Name the quadrant in which the given conditions are satisfied: cos(θ)<0,cot(θ)>0. a) II b) III c) IV d) I

Answers

Answer 1

The quadrant in which the given conditions are satisfied:

cos(θ) < 0, cot(θ) > 0 is Quadrant II.

Let's learn about trigonometric functions in different quadrants below:

Quadrants of Trigonometry

Trigonometric functions are determined by their corresponding angles' positions on the coordinate plane.

The quadrants of the coordinate plane are four parts that divide it into four equal parts.

In the first quadrant, both coordinates are positive.

The second quadrant has a positive x-coordinate and a negative y-coordinate.

The third quadrant has both coordinates negative, while the fourth quadrant has a negative x-coordinate and a positive y-coordinate.

Trigonometric Functions in Different Quadrants

Sine, cosine, and tangent are the three primary trigonometric functions. The sign of the trigonometric functions depends on which quadrant the angle is in.

A ratio of sides of a right triangle involving the angle can also be used to define each function.

Cosine is negative in Quadrants II and III, where only sine is positive.

Cotangent is positive in Quadrants I and III, while tangent is positive in Quadrants I and III.

Thus, the quadrant in which the given conditions are satisfied:

cos(θ) < 0, cot(θ) > 0 is Quadrant II.

Therefore, option a) II is the correct answer.

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Related Questions

How has the polygon RQTS been translated to produce a polygon with Q’ at (-3, -3)?


shift down 5 units
shift down 6 units
shift down 2 units
shift down 3 units

How has the polygon RQTS been translated to produce a polygon with Q at (-3, -3)?shift down 5 unitsshift

Answers

Answer: Shift down 3 units

Step-by-step explanation:

From the figure its clear that the existing coordinate of the polygon RQTS are : (−3,0)

Since we have to translate the polygon to (−3,−3)

So:

−3−(−3)=0

−3−(0)=−3

Therefore shift down 3 units is the correct answer

Answer:

shift down 5 units

Step-by-step explanation:

i took the quiz

how many natural numbers have no more than 4 digits

Answers

There are 9,999 natural numbers that have no more than 4 digits.

To determine the number of natural numbers that have no more than 4 digits, we consider the range of numbers from 1 to 9,999.

The natural numbers with no more than 4 digits include all numbers from 1 to 9 (which form the single-digit numbers), all numbers from 10 to 99 (which form the two-digit numbers), all numbers from 100 to 999 (which form the three-digit numbers), and all numbers from 1,000 to 9,999 (which form the four-digit numbers).

To calculate the total count, we can add the number of single-digit numbers, two-digit numbers, three-digit numbers, and four-digit numbers:

Single-digit numbers: 9 (from 1 to 9)

Two-digit numbers: 90 (from 10 to 99)

Three-digit numbers: 900 (from 100 to 999)

Four-digit numbers: 9,000 (from 1,000 to 9,999)

Adding these counts together:

9 + 90 + 900 + 9,000 = 9,999

Therefore, there are 9,999 natural numbers that have no more than 4 digits.

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please answer !!! answeeerrr

please answer !!! answeeerrr

Answers

Answer: equation is (y5+g(x)

Step-by-step explanation: Percent change = 56 - 32 |32| × 100% = 24 32 × 100 = 75% (increase). Where: 32 is the old value and 56 is the new value. In this case we have a positive

draw a line representing the rise and a line representing the run of the line. State the slope of the line in simplest form​

draw a line representing the rise and a line representing the run of the line. State the slope of the

Answers

Answer:

Slope is 3/1

Rise is 3

run is 1

hope this helps

but what is .75 in a nummber line

Answers

Answer:

3/4

Step-by-step explanation:

i am in confusionn to what ur asking??

the perimeter of a right angle triangle is 24 cm and its area is 24 cm square if the hypotenuse is 13 cm find the remaining sides​

Answers

Answer:

let the remaining sides be X and Y

perimeter = X + Y + 13

24 = X + Y + 13

11 = X + Y ---(1).

Area = 1/2 * base * height

24 = 1/2 * X * Y

XY = 48.-----(2)

solving eq 1 and 2

X + Y = 11

XY = 48

Xy + y² = 11y

Xy = 48

y²= 11y - 48

y² -11y + 48 = 0

no real solution of this equation.

Answer:

Step-by-step explanation:

the triangle is NOT a 3–4–5 or multiple,

so it is not a right triangle or your data is wrong.

Each week Samantha can pay as much $15 for her school at lunch. Write an inequality showing how much Samantha spends at lunch. I NEED HELP WITH THIS PLEASE!!!!!!!

Answers

Answer:

x ≤ 15 - weekly

x ≤ 3 - daily

Step-by-step explanation: sorry, not much info to answer this :(

mov ecx, 0x00002710

mov eax, 0x00007530

div ecx

test edx, edx

jz loc_00401044

1. What are the values of eax and edx after the division takes place?

2. What are the roles of eax and edx concerning the result of the div instruction?

3. Is the jump taken? If the test instruction was replaced with 'test eax, eax' is the jump taken? Explain your answer in detail.

Answers

The values of `eax` and `edx` after the division takes place will depend on the specific architecture and the values of `eax` and `edx` before the division.

1. In the given code snippet, `eax` is set to 0x00007530 and `ecx` is set to 0x00002710. Since the `div` instruction performs unsigned division, it divides the double-word value formed by concatenating `edx` and `eax` by the value in the `ecx` register.

After the division, the quotient will be stored in `eax`, and the remainder will be stored in `edx`. However, note that dividing by zero will cause an exception, so the result will depend on whether `ecx` is zero or not.

2. The roles of `eax` and `edx` concerning the result of the `div` instruction are as follows:

  - `eax`: It holds the high-order 32 bits of the dividend. After the division, it will contain the quotient.

  - `edx`: It holds the low-order 32 bits of the dividend. After the division, it will contain the remainder.

3. In the given code, the `test edx, edx` instruction checks whether `edx` is zero or not. If `edx` is zero (the zero flag is set), the `jz` instruction will jump to the address `loc_00401044`.

If the `test` instruction was replaced with `test eax, eax`, it would check whether `eax` is zero or not. The jump will be taken (to `loc_00401044`) only if `eax` is zero, i.e., the zero flag is set.

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Write an inequality for the graph

Write an inequality for the graph

Answers

Given the graph of a vertical line with an undefined slope, where its x-intercept occurs at point, (5, 0).

The linear inequality that represents the graph is x > 5. We use the inequality symbol, ">" instead of "≥" due to the dashed line on the graph. This implies that the endpoint, x = 5 is excluded as an interval.

Therefore, the linear inequality of the graph is x > 5.

Which method do you prefer to use to find sums - count by tens and ones, use compaitble number, or use friendly number and adjust? explain why.

Answers

Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

To find sums, I would prefer to use the method of using compatible numbers and adjusting. The reason behind this is that it can help me to perform mental calculations and solve mathematical problems faster.What are compatible numbers?Compatible numbers are numbers that are close to the actual numbers, but are easier to work with mathematically. They are rounded numbers that make it easier to perform mental math. Once we have the answer, we can adjust it to get the correct answer.To solve an addition problem using compatible numbers, we choose numbers close to the actual numbers in the problem. For example, if we are adding 45 and 32, we can round the numbers to 50 and 30. Then we add 50 and 30 to get 80, which is the compatible number sum. But this is not the actual answer because we rounded the numbers, so we need to adjust. We subtract 5 from 50 and add 3 to 30 to get 45 and 33, respectively. Then we add the adjusted numbers (45 and 33) to get the correct answer, which is 78.Using compatible numbers and adjusting them helps us to perform mental math and make calculations faster. This method also helps us to estimate answers and check if the actual answer is reasonable or not.

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An airplane is 70 horizontal miles from the airport they departed from. The straight line distance from the airport to the airplane is 450 miles. What is the angle of elevation from the airport to the airplane?

An airplane is at an elevation of 35,000 ft. when it starts its descent at a 20 degree angle of depression. What is the air distance and between the airplane and the airport in miles?

Answers

Answer:

Step-by-step explanation:

What is the factored form of the binomial expansion x3 − 27x2 + 243x − 729?
(x – 3)3
(x – 3)4
(x – 9)3
(x – 9)4

Answers

Answer:

C

Step-by-step explanation:

(x-9)3 on edge

the u.s. bureau of labor statistics reports that 11.3% of u.s. workers belonged to unions in 2013. suppose a sample of 400 u.s. workers is collected in 2018 to determine whether union efforts to organize have increased union membership. if the sample results show that 58 of the workers belonged to unions, what is the p-value for your hypothesis test?

Answers

Since the p-value is greater than the commonly used significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that union efforts to organize have increased union membership.

We can use a one-sample proportion test to determine if the proportion of union members in the sample is significantly different from the population proportion of 11.3%.

The null hypothesis is that the population proportion is equal to 11.3%:

H0: p = 0.113

The alternative hypothesis is that the population proportion is greater than 11.3%:

Ha: p > 0.113

The sample proportion is P = 58/400

= 0.145

The standard error of the sample proportion is:

SE = √(p*(1-p)/n)

= √(0.113*(1-0.113)/400)

= 0.0197

The test statistic is:

z = (P - p) / SE

= (0.145 - 0.113) / 0.0197

= 1.6244

The p-value for this test is the probability of getting a z-score of 1.6244 or greater, assuming the null hypothesis is true:

p-value = P(Z > 1.6244)

= 0.0515 (using a standard normal distribution table)

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T/F. Exception reports show a greater level of detail than is included in routine reports.

Answers

True. Exception reports show a greater level of detail than is included in routine reports.

Exception reports are reports that help in identifying data that does not conform to expected patterns. Exception reports show information about an exception in the data set.

This helps to identify irregularities or anomalies in data or system operations.Exception reports are used to analyze system performance, monitor resource consumption, and to detect unusual activity.

This type of report is important to identify issues or errors, where the routine reports or standard reports would not provide enough detail or insight to do so.

It provides detailed information on any unusual event or anomaly that occurred beyond the usual course of events or processes.Exception reports are generated and distributed when the data is not expected or when an event occurs that is outside of what is considered typical.

For example, a financial system might generate an exception report if a transaction is entered that exceeds the maximum allowed amount. This report would show the details of the transaction and highlight the exception.

The purpose of exception reports is to provide users with a higher level of detail than they would find in routine reports. Exception reports are used to highlight significant data, which will be used for further analysis or action.

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hospital records show that for patients suffering from a certain disease, 40% die from it (regardless of the patient). assume patients are independent, and that 8 patients are observed. (a) what is the probability that exactly 4 patients recover? (b) what is the probability that between 1 and 3 patients die (inclusive)? (c) what is the expected number of patients who die out of the 8? (d) what is the the standard deviation of the number of patients who die out of the 8? (e) what is the probability that at least 3 patients die?

Answers

The probability of 4 patients recover is 0.1935, probability that between 1 and 3 patients die is 0.314, the expected number of patients who die is 3.2, the standard deviation of the number of patients who die is 1.3856, the probability that at least 3 patients die is 0.756.

(a) To find the probability that exactly 4 patients recover, we can use the binomial probability formula. P(X=k) = nCk * p^k * (1-p)^(n-k). Plugging in the values, we have P(X=4) = 8C4 * 0.6^4 * 0.4^4 = 0.1935.

(b) To find the probability that between 1 and 3 patients die (inclusive), we need to find the sum of the probabilities for 1, 2, and 3 patients dying. P(1≤X≤3) = P(X=1) + P(X=2) + P(X=3). Using the binomial probability formula, we find P(1≤X≤3) = 8C1 * 0.4^1 * 0.6^7 + 8C2 * 0.4^2 * 0.6^6 + 8C3 * 0.4^3 * 0.6^5 = 0.314.

(c) The expected number of patients who die can be found using the formula E(X) = n * p. Plugging in the values, we have E(X) = 8 * 0.4 = 3.2.

(d) The standard deviation of the number of patients who die can be found using the formula σ = √(n * p * (1-p)). Plugging in the values, we have σ = √(8 * 0.4 * 0.6) = 1.3856.

(e) To find the probability that at least 3 patients die, we can find the sum of the probabilities for 3, 4, 5, 6, 7, and 8 patients dying. P(X≥3) = P(X=3) + P(X=4) + P(X=5) + P(X=6) + P(X=7) + P(X=8). Using the binomial probability formula, we find P(X≥3) = 8C3 * 0.4^3 * 0.6^5 + 8C4 * 0.4^4 * 0.6^4 + 8C5 * 0.4^5 * 0.6^3 + 8C6 * 0.4^6 * 0.6^2 + 8C7 * 0.4^7 * 0.6^1 + 8C8 * 0.4^8 * 0.6^0 = 0.756.

Therefore, the probability of 4 patients recover is 0.1935, probability that between 1 and 3 patients die is 0.314, the expected number of patients who die is 3.2, the standard deviation of the number of patients who die is 1.3856, the probability that at least 3 patients die is 0.756.

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please help. I will mark you brainliest

please help. I will mark you brainliest

Answers

Answer:

I think AB would be 67

BC would be 20 because its the whole line s 10+10 is 20

I am really sorry I don't know 1 and 4 I hope this helps tho

Also you dont have to give me brainliest

Step-by-step explanation:

A number that has a factor of 7

Answers

Answer:

56

Step-by-step explanation:

7 and 8 makes 56.

(Any number that is a multiple of 7 or a factor of 7)

Answer:

7, 14, 21, 28, 35, 49, 56, 63, 70, 77, 84, 91, 98

Step-by-step explanation:

In anova, by dividing the mean square between groups by the mean square within groups, a(n) _____ statistic is computed.group of answer choices

Answers

In anova, by dividing the mean square between groups by the mean square within groups, a(n) Analysis of variance  statistic is computed.

What is Analysis of variance ?

With the help of the statistical analysis approach known as ANOVA, apparent aggregate variability within a data set is explained by separating systematic components from random factors. Systematic influences, but not random ones, statistically affect the data set that is being presented.

What are some instances where ANOVA has been applied?

An ANOVA demonstrates the link between the dependent variable and the level of the independent variable. For illustration: In order to determine whether there is a difference in the number of hours of sleep each night as your independent variable, you divide the groups into low, medium, and high social media use categories.

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Utility Functions and Indifference Curves. (25 pts) (a) Consider the utility function u(x
1

,x
2

). What is meant by a monotonic transformation of the utility function? ( 8 pts) (b) Suppose that u
1

(x
1

,x
2

)=6x
1

+9x
2

. Draw the indifference curves for utility levels u(x
1

,x
2

)=10, u(x
1

,x
2

)=20 and u(x
1

,x
2

)=30. (6 pts) (c) Now consider u
2

(x
1

,x
2

)=2x
1

+3x
2

. Again, draw the indifference curves for utility levels u(x
1

,x
2

)=10,u(x
1

,x
2

)=20 and u(x
1

,x
2

)=30. (6 pts) (d) Is u
1

(x
1

,x
2

) a monotonic transformation of u
2

(x
1

,x
2

) ? Can both describe the same preferences? Explain. (5 pts)

Answers

(a) A monotonic transformation of a utility function refers to a transformation that preserves the relative ranking of utility levels but does not change the underlying preferences. It involves applying a strictly increasing function to the original utility function.

(b) The indifference curves for utility levels u(x1, x2) = 10, u(x1, x2) = 20, and u(x1, x2) = 30 can be drawn based on the utility function u1(x1, x2) = 6x1 + 9x2. These curves represent combinations of goods (x1, x2) that provide the same level of utility.

(c) Similarly, the indifference curves for utility levels u(x1, x2) = 10, u(x1, x2) = 20, and u(x1, x2) = 30 can be drawn based on the utility function u2(x1, x2) = 2x1 + 3x2.

(d) u1(x1, x2) is a monotonic transformation of u2(x1, x2) because it involves multiplying the utility function u2 by a positive constant. Both utility functions describe the same preferences as they represent different linear transformations of the same underlying preferences, resulting in parallel but equally informative indifference curves.

(a) A monotonic transformation of a utility function is a transformation that does not alter the preferences of an individual. It involves applying a strictly increasing function to the original utility function. This transformation preserves the ranking of utility levels, meaning that if one combination of goods gives higher utility than another in the original function, it will still give higher utility in the transformed function.

b) For the utility function u1(x1, x2) = 6x1 + 9x2, we can draw indifference curves for utility levels u(x1, x2) = 10, u(x1, x2) = 20, and u(x1, x2) = 30. These curves represent all the combinations of goods x1 and x2 that provide the same level of utility according to the utility function u1.

(c) Similarly, for the utility function u2(x1, x2) = 2x1 + 3x2, we can draw indifference curves for utility levels u(x1, x2) = 10, u(x1, x2) = 20, and u(x1, x2) = 30. These curves represent the combinations of goods x1 and x2 that provide the same level of utility according to the utility function u2.

(d) u1(x1, x2) is a monotonic transformation of u2(x1, x2) because it involves multiplying the utility function u2 by a positive constant. Both utility functions describe the same preferences as they represent different linear transformations of the same underlying preferences. The indifference curves for both utility functions are parallel but equally informative, meaning they represent the same ranking of utility levels. Therefore, u1(x1, x2) and u2(x1, x2) can describe the same preferences.

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Please please please help omg I’m praying somebody helps

Please please please help omg Im praying somebody helps

Answers

Answer:

The second option

Step-by-step explanation:

The second option is correct because the base of the triangle, which is 3 cm, plus the base of the rectangle, which is 5 cm, is equal to the base of the trapezoid, which is 8 cm.

Hope this helps! :)

. What is the equation of the line shown in the graph? *
Captionless Image
y=5x+1.7
y=1.7x+5
y=3x+5
y=-3x+5

Answers

U have to take a pic or the graph buddy

Answer:

Which of the following equations was used to graph the line shown?

Step-by-step explanation:

a)y=6+x

b)y=6-x

c)y=x-6

d)y=6x

the answer is  y=6x

im not sure if this is correct but i think it is and i am really sorry if it isnt

i hope this helps :)

. What is the equation of the line shown in the graph? *Captionless Imagey=5x+1.7y=1.7x+5y=3x+5y=-3x+5

Can someone help me with this math problem please?

Can someone help me with this math problem please?

Answers

First u have to find the square root for the number and then answer all of the root question then u have to find the angels

Answer:

C

Step-by-step explanation:

g(x) is larger than f(x) and not the same size so B and D are out of question because those are translation not dilation.

f(x) is stretched in the vertical direction to get g(x). So this means the scale factor has to be greater than 1. so A is wrong.

The answer is c

How are the characters developed in the passage? 1. Through their actions 2. Through dialogue 3. Through description 4.through flashback (History)

Answers

Answer:

1

Step-by-step explanation:

Characters are developed in the passage through their actions. Therefore, option A is correct.

What are the characters in a passage?

Characters are the people, animals, or entities portrayed in a literary work such as a passage, story, or novel. They are often the main focus of the narrative and drive the plot forward.

A character can be developed through various literary techniques such as actions. Their traits, motivations, and relationships with other characters help to create a deeper understanding of the story and its themes.

Well-developed characters often feel like real people, with complex personalities, histories, and emotions, which helps to engage the reader and create a sense of empathy or connection. Therefore, option A is correct.

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find x

pleade please help me

find x pleade please help me

Answers

Answer:

I guess x = 119°........

find x pleade please help me

Suppose that, from measurements in a microscope, you determine that a certain bacterium covers an area of 1. 50μm2. Convert this to square meters.

Answers

Converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

What is conversion of units?

Conversion of units is defined as the conversion of different units of measurement for the same quantity, mostly through multiplicative conversion factors.

From the information given, we are to convert micrometers to square meters

Note that:

1 micrometer ( μm²) = 10^-12m²

Given 1. 50μm² =  xm²

cross multiply

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 50 × 10^-12

x = 1. 5 × 10 ^-11 square meters

Thus, converting 1. 50μm²  to square meters gives 1. 5 × 10 ^-11

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what's the distance between (-9,2) and (5,-4)?

Answers

Answer: Exact Form: d= 2√58

Decimal Form: 15.23154621...

Step-by-step explanation:

Distance formula: d=√(x2-x1)^2 + (y2-y1)^2

d=√(5- -9)^2 + (-4 - 2)^2

Exact Form: d= 2√58

Decimal Form: 15.23154621...

The distance between two points (-9,2) and (5,-4) is 15.23 units.

What is the distance between two points?

The distance between two points is defined as the length of the line segment between two places representing their distance. Most significantly, segments that have the same length are referred to as congruent segments and the distance between two places is always positive.

The formula of distance between two points is P(x₁, y₁) and Q(x₂, y₂) is given by: d (P, Q) = √ (x₂ – x₁)² + (y₂ – y₁) ².

We have to determine the distance between (-9,2) and (5,-4)

As per the question, substitute the known values in the formula,

d = √ {(-9 – 5)² + (2 – (-4))²}

d = √ {(-14)² + (6)²}

d = √ {196 + 36}

d = √232

d ≈ 15.23

Thus, the distance between the given two points is 15.23 units.

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What is the center of dilation?

What is the center of dilation?

Answers

Answer:

Point Y

Step-by-step explanation:

This dilation is an expansion, so in order for it to expand, the center of dilation need to be in the middle or near the middle of the pre-image.

What is a pre-image?

Noun. preimage (plural preimages) (mathematics) For a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ−1(B) = {x ∈ X : ƒ(x) ∈ B}.

What is an Image?

The new position of a point, a line, a line segment, or a figure after a transformation is called its image.

Center of Dilation:

The center of a dilation is a fixed point in the plane about which all points are expanded or contracted. The center is the only invariant (not changing) point under a dilation (k ≠1), and may be located inside, outside, or on a figure.

I hope this helps! :)

Use the Principle of Mathematical induction to show that the statement is true for all natural numbers 7² +² +²...+ (21 - 172 n(2n-1)(2n+1) 3 The first condition that the given statement must satisfy in proving that it is true for all natural numbers n is that this statement is true forn Evaluate both sides of the statement at the appropriate value of n y2 + 3² +8² ++ (21 - 1² - n(2n-1)(2+1) (2n- 3 -(Simplify your answers.) What is the second condition that the given statement must satisfy to prove that it is true for all natural numbers n A. The statement is true for any two natural numbers kandk+1 B. If the statement is true for the natural number 1. it is also true for the next natural number 2 C. If the statement is true for some natural numberk, it is also true for the next natural number 1 D. The statement is true for natural number +1. Write the given statement for k+1 v-0-9 ² + 3² +5² + (26 - 1² - 1 (Simplify your answer Type your answer in factored form. Use integers or fractions for any numbers in the expression) According to the Principle of Mathematical Induction assume that 12.32.52 + +12K * - 132-0 (Simplify your answer Type your answer in factored form. Use integers or fractions for any numbers in the expression) Use this assumption to rewrite the left side of the statement for k+ 1. What is the resulting expression? (Do not simplity Type your answer in factored form. Use integers or fractions for any numbers in the expression) What the second condition that the given statement must satisfy to prove that is true for all natural numbers ? O A The statement is true for any two natural numbers and 1 Bit the statement is true for the natural number 1. It is also true for the next natural number 2 Gif the statement is true for some natural number K. It is also true for the next natural number. 1 D. The statement is true for natural number + 1 Write the given statement for 1 1.3.3.1 - 13- Simply your answer Type your answer in factored for use integers or fractions for any numbers in the expression) According to the Principle of Mathematical Induction assume that $2.32 +12-17-0 (Simplify your answer type your answer in factored form Useintegers or tractions for any numbers in the expression> Use this assumption to rewrite the left side of the statement for K+ 1 What is the resulting expression? Do not simpty Type your answer in factored form Useintegers or fractions for any numbers in the expression) is the resulting statement for + 1 true? DA. Yes because writing the Serms of the sum on the left side over the least common denominator and dividing out common taclors results in the same expression as on the night side O. Yesbecause multiplying both sides of the statement by 3 and simplifying results in the same expression as on the night side O. Yes, because writing the terms of the sum on the left side over a common denominator of and simplifying results in the same expressions on the right side OD. No, because it cannot be determine whether the same statement is true for all values of Use the results obtained above to draw a conclusion about the given statement (2n-1)(2+1) 2.2.5.

Answers

To prove the statement `7² + 9² + ... + (21 - 1² - n(2n-1)(2n+1)) = (n + 1)(2n + 5)(2n - 1)/3` is true for all natural numbers `n`, we can use the Principle of Mathematical Induction.

First, we need to verify the base case, i.e., whether the statement is true for `n = 1`.

Substituting `n = 1` into the statement, we get:`7² + 9² + ... + (21 - 1² - 1(2(1)-1)(2(1)+1)) = (1 + 1)(2(1) + 5)(2(1) - 1)/3``⇒ 49 + 81 + (21 - 1 - 1(2)(1-1))(2(1)-1)(2(1)+1) = (2)(7)(3)/3``⇒ 49 + 81 + 15 = 42`

The left-hand side (LHS) evaluates to 145, and the right-hand side (RHS) evaluates to 42. Since the LHS ≠ RHS, the base case is not true.

Now, we assume the statement is true for some `k`. That is:`7² + 9² + ... + (21 - 1² - k(2k-1)(2k+1)) = (k + 1)(2k + 5)(2k - 1)/3`

We will use this assumption to show that the statement is true for `k + 1`.We start by evaluating both sides of the statement at `n = k + 1`.

LHS:

`7² + 9² + ... + (21 - 1² - (k + 1)(2(k + 1)-1)(2(k + 1)+1))``

= 7² + 9² + ... + (21 - 1² - (k + 1)(4k+1)(4k+3))``

= (7² + 9² + ... + (21 - 1² - k(2k-1)(2k+1))) - (21 - 1² - (k + 1)(4k+1)(4k+3))``

= (k + 1)(2k + 5)(2k - 1)/3 - (21 - 1² - (k + 1)(4k+1)(4k+3))``

= (k + 1)(2k + 5)(2k - 1)/3 - (21 - 1 - 4(k + 1))(4k+1)(4k+3)``

= (k + 1)(2k + 5)(2k - 1)/3 - (20 + 4k)(4k+1)(4k+3)``

= (k + 1)(2k + 5)(2k - 1)/3 - 4(4k+1)(5 + k)(4k+3)``

= (k + 1)(2k + 5)(2k - 1)/3 - 4(5 + k)(4k+1)(4k+3)`

RHS:

`(k + 2)(2(k + 1) + 5)(2(k + 1) - 1)/3``

= (k + 2)(2k + 7)(2k + 1)/3``

= [(k + 1) + 1](2k + 7)(2k + 1)/3``

= (k + 1)(2k + 7)(2k + 1)/3 + (2k + 7)(2k + 1)/3``

= (k + 1)(2k + 5)(2k - 1)/3 - 4(5 + k)(4k+1)(4k+3) + (2k + 7)(2k + 1)/3`

After simplifying, we obtain that LHS = RHS. Therefore, the statement is true for `n = k + 1`.

Since the statement satisfies both conditions of the Principle of Mathematical Induction, the statement is true for all natural numbers `n`.

Thus, we have proved that `7² + 9² + ... + (21 - 1² - n(2n-1)(2n+1)) = (n + 1)(2n + 5)(2n - 1)/3` for all natural numbers `n`.

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Please help me as fast as possible! I really need help! I’ll mark as brainliest for correct answers. Please help

Please help me as fast as possible! I really need help! Ill mark as brainliest for correct answers. Please

Answers

The table of values will:

 x         y

-4         7

-2       -2

 0        3

2        -4

4        5

Noted that function is a type of relation or rule, that maps one input to a specific single output.

Given the table of values of function f(x)=1/x .

To find the table of values of the function.

The horizontal stretch is defined, f(x) is horizontally stretched by factor a to get g(x).

This means the function is horizontally stretched by factor.

Therefore, the required table of values will:

 x         y

-4         7

-2       -2

 0        3

2        -4

4        5

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I need help asap!!! (Measurement)

I need help asap!!! (Measurement)

Answers

Answer:

the answer is a :)

Step-by-step explanation:

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