In a right triangle,the altitude q from the right angle to the hipotenuse divides..........

Answer:

\(\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ........\)

The interval of convergence is:\((-\frac{2}{3},\frac{16}{3})\)

Step-by-step explanation:

Given

\(f(x)= \frac{9}{3x+ 2}\)

\(c = 6\)

The geometric series centered at c is of the form:

\(\frac{a}{1 - (r - c)} = \sum\limits^{\infty}_{n=0}a(r - c)^n, |r - c| < 1.\)

Where:

\(a \to\) first term

\(r - c \to\) common ratio

We have to write

\(f(x)= \frac{9}{3x+ 2}\)

In the following form:

\(\frac{a}{1 - r}\)

So, we have:

\(f(x)= \frac{9}{3x+ 2}\)

Rewrite as:

\(f(x) = \frac{9}{3x - 18 + 18 +2}\)

\(f(x) = \frac{9}{3x - 18 + 20}\)

Factorize

\(f(x) = \frac{1}{\frac{1}{9}(3x + 2)}\)

Open bracket

\(f(x) = \frac{1}{\frac{1}{3}x + \frac{2}{9}}\)

Rewrite as:

\(f(x) = \frac{1}{1- 1 + \frac{1}{3}x + \frac{2}{9}}\)

Collect like terms

\(f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2}{9}- 1}\)

Take LCM

\(f(x) = \frac{1}{1 + \frac{1}{3}x + \frac{2-9}{9}}\)

\(f(x) = \frac{1}{1 + \frac{1}{3}x - \frac{7}{9}}\)

So, we have:

\(f(x) = \frac{1}{1 -(- \frac{1}{3}x + \frac{7}{9})}\)

By comparison with: \(\frac{a}{1 - r}\)

\(a = 1\)

\(r = -\frac{1}{3}x + \frac{7}{9}\)

\(r = -\frac{1}{3}(x - \frac{7}{3})\)

At c = 6, we have:

\(r = -\frac{1}{3}(x - \frac{7}{3}+6-6)\)

Take LCM

\(r = -\frac{1}{3}(x + \frac{-7+18}{3}+6-6)\)

r = -\frac{1}{3}(x + \frac{11}{3}+6-6)

So, the power series becomes:

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}ar^n\)

Substitute 1 for a

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}1*r^n\)

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}r^n\)

Substitute the expression for r

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}(-\frac{1}{3}(x - \frac{7}{3}))^n\)

Expand

\(\frac{9}{3x + 2} = \sum\limits^{\infty}_{n=0}[(-\frac{1}{3})^n* (x - \frac{7}{3})^n]\)

Further expand:

\(\frac{9}{3x + 2} = 1 - \frac{1}{3}(x - \frac{7}{3}) + \frac{1}{9}(x - \frac{7}{3})^2 - \frac{1}{27}(x - \frac{7}{3})^3 ................\)

The power series converges when:

\(\frac{1}{3}|x - \frac{7}{3}| < 1\)

Multiply both sides by 3

\(|x - \frac{7}{3}| <3\)

Expand the absolute inequality

\(-3 < x - \frac{7}{3} <3\)

Solve for x

\(\frac{7}{3} -3 < x <3+\frac{7}{3}\)

Take LCM

\(\frac{7-9}{3} < x <\frac{9+7}{3}\)

\(-\frac{2}{3} < x <\frac{16}{3}\)

The interval of convergence is:\((-\frac{2}{3},\frac{16}{3})\)

Answer: AEC = 80

              X=30

YW ;)

Answer:

6 thirds

Step-by-step explanation:

you're welcome

Answer:

Cube B

Step-by-step explanation:

a = \(\sqrt[3]{125}\)

a = 5

6in x 6in = 36\(in^{2}\)

5 < 6 so A < B

The side length of Cube A ≈ 5 inches

The side length of Cube B = 6 inches

Cube B has a greater side length than Cube A.

We have,

To compare the side lengths of Cube A and Cube B, we need to find the side length of each cube.

For Cube A:

The volume of Cube A = side length³

125 = side length³

To find the side length of Cube A, we take the cube root of 125:

side length of Cube A = ∛125 ≈ 5 inches

For Cube B:

The area of one face of Cube B = side length²

36 = side length²

To find the side length of Cube B, we take the square root of 36:

side length of Cube B = √36 = 6 inches

Now, we can compare the side lengths of both cubes:

The side length of Cube A ≈ 5 inches

The side length of Cube B = 6 inches

Since 6 inches is greater than 5 inches, Cube B has a greater side length than Cube A.

Thus,

Cube B has a greater side length than Cube A.

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Answer:

Step-by-step explanation:

from the figure and the measurements it is a square, the diagonals are perpendicular and form 4 angles of 90°, so 90° is your answer.

Answer:

\(\pi\) radian

Step-by-step explanation:

We know that angle for a full circle is 2\(\pi\)

In the given figure shape is semicircle

hence,

angle for semicircle will be half of angle of full circle

thus, angle for given figure = half of  angle for a full circle = 1/2 * 2\(\pi\) = \(\pi\)

Thus, answer is \(\pi\) radian

alternatively, we also know that angle for a straight line is 180 degrees

and 180 degrees is same as \(\pi\) radian.

Answer:

What is a linear function? A linear function is a function whose graph is a straight line. The rate of change of a linear function is constant. The function shown in the graph below, y = x + 2, is an example of a linear function.

Graph of linear function

Graph of linear function

A linear function has a constant rate of change. The rate of change is the slope of the linear function. In the linear function shown above, the rate of change is 1. For every increase of one in the independent variable, x, there is a corresponding increase of one in the dependent variable, y. This gives a slope of 1/1 = 1.

A linear function is typically given in the form y = mx + b, where m is equal to the slope, or constant rate of change.

Examples of linear functions include:

If a person drives at a constant speed, the relationship between the time spent driving (independent variable) and the distance traveled (dependent variable) will remain constant.

Assuming no change in price, the relationship between the number of pounds of bananas a person buys (independent variable) and the total cost of the bananas (dependent variable) will remain constant.

If a person earns an hourly wage at their job, the relationship between the time spent working (independent variable) and the amount earned (dependent variable) will remain constant.

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Exponential Functions

What is an exponential function? An exponential function is a function that involves exponents and whose graph is a smooth curve. The rate of change in an exponential function is not constant. The functions shown in the graph below, y = 0.5x and y = 2x, are examples of exponential functions.

Graphs of exponential functions

Graphs of exponential functions

An exponential function does not have a constant rate of change. The rate of change in an exponential function is the value of the independent variable, x. As the value of x increases or decreases, the rate of change increases or decreases as well. Rather than a constant change, as in the linear function, there is a percent change.

An exponential function is typically given in the form y = (1 + r)x, where r represents the percent change.

Examples of exponential functions include:

Step-by-step explanation:

Answer:

Step-by-step explanation:

the waiter would receive an $8.44 tip

The probability that the first card is red and the second card is a 7 is 1/26.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

Probability that the first card is a red and the second is a 7 = (number of red cards / total number of cards) x (number of 7 / total number of card)

Probability that the first card is a red and the second is a 7 = (26 / 52) x (4/52) = 1/26

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ANSWER: 0,1 my friend have a good day

Answer:

D

Step-by-step explanation:

Took the test

A total of 8 workers are required for a building time of 15 days.

In this problem we find a case of inverse relationship, in which the number of workers (n) is inversely proportional to building time (t), in hours. The situation is represented by following formulas:

n ∝ 1 / t

n = k / t

Where k is the proportionality ratio, which can be eliminated by building the following formula:

n₁ · t₁ = n₂ · t₂

If we know that n₁ = 10, t₁ = 12 and t₂ = 15, then the required number of workers is:

n₂ = n₁ · (t₁ / t₂)

n₂ = 10 · (12 / 15)

n₂ = 10 · (4 / 5)

n₂ = 8

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Hello!

We have all angles of the triangle:

We will use the law of cosines. This relation is valid for all sides of any t

We have:

angle A = 12°

côté a = 10

angle B = 150°

This is therefore the first case of application of the sine law.

So:

\(\sf \dfrac{b}{sin~B} = \dfrac{a}{sin~A}\)

\(\sf b =\dfrac{sin~B~*~a}{sin~A} = \dfrac{sin~150~*~10cm}{sin~12} = \dfrac{arcsin~0.5~*~10cm}{arcsin~0.2079116908} = \dfrac{30~*~10cm}{12} = \dfrac{300cm}{12} = \boxed{\sf25cm}\)

your answer is -7+16i, because 4-11=-7 and 7i+9i is 16i

Answer:

coordinate  value is [-3,4].

Reltive is mio pie x 78.9 :)

hoped this helped :)

Answer:

The answer would be 5/100 or 1/20 in it's simplest form

Step-by-step explanation:

So let's say you have only 5% of a pie and the rest of your family gets the rest, if you put that in a form of a fraction, the answer would be 5 over 100 (5/100). But if you simplify, the answer would be 1/20 since 5 goes into 5 once and 20 goes into 100 5 times.

Ignore the messy writing, i was in a hurry.

Answer:

y = x + 2

Step-by-step explanation:

The slope-intercept equation is:

y = mx + b

First, you should use the point-slope formula to find the slope. Plug in the "x" and "y" values given from the points:

Point 1: (1,3)        Point 2: (2,4)

y₁ - y₂ = m(x₁ - x₂)               <--- Point-slope formula

(3 - 4) = m(1 - 2)                  <--- Plug in "x" and "y" values from points

-1 = -m                                <--- Simplify inside parentheses

1 = m                                  <--- Divide both sides by -1

Finally, use one of the points to solve for the y-intercept (b):

Point 1: (1,3)           m = 1

y = mx + b                       <--- Slope-intercept formula

3 = 1(1) + b                       <--- Plug in values from point and slope (m)

3 = 1 + b                          <--- Multiply slope and "x" value

2 = b                               <--- Subtract 1 from both sides

Since the slope = 1, it does not need to be included in the final formula. The final answer is:

y = x + 2

Answer:

Step-by-step explanation:

\(F(2)=\frac{1}[3} \cdot 4^{2}=\frac{16}{3}\)

We have a linear function that relates length of sides of squares and perimeter of the squares.

We can derive the function knowing that the perimeter is the sum of the length of the sides. If a square has 4 equal sides, the perimeter will be 4 times the length side.

Then, if perimeter is y and side length is x, we will have the relation:

Then, we can test for each value of x, what is the value of the perimeter y:

Answer: The only correct ordered pair is (3,12) [Option C]

Answer:

3(x+8)=5

Step-by-step explanation:

Hope it's correct and sorry if it's not

Answer:

8+5 (3 times x)

Step-by-step explanation:

Please mark me as brainliest

Answer:

The answer is given in attached file.

Step-by-step explanation:

Answer:

b=24

Step-by-step explanation:

the sides are equal to each other so

b+24=2b

24+24=2 times 24

48=48

so b=24

Answer:

D. y = 3/4x + 13

Step-by-step explanation:

lmk if you want an explanation

To find out how many flowers will be in each centerpiece, we can divide the total number of flowers by the number of centerpieces:

Total number of flowers: 1,064

Number of centerpieces: 28

Number of flowers in each centerpiece = Total number of flowers / Number of centerpieces

Number of flowers in each centerpiece = 1,064 / 28 = 38

Therefore, there will be 38 flowers in each centerpiece.

\(\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}\)

♥️ \(\large{\textcolor{red}{\underline{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}\)

Answer: 38

Step-by-step explanation:

The question is asking you to divided.

1064 divided by 28 = 38

So there will be 38 flowers in each centerpiece

When rolling a pair of dice, there are 36 possible outcomes, each representing a unique combination of the numbers on the two dice.

Event A: "at least one die is a 3" is not mutually exclusive with Event B: "at least one die is a 6" or Event C: "the sum is 11"

Event A and Event B are mutually exclusive because when one of the die is a 6, the other die cannot be a 3 and vice versa.

Event A and Event C are not mutually exclusive because there are some outcomes where at least one die is a 3 and the sum is 11. For example (3,8), (4,7) and (6,5) are all outcomes where at least one die is 3 and the sum is 11.

Event B and Event C are not mutually exclusive because there are outcomes where at least one die is a 6 and the sum is 11. For example (5,6) and (6,5) are both outcomes where at least one die is a 6 and the sum is 11.

So, in conclusion, Event A and Event B are mutually exclusive, but Event A and Event C and Event B and Event C are not mutually exclusive.

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Answer:

Its the first one

Step-by-step explanation:

It is a statistical question because the data may vary for each player. :)

Answer:

1 Collect like terms.

5(2x-1)+(30+20)

2 Simplify.

5(2x-1)+50

3 Expand by distributing terms.

10x-5+50

4 Collect like terms.

10x+(-5+50)

5 Simplify.

10x+45

Hope this helps!! <3

Answer:

10x + 55

Hope this helps :)

Answer:

Step-by-step explanation:

To find the direction of minimum rate of change for the function f(x, y) = x² + xy + y² at the point (5, 2), we need to find the gradient vector (also known as the gradient or the vector of partial derivatives) and then find the direction orthogonal to the gradient vector, as this direction will have the minimum rate of change.

First, let's find the gradient vector by computing the partial derivatives of f(x, y) with respect to x and y:

∂f/∂x = 2x + y

∂f/∂y = x + 2y

Now, evaluate the gradient vector at the point (5, 2):

∇f(5, 2) = (2(5) + 2, 5 + 2(2)) = (12, 9)

The gradient vector is (12, 9). To find the direction orthogonal to the gradient vector, we can swap the x and y components and negate one of them. Since the question asks for a vector with an x-component of 1, 0, or -1, we'll negate the x-component:

Orthogonal vector = (-1, 12)

So, the direction of minimum rate of change at point (5, 2) is given by the vector [-1, 12].

Answer:

$25.50

Step-by-step explanation:

8 tickets cost $204.

$204 ÷ 8 = $25.50

Total number of cards in the normal deck is 52

Number of spades in the normal deck = 13

Probability of drawing a spade(first card) = 13/52 = 1/4

Probability of not drawing a spade(first card) = 1 - 1/4 = 3/4

Since the first card is not replaced,

number of cards left = 52 - 1 = 51

number of spades left = 13

Probability of drawing a spade(second card) = 13/51

Since the second card is not replaced,

total number of cards left = 51 - 1 = 50

number of spades left = 13 - 1 = 12

Probability that the third card is a spade = 12/50 = 6/25

Thus, the probability that the first card is not a spade, the second card is a spade, and the third card is also a spade = 3/4 x 13/51 x 6/25 = 0.046