Answers
The appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].
What are the trig values?Given the equation and interval.
tanθ = -3, [ π/2 < θ < π ]
First, we use the definition of tangent to determine the known sides of the unit circle right triangle.
Note that; the quadrant determines the sign of each values.
tanθ = opposite / hypotenuse
We can use Pythagoras theorem to find the hypotenuse of the unit circle right triangle as the opposite and adjacent sides are known.
Hypotenuse = √( opposite² + adjacent² )
Hence, we have;
Hypotenuse = √( [3]² + [-1]² )
Hypotenuse = √( 9 + 1 )
Hypotenuse = √10
1) To find sinθ
sinθ = opposite / hypotenuse
sinθ = 3/√10
We simplify
sinθ = 3/√10 × √10/√10
sinθ = 3√10 / 10
[tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex]
2) cosθ
cosθ = adjacent / hypotenuse
cosθ = -1 / √10
Simplify
cosθ = -1 / √10 × √10/√10
cosθ = -√10 / 10
[tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex]
3) cotθ
cotθ = adjacent / opposite
cotθ = -1 / 3
[tex]cot\theta= -\frac{1}{3}[/tex]
4) secθ
secθ = hypotenuse / adjacent
secθ = √10 / -1
[tex]sec\theta=-\sqrt{10}[/tex]
5) cscθ
cscθ = hypotenuse / opposite
cscθ = √10 / 3
[tex]csc\theta= \frac{\sqrt{10} }{3}[/tex]
Therefore, the appropriate values are; [tex]sin \theta = \frac{3\sqrt{10} }{10 }[/tex], [tex]cos\theta = -\frac{\sqrt{10} }{10}[/tex], [tex]cot\theta= -\frac{1}{3}[/tex], [tex]sec\theta=-\sqrt{10}[/tex] and [tex]csc\theta= \frac{\sqrt{10} }{3}[/tex].
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Related Questions
look at image............
Answers
Answer:
f(x)=2x-3
Step-by-step explanation:
cause fir example if you put x=2 the y became 1.
Which expressions represent exponential decay? Check all that apply.
900(0.05)t
700(0.9)x
53(1.75)(0.3)x
90(1.2)t
300(2.4)(1.2)y
2x2 + 9
18 – 3y
Answers
The expressions that represent exponential decay are 900(0.05)^t, 700(0.9)^x and 53(1.75)(0.3)^x
How to determine the expressions?An exponential function is represented as:
y = ab^x
The above means that options (f) and (g) are not exponential functions
When b is less than 1, then the function is an exponential decay.
From the list of options, we have:
900(0.05)^t => b = 0.05
700(0.9)^x => b = 0.9
53(1.75)(0.3)^x => b = 0.3
Hence, the expressions that represent exponential decay are 900(0.05)^t, 700(0.9)^x and 53(1.75)(0.3)^x
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I NEED HELP QUICK!!!
Triangle ABC is transformed to triangle A′B′C′, as shown below:
A coordinate grid is shown from negative 4 to 0 to 4 on both x- and y-axes. A triangle ABC has A at ordered pair negative 1, 3, B at ordered pair 0, 1, C at ordered pair negative 3, 0. A triangle A prime B prime C prime has A prime at ordered pair negative 1, negative 3, B prime at ordered pair 0, negative 1, C prime at ordered pair negative 3, 0.
Which equation shows the correct relationship between the measures of the angles of the two triangles?
The measure of angle CAB = The measure of angle C prime B prime A prime
The measure of angle BCA = The measure of angle A prime B prime C
The measure of angle CAB = The measure of angle C prime A prime B prime
The measure of angle BCA = The measure of angle C prime A prime B prime
Answers
The equation that shows the correct relationship between the measures of the angles of the two triangles is;
Option D: The measure of angle BCA = The measure of angle C prime A prime B prime
How to Interpret Objects Transformation?We are told that Triangle ABC is transformed to triangle A′B′C′.
Now, the triangle ABC and A'B'C' are similar triangles and we know that similar triangles angles are congruent. Thus;
From the given coordinates, we can say that;
∠BAC = ∠B'A'C'
∠ABC = ∠A'B'C'
∠ACB = ∠A'C'B'
Thus, the equation that shows the correct relationship between the measures of the angles of the two triangles is;
The measure of angle BCA = The measure of angle C prime A prime B prime
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If m ∠4 = m ∠5, then r||s. Summarize the postulate or theorem that makes this a true statement.
can someone please explain how to solve this
Answers
The statement, m∠4 = m∠5, then then r||s is true based on the converse of corresponding angles theorem.
What is the Converse of Corresponding Angles Theorem?Based on the converse of corresponding angles theorem, if two corresponding angles, angles 4 and 5 are congruent or equal to each other, then the lines on which they lie on, lines r and s are congruent.
Therefore, based on the converse of corresponding angles theorem, m∠4 = m∠5, then then r||s.
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.
help me please gang
Answers
Answer:
Not similar
Step-by-step explanation:
There is only one side and one angle, which insufficient to prove triangle similarity.
Pls help me with the answer , ty
Answers
Using it's concept, the equivalent expression for the perimeter of the figure is:
2 + 3x2 + 4x2 + 5x2 + 8
What is the perimeter of a figure?The perimeter of a figure is given by the total length of it's boundary.
Hence, for the figure given in this problem, the perimeter is:
2 + 3 + 3 + 4 + 4 + 5 + 8 + 5
2 + 3x2 + 4x2 + 5x2 + 8
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Missing value of why worth 20 points pls help
Answers
A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The value of x, y and z is 90°, 53°, and 100°, respectively.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental form in geometry. The sum of all the angles of a triangle is always equal to 180°.
In ΔABD is made on the diameter of the circle, therefore, the measure of ∠BAD = 90°. Therefore,
x° = 90°
In ΔAOD, the measure of ∠AOD is 74°, also, the triangle is an isosceles triangle with OA and OD of equal length. Therefore, the sum of the angles can be written as,
y° + y° + 74° = 180°
2y° = 106°
y = 53°
Similarly, ΔBOC is an isosceles triangle with OB and OC having an equal length. Therefore, ∠OBC=∠OCB. Also, the sum of all the angles can be written as,
∠BOC + ∠OBC + ∠OCB = 180°
∠BOC + 40° + 40° = 180°
∠BOC = 100°
Hence, the value of x, y and z is 90°, 53°, and 100°, respectively.
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Solve each triangle – find any missing side and angle measures. Round answers to the nearest tenth.
Answers
Step-by-step explanation:
Please help ASAP
Please help ASAP
Please help ASAP
Please help ASAP
Answers
Substituting L = 7.29,
[tex]t = 2.01 \sqrt{7.29} \approx \boxed {5.4}[/tex]
HELP QUICKKK What is the difference between –4 and 6?
–10
–2
2
10
Answers
Answer:
10
Step-by-step explanation:
Plugin your answer: -4 + 10 = 6
Answer:
10
Step-by-step explanation:
Which of the following situations involve opposite quantities combining to make 0?
·Krista has a new piggy bank. She adds 3 quarters on Tuesday, and then adds another 3 quarters on Thursday.
·Carlyns opens a new checking account with $30. His first purchase, made with his new debit card, totals $28.
·Bekzod makes 1.5 liters of lemonade and drinks it all during the afternoon.
·Daisy is writing a novel. She wrote 4 new pages to finish Chapter 1. When she reviews Chapter 1, she discards these 4 pages and an additional 4 pages.
Answers
(−7)^-2 and more letters cause needed
Answers
Answer:
1/49.
Step-by-step explanation:
(−7)^-2
= 1 /(- 7)^2
= 1/49.
Write an equation to model this proportional relationship, where x represents the length of the rectangle and y represents the width of the rectangle.
Answers
When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle.
[tex]x\propto \frac{1}{y} [/tex]
We know that the area of a rectangle is given by the product of the length and width of the rectangle.
Area = Length*Width
In this given problem,
The length of the rerectanglctangle is represented by x
and the width of the rectangle is represented by y
If the area of the rectangle is represented by A now.
So by the formula,
A = x*y
When A is constant then,
x = A/y
[tex]\therefore x \propto \frac{1}{y}[/tex]
So from the above calculation we can conclude that about relation between length and width that,
"When Area of rectangle is constant, then the length x is inversely proportional to the width y of the rectangle."
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The following table shows a proportional relationship between jjj and mmm.
jjj mmm
444 333
121212 999
202020 151515
Write an equation to describe the relationship between jjj and mmm.
Answers
Answer:
The equation representing the proportional relationship between j and m is m = 3j/4 .
Step-by-step explanation:
Writing an Equation to Represent a Proportional Relationship
What is proportional relationship?
A proportional relationship between two quantities is when the two quantities vary directly with one and other. Meaning if one item is doubled, the other item is also doubled.
Going back to the given problem above, we have the table showing the proportional relationship between j and m.
j | 4 | 12 | 20 |
m | 3 | 9 | 15 |
Solution:
Step #1
The proportional relationship can be written as:
m/j = ¾ = 9⁄12 = 15⁄20 = ¾
Step #2
So, the equation representing this proportional relationship is:
m = ¾ × j/1 = 3j/4
Final Answer:
The equation representing the proportional relationship between j and m is m = 3j/4 .
Step-by-step explanation:
The following figure shows a square-based pyramid.
5
6
Which expression represents the surface area of the pyramid?
Choose 1 answer:
Answers
The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
The surface area of pyramid = sum of individual area of the surface
Surface area = (2 * 2) + 4(0.5 * 2 * 3)
The expression that shows the surface area of the pyramid is (2 * 2) + 4(0.5 * 2 * 3)
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number 8. use the Steps in the construction to determine which statement is true
Answers
Answer:
choice C
Step-by-step explanation:
The circle is circumscribed because circles drawn on the outside is known as circumscription. The circle is clearly outside touching the three vertices of the triangle.
Let $m$ be a positive integer such that $m$ has exactly 5 positive divisors. How many distinct prime factors does $m$ have
Answers
If m has exactly 5 positive divisors then there can only be one prime factor.
According to statement
m has exactly 5 positive divisors AND
Let A^p,B^q,.... are the possible factors of integer m then
assume that p and q ≥ 1.
then the number of possible divisors cannot be 5 because there are no two integers p, q ≥ 1, such that (p +1)(q + 1) = 5
So, If m has exactly 5 positive divisors then there can only be one prime factor.
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ILL MARK BRAINLIEST HELP PLS I NEED THE ANSWER TO 9 and 10
Answers
Answer:
28. Y=1x+c
29. -2/3x+c
Hope it helps :)
Given that y = 12 cm and 0 = 45°, work
out a rounded to 1 DP.
The diagram is not drawn accurately.
X
cm
Answers
The value of x is 8.5 cm
How to solve for x?The complete question is in the image
The given parameters are:
y = 12 cm
[tex]\theta = 45^o[/tex]
The value of x is calculated using the following sine ratio
[tex]\sin(\theta) = \frac xy[/tex]
This gives
[tex]\sin(45^o) = \frac x{12}[/tex]
Multiply by 12
[tex]x = 12 * \sin(45^o)[/tex]
Evaluate
x = 8.5
Hence, the value of x is 8.5 cm
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A room has a length of 8 m. A scale diagram is drawn of the room. In the diagram, the room has a length of 1 cm. What is the scale of the diagram? Give your answer as a ratio in the form 1 : k , where k is an integer.
Answers
The scale of the diagram as described in the task content is; 1: 8 where k= 8.
What is the scale of the diagram?It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.
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What term is used to describe the problem of using variables that strongly correlate with one another in a multiple linear regression model
Answers
Multicollinearity is used to describe the problem of using variables that strongly correlate with one another in a multiple linear regression model.
Multiple linear regression refers to a statistical technique that is used to predict the outcome of a variable based on the value of two or more variables. It is sometimes known simply as multiple regression, and it is an extension of linear regression. The variable that we want to predict is known as the dependent variable, while the variables we use to predict the value of the dependent variable are known as independent or explanatory variables.
Multicollinearity, also known as collinearity, is a phenomena in statistics when one predictor variable in a multiple regression model can be linearly predicted from the others with a high level of accuracy. In this case, minor adjustments to the model or the data may cause the multiple regression's coefficient estimates to fluctuate unpredictably. Multicollinearity only impacts calculations pertaining to specific predictors; it has no impact on the predictive capability or reliability of the model as a whole, at least within the sample data set. In other words, a multivariate regression model with collinear predictors can show how well the entire set of predictors predicts the outcome variable, but it might not provide accurate information about any particular predictor or about which predictors are redundant with respect to another predictor.
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The black graph is the graph of y= f(x). Choose the equation for the red graph
a. y=f(x+3)
b. y=f(x-3)
c. y+3=f(x)
d. y-3=f(x)
Answers
Answer:
[tex]D[/tex]
Step-by-step explanation:
Notice that the red graph does not globally differ from the black graph: it would have been approximately the same one unless it had been displaced by 3 units up. Therefore, it was only the ordinate axis that underwent our change: [tex]y - 3 = f(x) \Leftrightarrow y = f(x) + 3[/tex].
Answer:
C
Step-by-step explanation:
PLEASE HELPPPP!
Susan's calculator has a key that replaces the number displayed with its cube. If a² is displayed, how many times must Susan press the " cubing" key to display a number that is greater than 10?
Please explain it step-by-step! Also, I will give you a brainlist!!
Answers
Answer:
10
Step-by-step explanation:
This is because you would have to start with 109 = 23x
then solve it using logarithms
Then once you get the x value, it becomes
X>_10__(whatever number you found)
Please help! I can't figure this out, i'll give a brainliest
Answers
The linear equation that best fits the data is: y = 10x + 15.
How to Write the Linear Equation of a Data?First, find the slope/unit rate (m) and the y-intercept/starting value, then substitute the values into y = mx + b.
Using two points on the graph, (1, 25) and (2, 35), find the slope (m):
Slope (m) = (35 - 25)/(2 - 1)
Slope (m) = 10/1
Slope (m) = 10
Substitute (x, y) = (1, 25) and m = 10 into y = mx + b to find b
25 = 10(1) + b
25 - 10 = b
b = 15
Substitute m = 10 and b = 15 into y = mx + b
y = 10x + 15
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Please help ill give whoever answers the best the brainliest answer
Answers
7. A student on the cross-country team runs 30 minutes a day as a part of her training.
Write an equation to describe the relationship between the distance she runs in miles, , and her running speed, in miles per hour, when she runs:
a. at a constant speed of 4 miles per hour for the entire 30 minutes.
Answers
The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
The distance travelled in 30 minutes is:
Distance = speed * time = 4 mph * 0.5 h = 2 miles
The relationship between the distance she runs in miles, , and her running speed is Distance = speed * time
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CAN ANYONE HELP PLSS
Answers
Answer:
CD = 13
Step-by-step explanation:
since Δ ABD and Δ CBD are congruent , then corresponding sides are congruent, so
CD = DA = 13
Answer:
13
Step-by-step explanation:
We know that if two triangles are congruent, the corresponding element of those are also equal.
Given that,
ABD Δ ≡ CBD Δ
Therefore, the corresponding elements are also equal.
AD = CD
AD = 13 units
∴ CD = 13 units
A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles
Answers
A motorcycle traveling at 70 miles per hour overtakes a car traveling at 40 miles per hour that had a three-hour head start. How far from the starting point are the two vehicles.
----------------------
The car is 120 miles away when the motorcycle starts.
The bike gains on the car at 30 mph (70-40).
It takes 4 hours for the bike to close the gap (120/30).
In 4 hours, the bike and the car are 280 miles from the starting point.
---------
4*70 = 280
7*40 = 280
Since Distance = Speed x Time, and in this case, the distances are equal, we, therefore, have: 70T = 40(T + 3)
70T = 40T + 120
30T = 120
T=4, which makes the distance that both vehicles traveled, highlight_green280miles, calculated as (70 * 4), or (40 * 7).
It also means that the motorcycle took 4 hours to travel 280 miles, and the car took 3 hours more, or 7 hours to travel the same distance.
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Given that
x
= 8 cm and
y
= 23 cm, work out
∠
BCA rounded to 3 SF.
Answers
The value of the angle ∠BCA when approximated to 3 significant figures is; 20.4°
How to use Trigonometric Ratios?From the attached image of the triangle ABC showing the side lengths x and y, we can see clearly that it is a right angle triangle.
Now, since we want to find the value of the angle ∠BCA, then it means we have to use trigonometric ratio to get;
x/y = sin BCA
Plugging in the relevant values gives us;
8/23 = sin BCA
∠BCA = sin⁻¹(8/23)
∠BCA = 20.355
Approximating to 3 significant figures gives us;
∠BCA = 20.4°
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Members of the band sold juice and popcorn at a college football game to raise money for an
upcoming trip. Each juice bottle sold costs $2.50, and each container of popcorn sold costs
$1.25.
a. write an equation to represent how much money was made
b. be sure to specify what the variables represent.
Answers
Answer:
2.50x+1.25y=z
Step-by-step explanation:
Let the number of juice bottles = x
And the number of containers of popcorns=y
And the total number of juice bottles and containers of popcorns=z
Total number of juice bottles=x times $2.50
Total number of containers of popcorn= y times $ 1.25
equation; 2.50x+1.25y=z