Consider △DFE. What are the inputs or outputs of the following trigonometric ratios? Express the ratios in simplest terms.
sin(?) = 4/5
cos(F) = ?
tan(D) = ?
Answers
sin F = 4/5
cos F = 3/5
tan D = 3/4
Explanation:
First, we have sin an angle = 4/5
In a right-angled triangle:
sin theta = opposite / hypotenuse
This means that in triangle DFE:
The hypotenuse = 5 units
one of the sides = 4 units
Use Pythagoren theorem to get the other side as follows:
hypotenuse^2 = side1^2 + side2^2
5^2 = 4^2 + side2^2
side2^2 = 9
The second side of the triangle = 3 units
The special trig functions are as follows:
sin theta = opposite / hypotenuse
cos theta = adjacent / hypotenuse
tan theta = opposite / adjacent
From the attached figure and based on the calculations above:
sin F = 4/5
cos F = 3/5
tan D = 3/4
Hope this helps :)
Answer:
Sin(F)=4/5
Cos(F)=3/5
Tan(D)=3/4
Step-by-step explanation:
Related Questions
Find the perimeter and the area of the polygon with the given vertices. J (1,2), K (7,2), L (7,8), M (1,8)
Answers
recall, the perimeter is all sides summed up, and the area is just length * width.
Answer : The perimeter and the area of the polygon with the given vertices is, 24 unit and 36 unit² respectively.
Step-by-step explanation :
First we have to calculate the distance of JK, KL, LM and MJ.
Using distance formula:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
where,
d = distance between the two coordinates
x and y are the coordinates.
To calculate the distance of JK:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]d=\sqrt{(7-1)^2+(2-2)^2}[/tex]
[tex]d=\sqrt{(6)^2+(0)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of KL:
[tex]d=\sqrt{(x_3-x_2)^2+(y_3-y_2)^2}[/tex]
[tex]d=\sqrt{(7-7)^2+(8-2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(6)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of LM:
[tex]d=\sqrt{(x_4-x_3)^2+(y_4-y_3)^2}[/tex]
[tex]d=\sqrt{(1-7)^2+(8-8)^2}[/tex]
[tex]d=\sqrt{(-6)^2+(0)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
To calculate the distance of MJ:
[tex]d=\sqrt{(x_4-x_1)^2+(y_4-y_1)^2}[/tex]
[tex]d=\sqrt{(1-1)^2+(8-2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(6)^2}[/tex]
[tex]d=\sqrt{36}[/tex]
[tex]d=6[/tex]
The distance of JK, KL, LM and MJ is, 6, 6, 6 and 6.
Now we have to calculate the perimeter of the polygon.
Perimeter of polygon = JK + KL + LM + MJ
Perimeter of polygon = 6 + 6 + 6 + 6
Perimeter of polygon = 24 unit.
Now we have to calculate the area of polygon.
As the distance between the coordinates are equal that means the geometry will be square because in square the all four sides are equal.
Now we have to calculate the area of polygon by using area of square formula.
Area of polygon = Area of square = (side)²
Given: Side = 6
Area of polygon = Area of square = (6)²
Area of polygon = Area of square = 36 unit²
Thus, the area of polygon is, 36 unit²
Which statement is true about the function f(x)=-√-x
a.The domain of the function is all negative real numbers.
b.The range of the function is all positive real numbers.
c.The domain and range of the function have opposite signs.
d.The domain and range of the function are the same.
Answers
Answer: D.The domain and range of the function are the same.
Step-by-step explanation: Given function f(x)=-√-x.
The given function is a square root function and we have minus sign in front of x inside square root.
A square root always defined for positive values or 0.
In order to get a positive number or 0 inside square root, let us solve the inequality:
[tex]-x\geq 0[/tex]
On dividing both sides by -1, the inequality sign would get flip and we get
Domain: [tex]x \leq 0.[/tex]We can see that we have a negative sign in front of square root. So, the value of f(x) would be always a negative number or 0.
Therefore, range would also be :[tex]x \leq 0.[/tex].Therefore, correct option is D option.Answer:
hi thereee, the answer to this question is
d. the domain and range of the function are the same
hope this helps :)
have a good day!
Step-by-step explanation:
i just took the test
Two boats on opposite banks of a river start moving towards each other. They first pass each other 1400 meters from one bank. They each continue to the opposite bank, immediately turn around and start back to the other bank. When they pass each other a second time, they are 600 meters from the other bank. We assume that each boat travels at a constant speed all along the journey. Find the width of the river?
Answers
Let xx be the width of the river. It is given that, when they have met the first time, boat11 has travelled 14001400 m and boat22, (1400−x)(1400−x) metres.
When they meet for the second time, boat11 has travelled 600+(x−1400)=(x−800)600+(x−1400)=(x−800) m, and boat22, 1400+(x−600)=(x+800)1400+(x−600)=(x+800) m.
Note that, the relationship of the distances each traveled, is the same to both meetings. Thus,
14001400−x=x−800x+80014001400−x=x−800x+800⇒x=?⇒x=?Hope you can take it from here.an angle with measure between 90 and 180 is called
Answers
An angle with measure between 90° and 180° is called obtuse angle.
The definition of an obtuse angle in geometry states that an angle whose measure is greater than 90° and less than 180° is called an obtuse angle.
So, if the angle measure between 90 degree and 180 degree is obtuse angle.
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helppppppppppppppppppppppppppppppppppppppp
Answers
the answer is √2^5
Help me in this plz plz
Answers
3b. You can tell the system of linear equations has no solution if the equations result in a contradiction, such as 0 = 1. They will have infinite solutions if the result is a tautology, such as x = x or 0 = 0.
Word Problem
(a) There is actually no problem stated. If we assume the problem is to determine the length and width that meet the described conditions, then it would be appropriate to let variables represent the length (L) and width (W). The system of equations restates what the words state:
.. L - W = 2 . . . . . . length and width differ by 2 units
.. 2(L + W) = 40 . . the perimeter is 40 units
(b) You can solve this many ways. One way is to divide the second equation by 2, so you have a "sum and difference" problem
.. L - W = 2
.. L + W = 20
This is easily solved by adding the two equations to get
.. 2L = 22
.. L = 11
.. W = L -2 = 9
The solution is (L, W) = (11, 9). This is interpreted to mean the length of the rectangle is 11 units; the width is 9 units.
please help ASAP
the vertices of pqr are p(-3, 8), q(-6, -4), and r(1, 1). if you reflect pqr across the x-axis, what will be the coordinates of the vertices of the image p'q'r'?
Answers
Find the distance between the two points. Round to the nearest tenth if necessary. (10, –4), (5, 8)
169
7
13
16
Answers
If you ask this question may be you do not know the formula of the distance between two points or you do not know how to use it, so I am going to explain you both.
1) Formula of the distance betweer two points:
Say the point A has coordinates (x1, y1) and the point B has coordinates (x2, y2), the distance, d, between the points A and B is given by the formula:
[tex]d^2= (x_1-x_2)^2+(y_1+y_2)^2} = d=\sqrt{(x_1-x_2)^2+(y_1-y_2)^2} [/tex]
2) So, to apply that formula you need the coordinates of the two points.
In this case the coordinates of the point (10,-4) are: x = 10, y = -4
The coordinates of the point (5,8) are: x = 5, y = 8.
3) This is the application:
[tex]d= \sqrt{(10-5)^2+(-4-8)^2}= \sqrt{(5)^2+(-12)^2}= \sqrt{25+144} d= \sqrt{169}=13 [/tex]
So, the answer is 13.
Find the side of a square whose diagonal is of the given measure. Given = 12 square root 2ft.
Answers
diagonal^2 / 2 = side^2
144 * 2 / 2 = side^2
144 = side^2
side = 12
Help please.....!!!!!
Answers
______________________________________________________
Note:
_______________________________
When x = 0 ;
y = f(x) = 5(2)⁻ˣ = 5* (2)⁻⁰ = 5 * 1 = 5 .
_______________________________
By inspection of the graph, the only given answer choices with graphs that fall on the point "(0, 5)" are:
[A]: "Graph A" (the red graph) ; and:
[B]: "Graph B" (the green graph) .
________________________________________________________
Now, let us look at other points and see if the selected points are true values for the given function/ equation;
Start with "Graph B" (the green graph): Upon inspection, it is clear that "(0.5 , 7)" is a point on the graph; that is, for "Graph B" ,
when "x = 0.5" , y = 7" .
Let us plug these values into the equation: y = 5(2)⁻ˣ ; to see if the equation holds true; that is, when "x = 0.5" , does "y = 7" ?
5* 2^(-0.5) = 5 * 0.7071067811865475 ;
→ 5 * (√2/2) =
3.5355339059327375;
→ 3.5355339059327375 [tex] \neq [/tex] 7 .
________________________________________________
So; we are left with: Choice: [A]: "Graph A" {the red graph}.
________________________________________________
Combine like terms to simlify the expression: 2/5k—3/5+1/10k
Answers
(5/10)k - 3/5
(1/2)k - 3/5 is the answer to the question
THen
4/10K - 3/5 + 1/10k = 5/10k - 3/5
Simplify 5/10k
1/2k - 3/5 is your answer
Four sides of a octagon each measure 12 cm. The perimeter of the octagon is 70 cm. What is the length of each remaining side, if each remaining side has the same length?
Answers
4 * 12 = 48
70-48 = 22
so the remaining 4 sides need to = 22 cm
22 / 4 = 5.5
each remaining side = 5.5 cm
Answer:
It would be 5.5 cm
Step-by-step explanation:
Rhett decides to build a square room for his movie and music collection. If the area of the room is 9x^2 − 6x + 1 square feet, what is the length of one side of the room?
(3x + 1) feet
(9x − 1) feet
(3x − 1) feet
(9x + 1) feet
Answers
Choose the option that correctly completes the statement.
The sum of the measures of the interior angles of a quadrilateral is _____ degrees.
270
180
90
360
Answers
Answer:
D. 360 degrees.
Step-by-step explanation:
We have been given an incomplete statement. We are asked to complete the given statement using provided options.
Statement:
The sum of the measures of the interior angles of a quadrilateral is _____ degrees.
We know that a quadrilateral is a polygon with 4 vertices.
We can divide a quadrilateral into two triangles by drawing a diagonal. We know that sum of three angles of a triangle is equal to 180 degrees, so sum of angles of two triangles would be 360 degrees.
Therefore, the sum of the measures of the interior angles of a quadrilateral is 360 degrees and option D is the correct choice.
Find the length of both arc AB and arc APB, where
Answers
The measure of arc AB is twice that of angle APB, so is
2*108° = 216°.
The measure of arc APB is the difference between that and 360°, so is
360° -216° = 144°.
as you can see, the angle at P is the inscribed angle, and the intercepted arc is AB, thus 2P = arcAB.
and since a circle has a total of 360°, the other arc is just 360 - arcAB.
Choose the correct simplification of (7x3y3)2.
14x6y6
49x5y5
49x6y6
14x5y5
Answers
The correct simplification of (7x3y3)2 = 49x6y6
What is simplification?Simplification is defined as the removal of parentheses in an algebraic expressions in such a way that it would be understood.
From the expression given,
(7x3y3)2 = 2 × 7x × 3y × 3
= 49x6y6
Therefore, the correct simplification of (7x3y3)2 = 49x6y6
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True or false ? A car taking a turn at a constant speed is accelerating.
Answers
Mr burn's class is taking
a. field trip to the planetarium. The trip will cost $27 for each student. There are 18 students in his class.Use compatible numbers to estimate the total cost of field trip
Answers
Answer:
600
Step-by-step explanation:
The answer is 600
(60 POINTS)
The measure of angle E, the angle of elevation from point A to point B, is 5(x-2) degrees. The measure of D, the angle of depression from point B to point A is (x + 14) degrees. Find the measure of each angle.
Answers
[tex]\sf 5(x-2)=(x+14)[/tex]
Distribute 5 into the parenthesis:
[tex]\sf 5x-10=x+14[/tex]
Add 10 to both sides:
[tex]\sf 5x=x+24[/tex]
Subtract 'x' to both sides:
[tex]\sf 4x=24[/tex]
Divide 4 to both sides:
[tex]\sf x=6[/tex]
So this is our value of 'x', we can plug it into any of the two equations to find the measurement for both angles:
[tex]\sf x+14[/tex]
[tex]\sf 6+14[/tex]
[tex]\boxed{\sf 20\textdegree}[/tex]
So the length of both angle E and angle D is 20 degrees.
Answer:
measure of angle E equals 20 degrees, measure of angle D equals 20 degrees
What transformations change the graph F(x) to the graph g(x)
f(x) = 3x^2
G(x) = 9x^2-4
A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units
B. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated UP 4 units
C. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 1/3 and translated up 4 units
Answers
Final answer:
The transformation from f(x) = 3x^2 to g(x) = 9x^2 - 4 includes a vertical stretch by a factor of 3 followed by a vertical translation down by 4 units.
Explanation:
The transformations that change the graph f(x) = 3x2 to the graph g(x) = 9x2 - 4 involve two steps:
A vertical stretch by a factor of 3, which is achieved by multiplying the original function f(x) by 3, yielding 9x2. This transformation changes the original coefficient (3) in front of x2 to a new coefficient (9).
A vertical translation down by 4 units, which is represented by subtracting 4 from the result of the stretch transformation.
Therefore, the correct answer to the student's question is:
A. The graph of g(x) is the graph of f(x) stretched vertically by a factor of 3 and translated DOWN 4 units.
As a part of their weather unit, Anoki’s science class took a hot air balloon ride. As they passed over a fenced field, the angle of depression of the closer side of the fence was 32°, and the angle of depression of the farther side of the fence was 27°. If the height of the balloon was 800 feet, estimate the width of the field. Round your answer to the nearest foot. 2016_01_25_17_23_501.png The width of the field is about feet
Answers
Steps needed to find the width of the field (CD):
First, we should note that angle d would be equal to 27 degrees because there are two parallel lines that are cut by a transversal. Furthermore, angle a would be equal to 5 degrees since we just need to subtract 27 from 32.
We then subtract 27 and 5 from 180 to get angle c. [tex]180-27-5=148[/tex]. Angle c is therefore 148 degrees.
Next, we need to find angle e which is just the supplementary of angle c. Angle e therefore measures [tex]180-148=32[/tex] degrees.
For the next step we use sine law to find the length of segment AC:
[tex] \frac{sin(32)}{800} = \frac{sin(90)}{AC} [/tex]
[tex]AC=1509.66[/tex]
Lastly, we need to utilize the sine law again to find the length of segment CD or the width of the field:
[tex] \frac{sin(27)}{1509.66} = \frac{sin(5)}{CD} [/tex]
[tex]CD=290[/tex]
ANSWER: The width of the field is 290 ft.
How would you solve this?
Answers
I suppose as we don't see correctely the 2nd image, that it is the first one.
Angles DOY and DKY intersept then same arc are equals.
5x+15=3x+21
==>2x=6
==>x=3 and 5x+15=5*3+15=30°, 3x+21=3*3+21=30°
Angle OYK=15x=15*3=45°
Angle ODK=9x+18=9*3+18=45° =Angle OYK which intersept the same arc.
(35 points) Fred played golf and for the past 5 times had a score of 72, 79, 73, 81, and 70. What was his average score? A. 75 B. 77 C. 85 D. 375
Answers
A. 75
The average score of Fred is 75.
What is the average value?The common cost of a characteristic over language is described to be crucial of the feature divided by way of the period of the interval.
calculation:-
a score of 72, 79, 73, 81, and 70.
nu,ber of times = 5
total score = 72+79+ 73+ 81+ 70.
= 375
average score = 375/5
= 75
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A zoo has 15 emperor penguins. The emperor penguins make up 30% of all the penguins at the zoo. How many penguins live at the zoo?
Answers
1% = 15/30
= 1/2
100% = 100 x 1/2
= 50
there are 50 penguins in the zoo.
Answer:
30% = 15
1% = 15/30
= 1/2
100% = 100 x 1/2
= 50
there are 50 penguins in the zoo.
MATH HELP!
Kristen's gross annual income is $47,208. She is paid semimonthly and has 6% deducted from her paychecks for her 403(b). Her employer matches her deduction, up to 5%. How much is deposited into Kirsten's 403(b) each payday?
$98.35
$118.02
$196.70
$216.37
Answers
1967 * 0.06 = 118.02
1967 * 0.05 = 98.35
118.02 + 98.35 = 216.37
The amount deposited into Kristen's each payday is is 216.37
Kristen's gross annual income is $47,208.
What is the meaning of semimonthly?Twice a month
semimonthly per year means
12(2)=24
She paid semimonthly,
47,208 / 24 = 1967
6% deducted from her paychecks then,
1967 * 0.06 = 118.02
Her employer matches her deduction, up to 5% then,
1967 * 0.05 = 98.35
The amount deposited into Kristen's each payday is
118.02 + 98.35 = 216.37
Therefore,the amount deposited into Kristen's each payday is is 216.37
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Item 20The width of a rectangular room is 60% of its length. The length of the room is 10 feet. What is the area of the room?
Answers
A grocery bag can withstand 300 n of force before it rips apart. how many kilograms of apples can it safely hold?
Answers
The grocery bag can handle roughly 30.6 kg of apples safely. This conclusion is drawn based on the concept of forces, weight, and the Physics formula for calculating weight.
Explanation:The subject field for this question is Physics and it relates to the High School level. This question is about the concept in physics known as force, in particular, the force related to weight and how it pertains to carrying capacity.
In physics, force is typically given in units of Newton's (N), named after Sir Isaac Newton. The force exerted by a mass due to gravity is its weight. Specifically, weight is calculated through the formula F = m * g, where F is the force (weight), m is the mass in kilograms, and g is the acceleration due to gravity in m/s² (approximately 9.8 m/s² on Earth).
To find out how many kilograms of apples a bag can hold before it rips, we can use this formula and solve for m (mass). Given that the force the bag can withstand before ripping is 300 N, we have 300 N = m * 9.8 m/s². Isolating m gives us m = 300 N / 9.8 m/s² which is approximately 30.6 kg. Therefore, the bag can safely hold around 30.6 kg of apples.
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a rock is thrown from the top of a tall building. the distance, in feet, between the rock and the ground x seconds after it is thrown is given by f(x)=-16x62-4x+382 How long after the rock is thrown does it hit the ground
Answers
We have then:
f (x) = - 16x ^ 2-4x + 382
The moment the rock hits the ground we have f (x) = 0
0 = -16x ^ 2-4x + 382
We solve the polynomial looking for its roots which are:
x1 = -5.012803699004288
x2 = 4.762803699004288
We ignore the negative root. The solution is:
x = 4.76
Answer:
it hits the ground 4.76 s after is thrown
It takes approximately 5.0 seconds for the rock to hit the ground after it is thrown.
Explanation:To find the time when the rock hits the ground, we need to find the value of x when the distance between the rock and the ground is 0. In the given equation, f(x) = -16x^2 - 4x + 382, where f(x) represents the distance between the rock and the ground. We can set this equation equal to 0 and solve for x:
-16x^2 - 4x + 382 = 0
This is a quadratic equation. We can use the quadratic formula to solve for x:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Plugging in the values from the equation, we get:
x = (-(-4) ± sqrt((-4)^2 - 4(-16)(382))) / (2(-16))
This simplifies to:
x = (4 ± sqrt(16 + 24512)) / (-32)
x = (4 ± sqrt(24528)) / (-32)
x ≈ (-4 ± 156.49) / (-32)
Since we're dealing with time, the negative value doesn't make sense in this context. So, we take the positive root:
x ≈ (4 + 156.49) / (-32)
x ≈ 160.49 / (-32)
x ≈ -5.0
Therefore, it takes approximately 5.0 seconds for the rock to hit the ground after it is thrown.
Why must bowhunters use broadhead points when hunting big game?
Answers
There are states that require a certain measurement of the broadhead point arrows. Theses arrows must be solidly built and must always be razor sharp to ensure quick penetration to the animals thick skin and layers of tissues.
Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.
We have,
Bowhunters use broadhead points when hunting big game for several reasons:
- Greater Cutting Surface
Broadhead points have a larger cutting surface area compared to target or field points.
This increased surface area allows for more effective cutting and penetration, which is essential when hunting big game animals that have tough hides, muscles, and bones.
- Penetration and Lethality:
Big game animals often require deep penetration to reach vital organs for an ethical and humane kill.
Broadheads are designed to maximize penetration by creating large wound channels and causing significant tissue damage.
This helps ensure quick and effective kills, minimizing suffering for the animal.
- Blood Trails
- Terminal Performance
- Ethical Considerations
Thus,
Bowhunters use broadhead points when hunting big game for their greater cutting surface, penetration, lethality, blood trails, terminal performance, and ethical considerations.
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In which way do REITs resemble mutual friends
Answers
___________________________________________________________
REITs resemble mutual funds in that they both allow investors to pool their money to invest in a diversified portfolio. REITs consist of a variety of real estate properties, while mutual funds consist of stocks or bonds. Both provide individuals with an opportunity to invest in a professionally managed portfolio.
Explanation:REITs (Real Estate Investment Trusts) resemble mutual funds in that they both allow investors to pool their money together to invest in a diversified portfolio. Just as mutual funds consist of a variety of stocks or bonds from different companies, REITs consist of a variety of real estate properties such as office buildings, apartments, and shopping centers. Investors buy shares of a REIT and receive a return based on the performance of the real estate portfolio as a whole. Both REITs and mutual funds provide individuals with an opportunity to invest in a professionally managed portfolio without having to directly invest in individual stocks or properties.
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