What answer is the best one? Pls help me

The population was 6.98 million in 1900. The population of New York decreased with respect to time.

What is an exponential function?

An exponential function is a mathematical function with the formula f (x) = axe, where "x" is a variable and "a" is a constant that is called the function's base and must be greater than zero. The transcendental number e, which is approximately equal to 2.71828, is the most commonly used exponential function base.

The population of New York state can be modeled by

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513t}}\)

P is the population and t is the number of years since 1800.

The difference between the year 1900 to 1800 is 100.

Putting t = 100 in the given model:

\(P(t)=\frac{19.71}{1+61.22e^{-0.03513\times 100}}\)

\(P(t)=\frac{19.71}{1+61.22e^{-3.513}}\)

P(t) = 19.71/2.8248

P(t) = 6.9774

P(t) = 6.977 (rounded to the nearest thousands)

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JKLM is a parallelogram with four sides and four angles, meaning its measure of angle K is equal to the measure of angle M.

A parallelogram is a quadrilateral having four equal-length sides and opposing sides that are parallel. It is a two-dimensional form with two pairs of parallel sides and equal angles on all sides.

JKLM has four sides and four angles if it is a parallelogram. Because it is a parallelogram, the opposite sides of the figure will be parallel, as will the opposite angles. This signifies that the angle K measure is equal to the angle M measure. As a result, if the measure of angle M is known, the measure of angle K may be calculated.

For example, if angle M is 70 degrees, then angle K is also 70 degrees. In general, if the measure of angle M is x, the measure of angle K must be x as well.

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Answer:

7,8

Step-by-step explanation:

Answer: Creo que la respuesta es x+3

Espero haber ayudado :D

The angle of elevation of the sun is 18°.

According to the question,

We have the following information:

A 130 foot tall building has a shadow that is 400 feet long (this is the correct question).

Now, let's take the angle of elevation of the sun to be x°.

Now, the height of the building will become perpendicular and the shadow will serve as the base for the angle of elevation.

We will use the trigonometric function tan.

Tan x = Perpendicular/base

Tan x = 130/400

Tan x = 0.325

Now, the value of x is 18°.

Hence, the angle of elevation of the sun is 18°.

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By finding the roots of the polynomial, we conclude that the correct graph is the second one.

Here we have the polynomial:

\(f(x) = x^3 + x^2 - 2x\)

To identify it, we need to find the roots, we can rewrite the equation as:

\(f(x) = x*(x^2 + x - 2)\)

And we can rewrite the last part by using the Bhaskara's formula:

\(x = \frac{-1 \pm \sqrt{1^2 + 4*2} }{2} \\\\x = (-1 \pm 3)/2\)

Then the roots are:

x = -2

x = 1

Then we rewrite:

\(f(x) = x*(x + 2)*(x - 1)\)

So the roots are at x = 0, x = -2, and x = 1.

The graph with these roots is the second graph (top right).

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Answer:

y = -2x - 13

Step-by-step explanation:

Answer:

y = - 2x - 13

Step-by-step explanation:

First, distribute out the two on the right side of the equation.

y + 7 = - 2x - 6

Next, subtract 7 from both sides to isolate the y variable on the left side.

y = - 2x - 13

That is your answer in slop-intercept form.

Answer:

\(ln(\frac{(x+6)^{2} }{x^{7} } )\)

Step-by-step explanation:

In photos.

Answer:

Step-by-step explanation:

By the power property we know that 2*lnx = ln(x²)

Therefore 2*ln(x+6) = ln((x+6)²)

and 7*lnx = ln(x⁷)

finally by the product property we know that ln(a*b) = lna + lnb

so the recently transformed addition ln((x+6)²) + ln(x⁷) can be transformed into a product since the base of the logarithm are the same (base e for ln):

ln((x+6)²) + ln(x⁷)  = ln(x⁷*(x+6)²)

if you would want to further develop it (a+b)²=a²+2*a*b+b²

=ln(x⁷*(x²+12x+36))

by the distributive property of multiplication you can bring x⁷ into the parentheses by multiplying each element inside:

=ln(x⁹+12x⁸+36x⁷)

And I believe that would be the condensation of the expression provided to a single logarithm with coefficient 1.

Answer:5.97

Step-by-step explanation.  

you have to look at the question.

you have to look around the question

The very last step is you have to answer it  

Answer:

55,32,32,19,8,3

Step-by-step explanation:

Answer:

55,32,32,19,8,3

Step-by-step explanation:

Answer:

x = +2

y = +.5

Step-by-step explanation:

Above is how they increase in each column

The difference quotient for the given function is 9 -2/h.

The difference quotient for the given function can be calculated as:

[f(x+h) - f(x)]/h

= [(3(x+h)² - 2(x+h) + 5) - (3x² - 2x + 5)]/h

= (3x² + 6xh + 3h² - 2x - 2h + 5 - 3x² + 2x - 5)/h

= (6xh + 3h² - 2h)/h

= (6x + 3h -2)/h

Simplifying the expression further, we get:

(6x + 3h -2)/h = 6 + 3h/h -2/h

= 6 + 3 -2/h

= 9-2/h

Therefore, the difference quotient for the given function is 9 -2/h.

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"Your question is incomplete, probably the complete question/missing part is:"

Find the difference quotient [f(x+h)-f(x)]/h, where h≠0, for the function below.

f(x)=3x² -2x+5. Simplify your answer as much as possible.

Answer:

9 to the forth power * 7 to the 2nd power*

Answer:

9^4*7^2 is the answer espero que te sirva mucho

Answer:

2^5 *3

Step-by-step explanation:

You can solve this multiple ways but should get 2^5*3

Answer:

\(2^5*3\)

Step-by-step explanation:

\(96\\\\=2*48\\\\=2*2*24\\\\=2*2*2*12\\\\=2*2*2*2*6\\\\=2*2*2*2*2*3\\\\=2^{5}*3\)

Answer:

the slope is always X

Step-by-step explanation:

y=mx+b

X is the slope variable

1. Series:

\(\[\sum_{n=1}^{\infty} \frac{n}{{n^2 + 3}}\]\)

To determine the convergence or divergence of this series, we can use the comparison test or the limit comparison test.

Using the comparison test:

We compare the given series with a known series that we know to be convergent or divergent. Let's consider the series  \(\(\sum_{n=1}^{\infty} \frac{1}{n}\).\)

As \(\(n\)\) approaches infinity, the term  \(\(\frac{n}{{n^2 + 3}}\)\)  is always less than or equal to  \(\(\frac{1}{n}\).\)

Since the series  \(\(\sum_{n=1}^{\infty} \frac{1}{n}\)\)  is a known divergent harmonic series, and the terms of our series are less than or equal to the corresponding terms of the harmonic series, we can conclude that our series is also divergent.

Therefore, the first series is divergent.

2. Series:

\(\[\sum_{n=1}^{\infty} \left(\frac{n}{{n^2 + 3}}\right)^n\]\)

To test the convergence or divergence of this series, we can use the root test or the ratio test.

Using the root test:

We take the \(\(n\)th\) root of the absolute value of the series term and check the limit as \(\(n\)\) approaches infinity.

Let's calculate the limit:

\(\[\lim_{{n\to\infty}} \left(\frac{n}{{n^2 + 3}}\right)^n = \lim_{{n\to\infty}} \left(\frac{n^n}{{(n^2 + 3)^n}}\right) = \lim_{{n\to\infty}} \left(\frac{n^n}{{n^{2n} + 3n}}\right) = \lim_{{n\to\infty}} \left(\frac{n^n}{{n^{2n}}}\right) = \lim_{{n\to\infty}} \left(\frac{1}{{n^n}}\right) = 0\]\)

Since the limit is less than 1, the root test tells us that the series converges.

Therefore, the second series is convergent.

In summary:

1. The first series is divergent.

2. The second series is convergent.

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Answer:

(3x-2) (x-5)

Step-by-step explanation:

30 = -15 X -2

-17 = -15 + -12

3x2 - 15x - 2x +10

factorise

3x(x-5) - 2(x-5)

(3x-2) (x-5)

36x + 324 - 28x + 196

combine like terms: 36x - 28x = 8x and 324 + 196 = 520

8x+520

Answer:

-155

Step-by-step explanation:

-8\cdot \:9-83

-72-83

=-155

Answer:

The monomers are reacted to make prepolymers or a liquid, primitive macromolecule.

In the next step, the prepolymers are fed through a cell where it solidifies and attains the desired thickness. This process is called spinning.

Using a trigonometric equation, it is found that it will take 2.28 minutes until the two trains are first equidistant from the child.

The distance of the first train is:

\(y_1 = 2\cos^{2}x\)

The distance of the second train is:

\(y_2 = 3 + \cos{x}\)

When \(y_1 = y_2\), hence:

\(2\cos^{2}x = 3 + \cos{x}\)

The following substitution is made:

\(z = \cos{x}\)

Hence:

\(2z^2 = 3 + z\)

\(2z^2 - z - 3 = 0\)

Which is a quadratic equation with coefficients \(a = 2, b = -1, c = -3\), hence:

\(\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-3) = 13\)

\(z_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{13}}{4} = 1.5\)

\(z_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{1 - \sqrt{13}}{4} = -0.65\)

Then, applying the trigonometric equation, considering that \(-1 \leq z \leq 1\) due to the range of the cosine function:

\(z_2 = \cos{x_2}\)

\(x_2 = \arccos{z_2} = \arccos{-0.65} = 2.28\)

It will take 2.28 minutes until the two trains are first equidistant from the child.

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Answer:

Step-by-step explanation:

Since DM = DG + GM

The formula for the area of triangle is given by the expression 1/2 * base * height.

The formula for the area of a triangle is 1/2 multiplied by the base of the triangle multiplied by the height of the triangle.

To calculate the area of a triangle, you need to know the length of its base and the perpendicular height from the base to the opposite vertex. The formula for the area of a triangle is derived from the concept that the area of a rectangle is equal to the product of its length and width. Since a triangle is half of a rectangle, the area formula is modified by dividing the product of the base and height by 2, resulting in 1/2 * base * height. This formula applies to all types of triangles, including equilateral, isosceles, and scalene triangles. By plugging in the appropriate values for the base and height, you can calculate the area of any triangle.

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What is the formula for area of triangle?

Answer:100-K

Step-by-step explanation:

"100 decreased by a number K" can be written algebraically as:

100 - K

This expression represents the result of subtracting the value of K from 100.

Answer: x = -1 and y = -2

Step-by-step explanation:

You are given two expressions that have a relationship. There are two ways to solve this problem, but I will be going over the easy way. I'm assuming you know how to solve for one variable such as x? Well we can put the y varaible from the first equation in terms of x, from the second equation. Ill show you what I mean:

6x + 5(7x + 5) = -16

I replaced y in the first one in terms of x, so that we can solve just for x.

6x + 35x + 25 = -16

41x +25 = -16

41x = -41

x = -1

Now simply find y by plugging the now known x value into either equation

y = 7(-1) + 5

y = -2

Answer:

x = -1

y = -2

(  -1, -2 )

Step-by-step explanation:

6x + 5y = -16

They gave us what "y" is and its....

y = 7x + 5

We substitute the "y" in the equation with this "y = 7x + 5

"

6x + 5y = -16

6x + 5(7x + 5) = -16

Now we need to use the distributive property (multiply what is in the parenthesis by "5")

6x + 5 * 7x + 5 * 5 = -16

6x + 35x + 25 = -16

Combine Like Terms ( 6x and 35x)

41x + 35 = -16

Subtract 25 on both sides

41x + 35 - 25 = -16 - 25

41x = -41

Divide by 41 on both sides to isolate the variable

41x/41 = -41/41

x = -1

Now that we have what "x" is (-1) we can use that to find out what "y" is.

y = 7x + 5

Substitute the x with -1

y = 7x + 5

y = 7(-1) + 5

y = -7 + 5

y = -2

x = -1

y = -2

( x, y )

( -1, -2 )

Hope this helped!

Have a supercalifragilisticexpialidocious day!

Answer:

there aren't any options. but quadrant four would have a (x,-y) set up. positive x-values, but negative y-values.

Hi, you've asked an incomplete question. Here are the remaining questions:

a) Describe what each region in the Venn diagram represents.

Region I: In drama club, not in step team.

Region II: In both clubs.

Region III: In step team not in drama.

Region IV: Not in either club.

b) How many students were in only one of the two clubs?

c) How many students were in the drama club or in the step team?

d) How many students were surveyed?

Attached is the Venn diagram depicting the regions.

Explanation:

b) By adding the number of students that like drama club and those that like step club we can derive the answer:  34 + 27 = 61.

c) By adding 34 + 27 + those that like both (14) = 75.

d) The total number of students surveyed is gotten by summing any number in attached the diagram: 34 + 27 + 14 + 13 = 88.

The normal price of each chair is

The percentage off the normal price is

The percentage of the present price of each chair will be

To calculate the present value of one chair, we will use the formula below

By substituting the values, we will have

Since Mr .Krabs bought 4 chairs, the amount he spent will be

By substituting the values, we will have

Therefore,

The amount Mr.Krabs spent is = $6.30