How would you do a point circle problem like this without arctan?
Answers
To do this, we can use the Pythagorean theorem and trigonometric ratios instead.
1. Determine the coordinates of the given point, let's call it P(x, y), and the center of the circle, let's call it O(h, k). Also, note the radius, r.
2. Calculate the distance between point P and the center O using the Pythagorean theorem: d^2 = (x-h)^2 + (y-k)^2, where d is the distance.
3. Set d equal to the radius of the circle: r^2 = (x-h)^2 + (y-k)^2.
4. Now, let's find the angle θ between the x-axis and the line OP without using arctan. To do this, we'll use the sine and cosine ratios:
sin(θ) = (y-k) / r and cos(θ) = (x-h) / r
5. To eliminate the need for arctan, we can use the Pythagorean identity sin^2(θ) + cos^2(θ) = 1. Substitute the sine and cosine ratios we found earlier:
((y-k) / r)^2 + ((x-h) / r)^2 = 1
6. Simplify the equation by multiplying both sides by r^2:
(y-k)^2 + (x-h)^2 = r^2
You'll notice that this equation is the same as the one we found in step 3, confirming that the point P lies on the circle. You've now solved the point circle problem without using arctan, by employing the Pythagorean theorem and trigonometric ratios instead.
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Related Questions
If f(x) = StartFraction x Over 2 EndFraction + 8, what is f(x) when x = 10?
Answers
Answer:
13
Step-by-step explanation:
\( f(x) = \dfrac{x}{2} + 8 \)
\( f(10) = \dfrac{10}{2} + 8 \)
\( f(10) = 5 + 8 \)
\( f(10) = 13 \)
Answer:
13
Step-by-step explanation:
n a test of a random sample of 100 computer chips, 98 met the required specifications. Assume that the sample proportion from this test is a reliable estimate of the population proportion of success. Find the probability that at least 970 of 1000 computer chips will meet the required specifications. Please show your work.
Answers
A random sample of 100 computer chips, 98 met the required specifications. the probability that at least 970 of 1000 computer chips will meet the required specifications is approximately 0.9438 or 94.38%.
To solve this problem, we can use the normal approximation to the binomial distribution since both n (sample size) and p (probability of success) are sufficiently large.
Let's define the random variable X as the number of computer chips meeting the required specifications out of 1000.
The sample proportion of success is given by = 98/100 = 0.98.
The mean of the binomial distribution is given by μ = n * = 1000 * 0.98 = 980.
The standard deviation of the binomial distribution is given by σ = sqrt(n * * (1 - )) = sqrt(1000 * 0.98 * 0.02) = 6.244997998399387.
To find the probability that at least 970 of 1000 computer chips will meet the required specifications, we need to calculate the probability of X ≥ 970.
Using the normal approximation, we can standardize the distribution by converting X to a standard normal variable Z using the formula:
Z = (X - μ) / σ
Z = (970 - 980) / 6.244997998399387 = -1.598051288076399
We can then use the standard normal distribution table or a calculator to find the probability of Z ≥ -1.598.
P(Z ≥ -1.598) ≈ 0.9438
Therefore, the probability that at least 970 of 1000 computer chips will meet the required specifications is approximately 0.9438 or 94.38%.
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what is the denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity
Answers
The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity is equal to the number of total observations (N) minus the number of groups (k). So, it can be represented as (N - k).
The denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity depend on the sample size and the number of groups being compared.
In a two-sample test, the denominator degrees of freedom are equal to the total sample size minus the number of groups being compared. In a one-way ANOVA test, the denominator degrees of freedom are equal to the total sample size minus the number of groups being compared minus one. In a two-way ANOVA test, the denominator degrees of freedom are equal to the product of the degrees of freedom for each factor. In general, a higher denominator degrees of freedom value indicates a greater precision in the estimate of the population variance, which is important in determining the accuracy of the F statistic and the significance of the test.Thus, the denominator degrees of freedom of the F statistic for testing the null hypothesis of homoskedasticity is equal to the number of total observations (N) minus the number of groups (k). So, it can be represented as (N - k).Know more about the degrees of freedom
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Jayden evaluated the expression a + (2 + 1. 5) for a = 14. He said that the value of the expression was 8. 5. Select all the statements that are true. Jayden's solution is incorrect. Jayden added inside the parentheses before dividing. Jayden substituted the wrong value for a. Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
Answers
It is true that Jayden's solution is incorrect. It is false that Jayden added inside the parentheses before dividing.
It is false that Jayden substituted the wrong value for a. It is true that Jayden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
1) The correct solution is
Given,
a ÷ (2 + 1. 5)
Substituting the value of a which is 14
= 14 ÷ (2 + 1. 5)
= 14 ÷ 3.5
= 4
2) As there is no term which needs to be divided so, the second statement is false.
3) Jayden didn't substitute the wrong value of a he just solved the given expression without considering the bracket and divided the 14 which is the value of a by 2.
4) Jyaden divided 14 by 2 and then added 1. 5. Jayden added inside the parentheses before multiplying.
i.e. a ÷ (2 + 1. 5)
14 ÷ 2 + 1. 5
7+1.5
8.5
This is the way Jayden solved the equation due to which he arrived at the wrong solution.
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The Correct question is as below
Jayden evaluated the expression a ÷ (2 + 1.5) for a = 14. He said that the answer was 8.5. Choose True or False for each statement.
1. Jayden's solution is incorrect.
2. Jayden added in the parentheses before dividing.
3. Jayden substituted the wrong value for a.
4. Jayden divided 14 by 2 and added 1.5
Helppppppppppppp please
Answers
Answer:
105 Degrees
Step-by-step explanation:
Angle 3 is 105 degrees because it is cut in half on a striaght line. A line is 180 degrees so you subtract 75 from 180 and you get 105
Answer:
105°
Step-by-step explanation:
To find an exterior angle, subtract the interior angle from 180.
180 - 75 = 105
Therefore, angle 3 is 105°.
Let me know if I did something wrong.
a scoop of ice cream has a -centimeter radius and is served in a cone of the same radius. the scoop of ice cream is a sphere. how tall does the cone need to be in order to contain all of the ice cream if it completely melts?
Answers
The height of the cone needs to be 4 times the radius in order to contain all of the melted ice creams.
The volume of a sphere with a radius of r is given by the formula:
V = (4/3) × π × r^3
The volume of a cone with height h and base radius r is given by the formula:
V = (1/3) × π × r^2 × h
Since the scoop of ice cream has the same radius as the cone, we can set the two volumes equal to each other and solve for h:
(4/3) × π × r^3 = (1/3) × π × r^2 × h
Multiplying both sides by (3/4) gives:
π × r^3 = (1/4) × π × r^2 × h
Dividing both sides by π × r^2 gives:
r = (1/4) × h
So, the height of the cone needs to be 4 times the radius in order to contain all of the melted ice creams.
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(a) Let A∈Cm×m be tridiagonal and hermitian, with all its sub-and superdiagonal entries nonzero. Prove that the eigenvalues of A are distinct. (Hint: Show that for any λ∈C,A−λI has rank at least m−1.)
(b) On the other hand, let A be upper-Hessenberg, with all its subdiagonal entries nonzero. Give an example that shows that the eigenvalues of A are not necessarily distinct.
Answers
Answer:
Step-by-step explanation:
(a)
Let λ be an eigenvalue of A, and let x be the corresponding eigenvector. Then we have Ax = λx. Consider the matrix B = A - λI, where I is the identity matrix. We want to show that B has rank at least m-1.
Since A is tridiagonal, it follows that B is also tridiagonal. Moreover, since A is Hermitian, it follows that B is also Hermitian. Thus, B has the following form:
B = [b1 c1 ]
[a2 b2 c2 ]
[ a3 b3 c3 ]
[ . . ]
[ . cm-1 bm-1 cm]
where bi = ai - λ, for i = 1, 2, ..., m.
Now, let y be the vector obtained by setting the first entry of x to zero, i.e., y = [0 x2 x3 ... xm]T. Then we have By = Ax - λx = 0, since x is an eigenvector of A. It follows that y is in the nullspace of B.
Let z be a vector obtained by setting the second entry of x to zero, i.e., z = [x1 0 x3 ... xm]T. Then we have Bz = [b1 a2 0 ... 0]T, which is nonzero since bi is nonzero for all i. It follows that z is not in the nullspace of B.
Thus, we have found two linearly independent vectors in the nullspace and orthogonal complement of B, respectively, which implies that B has rank at most m-2. Since B is a square matrix of size m, it follows that B has rank at least m-1. Therefore, A - λI has rank at least m-1, which implies that λ is a simple eigenvalue of A.
(b)
Consider the matrix
A = [1 1 0]
[1 1 1]
[0 1 1]
which is upper-Hessenberg with all subdiagonal entries nonzero. The characteristic polynomial of A is given by
p(λ) = det(A - λI) = (1 - λ)(1 - λ)(1 - λ) - 1 = (λ - 2)λ(λ - 2).
Thus, the eigenvalues of A are λ = 0, 2, 2. Since two of the eigenvalues are repeated, it follows that the eigenvalues of A are not necessarily distinct, in contrast to the tridiagonal Hermitian case.
HEY CAN ANYONE PLS ASNWER DIS!!!!!1
Answers
Answer:
11 songs
Step-by-step explanation:
first you would multiply 1.80 by 3 which is 5.4
next you would subtract 12.0 by 5.4 and get 6.6
then you would divide 6.6 by .60 to get 11
Answer:
11 songs
Step-by-step explanation:
If you bought 3 movies that would cost $5.40 leaving you with $6.60 to spend on songs. If one song costs $0.60 then you would divide that by 6.60 to see how many songs you would be able to get.
Is 2(6 – 3x) + x equivalent to 2(3x) + x + 12?
Answers
Answer:
Step-by-step explanation:
Carry out indicated operations to see if they are equal
2(6-3x)+x=2(3x)+x+12
2(6)+2(-3x)+x=6x+x+12
12-6x+x=6x+x+12 combine like terms on both sides
12-5x=12+7x (we can see here they are unequal but we can continue) subtract 12 from both sides
-5x=7x divide both sides by x
-5=7
7 is not equal to -5 so the original expressions aren’t equivalent.
How many solutions does this system have? x minus y = negative 4. 3 x + y = 8. one two an infinite number no solution
Answers
Answer:
One solution
Step-by-step explanation:
Answer:
The correct answer is A.) one
Step-by-step explanation:
I just did the test on edge 2021 and got it right!
How many millimeters in a decimeter
Answers
Answer:
There are 100 millimeters in a decimeter
Step-by-step explanation:
Answer:
100 millimeters
Step-by-step explanation:
I NEED HELP!!! BUT FAST
Answers
Answer:
i think the answer is 63 millimeters
The continuous random variable X has a probability density function (pdf) given by f(x) Şi- & for 0 < x < 2 lo otherwise Part(a) Find the median of X, correct to 2 decimal places. 0.59 Part(b) Find P(X >>). Give your answer as a decimal, correct to 2 decimal places. 0.56 Part(c) Two independent observations of X are taken. Find the probability correct to 2 decimal places that one is less than and the other is greater than 2. The order in which we take observations matters. 0.25 Part(d) Find Var(X), correct to 2 decimal places. 0.22 Part(e) Find E(X), correct to 2 decimal places. 0.75 Part(f) Find the value of q such that P(X
Answers
The median of X is 1; P(X > 2) = 0; P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0; Var(X) is approximately 0.33; E(X) is 1 and the value of q such that P(X < q) = 0.95 is 1.9.
(a) To find the median of X, we need to find the value of x for which the cumulative distribution function (CDF) equals 0.5.
Since the PDF is given as f(x) = 1/2 for 0 < x < 2 and 0 otherwise, the CDF is the integral of the PDF from 0 to x.
For 0 < x < 2, the CDF is:
F(x) = ∫(0 to x) f(t) dt = ∫(0 to x) 1/2 dt = (1/2) * (t) | (0 to x) = (1/2) * x
Setting (1/2) * x = 0.5 and solving for x:
(1/2) * x = 0.5; x = 1
Therefore, the median of X is 1.
(b) To find P(X > x), we need to calculate the integral of the PDF from x to infinity.
For x > 2, the PDF is 0, so P(X > x) = 0.
Therefore, P(X > 2) = 0.
(c) To find the probability that one observation is less than 2 and the other is greater than 2, we need to consider the possibilities of the first observation being less than 2 and the second observation being greater than 2, and vice versa.
P(one observation < 2 and the other > 2) = P(X < 2 and X > 2)
Since X follows a continuous uniform distribution from 0 to 2, the probability of X being exactly 2 is 0.
Therefore, P(one observation < 2 and the other > 2) = P(X < 2) * P(X > 2) = 0 * 0 = 0.
(d) The variance of X can be calculated using the formula:
Var(X) = E(X²) - [E(X)]²
To find E(X²), we need to calculate the integral of x² * f(x) from 0 to 2:
E(X²) = ∫(0 to 2) x² * (1/2) dx = (1/2) * (x³/3) | (0 to 2) = (1/2) * (8/3) = 4/3
To find E(X), we need to calculate the integral of x * f(x) from 0 to 2:
E(X) = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1
Now we can calculate the variance:
Var(X) = E(X²) - [E(X)]² = 4/3 - (1)² = 4/3 - 1 = 1/3 ≈ 0.33
Therefore, Var(X) is approximately 0.33.
(e) The expected value of X, E(X), is given by:
E(X) = ∫(0 to 2) x * f(x) dx = ∫(0 to 2) x * (1/2) dx = (1/2) * (x²/2) | (0 to 2) = (1/2) * 2 = 1
Therefore, E(X) is 1.
(f) The value of q such that P(X < q) = 0.95 can be found by solving the following equation:
∫(0 to q) f(x) dx = 0.95
Since the PDF is constant at 1/2 for 0 < x < 2, we have:
(1/2) * (x) | (0 to q) = 0.95
(1/2) * q = 0.95
q = 0.95 * 2 = 1.9
Therefore, the value of q such that P(X < q) = 0.95 is 1.9.
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Given that the solutions of the previous question are W1= 20.27 and W2=-17.27, please answer question 9
Answers
Since we're talking about dimensions, the only solution that makes sense in the context of the problem is W1, because we cannot have negative measurements.
Which of the following best describes ethics?
it is a set of thoughts that are made about kinds of individuals
or their manners of conducting activities
it is a set of values that define r
Answers
Answer:
the second
Step-by-step explanation:
refers to well-founded standards of right and wrong that prescribe what humans should do, usually in terms of rights, obligations, benefits to society, justice
A scientist is measuring the amount of bacteria in a culture. This function f(x) = 200(3)x models the number of bacteria x hours after she began monitoring. What does the
200 in the function represent?
A.The bacteria multiply 200 times each hour
B.The culture started with 200 bacteria
C.The culture started with 3 bacteria
D.200 new bacteria grow each hour
Answers
Tyrone makes a scale drawing of his backyard. The scale from the backyard to the drawing is 2 ft to 1 in. The width of the patio on the drawing is 8 in. What is the width of Tyrone's actual patio?
Answers
Answer:
16:8 width
Step-by-step explanation:
Find the value of x.
(3x + 7)º
(4x – 18)°
X =
Answers
Answer:
X=25
Step-by-step explanation:
3x+7 = 4x-18
Subtract 3x from both sides
7=x-18
Add 18 to both sides
25=x
how to find the equation of a line that is parallel and passes through a point
Answers
Answer:
Step-by-step explanation:
Parallel line have the same slope. Put the reference line is y=mx+b format. m will be the slope. A parallel line must have the same m. Example:
y=2x+5 has a slope of 2 and a y-intercept of 5 (the value of y when x is 0). Any line witrh the same slope will be parallel. So with can write y=2x+b, where we'll change the y-interecpt so the the lines don't overlap. Once we know the parallel line must be y = 2x+b, we can enter the known point, e.g., (3,14), and calculate b:
y=2x+b
14=2*3+b
14=6+b
b=8
The parallel line to y=2x+5 is y=2x+8: It is parallel and goes through the point (3,14).
7. suppose a binary digit (0 or 1) needs to be transmitted across a series of 4 channels. each time, the digit is transmitted correctly to the next channel with probability 0.9, and is transmitted incorrectly (meaning that 1 is transmitted as 0, and 0 is transmitted as 1) with probability 0.1. if the digit 0 is sent, what is the probability that the digit that is received (after having been transmitted across the 4 channels) is a 0?
Answers
The probability that the digit that is received (after having been transmitted across the 4 channels) is 0.3645
In communication systems, it is common to face the challenge of transmitting information accurately over a noisy channel. In this scenario, errors can occur during transmission, and it is essential to quantify the probability of receiving the correct information at the end of the channel.
In this problem, we are asked to calculate the probability that the digit received after transmitting a 0 across four channels is also a 0. We know that each channel can either transmit the digit correctly with probability 0.9 or incorrectly with probability 0.1. Therefore, we can use the concept of conditional probability to solve this problem.
Using Bayes' theorem, we can rewrite this as:
P(CCCC | 0 received) x P(0 received) / P(CCCC)
Here, P(CCCC | 0 received) represents the probability that all four channels transmitted the 0 correctly, given that a 0 was received. This probability can be calculated as:
P(CCCC | 0 received) = P(C) x P(C | C) x P(C | C | C) x P(C | C | C | C)
Substituting the given probabilities, we get:
P(CCCC | 0 received) = 0.9 * 0.9 * 0.9 * 0.9 = 0.6561
Similarly, we can calculate the probability of receiving a 0 in general as:
P(0 received) = P(CCCC | 0 received) x P(0) + P(IIII | 0 received) x P(1)
where P(IIII | 0 received) represents the probability that all four channels transmitted the digit incorrectly, given that a 0 was received. This probability can be calculated similarly as:
P(IIII | 0 received) = P(I) * P(I | I) x P(I | I | I) x P(I | I | I | I) = 0.1 x 0.1 x 0.1 x 0.1 = 0.0001
Substituting the given probabilities, we get:
P(0 received) = 0.6561 x 0.5 + 0.0001 x 0.5 = 0.3281
Finally, we can calculate the denominator P(CCCC) as:
P(CCCC) = P(CCCC | 0 received) x P(0) + P(CCCC | 1 received) x P(1)
where P(CCCC | 1 received) represents the probability that all four channels transmitted the digit correctly, given that a 1 was received. This probability can be calculated similarly as:
P(CCCC | 1 received) = P(I) x P(I | C) x P(I | C | C) x P(I | C | C | C) = 0.1 x 0.9 x 0.9 x 0.9 = 0.0729
Substituting the given probabilities, we get:
P(CCCC) = 0.6561 * 0.5 + 0.0729 * 0.5 = 0.3645
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Please help!!!!
Tom, Lisa, and Jane are competing in a cooking competition. They all used different amounts of sugar from a can containing 4 pounds of sugar. Tom used 13% of the total sugar in the can. Lisa used 0.6 pounds of the total sugar in the can. Jane used 0.12 of the total sugar in the can. Who used the greatest amount of sugar from the can? Show your work and explain your answer in words.
Answers
Answer:
13 x 4
100
= 0.52 so tom used the most
Step-by-step explanation:
(x-14)÷7=12 I just need help
Answers
Answer:
x = 98
Step-by-step explanation:
Solve for x:
(x - 14)/7 = 12
Multiply both sides of (x - 14)/7 = 12 by 7:
(7 (x - 14))/7 = 7×12
(7 (x - 14))/7 = 7/7×(x - 14) = x - 14:
x - 14 = 7×12
7×12 = 84:
x - 14 = 84
Add 14 to both sides:
x + (14 - 14) = 14 + 84
14 - 14 = 0:
x = 84 + 14
84 + 14 = 98:
Answer: x = 98
x) sec’A + cosec?A
secA. cosecA
Answers
Answer:
(Sin A + Cos A)/Sin A. Cos A
Step-by-step explanation:
As we know
Sec A = 1/Cos A
and Cosec A = 1/Sin A
Given Equation
Sec A + Cosec A
Substituting the given values, we get -
1/cos A + 1/Sin A
(Sin A + Cos A)/Sin A. Cos A
An irrational number between 2 and 2.5
Answers
Answer:
Irrational number between 2 and 2.5 = √2*2.5 = √5
Step-by-step explanation:
2 < √5 < 2.5
We know that √5 is an irrational number.
So, √5 is the required irrational number between 2 and 2.5.
• Choose a topic from the list below: Argue why Josef Pieper conception of leisure is the best one in modernity, or instead why it might be a limited conception in comparison to another theory of leisure. • Argue why a life is better with leisure today, and why for the classical Greeks, an absence of leisure meant an absence of a happy life. • Argue why John Dewey and modern liberal thinkers did not agree with Aristotle's ideas on education or on leisure generally. • Argue how modern psychological conceptions of happiness and the classical idea of happiness in Aristotle differ. What was the "Greek Leisure Ideal" and how would it manifest today according to Sebastian De Grazia? What happened to it? • Argue why the liberal arts are so important in education and leisure, and explain its Greek origin and how that is received today. • You must choose from this list, but it can be modified slightly if you have an idea you wish to pursue. The main requirement is that you must contrast at least one ancient thinker and one modern one. • The paper must be well researched and contain a minimum of 6 sound academic sources. • Textbook or course readings may be used, but do not count in this total. DETAILS SCALCET8 1.3.039. 0/1 Submissions Used Find f o g o h. f(x) = 3x - 8, g(x) = sin(x), h(x) =x^2
Answers
To argue why the liberal arts are so important in education and leisure, one must discuss its Greek origin and how it is received today.
The term "liberal arts" comes from the Latin word "liberalis," which means free. It was used in the Middle Ages to refer to topics that should be studied by free people. Liberal arts refers to courses of study that provide a general education rather than specialized training. It encompasses a wide range of topics, including literature, philosophy, history, language, art, and science.The liberal arts curriculum is based on the idea that a broad education is necessary for individuals to become productive members of society. In ancient Greece, education was focused on developing the mind, body, and spirit.
The study of the liberal arts is necessary to create well-rounded individuals who can contribute to society in meaningful ways. While the importance of the liberal arts has been debated, it is clear that they are more important now than ever before. The study of the liberal arts is necessary to develop the skills that are required in a rapidly advancing technological world.
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The coordinates of a figure are (0, 2), (3, 4), (-1, -3), and (2, -1). What is the most specific classification?
A. quadrilateral
B. Parallelogram
C. isosceles trapezoid
D. rectangle
Answers
Answer:
B. Parallelogram
Step-by-step explanation:
It should look something like this which is a parallelogram.
Parallogram is like a rectangle or square that is kinda slanted.
________
/ /
/_______/
help please. this is area and the shaded region.
Answers
put the varible on the shaded half
Answer:
part A
Answer》78.50cm^2
part B
answer》A)21.5cm^2
Step-by-step explanation:
hope it helps you
have a great day!! ^_^
50 POINTS EACH!!!!! will give brian crown thing
Which expressions are equivalent to \(64^{1}\)?
Answers
Answer:
8^2
Step-by-step explanation:
8 squared is equal to 64. 64 to the power of 1 is also 64.
Which of the following ordered pairs represent points that lie on a horizontal line?
Answers
The ordered pairings (-2, 3), and (-5, 3), respectively, depict points along a horizontal line.
What is horizontal line?Let's go over some information on the horizontal line.
If the y-coordinates of every point along the line are equal, the line is horizontal.
The horizontal line's slope is zero and it is perpendicular to the x-axis.
Because the y-coordinates of every point on the line equal b, the equation of the horizontal line through point (a, b) is y = b.
Find the points with the same y-coordinates in order to identify the ordered pairs that represent points along a horizontal line.
Response A:
The paired numbers are (-2, 3), and (-5 , 3)
X is located between -2 and -5.
3 and 3 are the y-coordinates.
The two ordered pairs' y-coordinates are equivalent.
Points (-2, 3) and (-5, 3) are adjacent on a horizontal axis.
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The fastest lion ever recorded ran approximately 402 meters in 18 seconds. Which expression shows how to correctly determine the speed in meters per second?
O 402 meters + 18 seconds
O 18 seconds = 402 meters
O 402 seconds – 18 meters
O 18 meters = 402 seconds
Answers
Answer:
A. 402 meters ÷ 18 seconds
Answer: A 402 meters ÷ 18 seconds