|x-5|+8\\\\= -2|-5-5|+8\\\\= -12\)
Step-by-step explanation:
Thats the all rhe answers step by step
Solve for x.Enter the solutions from least to greatest.(3x – 6)(-x+ 3) = 0lesser x =greater x =
Answers
(3x – 6)(-x+ 3) = 0
then
3x - 6 = 0 or -x + 3 = 0
3x = 6 or -x = -3
Divide both sides by 3 and -1
3x/3 = 6/3 or -x/-1 = -3/-1
x = 2 or x = 3
lesser x = 2
greater x = 3
Can anyone help me here this is a mastery test by the way. Too tired to type it out so I put a photo.
^
|
Answers
Answer:
1st Question is 22r4
2nd Question is 22r16
3rd Question is 11r11
4th Question is 11r30
Step-by-step explanation:
Hope this helps. I'll give you my energy.
The radius of a circle is 4 miles. What is the length of a 45° arc?
45°
r=4 mi
Answers
The length of a 45° arc with a radius of 4 miles is approximately 3.14 miles, calculated using the formula for arc length.
To determine the length of a 45° arc given a radius of 4 miles, we can use the formula: Arc length = (angle measure / 360°) x 2πr, where r is the radius of the circle and π is a constant equal to approximately 3.14.
Substituting the given values into the formula, we get: Arc length = (45° / 360°) x 2π(4 mi)Arc length = (1/8) x 2π(4 mi)Arc length = (1/8) x 8π Arc length = π
The length of the 45° arc is approximately 3.14 miles.
Summary: To find the length of a 45° arc of a circle, we use the formula: Arc length = (angle measure / 360°) x 2πr. Given a radius of 4 miles, we can substitute the values into the formula to get the length of the 45° arc, which is approximately 3.14 miles.
For more questions on arc length
https://brainly.com/question/31341388
#SPJ8
Find the tangents of the acute angles in the right triangle. Write each answer as a fraction. WILL MAKE BRAINLIEST!!
tan G = ?
tan H = ?
Answers
The tangents of the acute angles in the right triangle gives:
tan(G) = 2
tan(H) = 1/2
How to find the tangents of angles?It should be noted that tangent is the ratio of opposite over adjacent. Thus:
tan(angle) = opposite/adjacent
So for reference angle G, we say,
tan(G) = JH/GJ = 2/1 = 2
We'll treat tan(H) in a similar fashion, but the opposite and adjacent sides swap roles. That means we'll apply the reciprocal to the result above to get 1/2 for tan(H)
So we have this interesting property where
tan(G)*tan(H) = 2*(1/2) = 1
In general,
tan(A)*tan(B) = 1 if and only if A + B = 90 degrees
Read more about tangents at: https://brainly.com/question/28035740
#SPJ1
Genny is making bracelets for her friends. She can make 3 bracelets in 15 minutes. How long will it take Genny to make a bracelet for all 10 of her friends?
Answers
Answer:
50 minutes
Step-by-step explanation:
15 / 3 = 5
5 x 10 = 50
Answer
50 minutes
Step-by-step explanation:
If Genny makes 3 bracelets in 15 minutes, she can make 9 bracelets in 45 minutes.
9/3 = 3
3 x 15 = 45 minutes
She needs to make one more bracelet. It takes 5 minutes to make one bracelet because: 15/3 = 5/1 (Five minutes = One bracelet)
45 mins + 5 mins = 50
A factory made 3 jars of creamy peanut butter and 97 jars of chunky peanut butter. What percentage of the jars of peanut butter were creamy?
Answers
Answer:
3%
Step-by-step explanation:
They made 97+3 total jars, 3 out of 100 is 3 percent.
A car is traveling at a speed of 85mph. The diameter of the wheel is 2 feet what is the angular speed in revolutions per second
Answers
Expand the expression.
1/5(15+10x-5)
Answers
Answer:
2x+2
Step-by-step explanation:
farthest it can go
A building in a city has a rectangular base. The length of the base measures 75 ft less than three times the width. The
perimeter of this base is 810 ft. What are the dimensions of the base?
ed
The width of the base is
ft.
Answers
Answer:
length = 285 ft
width = 120 ft
Step-by-step explanation:
Let the width = w.
length = 3w - 75
perimeter = 2(length + width)
810 = 2(3w - 75 + w)
405 = 4w - 75
480 = 4w
120 = w
w = 120
length = 3w - 75 = 3(120) - 75 = 285
A recent transportation survey of 500 college students yielded the following
information: 291 students own an automobile, 179 own a motorcycle, and 85 own
both an automobile and a motorcycle. What percent of the 500 students surveyed
own an automobile or a motorcycle?
Answers
The percent of the 500 students surveyed who own an automobile or a motorcycle is 555 / 500 x 100 = 111%.
What is surveys?Surveys are a type of data collection method used to gather information from a group of people. Surveys are typically administered through questionnaires, interviews, or focus groups. Surveys are used to collect information regarding an individual’s or group’s opinions, behaviors, beliefs, or preferences. Surveys are often used to measure public opinion on a variety of topics and to make predictions about potential outcomes. Surveys are valuable tools for gaining insight into a wide range of topics and can be used to inform decisions and strategies.
The total number of students who own an automobile or a motorcycle is the sum of students who own an automobile, students who own a motorcycle, and students who own both an automobile and a motorcycle. This sum is 291 + 179 + 85 = 555.
Therefore, the percent of the 500 students surveyed who own an automobile or a motorcycle is 555 / 500 x 100 = 111%.
To learn more about surveys
https://brainly.com/question/26851221
#SPJ1
the average of 10 numbers is 65 . the sum of the number is
Answers
Answer:
sum = 650
Step-by-step explanation:
average is calculated as
average = \(\frac{sum}{count}\)
given average = 65 and count = 10 , then
65 = \(\frac{sum}{10}\) ( multiply both sides by 10 )
10 × 65 = sum , that is
sum = 650
Your friend has a bag of yellow and purple candy. He wants to use them to play a game with you.
Purple is worth 2 points and yellow is worth three points. Pick 9 candies from the bag
Create a system of equations where the combination of the candies gives you a total of 22 points. Make sure you label and define your variables.
Answers
The system of equations where the combination of the candies gives you a total of 22 points are:
x + y = 9
2x + 3y = 22
How can we create system of equations?To create the equations, we shall first define the variables:
x = the number of purple candies
y = the number of yellow candies
Next, we shall use the given information that purple candies are worth 2 points and yellow candies are worth 3 points.
Then, we would make sure that the total number of candies selected is 9.
The first equation represents the total number of candies selected:
x + y = 9
The second equation represents the total number of points obtained:
2x + 3y = 22
Therefore, the system of equations is:
x + y = 9
2x + 3y = 22
This is a system of linear equations.
Learn more about system of linear equations at brainly.com/question/13729904
#SPJ1
salesperson earns $345 for selling $2300 in merchendice find the commison rate
Answers
Answer:
The commission rate is 15%
Step-by-step explanation:
commission = commission rate x sales
where the commission rate is expressed as a decimal.
In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:
345 = commission rate x 2300
To solve for the commission rate, we can divide both sides by 2300:
commission rate = 345/2300
Simplifying this expression, we get:
commission rate = 0.15
So, the commission rate is 15%
which of the following options is an odd function?
Answers
Answer: The answer is C
Step-by-step explanation:
PLEASE HELP ASAP!!
The table of values represents the function g(x) and the graph shows the function f(x). Which statement about the functions is true?
-all of the x-intercepts of f(x) are common to those of g(x)
-f(x) and g(x) intersect at exactly two points
-the minimum value of f(x) is less than the minimum value of g(x)
-f(x) and g(x) have the same y-intercept
Answers
Using function concepts, it is found that the correct statement is given by:
all of the x-intercepts of f(x) are common to those of g(x).
What are the x-intercepts of the functions?They are the values of x when x = 0, hence:
For g(x), it is of x = -1 and x = 1.For f(x), it is of x = -1.Hence, the first statement is correct, and the x-intercept x = -1 of f(x) is common to the x-intercept x = -1 of g(x).
More can be learned about function concepts at https://brainly.com/question/25537936
#SPJ1
PU
The data set below represents the different costs of a refrigerator at a local home improvement store.
$777, $498, $619. $379. $895, $1,256, $1,052
b. What is the median of the second half of the data? (third quartile) 379
T
Answers
Using the median concept, it is found that the third quartile is of is of $1,052.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
In this problem, the ordered data-set is:
$379, $498, $619, $777, $895, $1,052, $1,256.
Hence, the median of $777 divides the data-set into two halfs:
The first half is: $379, $498, $619.The second half is: $895, $1,052, $1,256.Hence, the third quartile, which is the median of the second half, is of $1,052.
More can be learned about the median concept at https://brainly.com/question/25215461
Andrea has 8 red buttons and 9 blue buttons. How many buttons does Andrea have?
Answers
Answer:
17 buttons
Step-by-step explanation:
Answer: 17
Step-by-step explanation:
8 + 9 = 17
he entire graph of the function is shown in the figure below.
Write the domain and range of using interval notation.
Someone please help me. I really nee help. this question is due tonight before 8 and im stuck.
Answers
The given graph shows that the function is periodic and fluctuates between y = -2 and y = 2. So, the range of the function is [-2,2].
The graph covers one period, which is from x = -3 to x = 3, and then repeats itself indefinitely in both directions. So, the domain of the function is (-∞, ∞).
In general, the domain of a function consists of all the possible input values that the function can take. In this case, since the function repeats itself indefinitely, it can take any input value from negative infinity to positive infinity.
So, the domain is (-∞, ∞). The range of a function, on the other hand, consists of all the possible output values that the function can produce.
In this case, the function oscillates between y = -2 and y = 2, so the range is [-2,2]. The interval notation for the domain is (-∞, ∞) and for the range is [-2,2].
for such more questions on function
https://brainly.com/question/11624077
#SPJ8