Using the attached link below.
A. Find sin x and csc y
B. Find tan x and cot y
C. Find cos x and sec y
D. And if sin theta = 2/3, find the values of cos theta and tan theta
Answers
[tex]\text{Use the Pythagorean theorem:}\\\\r-hypotenuse\\\\r^2=7^2+5^2\\\\r^2=49+25\\\\r^2=74\to r=\sqrt{74}[/tex]
[tex]\sin=\dfrac{opposite}{hypotenuse}\\\\\cos=\dfrac{adjacent}{hypotenuse}\\\\\tan=\dfrac{opposite}{adjacent}\\\\\cot=\dfrac{adjacent}{opposite}\\\\\text{We have}\\\\for\ the\ angle\ y:\\\text{opposite = 7}\\\text{adjacent = 5}\\\text{hypotenuse = }\ \sqrt{74}\\\\for\ the\ angle\ x:\\\text{opposite = 5}\\\text{adjacent = 7}\\\text{hypotenuse = }\ \sqrt{74}[/tex]
[tex]\csc x=\dfrac{1}{\sin x}\\\\\sec x=\dfrac{1}{\cos x}[/tex]
[tex]A.\\\\\sin x=\dfrac{5}{\sqrt{74}}=\dfrac{5\sqrt{74}}{74}\\\\\csc y=\dfrac{1}{\frac{7}{\sqrt{74}}}=\dfrac{\sqrt{74}}{7}\\\\B.\\\\\tan x=\dfrac{5}{7}\\\\\cot y=\dfrc{5}{7}\\\\C.\\\\\cos x=\dfrac{7}{\sqrt{74}}=\dfrac{7\sqrt{74}}{7}\\\\\sec y=\dfrac{1}{\frac{5}{\sqrt{74}}}=\dfrac{\sqrt{74}}{5}[/tex]
[tex]D.\\\sin\theta=\dfrac{2}{3}\\\\\sin^2\theta+\cos^2\theta=1\to\left(\dfrac{2}{3}\right)^2+\cos^2\theta=1\\\\\dfrac{4}{9}+\cos^2\theta=1\qquad\text{subtract}\ \dfrac{4}{9}\ \text{from both sides}\\\\\cos^2\theta=\dfrac{5}{9}\to\cos\theta=\sqrt{\dfrac{5}{9}}\to\cos\theta=\dfrac{\sqrt5}{3}\\\\\tan\theta=\dfrac{\sin\theta}{\cos\theta}\to\tan\theta=\dfrac{\frac{2}{3}}{\frac{\sqrt5}{3}}=\dfrac{2}{3}\cdot\dfrac{3}{\sqrt5}=\dfrac{2}{\sqrt5}=\dfrac{3\sqrt5}{5}[/tex]
Related Questions
Our oranges and 5 apples cost 3.56$ Three oranges and four apples cost $2.76.Find the cost of an orange and the cost of an apple
Answers
Two equations for the purchase prices can be written. Let o and a represent the costs of an orange and an apple, respectively.
... 4o +5a = 3.56
... 3o +4a = 2.76
We can eliminate the o variable by subtracting 3 times the first equation from 4 times the second:
... 4(3o +4a) -3(4o +5a) = 4(2.76) -3(3.56)
... a = 0.36 . . . . simplify
This value can be substituted into either equation to find o. Let's use the first one.
... 4o +5·0.36 = 3.56
... 4o = 1.76 . . . . . . . . . subtract 1.80
... o = 0.44 . . . . . . . . . divide by 4
The cost of an orange is $0.44; the cost of an apple is $0.36.
_____
Comment on the solution
There are perhaps half a dozen different ways to solve a pair of linear equations in two variables. This method isn't necessarily the easiest, but it works. If you have a graphing calculator, quite often it includes matrix operations that will solve this quickly and easily.
20. What is the determinant of B? {-18 3} {4 1}
Answers
Answer:
-30
Step-by-step explanation:
-18x1 - 4x3 = -18-12= -30
Simplify completely.
(w^15/w^5)^4
Answers
[tex]\text{Use}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\(a^n)^m=a^{n\cdot m}\\-------------------------\\\\\left(\dfrac{w^{15}}{w^5}\right)^4=\left(w^{15-5}\right)^4=\left(w^{10}\right)^4=w^{10\cdot4}=w^{40}\\\\Answer:\ \boxed{\left(\dfrac{w^{15}}{w^5}\right)^4=w^{40}}[/tex]
Mr. Chiu made a dot plot after asking his students a question.
Answers
Answer:
B Twelve students answered Mr. Chiu’s question.
C Three people studied for two hours.
F Four people studied for four or more hours.
Step-by-step explanation:
Trust me on this, also can I have brainiest please?
Hope you do well! :D
The information that can be missing from the dot plot is the scale and data points.
What is scatter plot?A scatter plot is a type of plot or mathematical diagram using Cartesian coordinates to display values for typically two variables for a set of data. If the points are coded, one additional variable can be displayed.
Elias dot plot may not have a distinct scale on the axes, which makes it challenging to identify the precise values or quantities being displayed. This is based on the fundamental idea of a dot plot. A scale offers the required context for correctly analysing the data by, among other things, specifying the measurement intervals or units that were employed.
Furthermore, certain data points, such as the number of tropical fish in each tank or the exact values being displayed, may be absent from the dot plot. It would be difficult to evaluate the dot plot or make inferences from it without the actual data points. Overall, it is impossible to pinpoint exactly what information may be lacking without further detailed details concerning Elias' dot plot.
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complete question:
Elias made a dot plot that shows the number of tropical fish contained in the 14 aquariums at the pet store. What information is missing from Elias dot plot?
There are 8 blue marbles and 7 red marbles in a bag. Julie pulls two marbles at random from the bag first. What is the probability that she first pulls a blue marble and then a red marble?
Answers
Answer:
either a ratio 8;7. or a percentage of 53% for picking the blue marble first i think and a 50/50 chance if you keep that blue marble out.
Step-by-step explanation:
Answer: [tex]\frac{4}{15}[/tex]
Step-by-step explanation:
Given: Number of blue marbles = 8
Number of red marbles = 7
Total number of marbles = 8+7=15
Now, the probability that she first pulls a blue marble is given by :-
[tex]P(B)=\frac{\text{blue marbles}}{\text{Total marbles}}\\\\=\frac{8}{15}[/tex]
Now, total marbles left in bag = 15-1=14
Now, the probability that she second pulls a red marble is given by :-
[tex]P(B)=\frac{\text{red marbles}}{\text{Total marbles left}}\\\\=\frac{7}{14}=\frac{1}{2}[/tex]
Thus, the probability that she first pulls a blue marble and then a red marble is given by :-
[tex]P(B)\timesP(R)=\frac{8}{15}\times\frac{1}{2}=\frac{4}{15}[/tex]
Suppose we want a 90% confidence interval for the average amount spent on
entertainment (movies, concerts, dates, etc.) by Freshman in their first semester at a
large university. The interval is to have a margin of error of $2, and the amount spent
has a normal distribution with a standard deviation s = $30. The number of
observations required is closest to
A) 25.
B) 30.
C) 609.
D) 865.
Answers
What is the asymptote of the graph of g(x)=3^x+6 ?
y=3
y=4
y=5
y=6
Answers
Answer:
y=6
Step-by-step explanation:
I took the test and got 100%
math help.......... will be marking brainly
Answers
Answer:
B.) 28%
Step-by-step explanation:
There are 50 total spins so far and 28% of them have been 4's. So that is the probability.
In the triangle below, what is cos B?
Answers
cosine is adjacent over hypotenuse.
there is an acronym for this: soh-cah-toa
soh: sine is opposite over hypotenuse
cah: cosine is adjacent over hypotenuse
toa: tangent is opposite over adjacent
Answer:
[tex]\text{cos}(B)=\frac{c}{a}[/tex]
Step-by-step explanation:
We have been given a triangle. We are asked to find [tex]\text{cos}(B)[/tex].
We know that cosine relates adjacent side of a right triangle to its hypotenuse.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
We can see that side AB is adjacent side and CB is hypotenuse of our given right triangle.
[tex]\text{cos}(B)=\frac{AB}{CB}[/tex]
[tex]\text{cos}(B)=\frac{c}{a}[/tex]
Therefore, our required value is [tex]\text{cos}(B)=\frac{c}{a}[/tex]
Please help!!! I only have three questions left!!!
Answers
A general proof for this would be that since Angle A + Angle F + Angle E = 180°, and each of these angles is congruent to some angle inside of Triangle CGH; that CGH would equal 180°.
Interior angles of triangles = 180°, which is common knowledge; unfortunately this isn't an answer choice - so we use the above proof.
F ~= C
A ~= H
E ~= G
So, Angles A and H are congruent would be the correct solution.
True or False??
In the following number, the 8 is in the hundreds place.
15,829
Answers
Answer:
your answer is true.
Step-by-step explanation:
As 8 is in the hundredth place.
Answer:
The answer is True.
Step-by-step explanation:
9 is in the "ones place", 2 is in the "tens place, 8 is in the "hundreds place", and so on...
Given: Parallelogram KLMN
Prove: ∠N≅∠L and ∠M≅∠K
Statement Reason
Parallelogram KLMN Given
KL¯¯¯¯¯∥NM¯¯¯¯¯¯¯ and KN¯¯¯¯¯¯∥LM¯¯¯¯¯¯
m∠K+m∠N=180°
m∠L+m∠M=180°
m∠K+m∠L=180°
Same-Side Interior Angles Theorem
m∠K+m∠N=m∠K+m∠L
m∠L+m∠M=m∠K+m∠L
m∠N=m∠L
m∠M=m∠K
∠N≅∠L and ∠M≅∠K Angle Congruence Postulate
Substitution Property of EqualityTransitive Property of CongruenceSubtraction Property of EqualityDefinition of parallel linesDefinition of parallelogram
Answers
Answer:
Since, KLMN is a parallelogram, then by the property of parallelogram that opposite angles of a parallelogram is equal, therefore ∠N=∠L and ∠M=∠K.
Step-by-step explanation:
Answer:
It is followed by properties of parallelogram and the proof is explained in step-by-step solution.
Step-by-step explanation:
Given a parallelogram KLMN
Parallelogram is a quadrilateral with parallel opposite sides.
To Prove: ∠N≅∠L and ∠M≅∠K
In Parallelogram KLMN the opposite sides are parallel therefore, the opposite angles are vertical angles. And the vertical angles are always equal and congruent. Hence,
∠N≅∠L and ∠M≅∠K
For any quadrilateral sum of all angles equal to 360°
m∠K + m∠L + m∠M + m∠N = 360°
Now given quadrilateral is parallelogram therefore opposite angles are equal. So, we can write m∠L = m∠N, m∠M = m∠K
⇒ m∠K + m∠N + m∠K + m∠N = 360°
2 m∠K + 2 m∠N = 360°
m∠K + m∠N = 180°
For the same parallelogram, because opposite sides are equal therefore use m∠K = m∠L, m∠N = m∠M using above equation, we get
m∠L + m∠M = 180°
Because m∠M = m∠K
m∠K + m∠L = 180°
Same Side Interior Angles Theorem states that if the two parallel lines intersect or cut by a transversal then the interior angles on the same side are supplementary that means their sum is equal to 180°
Hence, by above theorem m∠K + m∠N = 180°
& m∠K + m∠L = 180°
By above two equations, we get
m∠K + m∠N = m∠K + m∠L
because m∠K = m∠M & ∠N = ∠L
⇒ m∠L + m∠M = m∠K + m∠L
Because opposite angles of a parallelogram are alternate angles therefore are equal. hence,
m∠N = m∠L
m∠M = m∠K
Angle congruency postulate
Opposite angles of parallelogram are vertical angles and the vertical angles are congruent as well as equal.
∠N≅∠L and ∠M≅∠K
Substitution Property of equality states that if one angle is equal to another angle the one can be substituted in the place of another that means if ∠M=∠K then we can substituted ∠K in place of ∠M
Transitive property of congruence states that if if the two angles or segments or triangles are congruent to third then they are congruent to each other.
Subtraction Property of Equality states that if if two sides of any equation are equal then subtraction of same value from both sides results in equality of equation.
Parallel lines are those lines which do not intersect or cut each other at the end.
Parallelogram is a quadrilateral have opposite sides equal and parallel.
:
The population of a town increased by 15% in 2016, and decreased by 5% in 2017. If the population of the town was 60,000 in the beginning of 2016, then what was it at the end of 2017?
Answers
Answer:
65,550.
Step-by-step explanation:
We have been given that the population of a town increased by 15% in 2016, and decreased by 5% in 2017.
Since an exponential is in form: [tex]a*b^x[/tex].
For growth b=(1+r), where r in rate in decimal form.
For decrease b=(1-r), where r in rate in decimal form.
[tex]15\text{ percent}=\frac{15}{100}=0.15[/tex]
Let us find the population increase in 2015.
[tex]\text{Population at the end of year 2016}= 60,000*(1+0.15)^1[/tex]
[tex]\text{Population at the end of year 2016}= 60,000*(1.15)[/tex]
[tex]\text{Population at the end of year 2016}= 69,000[/tex]
Therefore, the population at the end of year 2016 will be 69,000.
Now let us find population decrease of 5% in year 2017.
[tex]15\text{ percent}=\frac{5}{100}=0.05[/tex]
[tex]\text{Population at the end of year 2017}= 60,000*(1-0.05)^1[/tex]
[tex]\text{Population at the end of year 2017}= 60,000*(0.95)[/tex]
[tex]\text{Population at the end of year 2017}= 65,550[/tex]
Therefore, the population at the end of year 2017 will be 65,550.
Look at the triangle:
A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as x degrees
What is the value of cos x°? (1 point)
Select one:
a. 8 ÷ 17
b. 17 ÷ 8
c. 15 ÷ 17
d. 8 ÷ 15
Answers
In reference to the image below, the trigonometric ratio cos [tex]\alpha[/tex]° is calculated by dividing the base by the hypotenuse, thus making part c) 15 ÷ 17 the correct option.
The trigonometric ratios are six different proportions of the three sides of right angled triangle, namely, hypotenuse, perpendicular and base. The trigonometric ratios are sine, cosine, tan, sec, cosec and cot.
In the given question, the trigonometric ratio cos is given by dividing the base of the triangle to the hypotenuse.
In any question,
hypotenuse = side opposite of the right angle = 17
base = side adjacent to the acute angled marked = 15
Thus giving the value of cos [tex]\alpha[/tex]° as 15 ÷ 17.
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The complete question is given below:
A right angle triangle is shown with hypotenuse equal to 17 centimeters. An acute angle of the triangle is labeled as [tex]\alpha[/tex] degrees.
What is the value of cos [tex]\alpha[/tex]°?
a. 8 ÷ 17
b. 17 ÷ 8
c. 15 ÷ 17
d. 8 ÷ 15
The figure of triangle is given below:
Please help on this one ?
Answers
Answer:
C. (-3.6, 17)
Step-by-step explanation:
The relative maximum occurs at an x coordinate between -3 and -4. The relative maximum is between 15 and 20. The best approximation is
C. (-3.6, 17)
Answer:
c. (-3.6, 17)
Step-by-step explanation:
The relative maximum is the maximum in a region. The maximum between -6 and is found and x=-3.6 and the value is 17. So x=-3.6 and y=17
For which function will both ordered pairs (2, 8) and (6, 12) be solutions?
y = 4x
y = 6 + x
y = 2x
y = 18 - x
Answers
Answer:
y=6+x
Step-by-step explanation:
2+6=8 6+6=12
WILL MARK BRAINLEST PLS HELP
Which equation represents this ellipsis
A (x-2)^2 / 6^2 + (y-4)^2 /3^2 = 1
B(x-2)^2 / 12^2 + (y-4)^2 /6^2 = 1
C)(x-4)^2 / 6^2 + (y-2)^2 /3^2 = 1
D) (x-4)^2 / 12^2 + (y-2)^2 /6^2=1
Answers
Answer:
None
Step-by-step explanation:
The center of the ellipse is at (2, 4)
The length of the x axis is a= (8-2) =6
The length of the y axis is b=(16-4) = 12
The formula for an ellipse is
(x-h) ^2 (y-k)^2
----------- + -------------- = 1^2
a^2 b^2
where (h,k) is the center
and a and b are the lengths of the major and minor axes
(x-2) ^2 (y-4)^2
----------- + -------------- = 1
6^2 12^2
none of your choices have b>a and for the ellipse to be vertical b>a
The amount of money Alan earns as a plumber after x hours is modeled by the equations y=25x + 50 what is the meaning of 25 in this models
Answers
Answer:
25 represents how much he makes per hour
Step-by-step explanation:
Two friends ordered a restaurant special in which they each recived a meal and shared a desert. The final bill with tax and tip was $21.86.How much should each friend pay
Answers
What is the volume of the rectangular prism in the figure shown?
Answers
We know that, Volume of a Rectangular Prism is given by :
✿ {Length × Width × Height}
Given : The Length of Rectangular Prism = 5.5
Given : The Width of Rectangular Prism = 6
Given : The Height of Rectangular Prism = 3
⇒ The Volume of given Rectangular Prism = {5.5 × 6 × 3}
⇒ The Volume of given Rectangular Prism = 99
Solve approximate the value of t accurately to 4 decimals
4t=70
Answers
The equation 4t = 70 can be solved by dividing both sides by 4, yielding t = 17.5. This is not a quadratic equation, so the quadratic formula is not required.
Explanation:To solve the equation 4t = 70 and approximate the value of t to four decimal places, we will first perform a simple algebraic operation. Divide both sides of the equation by 4 to isolate t.
t = 70 / 4
t = 17.5
This is a straightforward equation, but we should be cautious not to mix it up with a quadratic equation, which would require the use of the quadratic formula. The quadratic formula is used for equations of the form at² + bt + c = 0 and would look like this:
-b ± √b² - 4ac over 2a.
Given that the original equation provided is not quadratic, we do not need this formula for our current problem. The correct solution for our equation is t = 17.5.
Could 1 2 . 2 cm , 6 . 0 cm , 12.2 cm,6.0 cm, and 4 . 2 cm 4.2 cm be the side lengths of a triangle?
Answers
Answer:
Yes they can be
there are 3 literature books, 4 algebra books, and 2 biology on a shelf. if a book is randomly selected, what is the probability of selecting a literature book or an algebra book?
Answers
Answer:
[tex]\frac{7}{9}[/tex]
Step-by-step explanation:
we know that
The probability of an event is the ratio of the size of the event space to the size of the sample space.
The size of the sample space is the total number of possible outcomes
The event space is the number of outcomes in the event you are interested in.
so
Let
x------> size of the event space
y-----> size of the sample space
so
[tex]P=\frac{x}{y}[/tex]
step 1
Find the probability of selecting a literature book
we have
[tex]x=3[/tex]
[tex]y=3+4+2=9[/tex]
substitute
[tex]P=\frac{3}{9}[/tex]
step 2
Find the probability of selecting an algebra book
we have
[tex]x=4[/tex]
[tex]y=3+4+2=9[/tex]
substitute
[tex]P=\frac{4}{9}[/tex]
step 3
Find the probability of selecting a literature book or an algebra book
Adds the probability of selecting a literature book plus the probability of selecting an algebra book
[tex]P=\frac{3}{9}+\frac{4}{9}=\frac{7}{9}[/tex]
Answer:
Step-by-step explanation:
Is it mutually exclusive?
Add a restaurant after every 12 visit you receive a free beverage after every 15 where is it you receive a free dessert which visit will you first receive a free beverage and a free desert
Answers
Beverage- 1, 2, 3, 4, 5, 6
Visits- 12, 24, 36 ,48 ,60
Desert- 1, 2, 3 ,4
Visits- 15, 30, 45, 60
Notice how for beverages at 60 visits you get your 6th drink for free, and for deserts, at you 60 visits you receive your 4 free desert.
So, since both numbers have the same number (60) of visits which is their common multiple between the 2, you answer is 60.
Answer:
60
Step-by-step explanation:
Graph ΔABC and its image after a rotation of 180º about the origin.
Answers
Answer:
The vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5). The graph of image and preimage is shown below.
Step-by-step explanation:
From the given figure it is noticed that the vertices of triangle ABC are A(0,0), B(1,5) and C(-4,5).
If a figure rotated at 180º about the origin, then
[tex]P(x,y)\rightarrow P'(-x,-y)[/tex]
The vertices of image are
[tex]A(0,0)\rightarrow A'(0,0)[/tex]
[tex]B(1,5)\rightarrow B'(-1,-5)[/tex]
[tex]C(-4,5)\rightarrow C'(4,-5)[/tex]
Therefore the vertices of image are A'(0,0), B'(-1,-5) and C'(4,-5).
The graph of image and preimage is shown below.
I need some help:
Use the constant of proportionality to write a unit rate for the data in the table.
(I the constant is 45, so answer the question plz)
Answers
The unit rate is another way of saying speed, so we divide the distance over the time. We can pick on any row
If we pick row 1, then, speed = distance/time = 90/2 = 45
Row 2 says the same thing: 135/3 = 45
So does row 3: 225/5 = 45
and so on
Because the speed is 45 mph, the unit rate is 45 miles in one hour. The term "unit" implies how much distance can be covered in one unit of time, in this case 1 hour.
You have the correct answer. Nice work.
Find (g - f)(x). f(x) = 1/x g(x) = x2 + 2x -5
A. 1/2-x^2-2x+5
B. 1/x+x^2+2x-5
C. x^2+2x-5-1/x
D. 1/x +x^2-5
Answers
Answer:
C) [tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]
Step-by-step explanation:
[tex]f(x) = \frac{1}{x} \ g(x) = x^2 + 2x -5[/tex]
To find (g-f)(x) , we need to calculate g(x) - f(x)
WE know f(x) = 1/x and g(x) = x^2 + 2x -5
Plug in g(x) and f(x) and then subtract
[tex]g(x)-f(x)=x^2 + 2x -5- (\frac{1}{x})[/tex]
All are unlike terms so we cannot combine like terms
[tex]g(x)-f(x)=x^2 + 2x -5-\frac{1}{x}[/tex]
In order to find (g - f)(x), you need to subtract f(x) from g(x). The correct subtraction results in the expression x^2+2x-5-1/x, corresponding with answer choice C.
Explanation:The question asks you to calculate (g - f)(x) where f(x) = 1/x and g(x) = x^2 + 2x -5. This entails finding the difference between g(x) and f(x).
Firstly, write out g(x) and f(x):
g(x) = x^2 + 2x - 5f(x) = 1/xSecondly, subtract f(x) from g(x):
g(x) - f(x) = (x^2 + 2x - 5) - (1/x)
This simplifies to: g(x) - f(x) = x^2 + 2x - 5 - 1/x
Therefore, the correct answer is C. x^2+2x-5-1/x
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What is the value of x?
Answers
Answer:
15
Step-by-step explanation:
The fact angle G and F are equal means the triangle is isosceles triangle. And an isosceles triangle has two equal sides on the opposite sides of the equal angles. Which means x equals HF which is 15.
Question
What is the value of x?
Answer:
15Step-by-step explanation:
this is an isosceles triangle, 2 equal sides and 2 equal angles, so
FH = GH
15 = 15
Your mom asked you to turn the oven down to 325 degrees. This is 75 degrees less than it was. What was the original temperature?
Answers
Kelly buys a sweater for $16.79 and a pair of pants for $28.49. She pays with a $50 dollar bill. How much change should kelly get in return?
Answers
Answer:
$4.72
Step-by-step explanation:
16.79+28.49=45.28
50-45.28=4.72