Identify the standard form of the equation by completing the square.
4x2 − 9y2 − 8x + 36y − 68 = 0

Based on the information, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function

The given parameters from the question are:

P(n) = 1200(1.68)^n

Where

n represent the number of months

An exponential growth function is represented as:

P(n) = a * (1 + r)^n

Where

a represents the initial value

r represents the rate

By comparison, we have

a = 1200

1 + r = 1.68

This gives

r = 0.68 = 68%

Hence, there were initially 1200 ferns; the monthly percent rate of change is 68% and this situation is modeled by an exponential growth function

Read more about exponential growth function at:

https://brainly.com/question/2456547

#SPJ1

1,200

68

growth

Got it right on Edmentum

Answer:

Hey there!

Step-by-step explanation:

This is ur answer...

Hope it helps!

Brainliest pls!

Have a good day!^^

Answer:

Step-by-step explanation:

integer and rational

Answer:

f(x) = 5x - 5

Step-by-step explanation:

f(x) = 5x - 5 is a linear equation as it has no power.

The power series representation for the function, so the interval of convergence is (-9,9).

The definition of convergence refers to 2 or more matters coming together, joining collectively, or evolving into one. An example of convergence is when a crowd of people all move collectively into a unified organization.

Convergence is when two or extra matters come collectively to shape a brand new whole, like the convergence of plum and apricot genes within the plucot. Convergence comes from the prefix con-, meaning collectively, and the verb verge, because of this to show closer to.

The simple concept of convergence permits multiple responsibilities to be accomplished on a single device, which efficiently conserves space and power. for example, as opposed to wearing separate devices – like a cell cellphone, digital camera, and virtual organizer – each era converges on a single tool or telephone.

We have given f(x)=1/(9+x)

f(x)=(1/9)*(1/(1-(-x/9))

f(x)=summation of (n=0 to infinity) [1/9*(-x/9)n]

=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]

f(x)=summation of (n=0 to infinity) [(-1)n*(xn/9n+1)]

Let an=(-1)n*(xn/9n+1)

using the Ratio Test

L=lim n-->infinity|an+1/anL=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]/[(-1)n*(xn/9n+1)]|

=lim n-->infinity|[(-1)n+1*(xn+1/9n+2)]*[9n+1/(-1)n*(xn)]|

=lim n-->infinity|(-1)*(x)/9)|

=|-x/9|<1

x/9<1 and x>9>-1

x<9  and x>-9

x is -9<x<9

for x=9 the series ,summation of (n=0 to infinity) [(-1)n*(9n/9n+1)] =summation of (n=0 to infinity) [(-1)n*(/9)]

=1/9*summation of (n=0 to infinity) [(-1)n]

By the geometric series this summation of (n=0 to infinity) [(-1)n] diverges

=1/9*diverges

the series diverges for x=9

for x=-9 the series ,summation of (n=0 to infinity) [(-1)n*(-9)n/9n+1)] =summation of (n=0 to infinity) [(-1)2n*(/9)]

=1/9*summation of (n=0 to infinity) [(-1)2n]

which is diverges

so the interval of convergence is (-9,9)

Learn  more about convergence here https://brainly.com/question/21089324

#SPJ4

Answer:

19

Step-by-step explanation: (75/5) + 4= p

15+4=p

19=p

The original price for one lunch meal is $19

p = $15 + $4

p = $19

Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Given solution of a question done by two people.

Jenna's method

5(30+4)

(5)(30)+(5)(4)

150+20=170

Mia's method

5(30+4)

5(34)=170

We are required to find why they have achieved at the same answer.

Jenna and Mia have achieved at the same answer because they both have adopted the right method.Jenna's method is the equation in its simplest form. Addition of that is easily understood. While Mia's method is just valid as Jenna's some people may have trouble remembering the steps of multiplication within parantheses as well as being able to look at large multiplication problem and automatically knowing the answer or being able to get the answer as fast as simple addition.

Hence Jenna and Mia arrived at the same answer because both the methods they have adopted are correct.

Learn more about multiplication at https://brainly.com/question/10873737

#SPJ1

Answer:

1. Given

2. Definition of Congruent Angles

3. Triangle Interior Angle Sum Theorem

4. Transitive Property of Equality

5. Substitution Property of Equality

6. Definition of Congruent Angles

Using it's concept, there is a 0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

For each block, there are 8 outcomes, since there are 2 blocks, there are 8² = 64 total outcomes. For the desired outcomes, we have that:

Hence there are 8 + 7 = 15 desired outcomes, and the probability is given by:

p = 15/64 = 0.2344.

0.2344 = 23.44% probability that you will choose a block labeled with a T or a block labeled with a 6.

More can be learned about probabilities at https://brainly.com/question/14398287

#SPJ1

The number of people that have watched the video is 858 people

A function is a mathematic rule. We know that a function shows the rule that is to  be carried out and is often written in the form of an equation.

Now we have the function shown as; f(x) = 33(1.3)x. Since we know that the term x is referred as the number of days the video has been online.

Thus,  f(x) = 33(1.3)(20) thus we can now say that the number of people who have vied the video in twenty days is 858 people.

Learn more about mathematical function:https://brainly.com/question/26382648

#SPJ1

Answer: the answer is B or 858

Step-by-step explanation: The answer is B or 858

Answer:

supposed to make the subject y then slope is -2

Answer: 16482

Step-by-step explanation:

Let's divide the number into three parts:

sixteen thousand | four hundred |eighty-two

A thousand is 1000, so sixteen thousand should be 16000.

A hundred is 100, so four hundred should be 400.

Eighty-two is just 82.

Let's add all of these:

[tex]16000+400+82=16482[/tex]

The equation that represents the function is y = -x - 1

The complete question is added as an attachment

From the table of values, we have the following points

(x, y) = (-1,0) and (0,-1)

Calculate the slope (m) using

m = (y2 - y1)/(x2 - x1)

Substitute the known values in the above equation

m = (-1 -0)/(0 + 1)

Evaluate the exponent

m = -1

The equation is then calculated as:

y = mx + c

This gives

y = -x + c

Using the point (0,-1), we have:

0 = 1 + c

Solve for c

c = -1

So, we have

y = -x - 1

Hence, the equation that represents the function is y = -x - 1

Read more about linear functions at:

https://brainly.com/question/1884491

#SPJ1

Answer:

$700

Step-by-step explanation:

If he made a loss of 15%, then it means that selling price is 85% of the cost price.

If the cost price is x, then we have;

0.85x = 595

x = 595/0.85

x = $700

The lifetime of meson according to laboratory clocks would be 14 μs.

In this question,

Meson decay, Δt = 2μs

Velocity, y = 0.99C, where C is the speed of the light

Time measurement depends on the reference frame of clock.

Time dilation, Δt' = y Δt

⇒  [tex]\frac{\Delta t }{\sqrt{1-\frac{v^{2} }{c^{2} } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-\frac{(0.99c)^{2} }{c^{2} } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.99^{2} } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{1-0.9801 } } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{\sqrt{0.0199} } }[/tex]

⇒ [tex]\frac{2(10^{-6} ) }{0.1410} } }[/tex]

⇒ 14.18 × 10⁻⁶ ≈ 14 μs

Hence we can conclude that the lifetime of meson according to laboratory clocks would be 14 μs.

Learn more about lifetime at laboratory clocks here

https://brainly.com/question/23455167

#SPJ4

The y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought. Therefore, option B is the correct answer.

Given that, Ethan bought 3 pints of raspberries for $5 per pint and x pints of blueberries for $3 per pint.

The average is (15 + 3x)/(3+x) per pint.

We need to find what quantity will be represented by the y-intercept of the graph.

Since the y-intercept always has a corresponding x-value of 0, replace x with 0 in the equation and solve for y. On a graph, the y-intercept can be found by finding the value of y when x=0. This is the point at which the graph crosses through the y-axis.

Now, the graph of y=(15 + 3x)/(3+x)is given below.

To find the x-intercept, substitute in 0 for y and solve for x. To find the y-intercept, substitute in 0 for x and solve for y.

x-intercept(s): (−5,0)

y-intercept(s): (0,5)

So, the y-intercept represents the average cost, in dollars per pint, of all the raspberries Ethan bought.

Therefore, option B is the correct answer.

To learn more about y-intercept visit:

https://brainly.com/question/14180189.

#SPJ1

The solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5

Linear equations are equations that have constant average rates of change, slope or gradient

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x- y = 3

y - x = 1

Make y the subject in the second equation, by adding x to both sides of the equation

y - x + x = x + 1

This gives

y = x + 1

Substitute y = x + 1 in 2x- y = 3

2x- x - 1 = 3

Evaluate the like terms

x = 4

Substitute x = 4 in y = x + 1

y = 4 + 1

Evaluate

y = 5

Hence, the solution for the system of linear equations 2x- y = 3 and y - x = 1 are x = 4 and y = 5

Read more about system of linear equations at

https://brainly.com/question/14323743

#SPJ1

Answer:

  (a)  x = -1.10 and x = 1.10

Step-by-step explanation:

A straightforward square root will give the value of x.

Divide by the coefficient of x^2:

  x^2 -30/25 = 0

  x^2 -1.20 = 0

Add 1.20, and take the square root.

  x^2 = 1.20

  x = ±√1.20 ≈ ±1.0954

  x ≈ -1.10 and 1.10 . . . . . round to hundredths

__

Additional comment

For small values of x, the root of (1+x) is approximately 1+x/2. For a root accuracy to the nearest hundredth, x < 0.21 (as here). For accuracy to the nearest thousandth, x < 0.064.

The coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

Binomial expansion is the expansion of two term expressions such as (a + b)ⁿ where n is a rational number.

Pascal's triangle is atriangle used in determining the coefficients of a binomial expansion.

The general term for the expansion (a + b)ⁿ = ∑ⁿCₓaˣbⁿ⁻ˣ.

So, each term is ⁿCₓaˣbⁿ⁻ˣ.

Comparing (a + b)ⁿ with (2t + s)⁷,

So, its general term is ⁿCₓ(2t)ˣsⁿ⁻ˣ = ⁷Cₓ(2t)ˣsⁿ⁻ˣ

= ⁷Cₓ(2)ˣtˣsⁿ⁻ˣ

So, the coefficient term is ⁷Cₓ(2)ˣ

Now for the term t²s⁵, x = 2.

So, the coeficient term is  ⁷Cₓ(2)ˣ =  ⁷C₂(2)²

= 7!/2!(7 - 2)! × 4

= 7!/2!5! × 4

= 7 × 6 × 5!/(2! × 5!) × 4

= 7 × 6/2 × 4

= 7 × 3 × 4

= 84

So, the coefficient of t²s⁵ in the expansion of (2t + s)⁷ is d. 84

Learn more about binomial expansion here:

https://brainly.com/question/25086608

#SPJ1

Answer:

okay it's name is Muhammad Deco alfansia ( ◜‿◝ )

Answer:

Slope, sometimes referred to as gradient in mathematics, is a number that measures the steepness and direction of a line, or a section of a line connecting.

Step-by-step explanation: Hope this helps you!

Answer:

ummation of n=1 to n=7 (-2)^n

Step-by-step explanation:

summation of n=1 to n=7 (-2)^n

The Total surface area of the rectangular prism = 168 in.²

The Volume of the rectangular prism = 108 in.³

The total surface area of a rectangular prism is given as: SA = 2(wl + hl + hw), where:

w = width of the rectangular prism

h = height of the rectangular prism

l = length of the rectangular prism

The volume of a rectangular prism = l × w × h

Find the Total surface area of the rectangular prism:

Length (l) = 9 in.

Width (w) = 2 in.

Height (h) = 6 in.

Total surface area of the rectangular prism = 2(wl+hl+hw) = 2·(2·9+6·9+6·2) = 168 in.²

Find the volume of the rectangular prism:

Length (l) = 9 in.

Width (w) = 2 in.

Height (h) = 6 in.

Volume of the rectangular prism = l × w × h = 9 × 2 × 6

Volume of the rectangular prism = 108 in.³

Learn more about the rectangular prism on:

https://brainly.com/question/1015291

#SPJ1

The time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds

The function is given as:

y = -16x^2 + 48x

When the ball hits the ground, we have

y = 0

Substitute the known values in the above equation

-16x^2 + 48x = 0

Factor out -16x

-16x(x - 3) = 0

Divide through by -16x

x - 3 = 0

Add 3 to both sides

x = 3

Hence, the time, in seconds, it takes from the moment the soccer ball is kicked until it returns to the ground is 3 seconds

Read more about quadratic functions at:

https://brainly.com/question/8992769

#SPJ1

The groups which would be most representative of the opinions of all employees in the company are: A sample of 5% of randomly selected employees from each office location, Employees who are randomly selected by a computer from a list of all company employees and Employees who have worked for the company for more than 10 years.

Options (A),(C) and (D) are correct.

A sizable business has locations around the nation. The company's facilities director was tasked with asking employees about their office furnishings. Instead of polling every worker at the company, the director chose to select a sample. We are supposed to find the groups which would be most representative of the opinions of all employees in the company.

Learn more about samples here:

https://brainly.com/question/17831271

#SPJ1

The probability that it will rain both days is [tex]\frac{1}{4}[/tex].

According to the question

Mr. and mrs. smith plan to roof the cabin on 2 consecutive days.

Assuming that the chance of rain is independent of the day

Probability is the chance that some event will happen.

It is the ratio of the number of ways a certain event can occur to the number of possible outcomes.

Probability = Number of ways it can occur/Total number of outcomes

Probability of rain on first day = 1/2

Probability of rain on second day = 1/2

Then

Probability of rain on both days = [tex]\frac{1}{2}[/tex] × [tex]\frac{1}{2}[/tex] = 1/4

Hence,

The probability that it will rain both days is [tex]\frac{1}{4}[/tex].

Find out more information about probability here

brainly.com/question/13605042

#SPJ4

For a circle k(O) with diameter AB and CD ⊥ AB, it is proved that AD·CB=AC·CD, using similarity of triangles.

Given:

circle k(O) with diameter AB

CD ⊥ AB

To Prove: AD·CB=AC·CD

Proof:

In ΔADC and ΔCDB,

∠ADC = ∠CDB = 90°  

[∵Both are right angle triangles]

CB = CB [Common side]

⇒ AC / CB = CD / DB

Thus, ΔACD is similar to ΔCDB by RHS similarity.

Therefore, we can write,

AD/CD = AC/CB [Since corresponding sides of similar triangles are proportional]

⇒ AD·CB = AC·CD

Hence proved.

Learn more about similarity here:

https://brainly.com/question/25882965

#SPJ1

The circumference of the given circle is 25.1 cm.

According to the statement

we have given that the the radius of circle which is 4cm.

And we have to find the circumference of the circle.

So, For this purpose

The circumference is the length of any great circle, the intersection of the sphere with any plane passing through its center.To calculate the circumference of a circle, multiply the diameter of the circle with π (pi).

The formula to calculate it is

C = 2(pi)r

So, substitute the values in it then

Here use pi value is 3.14

C = 2 *3.14*4

C = 25.12.

The circumference of the given circle is according to one decimal place is 25.12 cm.

So, The circumference of the given circle is 25.1 cm.

Learn more about circumference here

https://brainly.com/question/4233129

#SPJ1

Answer:

We note that,

x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³

now we can use binomial series on (1+x²)²ᐟ³

(1+x²)²ᐟ³ = ( 1+2x²/3+((2/3)*(2/3 -1)/2) x⁴ + ((2/3)*(2/3 -1)(2/3–2)/6) x⁶ +o(x⁶) =

= 1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶)

The last step is to differentiate,

x/³√(1+x²) dx = (3/4) d/dx (1+x²)²ᐟ³

= (3/4) d/dx (1 + 2x²/3 - x⁴/9 +4x⁶/81 +o(x⁶) )

= (3/4) ( 0 + (4/3)x - 4/9 x³ + 24x⁵/81 + o(x⁵))

= x - x³/3 + 2x⁵/9 + o(x⁵)

The complete Question is- How do I find the Maclaurin series using binomial series in the function f(x) = x/³√1+x^2?

Learn more about binomial series here:

https://brainly.com/question/14004514

#SPJ4

Part a

[tex]\frac{2x+1}{x}=\frac{1}{x-2}\\\\(2x+1)(x-2)=x\\\\2x^2 -3x-2=x\\\\2x^2 - 4x-2=0\\\\x^2 - 2x-1=0\\\\x=\frac{2 \pm \sqrt{8}}{2}\\\\x=1 \pm \sqrt{2}[/tex]

Part C

[tex]\frac{x+3}{1-x}=\frac{x+1}{x+2}\\\\(x+3)(x+2)=(1-x)(x+1)\\\\x^2 +5x+6=-x^2 +1\\\\2x^2 + 5x+5=0\\\\x=\frac{-5 \pm \sqrt{-15}}{4}\\\\x=\frac{-5 \pm i\sqrt{15}}{4}[/tex]

Answer:

Graph B

Step-by-step explanation:

Transform the given equation into the slope intercept form, y = mx + b, where m represents the slope and b represents the y-intercept.

3x - 2y = -12

2y = 3x + 12

y = 3/2x + 6

Graph B represents y = 3/2x + 6 because it has a y-intercept at (0,6) and a slope of 3/2.