PLSSSS HELPPPP I WILLL GIVE BRAINLIEESTTT!!!!!!!!!!

PLSSSS HELPPPP I WILLL GIVE BRAINLIEESTTT!!!!!!!!!!

Answers

Answer 1
yes, it is. linear function
Answer 2
Yes it is a linear function!

Related Questions

I need three examples on how math is used in psychology.

Answers

Answer: 1) Error response times

2) Memory Scanning, visual search

3) Stimulus identification

Step-by-step explanation:1) response times reflext the time it takes to interpret a stimulus,get info from memory, initiate a muscle response

2) The hippocampus retrieves info from the working memory and begins to change the brains physical neural wiring

3) A decisive role in our perception and cognition

In general, there are two areas of psychology where mathematics is heavily utilized: mathematical modeling of psychological theories and experimental phenomena, which gives rise to mathematical psychology, and statistical approaches to quantitative measurement practices in psychology, which give rise to psychometrics.

match the correct term with its definition chord [ choose ] tangent [ choose ] secant [ choose ] diameter [ choose ]

Answers

Chord [a straight line segment that joins two points on the circumference of a circle]

Tangent [a straight line that touches a circle or sphere at a single point]

Secant [a straight line that intersects a circle at two points]

Diameter [a straight line passing through the center of a circle and connecting two points on the circumference]

In geometry, there are several terms related to circles, such as chord, tangent, secant, and diameter. Here are their definitions:

Chord: A chord is a line segment connecting any two points on the circumference of a circle. It is the longest segment that can be drawn inside a circle.

Tangent: A tangent is a line that touches the circumference of a circle at only one point, called the point of tangency. It is perpendicular to the radius at the point of tangency.

Secant: A secant is a line that intersects a circle at two points. It can be a line that passes through the center of the circle, in which case it is the diameter of the circle.

Diameter: The diameter is the longest chord of a circle, and it passes through the center of the circle. It is twice the length of the radius.

Understanding these terms is important in solving problems related to circles and their properties. For example, in finding the length of an arc or the area of a sector, we need to know the chord or diameter of the circle, and the angle or central angle subtended by the arc or sector. In constructing tangents to circles, we need to know the point of tangency and the radius or diameter of the circle.

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Kehlani has p pennies and n nickels. She has at least 20 coins altogether. Write this situation as an inequality.

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Let's represent the number of pennies Kehlani has with "p" and the number of nickels with "n".

To write the situation as an inequality, we need to express that Kehlani has at least 20 coins.

The total number of coins Kehlani has is p + n. So, the inequality can be written as:

p + n ≥ 20

This means that the sum of the number of pennies and nickels Kehlani has must be greater than or equal to 20 for the situation to be true.
P=10 n=2 because p is 1 cents and we need 10 and n is 5 cents per cent so we 2 of those

The mean mass of five men is 76 kg. The masses of four of the men are 72 kg, 74 kg, 75 kg and 81 kg. What is the mass of the fifth man

Answers

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

(72+74+75+81+x)/5=76
x=(76.5)-302
x=380-302=78

Consider the vectors: a=(1,1,2),b=(5,3,λ),c=(4,4,0),d=(2,4), and e=(4k,3k)
Part(a) [3 points] Find k such that the area of the parallelogram determined by d and e equals 10 Part(b) [4 points] Find the volume of the parallelepiped determined by vectors a,b and c. Part(c) [5 points] Find the vector component of a+c orthogonal to c.

Answers

The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

a) Here the area of the parallelogram determined by d and e is given as 10. The area of the parallelogram is given as `|d×e|`.

We have,

d=(2,4)

and e=(4k,3k)

Then,

d×e= (2 * 3k) - (4 * 4k) = -10k

Area of parallelogram = |d×e|

= |-10k|

= 10

As we know, area of parallelogram can also be given as,

|d×e| = |d||e| sin θ

where, θ is the angle between the two vectors.

Then,10 = √(2^2 + 4^2) * √((4k)^2 + (3k)^2) sin θ

⇒ 10 = √20 √25k^2 sin θ

⇒ 10 = 10k sin θ

∴ k sin θ = 1

Therefore, sin θ = 1/k

Hence, the value of k is 1.

Part(b) The volume of the parallelepiped determined by vectors a, b and c is given as,

| a . (b × c)|

Here, a=(1,1,2),

b=(5,3,λ), and

c=(4,4,0)

Therefore,

b × c = [(3 × 0) - (λ × 4)]i + [(λ × 4) - (5 × 0)]j + [(5 × 4) - (3 × 4)]k

= -4i + 4λj + 8k

Now,| a . (b × c)|=| (1,1,2) .

(-4,4λ,8) |=| (-4 + 4λ + 16) |

=| 12 + 4λ |

Therefore, the volume of the parallelepiped is 12 + 4λ.

Part(c) The vector component of a + c orthogonal to c is given by [(a+c) - projc(a+c)].

Here, a=(1,1,2) and

c=(4,4,0).

Then, a + c = (1+4, 1+4, 2+0)

= (5, 5, 2)

Now, projecting (a+c) onto c, we get,

projc(a+c) = [(a+c).c / |c|^2] c

= [(5×4 + 5×4) / (4^2 + 4^2)] (4,4,0)

= (4,4,0.5)

Therefore, [(a+c) - projc(a+c)] = (5,5,2) - (4,4,0.5)

= (1,1,1.5)

Therefore, the vector component of a + c orthogonal to c is (1,1,1.5).

Conclusion: The value of k is 1, the volume of the parallelepiped is 12 + 4λ, and the vector component of a + c orthogonal to c is (1,1,1.5).

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the probability of bill serving an ace in tennis is 0.15, and the probability that he double faults is 0.25. what is the probability that bill does not serve an ace or a double fault? a. 0.5 b. 0.15 c. 0.4 d. 0.9 e. 0.6

Answers

The probability that Bill does not serve an ace or a double fault is 0.6.Option E (0.6) is the correct answer.

The probability of bill serving an ace in tennis is 0.15, and the probability that he double faults is 0.25. The probability that Bill does not serve an ace or a double fault is 0.6.What is probability?Probability refers to the chance that an event or circumstance will happen. It's the likelihood of something happening. Probability is usually expressed as a fraction or percentage. In many everyday situations, probability is used to make informed decisions. A probability of 1 indicates that an event is guaranteed to happen, while a probability of 0 indicates that an event is impossible to occur. A probability of 0.5 or 50% implies that an event is equally likely to happen or not. Probabilities can range from 0 to 1.What is the probability that Bill does not serve an ace or a double fault?The probability of Bill serving an ace is 0.15. The probability that he double faults is 0.25. The probability that he serves neither an ace nor a double fault is therefore 1 - (0.15 + 0.25) = 0.6Therefore, the probability that Bill does not serve an ace or a double fault is 0.6.Option E (0.6) is the correct answer.

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Consider the matrix A-1 0 1 101 a) Find all eigenvalues of A. (4 marks) b) Find the eigenvector and the basis for the eigenspace corresponding to the smallest eigenvalue of A obtained in a). (7 marks) c) Given the basis for the largest eigenvalue is 1. Show that A is diagonalizable. (2 marks) d) Find the diagonal matrix D and the invertible matrix P such that D=P-¹AP (if exists). (2 marks) e) Based on the obtained eigenvalues in a), i) find the trace and the determinant of A. ii) find all eigenvalues of A³. (Hint: Do not use |A- = 0)

Answers

a - the eigenvalue of matrix A is λ = 1.

b- the eigenvector corresponding to the smallest eigenvalue is [0; 1], and the basis for the eigenspace is { [0; 1] }.

c -A has a complete set of linearly independent eigenvectors and is diagonalizable.

d - Matrix D is the diagonal matrix, and matrix P is the invertible matrix that diagonalizes matrix A if it exists.

e -i)the trace of A is 1.

ii) eigenvalues of A^3 are the same as the eigenvalue of A, which is 1.

a) To find the eigenvalues of matrix A, we need to solve the equation det(A - λI) = 0, where λ is the eigenvalue and I is the identity matrix.

A = [1 0; 1 1]

Subtract λI from A:

A - λI = [1-λ 0; 1 1-λ]

Calculate the determinant:

det(A - λI) = (1-λ)(1-λ) - (0)(1) = (1-λ)^2

Set the determinant equal to zero and solve for λ:

(1-λ)^2 = 0

λ = 1

Therefore, the eigenvalue of matrix A is λ = 1.

b) To find the eigenvector and eigenspace corresponding to the smallest eigenvalue (λ = 1), we need to solve the equation (A - λI)v = 0, where v is the eigenvector.

(A - λI)v = (A - I)v = 0

Subtract I from A:

A - I = [0 0; 1 0]

Solve the system of equations:

0v1 + 0v2 = 0

v1 + 0v2 = 0

The solution to the system is v1 = 0 and v2 can be any non-zero value.

Therefore, the eigenvector corresponding to the smallest eigenvalue is [0; 1], and the basis for the eigenspace is { [0; 1] }.

c) To show that matrix A is diagonalizable, we need to prove that it has a complete set of linearly independent eigenvectors. Since we already found one eigenvector [0; 1], which spans the eigenspace for the smallest eigenvalue, and there is only one eigenvalue (λ = 1), this means that A has a complete set of linearly independent eigenvectors and is diagonalizable.

d) To find the diagonal matrix D and the invertible matrix P such that D = P^(-1)AP, we need to find the eigenvectors and construct matrix P using the eigenvectors as columns.

Since we already found one eigenvector [0; 1] corresponding to the eigenvalue λ = 1, we can use it as a column in matrix P.

P = [0 ?]

[1 ?]

We can choose any non-zero value for the second entry in each column to complete matrix P. Let's choose 1 for both entries:

P = [0 1]

[1 1]

Now, we calculate P^(-1) to find the invertible matrix:

P^(-1) = (1/(-1)) * [1 -1]

[-1 0]

Multiplying A by P and P^(-1), we obtain:

AP = [1 0] P^(-1) = [1 -1]

[2 1] [-1 0]

D = P^(-1)AP = [1 -1] [1 0] [0 1] [1 0] [0 0]

[-1 0] * [2 1] * [1 1] * [1 1] = [0 0]

Therefore, D = [0 0]

[0 0]

Matrix D is the diagonal matrix, and matrix P is the invertible matrix that diagonalizes matrix A if it exists.

e) Based on the obtained eigenvalue (λ = 1) in part a):

i) The trace of matrix A is the sum of the diagonal entries, which is equal to the sum of the eigenvalues. Since we have only one eigenvalue (λ = 1), the trace of A is 1.

ii) To find the eigenvalues of A^3, we can simply raise the eigenvalue (λ = 1) to the power of 3: λ^3 = 1^3 = 1. Therefore, the eigenvalues of A^3 are the same as the eigenvalue of A, which is 1.

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Monday through Thursday, the movie theater sold 439 tickets. Over the weekend,
999 tickets were sold. How many more tickets were sold over the weekend?

Answers

Answer:

560

Step-by-step explanation:

You subtract 439 from 999 and you get the left over tickets that were sold over the weekend

if 11x+5y = 9
11x +3y=1​

Answers

Y=4 x=-1. because I’m right! Plug them in and see -11 plus 12 equals 1.

.

\(the \: value \: of \: x \: is \: - 1. \\ the \: value \: of \: y \: is \: 4 \\ please \: see \: the \: attached \: picture \: for \: full \: solution \\ hope \: it \: helps\)

if 11x+5y = 911x +3y=1

Not equivalent to 3x -6

Answers

The equivalent equation for 3x - 6 is 3(x - 2).

What is equation?

Equation: A statement that two variable or integer expressions are equal. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for the answers to these questions.

Given equation:

3x - 6

Take 3 as common from both the term,

= 3(x - 2)

Therefore, the equivalent equation for 3x - 6 is 3(x - 2).

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Jack challenged Jill to a race around a curve of a track. Jack took lane 8 with Jill at lane 1. If the radius of lane 1 is half of lane 8, what is the distance in metres Jack has to run if Jill ran a distance of 50m?

Answers

Answer:jac ganko

Step-by-step explanation:

25m if it’s half the length of 8

if the mean of a sample is 4, and the standard deviation is 4, what is the z-score for a raw score of 6?

Answers

The z-score for a raw score of 6 is 0.5.A z-score indicates how many standard deviations a raw score is away from the mean.

To calculate the z-score for a raw score of 6 given a mean of 4 and a standard deviation of 4, we can use the formula:

z = (raw score - mean) / standard deviation

Substituting the values into the formula, we get:

z = (6 - 4) / 4

z = 0.5

Therefore, the z-score for a raw score of 6 is 0.5.

In this case, a z-score of 0.5 indicates that the raw score of 6 is half a standard deviation above the mean of 4.

Z-scores are useful because they allow us to compare scores from different distributions. For example, if we have two sets of data with different means and standard deviations, we can convert them into z-scores to compare them directly. A positive z-score means that the raw score is above the mean, while a negative z-score means that the raw score is below the mean. The magnitude of the z-score indicates how far the raw score is from the mean in terms of standard deviations.

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Using the definition of martingales

Let two martingales in respect to the same filtration. Prove that the process is a supermartingale.

Answers

In a supermartingale , the current variable (\(X_{t}\)) is an overestimate for the upcoming \(X_{t + 1}\).

A sequence of random variable (\(X_{t}\)) adapted to a filtration (\(F_{t}\)) is a martingale (with respect to (\(F_{t}\))) if  all the following holds for all t :

(i)   E|\(X_{t\)| < ∞

(ii) E[ \(X_{t + 1}\)|\(F_{t}\)] = \(X_{t}\)

If instead of condition (ii) we have E [\(X_{t + 1}\)|\(F_{t}\)]  ≥ \(X_{t}\) for all t , we then say that (\(X_{t}\))  is submartingale with respect to (\(F_{t}\)).

If instead of condition (ii) we have E [ \(X_{t + 1}\) | \(F_{t}\)] ≤\(X_{t}\) for all t , we then say that (\(X_{t}\)) is supermartingale with respect to (\(F_{t}\)).

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Americans work an average of 34 years before retiring.
State the null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the appropriate parameter (μ or p).
H0: μ ≤ 34, Ha: μ > 34
H0: p = 34, Ha: p ≠ 34
H0: μ ≠ 34, Ha: μ = 34
H0: μ ≥ 34, Ha: μ < 34
H0: μ = 34, Ha: μ ≠ 34
H0: p ≤ 34, Ha: p > 34
H0: p ≠ 34, Ha: p = 34
H0: p ≥ 34, Ha: p < 34

Answers

Null hypothesis, H0, and the alternative hypothesis, Ha, in terms of the appropriate parameter (μ or p) is;

H0: μ ≤ 34, and also Ha: μ > 34

How to find H0 and Ha?

When a hypothesis testing is conducted, the null hypothesis (H0) and the alternative hypothesis (Ha) are set.

We will state the null hypothesis, and also the alternative hypothesis, w.r.t of the appropriate parameter.

The appropriate parameter for the given statement is the population mean (μ).

Americans works with an average years of 34 before retiring.

Null hypothesis (H0):

The population mean is less than or equal to 34.

H0: μ ≤ 34

Alternative hypothesis (Ha):

The population mean is greater than 34.

Ha: μ > 34

This hypothesis test is a two-tailed test because we are interested in testing whether the population mean is significantly different from 34, without specifying the direction of the difference.

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Can somebody help me with this question plz!

Can somebody help me with this question plz!

Answers

x=8.5 because angle B and angle D are congruent using alternate interior angles theorem. so you would find the measure of B by adding 50+45 to get 95, then subtract 95 from 180 to get 85 degrees for angle B. Now your equation is 10x=85 so if you divide 85/10 you get x=8.5! hope this helped :)

Answer:

x = 5°

Step-by-step explanation:

Because of the given congruency,

Angle A = Angle D = 50° = 10x

10x = 50

x = 5°

HOPE IT HELPS!!!

There were two candidate A and B conteting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, find the number of vote received by B

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There were two candidate A and B contesting for the municipal corporation election in a town. The total number of voter in the town were 80,000. If 90% of the voter had voted and 60% of vote polled were cat in favour of A, 28,800 the number of vote received by B.

What is municipal corporation election?

A state-incorporated city, town, village, or county that has the power to manage local governmental matters, such as creating a police force. A municipal corporation is established by a state's legislature, which also determines its lifespan, privileges, and powers. likewise known as a municipality.

A local governing body, such as cities, counties, towns, townships, charter townships, villages, and boroughs, is referred to legally as a "municipal corporation." Municipally-owned companies can also be referred to as this

Regulation of building construction and land usage. Town planning is included in urban planning. preparing for social and economic progress. water supply for residential, commercial, and industrial uses.

Given that,

Total number voters = 80,000

Total number of votes polled = 90%

Thus,

= (90/100) × 80,000

= 72,000

So, total percent of votes received by B if A gets 60% of polled votes.

= 100% - 60%

= 40%

Hence, total number of votes received by B

= (40/100) × 72,000

= 28,800

Therefore, the number of votes received by B, out of total votes polled is 28,800 votes.

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Solve the problem.

Which is greater, E or P, and by how much?

E = 1+3+5+7+. +91

P= 2+4 +6+8+. +92

Answers

P is greater than E by 46

The sum of the series E is equal to the average of the first and last term of the series, multiplied by the number of terms in the series. The first term of the series is 1, the last term is 91, and there are 46 terms in the series, so the sum of the series E is:

E = (1 + 91) / 2 * 46

= 46 * 46

= 2116

The sum of the series P is equal to the average of the first and last term of the series, multiplied by the number of terms in the series. The first term of the series is 2, the last term is 92, and there are 46 terms in the series, so the sum of the series P is:

P = (2 + 92) / 2 * 46

= 47 * 46

= 2162

Subtract the two sums to get how much one is greater than the other.

2162 - 2116 = 46

Therefore, P is greater than E by 46.

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False associations between two variables which are actually influenced by a third variable are known as:

Answers

False associations between two variables which are actually influenced by a third variable are known as the Spurious Relationship

How to determine the relationship

Within the context of the question, there are two types of relationships between variables.

These relationships are:

Spurious RelationshipNon-spurious Relationship

When two variables are influenced by another factor or variable, then the relationship is said to be a spurious relationship;

Otherwise, the relationship is non-spurious relationship

Using the above highlight as a guide, the term that completes the given definition is spurious relationship

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Centerville has a population of 18,000. People under the
age of 18 make up 23% of the town's population. How
many people under the age of 18 live in Centerville??

Answers

Answer:4140

Step-by-step explanation: I’m just to beast

A Spanish company imports the following products: "Glazed ceramic flags and paving, hearth or wall tiles; glazed ceramic mosaic cubes and the like, whether or not on a backing" Which amount will you have to regulate at the Spanish border, if the goods come from Mexico? N.B: Take into account the importance of the agreements of free trade.

Answers

If the Spanish company imports glazed ceramic flags and paving, hearth or wall tiles, glazed ceramic mosaic cubes, or similar products from Mexico, the amount to be regulated at the Spanish border will depend on the specific customs regulations and trade agreements between Spain and Mexico.

Free trade agreements between the two countries may result in reduced or eliminated customs duties for qualifying goods.The amount to be regulated at the Spanish border for the importation of glazed ceramic products from Mexico will be determined by the applicable customs regulations and trade agreements in place.

If Spain and Mexico have a free trade agreement, such as the one between the European Union and Mexico, the imported goods may be eligible for preferential treatment, including reduced or eliminated customs duties.

Under a free trade agreement, the customs duties that would normally apply to imported goods may be waived or reduced, promoting trade between the countries.

However, it is important to note that free trade agreements often have specific rules of origin criteria that must be met to qualify for preferential treatment. These criteria may include requirements related to the manufacturing or sourcing of the goods, such as a certain percentage of value added in the exporting country.

To determine the exact amount to be regulated at the Spanish border, it is necessary to consult the specific customs regulations and trade agreements between Spain and Mexico, taking into account the provisions regarding the importation of glazed ceramic products or seeking guidance from customs authorities or trade experts.

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In one ancient civilization, hunters shared fresh meat with other individuals in a group without an explicit timeframe or agreement about who would do what in return. However, the favor would surely be returned by those in the tribe who could cook, take care of children, and provide shelter. What type of economy does this MOST closely describe? A. socialist economy B. gift economy C. market economy D. planned economy

Answers

Answer:

It is a gift economy

Step-by-step explanation:

This is correct on playto, but let me give you an explanation. A gift economy is a explicit agreement between two parties that if a favor is given, it'd be returned at a later time. If a hunter shared meat with others, the hunter expects to get something later in returned. By defintion, this is the role of a gift economy.

Solve for x: 7x + 15 = 38 (5 points)
Group of answer choices

twenty-three sevenths

fifty-three sevenths

53

23

Answers

Answer: twenty-three sevenths (3.3)

Steps:
7x + 15 = 38
7x = 38 - 15
7x = 23
x = 23/7
x = 3.3

Answer:

twenty-three sevenths

represent the number of books a student buys at the next book fair. what is the expected value of

Answers

The following is the expected value of a number of books a student buys at the next book fair is 2.404 books.

How to determine a discrete probability distribution's expected value?The sum of each result of a discrete probability distribution times its corresponding probability is the distribution's anticipated value.The distribution is stated as follows based on the histogram provided by the picture just at end of the answer:

P(X = 1) = 0.285P(X = 2) = 0.333P(X = 3) = 0.168P(X = 4) = 0.136P(X = 5) = 0.063P(X = 6) = 0.015

The random variable b's expected value is then calculated as follows:

E(X) = 1 x 0.285 + 2 x 0.333 + 3 x 0.168 + 4 x 0.136 + 5 x 0.063 + 6 x 0.015 E(X)  = 2.404 books.

Thus, the expected value of discrete probability distribution is 2.404 books.

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The graph for the question is attached.

represent the number of books a student buys at the next book fair. what is the expected value of

If a cheetah travels 50 miles per day, how many feet per hour does the cheetah travel?


HELP FAST

Answers

26400 is what they travel in feet in a day divide that by 24 and that should be your answer

Consider an example of an apartment: the number of bedrooms, bathrooms, and the floor of an apartment determines its price. Which is/are the predictor variable(s) in this example?.

Answers

By using function, it can be concluded that-

The predictor variables are bed, bath, floor

What is function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

In a function y = f(x), x is the independent variable and y is the dependent variable.

The price of an apartment is dependent on the number of bedrooms, bathrooms and the floor of the apartment

So the required function is p = f(bed, bath, floor) where p is the price of the apartment

The predictor variables are bed, bath, floor

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POINTS
need answesrs to this, thank y ou

POINTSneed answesrs to this, thank y ou

Answers

Answer:

(-4, -1)

Step-by-step explanation:

The midpoint formula is [ (x1+x2/2,y1+y2/2) ]

(-1+(-7)/2, 2+(-4)/2)

(-8/2, -2/2)

(-4, -1)

Best of Luck!

Can someone help me with this?

Can someone help me with this?

Answers

Answer:

\( \sqrt{30} \)

I need help on this

Answers

\(\begin{gathered} \frac{19}{5x^3y^2}-\frac{1}{5xy} \\ \\ \frac{19(5xy)-5x^3y^2}{(5x^3y^2)\cdot(5xy)} \\ \\ \frac{95xy-5x^3y^2}{25x^4y^3} \\ \\ \frac{5xy(19-x^2y)}{5xy(5x^3y^2)} \\ \\ \frac{19-x^2y}{5x^3y^2} \\ \\ \text{The simplification of }\frac{19}{5x^3y^2}-\frac{1}{5xy}\text{ is }\frac{19-x^2y}{5x^3y^2} \end{gathered}\)

Which triangles are similar by the angle-angle criterion for similarity of triangles?

Which triangles are similar by the angle-angle criterion for similarity of triangles?
Which triangles are similar by the angle-angle criterion for similarity of triangles?
Which triangles are similar by the angle-angle criterion for similarity of triangles?
Which triangles are similar by the angle-angle criterion for similarity of triangles?

Answers

Answer:

for first:

<D=<B(corresponding angle)

<E=<C(corresponding angle)

<A=<A(common angle)

so

∆AED~ ∆ACB by A.A.A. axiom

is your answer

other are CONGRUENT TRAINGLE.

PLEASE HELP!! determine asymptotes, intercepts, and multiplicities!!!

PLEASE HELP!! determine asymptotes, intercepts, and multiplicities!!!

Answers

The vertical asymptotes of the function are -5 and 3, and the horizontal asymptote is 1.

What is the asymptotes of the function?

The asymptotes of the function, f(x) = (x² + 5x) / (x² + 2x - 15), is calculated as follows;

For vertical asymptotes;

x² + 2x - 15 = 0

(x + 5)(x - 3) = 0

x = -5 or 3, this is the vertical asymptotes.

The horizontal asymptotes is calculated as;

divide the numerator and denominator by x²;

f(x) = (x² + 5x) / (x² + 2x - 15)

= (1 + 5/x) / (1 + 2/x - 15/x²)

As x approaches infinity, both 5/x and 2/x become very small, and 15/x² becomes even smaller.

The limit of the function:

f(x) → 1 / 1 = 1

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