he functions f(x) and g(x) are graphed.

On a coordinate plane, a curved red line with an upward arc, labeled g of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0). A straight blue line with a negative slope, labeled f of x, crosses the y-axis at (0, 4) and the x-axis at (2, 0).



Which represents where f(x) = g(x)?

f(2) = g(2) and f(0) = g(0)
f(2) = g(0) and f(0) = g(4)
f(2) = g(0) and f(4) = g(2)
f(2) = g(4) and f(1) = g(1)

Answer:

  18.5 m

Step-by-step explanation:

The diameter in meters is 5.90, so the circumference of the room is ...

  C = πd = 5.90π m ≈ 18.5 m

The perimeter of the room is about 18.5 m.

The range of C(t), the function of the average monthly cost of owning the cell phone, is (60, 560].

The range of a function is the set of all y-values obtained after substituting all possible x-values.

Steps to find the range of a function:

For the given problem:

The price of the device = $500

Monthly plan = $60

C(t) is defined as the average monthly cost of owning the phone.

Let t = number of months of owning the cell phone.

Then, total cost after t month = 500 + 60 t.

Hence, the average is:

C(t) = (500 + 60t)/t

C(t) =  500/t + 60

For t = 1, C(1) = 500 + 60 = 560

For t > 1, C(t) < 560

Therefore the maximum value of C(t) = 560

For t →∞  then 500/t will approach zero, hence:

C(t) →(0 + 60), or C(t) will approach 60.

Therefore, we can conclude that 60 < C(t) ≦ 560, or the range of C(t) is (60, 560].

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The first step to solve this exercise is to write the Mixed number as a decimal number. You can do it by dividing the numerator by the denominator of the fractional part and adding the quotient to the Whole number part, as follows:

So:

Knowing that Positive numbers are greater than zero and knowing that Negatives numbers are less than zero, we can order the given numbers from greatest to least, as you can see below:

Answer:

1/2 1/6 1/6

Step-by-step explanation:

Answer:

See below ↓↓

Step-by-step explanation:

a₁ refers to the first term of the sequence.

That is clearly : a₁ = 6

The formula for the nth term is :

Therefore, the nth term is :

Answer:

V = πr²h

Step-by-step explanation:

r = radius of circle

h = height of cylinder

Step-by-step explanation:

The formula for the volume of a cylinder is V=Bh or V=πr2h . The radius of the cylinder is 8 cm and the height is 15 cm. Substitute 8 for r and 15 for h in the formula V=πr2h . ... Therefore, the volume of the cylinder is about 3016 cubic centimeters.

Answer:

1: No, they're not similar polygons

2: Yes, they're similar polygons

Step-by-step explanation:

1: DF/AC = 8/6 = 1.3repeating

  FE/CB = 6/4 = 1.5

there is no constant of proportionality

2: 48/40 = 1.2

   35/30 = 1.2

the constant of proportionality is 1.2

a. Media usage is categorical and Tiredness is quantitative. The effect of media is the explanatory variable and Tiredness is the response variable.

b. Yes, this is an observational study.

This research was done via observation. The researchers are not modifying or controlling any variables; instead, they are watching and assessing the correlation between media use and fatigue. By visiting randomly chosen households and interviewing the adult household member with the closest birthday, they are gathering data.

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r = 1/15

a branliest from the answer will be appreciated

Step-by-step explanation:

1/x-9= 6

cross multiply

1= 6×{x-9}

1= 6x - 54

collect like terms

1+54= 6x

55= 6x

x= 55/6 or 9.1667

no, this is false. 1 is greater than 12/20.

Answer:

No. Its not cause 20/20 is what makes ita whole 1 so if ita 12 than its not equal to 1

The general solution of the given differential equation is \(y(x) = c₁(7) + c₂e^-2x) + c₃e^4x)\), where c₁, c₂, and c₃ are arbitrary constants.

To verify that y₁ = 7, y₂ = e^-2x), and \(y₃ = e^4x\)) are solutions of the given differential equation y‴ - 2y″ - 8y′ = 0, we need to substitute them into the equation and check if they satisfy it.

Let's start with y₁ = 7:

y₁' = 0

y₁″ = 0

y₁‴ = 0

Substituting these derivatives into the differential equation, we have:

0 - 2(0) - 8(0) = 0

The equation holds true, so y₁ = 7 is a solution.

Now, let's check y₂ = e^-2x):

\(y₂' = -2e^-2x)\\y₂″ = 4e^-2x)\\y₂‴ = -8e^-2x)\\\)

Substituting these derivatives into the differential equation:

\(-8e^-2x) - 2(4e^-2x)) - 8(-2e^-2x)) = 0\)

Simplifying this expression, we get:

\(-8e^-2x) + 8e^-2x) + 16e^-2x) = 0\)

The equation holds true, so \(y₂ = e^-2x\)) is a solution.

Lastly, let's check\(y₃ = e^4x):\)

\(y₃' = 4e^4x)\\y₃″ = 16e^4x)\\y₃‴ = 64e^4x)\\\)

Substituting these derivatives into the differential equation:

\(64e^4x) - 2(16e^4x)) - 8(4e^4x)) = 0\)

Simplifying this expression, we get:

\(64e^4x) - 32e^4x) - 32e^4x) = 0\)

The equation holds true, so \(y₃ = e^4x\)) is a solution.

Now, let's move on to part B and show that y₁, y₂, and y₃ form a fundamental set of solutions of the differential equation on (-∞, ∞).

To prove this, we need to show that the Wronskian determinant is non-zero, where the Wronskian is defined as:

W(x) = |y₁ y₂ y₃|

|y₁' y₂' y₃'|

|y₁″ y₂″ y₃″|

Calculating the Wronskian determinant, we have:

\(W(x) = |7 e^-2x) e^4x)|\\|0 -2e^-2x) 4e^4x)|\\|0 4e^-2x) 16e^4x)|\\\)

Expanding the determinant, we get:

\(W(x) = 7(-2e^-2x) * 16e^4x)) - e^-2x)(0 * 16e^4x)) + e^4x)(0 * 4e^-2x))\\= -224e^2x) + 0 + 0\\= -224e^2x)\\\)

The Wronskian determinant is non-zero for all x, which confirms that y₁, y₂, and y₃ form a fundamental set of solutions of the differential equation on (-∞, ∞).

The general solution of the differential equation is then given by:

y(x) = c₁y₁(x) + c₂y₂(x) + c₃y₃(x)

Substituting the solutions, we have:

\(y(x) = c₁(7) + c₂e^-2x) + c₃e^4x)\)

where c₁, c₂, and c₃ are arbitrary constants.

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Answer:

detail below

Step-by-step explanation:

slope = difference of y/difference of x

m1 = (3-2) / (7-5) = 1/2

m2 = (-3 - -1) / (5 - 2) = -2/3

m3 = (3 - 6) / (-1 - -4) = -3/3 = -1

IIIIIIIIDDDDDDDDDDDDKKKKKKKKKK

Answer:

F(x) = (x+2)(-x+3)(x-2)^2. I think answer should be like this

The base length of the cross section is 4 cm.

The volume of the triangular prism below is 396 cm³. The base length of the the cross section can be found as follows:

Therefore,

volume of a triangular prism = base area × height

volume of the triangular prism = 396 cm³

height = h

base area = 1 / 2 bh

where

Therefore,

base area = 1  / 2 × b × 11

base area = 11 / 2 b

Hence,

396 = 11  / 2 b × 18

396 = 99b

b = 396 / 99

b = 4

Therefore,

base length =  4 cm.

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The first value in a sequence or series, or the starting point in mathematics, is referred to as the initial number. For instance, the first number in the series 1, 3, 5, 7, and 9 is 1. To find the initial number of fish in the pond, we need to use the formula given to us:

P = 3000 / (1 + 2e^(-0.9t))

Here, P represents the population of fish at any given time t. We are looking for the initial population, which means we need to find P when t is equal to 0.

So, let's substitute 0 for t in the formula:

P = 3000 / (1 + 2e^(-0.9*0))
P = 3000 / (1 + 2e^0)
P = 3000 / (1 + 2*1)
P = 3000 / 3
P = 1000

Therefore, the initial number of fish in the pond was 1000.

To explain it in detail, the formula for the growth of the fish population in a newly dug pond is given as P=3000/1+2e^-0.9t, where P is the population of fish at any given time t.

We can find this by substituting 0 for t in the given formula, which gives us the population of fish at the initial time. When t=0, we get P=3000/1+2e^-0.9*0.

The exponent of e^-0.9*0 is 0, so it becomes 1.

Substituting this value in the formula, we get P=3000/1+2*1, which simplifies to P=3000/3, which is 1000.

Therefore, the initial number of fish in the pond was 1000.

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Answer:

586%

Step-by-step explanation:

5.86 times 100 to change to a percent

586 %

Answer:

A. 586%

Step-by-step explanation:

Multiply 5.86 by 100.

Drop the decimal.

Add the percent symbol.

Nathan played 4 games and went on 8 rides.

Nathan went to a carnival and spent $34. Games cost $1 each and rides cost $3.75 each. Let's say Nathan played x games and went on y rides. We know that x + y = 34 and y = 2x. We can substitute the second equation into the first equation to get x + 2x = 34. Solving for x, we get x = 4. Plugging this value back into y = 2x, we get y = 8.

Here is a table of Nathan's expenses:

Item    Cost                            Quantity                       Total Cost

Games $1                                        4                               $4                          

Rides $3.75                                8                               $29.00

Total $34.00

Nathan had a great time at the carnival and spent his money wisely. He played four games and went on eight rides, which is a good amount of entertainment for the price.

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Answer:

Step-by-step explanation:

(x / -5) + 7 ≥ 1

Answer:

21... 27.... 38...

Step-by-step explanation:

Add prime numbers to the number in alternate.

4 + 3 = 7

5 + 5 = 10

7 + 7 = 14

10 + 11 = 21

14 + 13 = 27

21 + 17 = 38

Answer:

Step-by-step explanation:

4x+8=.1x+3+3.9x

4x+8=4x+3

No solution since the 4x's will cancel each other out

The probability that one spin of the spinner will land in a shaded sector is 2/3.

The likelihood that something will happen is the straightforward definition of probability. When we are unsure of how an event will turn out, we might talk about the probabilities of various outcomes or how likely they are. The study of events subject to probability is referred to as statistics.

Probability is a branch of mathematics that deals with numerical representations of the likelihood of an event occurring or of a proposition being true.

When the spinner is released, there is a low likelihood that the part will rest on four.

Information: A particular spinner has equal-sized sectors, and it is equally likely to land in any of them. The remaining sectors are not coloured, and four of the sectors are shaded.

Four of the sectors are shaded, while the remaining sectors are not, according to the enigma.

The spinner has two unshaded areas and four shaded areas.

P(E)=4/6

P(E)=2/3

As a result, there is a simple 2/3 chance that the spinner will rest on four when it is spin.

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The complete question is:

"A certain spinner is divided into 6 sectors of equal size, and the spinner is equally likely to land in any sector. Four of the 6 sectors are shaded, and the remaining sectors are not shaded. What is the probability that one spin of the spinner will land in a shaded sector?"

The derivative of a function represents the rate of change of the function at a specific point. In this case, f'(0) = 1 indicates that at x = 0,

To find f'(0), we need to calculate the derivative of f(x) with respect to x and then evaluate it at x = 0.

Using the product rule and chain rule, we can differentiate f(x) = (x-1)^2 sin(x) as follows:

f'(x) = 2(x-1) sin(x) + (x-1)^2 cos(x)

Now, let's substitute x = 0 into the derivative expression:

f'(0) = 2(0-1) sin(0) + (0-1)^2 cos(0)

= -2(0) + 1^2 (1)

= 0 + 1

= 1

Therefore, f'(0) = 1.

the function f(x) = (x-1)^2 sin(x) is increasing with a rate of 1. It means that as we move along the x-axis from negative values towards x = 0, the function is getting steeper and the slope at x = 0 is positive.

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Answer:

The 24

Step-by-step explanation:

The 30 represents how many problems there were in all

Hope I was Helpful!!

Ohhhhh No wait the answer is . 80 Im so sorry

B. 0.80

So, 24 out of 30 is equal to 80%.

If 100% = 1.0

Then 80% = 0.80

Hope this helps you out! Good luck. :)

Answer:

The correct answer is c.) 3/36.There are three favorable outcomes (2, 11, and 12) out of a total of 36 possible outcomes (assuming a fair six-sided number cube). Therefore, the probability of X being a 2, 11, or 12 is 3/36, which can be simplified to 1/12.

Step-by-step explanation:

Answer:

4 years and 2 months

Step-by-step explanation:

Simple interest formula

A = P(1 + rt)

where:

Given:

Substitute the given values into the formula and solve for t:

\(\implies \sf 1000 = 500(1 + 0.24t)\)

\(\implies \sf \dfrac{1000}{500}=(1 + 0.24t)\)

\(\implies \sf 2=1 + 0.24t\)

\(\implies \sf 1 = 0.24t\)

\(\implies \sf t=\dfrac{1}{0.24}\)

\(\implies \sf t=4 \frac{1}{6} \:years\)

\(\implies \sf t=4\:years\:2\:months\)

Therefore, it takes 4 years and 2 months for the initial investment of $500 to double at a simple interested rate of 24%.

In 2009, the naming rights for the 122 teams in the four major US professional sports leagues (NFL, NBA, MLB, and NHL) earned those franchises approximately $3.6 billion.

In 2009, the naming rights deals for the 122 teams across the NFL, NBA, MLB, and NHL generated approximately $3.6 billion for those franchises. These deals allow companies to attach their name to a stadium or arena, which can provide valuable exposure and brand recognition.

The amount earned from these deals can vary widely based on factors such as the popularity of the team and the location of the stadium or arena. Despite fluctuations in the economy and the sports industry, naming rights deals have remained a significant source of revenue for professional sports franchises.

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