Answers
step 1
Find out sine
Remember the identity
[tex]cos^2\theta+sin^2\theta=1[/tex]substitute the given value of cosine
[tex]\begin{gathered} (\frac{5}{9})^2+s\imaginaryI n^2\theta=1 \\ \\ s\imaginaryI n^2\theta=1-\frac{25}{81} \\ \\ s\mathrm{i}n^2\theta=\frac{56}{81} \\ \\ sin\theta=\frac{\sqrt{56}}{9} \\ \\ sin\theta=\frac{2\sqrt{14}}{9} \end{gathered}[/tex]step 2
Find out cosecant
[tex]\begin{gathered} csc\theta=\frac{1}{sin\theta} \\ \\ csc\theta=\frac{9}{2\sqrt{14}}*\frac{\sqrt{14}}{\sqrt{14}}=\frac{9\sqrt{14}}{28} \\ \\ csc\theta=\frac{9\sqrt{14}}{28} \end{gathered}[/tex]step 3
Find out secant
[tex]\begin{gathered} sec\theta=\frac{1}{cos\theta} \\ \\ sec\theta=\frac{9}{5} \end{gathered}[/tex]step 4
Find out tangent
[tex]\begin{gathered} tan\theta=\frac{sin\theta}{cos\theta} \\ \\ tan\theta=\frac{\frac{2\sqrt{14}}{9}}{\frac{5}{9}}=\frac{2\sqrt{14}}{5} \end{gathered}[/tex]step 5
Find out cotangent
[tex]\begin{gathered} cot\theta=\frac{1}{tan\theta} \\ \\ cot\theta=\frac{5}{2\sqrt{14}}*\frac{\sqrt{14}}{\sqrt{14}}=\frac{5\sqrt{14}}{28} \\ \\ cot\theta=\frac{5\sqrt{14}}{28} \end{gathered}[/tex]Related Questions
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Which inequality correctly compares 118%, 0.34, and two and one fifth?
0.34 < 118% < two and one fifth
118% < 0.34 < two and one fifth
0.34 < two and one fifth < 118%
two and one fifth < 0.34 < 118%
Answers
Which inequality correctly compares 118%, 0.34, and two and one fifth?
0.34 < 118% < two and one fifth
118% < 0.34 < two and one fifth
0.34 < two and one fifth < 118%
two and one fifth < 0.34 < 118%
118% = 118%
0.34 = 34%
2 and 1/5 = 200.2%
34% < 118% < 200.2%
What can you conclude from the information in the diagram?
Answers
Answer:
Triangle UVT and TSR are isosceles triangles (two equal sides).
Angle WUV = Angle WTV (base angles of isosceles triangle)
Angle RTS = Angle TRS (base angles of isosceles triangle)
Line VW is perpendicular to line UT.
Angle WTV = Angle RTS (vertically opposite angles)
Angle WTR = Angle VTS (vertically opposite angles)
Describe the transformation of f(x)= x2 represented by g. then graph.
Answers
help meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee
Answers
Answer:
d
Step-by-step explanation:
The number of years must be non-negative.
This eliminates all of the options except for d.
5. Which equation is solved for the height of the cone based on theinformation given below ?
Answers
The equation for the Volume (V) of the cone given is,
[tex]V=\frac{1}{3}\pi r^2h[/tex]We are to isolate 'h' in the equation above
SOLUTION
Multiply both sides by 3
[tex]3V=3\times\frac{\pi}{3}r^2h[/tex]Simplify
[tex]3V=\pi r^2h[/tex]Divide both sides by πr²
[tex]\frac{3V}{\pi r^2}=\frac{\pi r^2h}{\pi r^2}[/tex]Simplify
[tex]h=\frac{3V}{\pi r^2}[/tex]Hence, the answer is
[tex]h=\frac{3V}{\pi r^2}\text{ (OPTION D)}[/tex]A large pizza pie with 15 slices is shared among x students such that each student's share is 3 slices. Write it as a mathematical statement.
Answers
15/x = 3
Explanation:Total number of slices = 15
Number of students = x
Each student's share = 3
(Total number of slices)/(Number of students) = Each student's share
Therefore, the mathematical statement representing the illustration is:
15/x = 3
A student is initially outside. He is given the choice with a probability of 0.4 of going to the playground, 0.3 of shopping in the mall and 0.3 of returning home. If he is in the playground, he takes 2 hrs of time and then decides to stay in the playground again or return back home. (he can continue to decide to stay in playground like a recursive process) Similarly, If he is in the mall, he takes 3 hrs of time and then decides to stay in the mall again or return back home. (he can continue to decide to stay in mall like a recursive process) For all cases, it takes 1 hr to return home. what is the expected hours the student was outside home?
Answers
Based on the probability values, it will take the student 2 hours to stay outside the home
How to determine the expected value of the student?The given parameters are:
Probabilities
P(1) = 0.4
P(2) = 0.3
P(3) = 0.3
Time
Time 1 = 2 hours
Time 2 = 3 hours
Time 3 = 1 hour
When the above are represented on a table, we have the following table of values
Time (x) | 2 3 1
Probability (P(x)) | 0.4 0.3 0.3
The expected value of the student is then calculated as
E(x) = ∑ x * P(x)
Substitute the known values in the above equation
E(x) = 2 * 0.4 + 3 * 0.3 + 1 * 0.3
Evaluate the products
E(x) = 0.8 + 0.9 + 0.3
Evaluate the sum
E(x) = 2
Hence, the expected value is 2
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Line k is shown below.Vai4 321 (2, 1)x-5 -4 -3 -2I NON0 1 2 3 4 5k(-4,-2) 3-5Which ratio represents the slope of a line parallelto line k??221O-221
Answers
hello
to solve this problem, we have to use the formula of slope of a line
[tex]\begin{gathered} \text{slope(m)}=\frac{y_2-y_1}{x_2-x_1} \\ y_2=1 \\ x_2=2 \\ y_1=-2 \\ x_1=-4 \end{gathered}[/tex]substitute the values into the equation (formula)
[tex]m=\frac{1-(-2)}{2-(-4)}=\frac{1+3}{2+4}=\frac{4}{6}=\frac{2}{3}[/tex]from the calculations above, the slope of the line is equal to 2/3
Solve the following quadratic equation by the square root method. If needed, write your answer as a fraction reduced to lowest term
Answers
Solution
Solve the following quadratic equation by the square root method.
[tex]\begin{gathered} y^2-10y+25=-49 \\ y^2-10y+25+49=0 \\ y^2-10y+74=0 \end{gathered}[/tex]Therefore the correct answer for y are
[tex]y=5+7i,\text{ 5-7i}[/tex]the recommended amount of meat to serve 1 and 1/2 dozzen people is 4 and 1/2 pounds. how many pounds of meat are recommended to feed 1 dozzen people? how many pounds are recommended to feed 4 people? and how many pounds are recommended to feed 1 person
Answers
First, 1 dozen is 12 units, so
[tex]1\frac{1}{2}\text{ dozen people }=\text{ 12 people + 6 people = 18 people}[/tex]Now, to solve the exercise you can use the rule of three. So, you have
*How many pounds of meat are recommended to feed 1 dozen people?
[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 12\text{ people}\rightarrow x\text{ pounds} \\ x=\frac{12\text{ people }\ast\text{ 4.5 pounds}}{18\text{ people}} \\ x=\frac{54}{18}\text{ pounds} \\ x=3\text{ pounds} \end{gathered}[/tex]Therefore, 3 pounds of meat is recommended to feed a dozen people.
*How many pounds are recommended to feed 4 people?
[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 4\text{ people}\rightarrow x\text{ pounds} \\ x=\frac{4\text{ people }\ast\text{ 4.5 pounds}}{18\text{ people}} \\ x=\frac{18}{18}\text{ pounds} \\ x=1\text{ pound} \end{gathered}[/tex]Therefore, 1 pound of meat is recommended to feed 4 people.
*How many pounds are recommended to feed 1 person
[tex]\begin{gathered} 18\text{ people}\rightarrow4.5\text{ pounds} \\ 1\text{ person}\rightarrow x\text{ pounds} \\ x=\frac{1\text{ person}\ast4.5\text{ pounds}}{18\text{ people}} \\ x=\frac{1}{4}\text{ pounds} \end{gathered}[/tex]Therefore, 1/4 pound of meat is recommended to feed 1 person.
Choose the equation of a circle with radius 9 and center (3,-4).
Choose the correct answer below.
○ A. (x+3)² + (y− 4)² = 81
○ B. (x − 3)² + (y+4)² = 81
○ C. (x+3)² + (y−4)² = 9
OD. (x-3)²+(y+4)² =
Answers
Answer:
B. (x − 3)² + (y+4)² = 81
Step-by-step explanation:
If a circle has center located at (a, b) and radius of r, the equation of this circle is
(x - a)² + (y-b)² = r²
We have a = 3, b = -4 and r = 9
So equation is
(x - 3)² + y - (-4))² = 9²
==> (x − 3)² + (y+4)² = 81
a table shows the cost (in cents) of producing and distributing each coin for the years 2007 and 2014
which coin has a cost in 2014 that is less than 0.95 times the cost in 2007
2007. 2014
quarter. 9.78. 8.95
dime. 4.09. 3.91
nickel. 9.53. 8.09
penny. 1.67. 1.66
Answers
The dime has a cost in 2014 that is less than 0.95 times the cost in 2007.
To solve this problem by finding out the ratio. We can solve this problem by following a few steps.
According to the question, the cost in 2014 is less than 0.95 times the cost in 2007.
So the ratio is 1: 0.95. Which can be written as, 1/ 0.95 = 100/95 = 20/19 = 20: 19.
Now, we have to find among all those coins which follow the trend of 20: 19.
For the quarter, the ratio is 9.78: 8.95 = 9.78 / 8.95 ≠ 20 : 19For the dime, the ratio is 4.09: 3.91 = 4.09/3.91 ≈20: 19For the nickel, the ratio is = 9.53: 8.09= 9.53. 8.09 ≠ 20: 19For the penny, the ratio is = 1.67: 1.66 = 1.67/1.66 ≠ 20: 19Here only the price of a dime has declined 0.95 times.
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a survey survey asked 200 students to name their favorite fruit the table shows the results of a survey
Answers
Part A
Fraction of peach 2/5
Total = 200
number of students that pick peach as their favorite fruits
[tex]\begin{gathered} =\text{ }\frac{2}{5}\text{ x 200} \\ =\text{ }\frac{2\text{ x 200}}{5} \\ =\text{ }\frac{400}{5} \\ =\text{ 80 students} \end{gathered}[/tex]Part B
number of students that pick orange as their favorite fruits
[tex]\begin{gathered} =\frac{3}{8}\times200^{} \\ =\text{ }\frac{3\text{ x 200}}{8} \\ =\text{ }\frac{600}{8} \\ =\text{ 75} \end{gathered}[/tex]number of students that pick plum as their favorite fruits
[tex]\begin{gathered} =\text{ }\frac{1}{10}\text{ x 200} \\ =\text{ }\frac{200}{10} \\ =\text{ 20} \end{gathered}[/tex]There are 55 more students that chose orange rather than plum.
A ticket to see your favorite baseball team costs $30.86. That price decreases by $0.35 for every game lost during the regular season. What equation could you use to find the cost C of a ticket after L losses? Represent the total change in the cost of a ticket after the team loses 31 games. What is the price of a ticket after the team loses 31 games?
Answers
Answer:20.01
Step-by-step explanation:
0.35x31=10.85
30.86-10.85=20.01
11. Find the length of the missing side. 16 25 19
Answers
Answer:
x = 14.12
Explanation:
To find the missing side, we will use the cosine law:
[tex]c^2=a^2+b^2-2ab\cos (C)[/tex]Where a, b, and c are the length of the sides of the triangle and C is the measure of the angle formed by the sides a and b.
So, we can use the equation to find the angle formed by the side of length 35 and the side of length 44 (25 + 19 = 44). So, replacing a by 35, b by 44, and c by 16, we get:
[tex]16^2=35^2+44^2-2(35)(44)\cos (\theta)[/tex]Then, solving for θ, we get:
[tex]\begin{gathered} 256=1225+1936-3080\text{cos(}\theta) \\ 256=3161-3080\cos (\theta) \\ 256-3161=-3080\cos (\theta) \\ -2905=-3080\cos (\theta) \\ \frac{-2905}{-3080}=\cos (\theta) \\ 0.9432=\cos (\theta) \\ \cos ^{-1}(0.9432)=\theta \\ 19.41=\theta \end{gathered}[/tex]Now, we can calculate the length of the missing side, using the angle θ = 19.41°, the side with length 35 and the side with length 25 as:
[tex]x^2=35^2+25^2-2(35)(25)\cos (19.41)[/tex]Therefore, the value of x is:
[tex]\begin{gathered} x^2=1225+625-1650.56 \\ x^2=199.44 \\ x=\sqrt[]{199.44} \\ x=14.12 \end{gathered}[/tex]So, the length of the missing side is 14.12
In a single throw of a fair die, what is the probability that an odd number or a perfect square greater than one shows up?
Answers
The probability that an odd number or a perfect square greater than one shows is 2/3.
Probability - The area of mathematics known as probability deals with numerical representations of the like that an event will occur or that a statement is true.
The probability of an event is a value between 0 and 1.total no. of outcomes - 1,2,3,4,5,6
odd number = 1,3,5
or a perfect square = 4
probability - dividing the favorable number of outcomes by the total number of possible outcomes.
probability = favorable outcomes / total no. of outcomes
= 4/6
= 2/3
The probability that an odd number or a perfect square greater than one shows is 2/3.
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What would the simplified form be to-√12+3√3
Answers
Construct a difference table to predict the next term of sequence. 6, 1, 0, 10, 38, 91,.......
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Number..................Difference1........... Difference 2.....Difference 3
6...........................................................................................
1................................ -5......................................................
0.............................. -1....................................4..............
10.............................. 10..................................11......................7
38.............................. 28................................18..................... 7
91.............................. 53................................25................... 7
176............................85..............................32
Answer:
Next number in sequence 176
If A={h,y,d,r,o,p,l,a,n,e,s} and U={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}, find A′
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Answer:
A' = { b,c,f,g,i,j,k,m,q,t,u,v,w,x,z }
Step-by-step explanation:
Write an equation that represents the line.
Use exact numbers.
Answers
Answer:
y = 0.75x + 2
Step-by-step explanation:
Take two distinct points on the graph
Compute the slope m and y-intercept b
Equation of line in slope-intercept form is
y = mx + b
Take points (0, 2) and (4, 5)
Slope m = (5 - 2) /(4-0) = 3/4
y-intercept from the graph is 2
So y = 3/4 x + 2 =0.75x + 2
please i need help
Answers
Answer:
they both go up by 2
A teacher was helping me but I got force quite the app due to lag can you help me with question C, D, and E !!!
Answers
Parts C, D and E
Answer:
Explanation:
C) The maximum height is the highest point on the graph. On the x axis of the graph, each small square is 0.25 units. Thus, the x coordinate of the maximum height is is 1.25. The ball reached maximum height after 1.25 seconds
D) There were two different times when the ball was at 10m.
When y = 10 m, x = 0.5
when y = 10, x = 2
At 0.5 and 2 seconds, the ball was at 10m
E) A the time the when the ball hit the ground, the height is 0. Thus, the time when the ball hits the ground is 3 seconds
Hello, I need some assistance with this precalculus homework question, please?HW Q2
Answers
Answer:
A. The solution set is {4096}.
Explanation:
Given the logarithmic equation:
[tex]\frac{1}{2} \log _{6} x=3 \log _{6} 4[/tex]Multiply both sides of the equation by 2:
[tex]\begin{gathered} \frac{1}{2}\times2\log_6x=3\times2\log_64 \\ \log_6x=6\log_64 \end{gathered}[/tex]Next, apply the power law of logarithms to the right side of the equation.
[tex]\begin{gathered} \log_6x=\log_64^6 \\ \implies\operatorname{\log}_6x=\operatorname{\log}_64096 \end{gathered}[/tex]Since the bases are the same, equate the numbers:
[tex]x=4096[/tex]The solution set is {4096}.
Write a quadratic equation in standard form with the given root(s) -7,3/4 and can you explain how you did it? i need it ASAP please and thank you
Answers
The equation of the quadratic equation is P(x) = x² + 23/4x - 21/4
What are quadratic equations?Quadratic equations are second-order polynomial equations and they have the form y = ax^2 + bx + c or y = a(x - h)^2 + k
How to determine the quadratic equation?The given parameters are
Zeros = -7 and 3/4
The sum of multiplicities of the quadratic equation must be equal to the degree.
This means that the multiplicity of the zeros -7 and 3/4 is 1
The equation of the quadratic equation is then calculated as
P(x) = (x - zero)^ multiplicity
So, we have
P(x) = (x + 7)(x -3/4)
Expand
P(x) = x² + 7x - 3/4x - 21/4
This gives
P(x) = x² + 23/4x - 21/4
Hence, the equation is P(x) = x² + 23/4x - 21/4
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2. Tony's bill at a restaurant was $47.24. He planned to leave an 18% tip for the waiter. How muchdid he pay overall? (2 points)
Answers
Determine the amount paid by the Tony overall.
[tex]undefined[/tex]Write the augmented matrix for the following system of equations.
9y-5+9z = 0
7x=-3y+7+z
5x + 7y = 5
Answers
The augmented matrix is [tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex].
What is a matrix?
A rectangular array or table containing numbers, symbols, or phrases that are arranged in rows and columns is known as a matrix.
The given system of equations is:
9y - 5 +9z = 0
7x = -3y +7 + z
5x + 7y = 5
Rewrite the equations as:
0x + 9y + 9z = 5
7x +3y -1z = 7
5x + 7y + 0z= 5
Therefore, the augmented matrix for the system of equations is:
[tex]\begin{bmatrix}0&9&9&|&5\\7&3&-1&|&7\\5&7&0&|&5\end{bmatrix}[/tex]
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Find the tangent of
Answers
To find tan S, we will use the trigonometric ratio:
[tex]\text{tan}\theta=\frac{opposite}{adjacent}[/tex]From the question,
θ=S opposite=55 adjacent = 48
substitute the values into the formula
[tex]\tan S=\frac{55}{48}[/tex]Complete the mapping of the vertices of ADEF. D(2,-4) - D E(1,-1) - E F(5, 1) - F >
Answers
The vertices of the ΔDEF are given by (-4, 2)D', (-1, 1)E' , (1, 5)F' through mapping.
what is mapping?
Any set, including all whole integers, all the points on a line, or all the objects inside a circle, can be mapped. A mapping of the set of all whole numbers onto the set of even numbers is defined by the expression "multiply by two," for instance. A rotation is an internal map of a plane or of all of space.
The vertices of ΔDEF are given by D(2,-4) - D E(1,-1) - E F(5, 1).
According to the rule defining a reflection across the line, y=x should be stated when reflecting a point across the line. Then, the x and y coordinates are switched as follows:
y(x, y) → (y, x)
Let's now use the aforementioned rule to finish mapping the vertices of DEF. Change the x and y coordinate locations as follows:
D(2, –4) gives (-4, 2)D'E(1, –1) gives (-1, 1)E'F(5, 1) gives (1, 5)F'The vertices of the ΔDEF are given by (-4, 2)D', (-1, 1)E' , (1, 5)F' through mapping.
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Which expression is equivalent to -4(2 - 6x) - 2.5x ?
Answers
Rewriting the expression, we have:
[tex]\begin{gathered} -4\mleft(2-6x\mright)-2.5x \\ =-8+24x-2.5x \\ =21.5x-8 \end{gathered}[/tex]So an equivalent expression is 21.5x - 8.
Find the greatest common factor (GCF) of 64 and 72.A. 8B. 9C. 4D. 12
Answers
Okay, here we have this:
Let's decompose each number and then we see their common factors:
64=2*2*2*2*2*2
72=2*2*2*3*3
The factors common to both are: 2*2*2, and by multiplying we obtain that the greatest common divisor is 8. The correct answer is option A.