Given the right triangle shown below, prove cos2(θ) + sin2(θ) = 1.
A triangle with sides x, y, and hypotenuse r. Angle theta is opposite to side y.
By
, cos(θ) = StartFraction x Over r EndFraction, and by
, sin(θ) = StartFraction y Over r EndFraction.
Multiplying both sides of the above equations by r, we get that x = r cos(θ) and y = r sin(θ).
The
states that x2 + y2 = r2.
By
, we have [r cos(θ)]2 + [r sin(θ)]2 = r2.
Applying the
, the equation can be written as r2 cos2(θ) + r2 sin2(θ) = r2.
Dividing both sides of the equation by r2 results in cos2(θ) + sin2(θ) = 1.
Answers
The blanks are filled by
Laws of Cosine,
Laws of Sine,
Pythagorean Theorem,
Substitution method,
Laws of Exponents
respectively.
What are the Laws of Cosine?A triangle with sides x, y, and hypotenuse r.
Angle θ is opposite to side y.
[tex]cos(\theta)=\frac{\mbox{adjacent side}}{\mbox{hypotenuse}}=\frac{x}{r}[/tex]
What are the Laws of Sine?A triangle with sides x, y, and hypotenuse r.
Angle θ is opposite to side y.
[tex]sin(\theta)=\frac{\mbox{opposite side}}{\mbox{hypotenuse}}[/tex]
What is Pythagorean Identity?A triangle with sides x, y, and hypotenuse r.
Angle θ is opposite to side y.
Then the property
x²+y²=r²
is called the Pythagorean Identity.
How to fill the blanks?Given the right triangle shown below, prove cos²(θ) + sin²(θ) = 1.
A triangle with sides x, y, and hypotenuse r.
Angle θ is opposite to side y.
By Laws of Cosine
, cos(θ) = x/r, and
by Laws of Sine
, sin(θ) = y/r.
Multiplying both sides of the above equations by r, we get that
x = r cos(θ) and
y = r sin(θ).
The Pythagorean Theorem states that x² + y² = r².
By Substitution method , we have [r cos(θ)]² + [r sin(θ)]²= r².
Applying the Laws of Exponents, the equation can be written as r² cos²(θ) + r² sin²(θ) = r².
Dividing both sides of the equation by r² results in cos²(θ) + sin²(θ) = 1.
Hence, the blanks are filled by
Laws of Cosine,
Laws of Sine,
Pythagorean Theorem,
Substitution method,
Laws of Exponents
respectively.
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Answer:
the above is right
Step-by-step explanation:
Just took the test
Related Questions
6x+3(4x-2)
Step by Step
Answers
Answer:
18x-6
Step-by-step explanation:
simplify the expression
help help help please
Answers
Answer:
see explanation
Step-by-step explanation:
To evaluate f(8), substitute x = 8 into f(x) , that is
f(8) = [tex]\sqrt{2(8)+9}[/tex] = [tex]\sqrt{16+9}[/tex] = [tex]\sqrt{25}[/tex] = ± 5
-----------------------------------------------------
Equating
[tex]\sqrt{2x+9}[/tex] = 3 ( square both sides )
2x + 9 = 9 ( subtract 9 from both sides )
2x = 0 ⇒ x = 0
Thus
f(0) = 3
Which equation best matches the graph shown below?
Answers
The quadratic function that best matches the graph is given as follows:
y = -0.2(x + 3)² + 5.
How to define the quadratic function given it's vertex?The quadratic function of vertex(h,k) is given by the rule presented as follows:
y = a(x - h)² + k
In which:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The coordinates of the vertex for this problem are given as follows:
(-3, 5).
Hence:
y = a(x + 3)² + 5
When x = 0, y = 3, hence the leading coefficient a is obtained as follows:
3 = 9a + 5
9a = -2
a = -0.2. (rounded).
Hence the function is:
y = -0.2(x + 3)² + 5.
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A movie was 3 and one-half hours long. If Lily turned the movie off One-fourth of the way through, how much time did she spend watching it? StartFraction 1 Over 14 EndFraction of an hour StartFraction 7 Over 8 EndFraction of an hour 1 and StartFraction 1 Over 7 EndFraction of an hour 14 hours
Answers
Answer:
StartFraction 7 Over 8 EndFraction of an hour
7/8 hour
Step-by-step explanation:
Total movie time = 3 1/2 hours
Lily turned the movie off One-fourth of the way through,
1/4 of 3 1/2
= 1/4 ×7/2
= 7/8 hour
how much time did she spend watching it.
Time spent watching the movie = 3 1/2 hour - 7/8 hour
= 7/2 - 7/8
= 14-7/8
= 7/8 hour
StartFraction 7 Over 8 EndFraction of an hour
Answer:
7/8 of an hour
Step-by-step explanation:
Please help I’m being timed on this! ://
Write an algebraic rule to describe the translation P(-8,6) ► P(-10,2).
A (x,y) (- 18.y+8)
B. (x,y) → (x+2,y+4)
C. (x,y) → (x +4,y - 2)
D. (x,y) → (x-2,y-4)
Answers
Answer:
its going to be D (x,y) - (x-2,y-4)
Step-by-step explanation:
One pencil is randomly selected from a case containing 3 red, 4 green, 2 black, and 6 blue pencils. Find the probability for green and black.
Answers
Answer:
black= 2/15 green= 4/15
Step-by-step explanation:
so first we find out what this is out of so we add them all together which comes to 15. so there are 15 pencils. Since they're 4 green out of all 15 pencils it will be a 4/15 its same for black with 2/15. (sorry if it's not good, I hope this helped)
If an explanatory variable is exogenous it implies that: a. the variable cannot be correlated with other explanatory variables. b. the variable is not correlated with the regression error. c. the variable must have zero mean. d. the value of the variable must be randomly assigned.
Answers
b. the variable is not correlated with the regression error. if an explanatory variable is exogenous, it means that the variable is not correlated with the regression error term. This assumption is important for obtaining unbiased and consistent parameter estimates in regression analysis.
If an explanatory variable is exogenous, it implies that the variable is not correlated with the regression error term. In other words, the exogenous variable is unrelated to the factors that are not explicitly included in the regression model and captured by the error term.
Exogeneity is an important assumption in regression analysis, as violating this assumption can lead to biased and inconsistent parameter estimates. When an explanatory variable is exogenous, it means that its value is determined independently of the other variables in the model and the error term.
Let's briefly discuss the other options:
a. The variable cannot be correlated with other explanatory variables: Exogeneity does not necessarily imply that the variable cannot be correlated with other explanatory variables. Explanatory variables can be correlated with each other as long as they are not correlated with the regression error term.
c. The variable must have zero mean: Exogeneity does not require that the variable has a zero mean. Exogeneity refers to the lack of correlation between the variable and the regression error, not its mean value.
d. The value of the variable must be randomly assigned: Exogeneity does not require that the value of the variable is randomly assigned. Exogeneity implies that the variable is not affected by the regression error and is determined independently of the other variables in the model, but it does not necessarily imply a random assignment of values.
In summary, if an explanatory variable is exogenous, it means that the variable is not correlated with the regression error term. This assumption is important for obtaining unbiased and consistent parameter estimates in regression analysis.
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Whoever can answer this question is among one of the smartest people I have come across! PLUS I Will Mark Brainliest
Answers
Answer:
So I don't think an 11 year old like me can solve this question because I don't even know the concept used for this but from what I can see, this is somewhat easy.
y = 6.5
Step-by-step explanation:
If 3x = 5.5 on the table, then
y = 3x + 1 turns into y = 5.5 +1
5.5 + 1 = 6.5
So y = 6.5
how many are 15 x 15 ?
Answers
Answer:
225
Step-by-step explanation:
Answer:
225
Step-by-step explanation:
15x15
5x5=25
5x1+2=7
add 0
1x5=5
1x1=1
75+150=225
The width of a rectangle is 33 centimeters. The perimeter is at least 776 centimeters. Write and solve an
inequality to find the possible lengths of the rectangle.
Answers
Step-by-step explanation:
length is x
p=(33+×)2
(33+×)2>776
66+2×>776
×>710
×>355
the length of the rectangle is greater/equals 355
What is 7! Like seven times all the numbers below it
Answers
Lemmings are small mammals that reproduce quickly. A lemming population often grows so quickly that there is not enough food for all of the lemmings to eat. This results in a decline of the lemming population.
This example best supports the ideas of which scientist?
Malthus
Darwin
Lamarck
Linnaeus
Answers
Answer:
A(Malthus)
Step-by-step explanation:
because i'm stunning and cunning for miraculis ladybug and legacies
What is the range of the function represented by these ordered pairs? (
{(-1, -3), (-2, 0), (-3,5), (1, -3), (2, 0), (3,5)}
Answers
Answer:
6
Step-by-step explanation:
smallest x value is -3
largest x value is 3
so distance between them is 6
3- (-3)=6
Answer:
Step-by-step explanation:
How far would the plane fly in 3 hours at this speed? explanation
Answers
Answer:
The plane will fly 1830mph.
Step-by-step explanation:
Just multiply 610 (mph) by 3 (# of hours)
Answer:
1830 miles
Step-by-step explanation:
3 hours x 610 mph = ? how far the plane will fly
3 x 610 = 1830
the plane will fly 1830 miles in 3 hours
2g-h/f=5 solve for g
Answers
2g-m=5-gh solve for g
2g+gh=5+m
g(2+h)=5+m
g=(5+m)/(2+h)
Cheers,
Stan H.
Find (a) the perimeter and (b) the area of the figure. Use 3.14 or 22/7 for Pi. Round your answer to the nearest hundredth, if
necessary.
Answers
a. Total perimeter = 89.12 ft
b. Total area = 174. 24 ft²
How to determine the valuesTo determine the perimeter, we have;
Perimeter of triangle = a + b + c = 8 + 6 + 10 = 24ft
Circumference of a circle is expressed a;s
= 2πr
Circumference = 2× 3.14 × 4
Multiply the values
Circumference = 25. 12 ft
Perimeter of a square = 4a)
Perimeter = 40 ft
Total perimeter = 40 + 25.12 + 24 = 89.12 ft
For area;
Triangle = 1/2bh = 1/2 (48) =24 ft²
Square = a² = 100ft²
Circle = 3.14 × 4² = 50.24ft²
Total area = 174. 24 ft²
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Find the value of so that the polynomial p(x) is divisible by (x + 2) p(x) = 4x ^ 3 + c * x ^ 2 + x + 2
Answers
Answer:
8
Step-by-step explanation:
Steve has 12 guppies. Their population decreases by 3% each year. How many guppies will there be in one year?
Answers
Answer:
11 guppies
Step-by-step explanation:
my teacher told me the answer
Which expression is equivalent to (7 to the power of -8) (7 to the power of 3) ?
Answers
Answer:
7^-5
Step-by-step explanation:
7^-8 .* 7^3=7^-8+3 =7^-5
QUESTION 30 Given the following probability distributions, what are the expected returns for the market and for Security J? State Pr i ᵣM ᵣJ
1 0.3 -10% 40% 2 0.4 10 -20 3 0.3 30 30
Answers
Expected return for the marketE(RM) = ∑ Pr(RM) = 0.3(-10%) + 0.4(10%) + 0.3(30%)= -3% + 4% + 9%= 10%Therefore, the expected return for the market is 10%Expected return for Security JE(RJ) = ∑ Pr(RJ) = 0.3(40%) + 0.4(-20%) + 0.3(30%)= 12% - 8% + 9%= 13%Therefore, the expected return for Security J is 13%..
The above calculation represents the probability distributions of returns for the market and Security J. From the above calculation, it can be observed that the expected return for the market is 10%.
The expected return is a prediction that helps investors to get an idea about the possible returns of an investment.
The expected return is calculated by multiplying each possible outcome by its corresponding probability and then adding all the products.
By calculating the expected return for the market, investors can predict the market performance and make investment decisions accordingly. Similarly, the expected return for Security J is 13%, which implies that Security J has a higher expected return than the market.
By analyzing the expected return, investors can decide which investment would be more profitable for them.
In conclusion, the expected return for the market and Security J can be calculated using probability distribution. The calculation of the expected return is beneficial for investors to understand the market performance and make investment decisions accordingly.
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Suppose you own a tour bus and you book groups of 20 to 70 people for a day tour. The cost per person is $30 minus $0.25 for every ticket sold. Gas and other miscellaneous costs are $200. Write the revenue and cost functions for this situation. Write the profit function for this situation. Find the number of tickets needed to maximize profit and give the maximum profit
Answers
Let's denote the number of tickets sold as .
The revenue function can be calculated by multiplying the number of tickets sold by the ticket price:
Revenue() = * (30 - 0.25)
The cost function consists of two components: the cost per person and the fixed costs for gas and miscellaneous expenses:
Cost() = * 30 - 0.25^2 + 200
To find the profit function, we subtract the cost function from the revenue function:
Profit() = Revenue() - Cost()
Profit() = * (30 - 0.25) - ( * 30 - 0.25^2 + 200)
Profit() = -0.25^2 + 30 - 0.25^2 + 200
To maximize profit, we need to find the value of that maximizes the profit function. This can be achieved by finding the vertex of the quadratic equation () = -0.25^2 + 30 + 200.
The x-coordinate of the vertex can be calculated using the formula = - / (2), where = -0.25 and = 30:
= -30 / (2 * -0.25)
= -30 / -0.5
= 60
Therefore, the number of tickets needed to maximize profit is 60.
To find the maximum profit, we substitute = 60 into the profit function:
Profit(60) = -0.25 * (60)^2 + 30 * 60 + 200
Profit(60) = -0.25 * 3600 + 1800 + 200
Profit(60) = -900 + 2000
Profit(60) = 1100
Hence, the maximum profit is $1100.
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Is the mean greater than, less than, or equal to the median?
Answers
Answer:
One of the basic tenets of statistics that every student learns in about the second week of intro stats is that in a skewed distribution, the mean is closer to the tail in a skewed distribution. So in a right skewed distribution (the tail points right on the number line), the mean is higher than the median.
Step-by-step explanation:
Is the mean always greater than the median in a right skewed distribution?
by Karen Grace-Martin Leave a Comment
One of the basic tenets of statistics that every student learns in about the second week of intro stats is that in a skewed distribution, the mean is closer to the tail in a skewed distribution.
So in a right skewed distribution (the tail points right on the number line), the mean is higher than the median.
It’s a rule that makes sense, and I have to admit, I never questioned it.
But a great article in the Journal of Statistical Education shows that it really only holds in ideali
12:35 on Sunday.
I am back with a handful of geometry questions. I would like you to answer this question and explain or show all of your work.
I will mark Brainlest for an accurate answer!
If the image is to blurry try clicking on it. If it is still to blurry, let me know in the comments. If you have any other questions about the problem, let me know.
Please only answer of you have a "real" answer and not a comment. Save your comments for the comment box!
If you would like to help me out some more, go check out my profile and answer the questions that have 12:35 on Sunday questions on them.
God Bless.
Answers
Answer:
(x, y) ⇒ (x, y+6)
Step-by-step explanation:
Reflection of a value a across a point p to make b requires that a, b, and p satisfy the relation ...
p = (a+b)/2
2p = a + b
b = 2p - a
This is true for any sort of reflection. Here we have a reflection across the horizontal line y=-1, followed by a reflection across the horizontal line y=2. These reflections do not change the x-coordinate of a point, but they change the y-coordinate in accordance with the above relation.
Reflection across y = -1:
(x, y) ⇒ (x, 2(-1)-y) = (x, -2-y)
Reflection of that across y = 2:
(x, -2-y) ⇒ (x, 2(2) -(-2-y)) = (x, y+6)
The composition of the two reflections results in a translation upward of 6 units: (x, y) ⇒ (x, y+6)
Please help me please please. Thank you!!!
Answers
3.3.IP-14
Question Help $
A ranger hiked 605 feet to and from the peak of a mountain, each way. The ranger hiked 4 times in
the past four weeks. How far did the ranger hike on the mountain over the past four weeks?
The ranger hiked feet.
(Type a whole number.)
Help
Answers
Simon neatly arranged 35 radio-controlled cars in 5 rows on the shelf.Find the number of cars placed in each row.
Answers
Answer:
7
Step-by-step explanation:
35 / 5 = 7
Answer:
7 = 35 cars/5 rows= 7 cars per row
Solve the equation and show your work W + 87 = 102
Answers
Exercise #1: Kirk's bank account has $100 in it. He writes a check for $300 which is
then withdrawn from his bank account. How much money does he have now in the
account?
Answers
Answer:
-200
Step-by-step explanation:
100-300=-200
or 400
A closed container has 5.04 ⋅ 1023 atoms of a gas. Each atom of the gas weighs 1.67 ⋅ 10–24 grams.
Which of the following shows and explains the approximate total mass, in grams, of all the atoms of the gas in the container?
Answers
Answer:
Step-by-step explanation:
Each atom of the gas weighs 1.67 ⋅ 10−24 grams. 6.71 grams, because (5.04 + 1.67) ⋅ (1023⋅ 10−24 ) = 6.71. ... 0.67 grams, because (5.04 + 1.67) ⋅ (1023⋅ 10−24 ) = 6.71 ⋅ 10−1.
Nosaira solved an equation. Her work is shown below:
3(2x + 1 ) = 2(x + 1) + 1
6x + 3 = 2x + 2 + 1
6x + 3 = 2x + 3
4x = 0
x = 0
She determines the equation has no solution.
Which best describes Nosaira’s work and answer?
Her work is correct, but there is one solution rather than no solution.
Her work is correct and her interpretation of the answer is correct.
Her work is incorrect. She distributed incorrectly.
Her work is incorrect. She moved terms across the equals sign incorrectly.
Answers
Answer:
yeah its A
Step-by-step explanation:
Nosaira's work is correct, but there is one solution and rather than no solution.
The correct option is A.
What is an equation?A pair of algebraic equations with the equal symbol (=) in the center and the same value is referred to as an equation.
The steps she used to solve the equation are valid, and she correctly determined that x = 0.
As per the information provided,
3(2x + 1 ) = 2(x + 1) + 1
6x + 3 = 2x + 2 + 1
6x + 3 = 2x + 3
4x = 0
x = 0
However, this means that the equation does have a solution, contrary to her conclusion that there is no solution.
This is likely a mistake in her interpretation of the solution, rather than an error in her algebraic work.
Therefore, there is only one solution.
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