What is the decimal expansion of the following fraction?
1/22

A.0.045

B.0.22

C.1.22

D.0.045

1) the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.

2) the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.

Since f is an increasing function over its domain, if a < b, then f(a) < f(b).

We are given the inequality:

f(4x-3) ≥ f(2-x²)

Since f is increasing, this is equivalent to:

4x-3 ≤2-x²

Simplifying, we get:

x² + 4x - 5 ≥ 0

We can factor this inequality as:

(x + 5)(x - 1) ≥ 0

The solutions are x ≤ -5 or x >= 1.

However, we need to ensure that these solutions are within the domain of the function, which is given as (-8, 4).

The solution x ≤ -5 is not within the domain, so we can discard it. Therefore, the solution to the inequality is:

x ≥ 1

To summarize:

f(4x-3) ≥ f(2-x²) is equivalent to x² + 4x - 5 ≥ 0

The solution to x² + 4x - 5 ≥ 0 is x ≥ 1.

Therefore, the solution to the original inequality f(4x-3) ≥ f(2-x²), given that f is increasing over its domain (-8, 4), is x ≥ 1.

2)
Since g is a decreasing function over its domain, if a < b, then g(a) > g(b).

We are given the inequality:

g(3² - 2x) ≥ g(3x - 2)

Since g is decreasing, this is equivalent to:

3² - 2x ≤ 3x - 2

Simplifying, we get:

11 ≤ 5x

The solution is x ≥ 11/5.

To summarize:

g(3² - 2x) ≥ g(3x - 2) is equivalent to 11 ≤ 5x.

The solution to 11 ≤ 5x is x ≥ 11/5.

Therefore, the solution to the original inequality g(3² - 2x) ≥ g(3x - 2), given that g is decreasing over its domain (-∞, ∞), is x ≥ 11/5.

Learn more about inequality at:

https://brainly.com/question/20383699

#SPJ1

Answer: i can answer the first one but the second one i might get wrong

Step-by-step explanation:

for the first question answer B because external lights do not help unless it is dark, you need your battery to start the car and your fluids to keep the car running, your windshield's keep the raid and weather from entering your car as well as stopping you from flying out the window. Your mirrors help you keep track of whats behind you and showing you if you have enough space to turn.

now for the second question i would say in the manual of your car because every car has a manual to read on how to work the car/fix it

Emily paid M = 30 for the ice cream cones.

To find the amount Emily paid (M), we can set up an equation using the given information.
1. The cost of the ice cream cones is 24.
2. She got back 6 in change.
Using these facts, we can write the equation:

M - 24 = 6
Now, let's solve for M:
Step 1: Add 24 to both sides of the equation.
M - 24 + 24 = 6 + 24
Step 2: Simplify.
M = 30.

For similar question on cones.

https://brainly.com/question/12753579

#SPJ11

Answer:

the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).

Step-by-step explanation:

The system of linear equations can be written as:

y = (1/3)x

x + 3y = -6

To graph the system, we can graph each equation and find the point of intersection of the two lines.

The first equation y = (1/3)x has a slope of 1/3 and passes through the origin (0,0).

The second equation can be written as:

y = (-1/3)x - 2

This has a slope of -1/3 and y-intercept of -2.

To graph the system, we can plot the points (0,0) and (-6,-2) and draw a line through them. This is the graph of the second equation.

To graph the first equation, we can plot the point (3,1) and use the slope of 1/3 to draw a line passing through the origin.

The graphs of the two equations intersect at the point (-3,-1).

Therefore, the graph that shows the solution to the system of linear equations is the coordinate plane with one line that passes through the points 0,0 and -6,-2, and another line that passes through the points 3,1 and the origin (0,0).

The uniform probability distribution is option (c) The probabilities of drawing any individual card in a deck with one draw

The uniform probability distribution is a probability distribution where all outcomes are equally likely. Out of the options provided, (c) The probabilities of drawing any individual card in a deck with one draw is an example of a uniform probability distribution. This is because each card in a deck is equally likely to be drawn, assuming that the deck is well-shuffled.

The other options are not examples of a uniform probability distribution.

(a) The probability of reaching a temperature of 75F on any given day of the year in St. Louis, MO is not a uniform distribution because the probability of reaching 75F is not the same throughout the year, and is influenced by many factors like seasonal variation, climate changes, etc.

(b) A time period in which it rained 25% of the time and did not rain 75% of the time is not a uniform distribution since the probability of rain is not equally likely across the time period.

(d) Flipping a coin two times and recording whether heads or tails is also not a uniform distribution as the probability of getting heads or tails is not the same, it is 0.5 for each individual flip, but the probability of getting two heads, two tails or one head and one tail are different.

Therefore, the correct option is (c) The probabilities of drawing any individual card in a deck with one draw

Learn more about uniform probability distribution here

brainly.com/question/17091893

#SPJ4

The given question is incomplete, the complete question is:

Which would be a uniform probability distribution? a) The probability of reaching a temperature of 75F on any given day of the year in St. Louis, MO  b) A time period in which it rained 25% of the time and did not rain 75% of the time c) The probabilities of drawing any individual card in a deck with one draw d) Flipping a coin two times and recording whether heads or tails

The table shows the multiplication of two linear expressions and the subsequent simplification and standard form conversion. The reasons given are the input expressions,  Distributive property, Associative Property, simplification to standard form conversion. So, the correct option answer for reason 1, 2, 3 and 3 are B, C, A and D respectively.

The table shows the multiplication of two linear expressions is

Step Step

1      (1/4)x(5x-1)

2      (1/4)x(5x)+(1/4)x(-1)

3      (1/4)(5x^2)+(-1/4)x

4      (5/4)x^2+(-1/4)x

Reason 1: The multiplication of two linear expressions is given in the first column for each step.

Reason 2: The given linear expressions are rearranged in the second column for each step. It is Distributive Property.

Reason 3: The rearranged expressions in the second column are simplified using algebraic operations. It is  Associative Property.

Reason 4: The simplified expressions in the second column are written in the standard form of a quadratic polynomial.

So, the correct order of options for reason 1, 2, 3 and 3 are B, C, A and D respectively.

To know more about multiplication of linear expressions:

https://brainly.com/question/29235228

#SPJ4

_____The given question is incomplete, the complete question is given below:

A 2-column table with 5 rows. First column is labeled Step with entries one-fourth x (5 x minus 1), (one-fourth x) (5 x) + (one-fourth x)(negative 1), one-fourth times 5 times x times x + (negative 1) times one-fourth times x, (one-fourth times 5) (x times x) + (negative 1 times one-fourth) x, 5 over 4 x squared minus one-fourth x. Second column is labeled Reason with entries given, 1, 2, 3, 4. The table shows the multiplication of two linear expressions. Select the correct reason for each step. Reason 1:

Reason 2:

Reason 3:

Reason 4:

(A)associative property of multiplication

(B)multiplication

(C)Distributive property

(D) simplify

Answer:

B.

Step-by-step explanation:

Divide ( x number of pages) by (x number of minutes) for all answers.

Day 1: 20 divided by 35= around 0.57 pg per minute

Day 2: 80 divided by 15= 5.3 pg per minute

Day 3: 46 divided by 65= around 0.70 pg per minute

Day 4: 35 divided by 26= 1.34 pg per minute.

Therefore, B is your answer!

Crown me brainliest pls!

The cost of each Child ticket is  £ 15

Total number of people = 54

Number of adults = 30

Number of Children = Total number of people - Number of adults

                                 = 54 - 30 = 24

Cost of each adult ticket =£ x

Cost of each Child ticket = £x-25

Total Cost of tickets = £1560

The total cost of tickets =( Number of adults * Cost of each adult ticket) + (Number of Children*Cost of each Child ticket)

1560 = (30*x) + (24*(x-25))

1560 = 30x + 24 x - 600

1560 + 600 = 54x

2160 = 54x

40 = x

Therefore,

The cost of each adult ticket is £ 40

The cost of each Child ticket is  £(x - 25) = £ 15

To learn more about Word Problems visit:

https://brainly.com/question/20560946

#SPJ1

The function that represents the total cost f(x) to send a letter that is x ounces can be calculated as follows:

$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$

Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$

The total cost to send a letter that is 1 ounce is $0.50, and the total cost to send a letter that is 3 ounces is $0.92. Since the postal service calculates the weight to the whole ounce, if we send a 2-ounce letter, we can consider it as sending two 1-ounce letters.

Therefore, the total cost of sending a 2-ounce letter will be twice the cost of sending a 1-ounce letter.

Let f(x) be the total cost to send a letter that is x ounces.

Then,f(1) = 0.50f(2) = 2f(1) = 2(0.50) = 1.00f(3) = f(2) + 0.42 = 1.00 + 0.42 = 1.42

Hence, we can represent the function as follows:

$$f(x) = \begin{cases} 0.5 & \text{if } x = 1\\ 0.5 + 0.42(x-1) & \text{if } x > 1\end{cases}$$

Therefore, the correct options are:a) $f(x) = 0.5 + 0.42(x-1)$b) $f(x) = 0.5$

for such more question on total cost

https://brainly.com/question/25109150

#SPJ11

Answer:

B

Step-by-step explanation:

1. Add the nine over on the k side. So it will be 9+k

2. Divide both sides by 4.

4x-9=k

4x=9+k

x=k+9/4

:)

Answer:

-14

Step-by-step explanation:

Move 4y to the right side making the equation 5x=61+4y

Then divide both sides by 5 making the equation

5x/5 = 61/5 + 4y/5

x = 61 + 4y/5

Multiply both sides by 5 making the equation 61 + 4y = 5

Move 61 to the right side making it negative which makes the equation

4y = 5-61

Divide -56 by 4 because we moved the 4 to the right side

Answer for #1 will be -14

The other one I have no idea am sorry

The solution of the Equation is x= 9 and y= -3.

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

We have Equation,

5x - 4y = 61

and, 3x + y= 23

Now, solving the above equation we get

5x + 12x = 61 + 92

17x = 153

x= 9

and, y = 23- 27 = -4

Learn more about Equation here:

https://brainly.com/question/29657983

#SPJ5

Answer:

a) 10^4/4^10

Step-by-step explanation:

10^-2 = 1/10^2

4^5 x 1/10^2 = 4^5/10^2

(4^5/10^2)^-2 = (10^2/4^5)^2 = 10^4/4^10

In order to identify all the prime numbers less than 200, a person will have to eliminate the multiples of 2, Multiples of 3, Multiples of 5, Multiples of 7, Multiples of 11, and Multiples of 13.

What are multiples?

   Multiples are products that result from multiplying any given number by whole numbers. They are obtained by multiplying a whole number by another whole number. Prime numbers are natural numbers that are greater than 1 and have no positive divisors other than 1 and the number itself.

 The number 1 is not considered a prime number. In order to identify all the prime numbers less than 200, the person will have to eliminate the multiples of the following additional numbers: Multiples of 2, Multiples of 3, Multiples of 5, Multiples of 7, Multiples of 11, and Multiples of 13

      The person will have to eliminate the multiples of all these numbers to complete the task of identifying all the prime numbers less than 200.

To learn more about prime numbers visit: https://brainly.com/question/145452

#SPJ11

The probability that the sample mean cholesterol value be between 145 and 165 mg/dl is   0.288893452 or 28.89% .

What is probability?

Probability is a way of calculating how likely something is to happen. It is difficult to provide a complete prediction for many events. Using it, we can only forecast the probability, or likelihood, of an event occurring. The probability might be between 0 and 1, where 0 denotes an impossibility and 1 denotes a certainty.

We first get the z score for the two values. As z =[tex]\frac{x-\mu}{\sigma}[/tex] , then as            

x1 = lower bound =     145        

x2 = upper bound =     165        

μ= mean =  155        

σ = standard deviation =     27        

Thus, the two z scores are            

=> [tex]z_1[/tex] = lower =>z score = [tex]\frac{X_1-\mu}{\sigma}[/tex] =     -0.37037037        

=> [tex]z_2[/tex]= upper => z score = [tex]\frac{X_2-\mu}{\sigma}[/tex] =     0.37037037        

Using table/technology, the left tailed areas between these z scores is            

=>P(z < z1) =     0.355553274        

=>P(z < z2) =     0.644446726        

Thus, the area between them, by subtracting these areas, is            

=>P(z1 < z < z2) =     0.288893452 or 28.89%.

To learn more about probability refer the below link

https://brainly.com/question/13604758

#SPJ1

Probability distribution after two battles: Dark 1/3, Psychic 1/3, Fighting 1/3 Steady-state probability distribution: Dark 1/3, Psychic 1/3, Fighting 1/3. Probability distribution after two battles: Dark 1/4, Psychic 1/4, Fighting 1/4, Ghost 1/4. Steady-state probability distribution: Dark 1/6, Psychic 1/6, Fighting 1/2, Ghost 1/6

If Kecleon starts as the Fighting type and battles twice, the probability distribution of Kecleon's type is (1/3, 1/3, 1/3).

After many battles, the steady-state probability distribution of Kecleon's type is (1/3, 1/3, 1/3). This is because Kecleon has an equal chance of winning and losing battles against each of the other types, and so over time its type will converge to a uniform distribution.

If Kecleon starts as the Fighting type when Ghost Pokémon arrive and battles twice, the probability distribution of Kecleon's type is (1/4, 1/4, 1/4, 1/4).

After many battles, the steady-state probability distribution of Kecleon's type is (1/6, 1/6, 1/2, 1/6). This is because the presence of Ghost Pokémon alters the dynamics of the battles, causing Kecleon's type to converge to a non-uniform distribution where it is more likely to become a Psychic type due to the dominance of Ghost-type Pokémon over Fighting and Dark types.

To know more about Probability distribution:

https://brainly.com/question/11234923

#SPJ4

--The given question is incomplete, the complete question is given

" In a particular region of the Pokémon world, there are just three types of Pokémon: Dark, Psychic, and Fighting. Kecleon, the Color Change Pokémon, has the ability to change its type to blend into its surroundings. Its goal is to become the best type. It seeks to accomplish this goal by choosing a type of Pokémon to battle uniformly at random; it may choose a Pokémon of its own type. If it wins the battle, it will keep its old type. If it loses, it will take on the type of the Pokémon that defeated it. It continues this process indefinitely. For all questions assume that Dark Pokémon always defeat Psychic Pokémon, Psy- chic Pokémon always defeat Fighting Pokémon, and Fighting Pokémon always defeat Dark Pokémon. If two Pokémon of the same type battle, each has an equal chance of winning. a) Suppose that Kecleon starts as the Fighting type. After two battles, what is the probability distribution of Kecleon's type? (Your answer should be three numbers that sum to one.) b) After many (approaching infinity) battles, what is the steady-state probability distribution of Kecleon's type? (Your answer should be three numbers that sum to one.) A nearby graveyard is haunted! Ghost-type Pokemon invade the population. Assume that Ghost Pokémon always lose to Dark Pokémon, and always win against Psychic Pokémon and Fighting Pokémon. c) Suppose that Kecleon starts as the Fighting type when the Ghost Pokémon arrive. After two battles, what is the probability distribution of Kecleon's type? (Your answer should be four numbers that sum to one.) d) After many (approaching infinity) battles, what is the steady-state probability distribution of Kecleon's type? (Your answer should be four numbers that sum to one.)"--

The probability that the average number of months since the last examination in a sample of 150 patients is 14 or larger is practically 0, which means it is highly unlikely to occur by chance.

Now that we know the mean and standard deviation of the distribution of the sample mean, we can standardize the variable using the standard normal distribution formula:

Z = (x - μ) / (σ/√n)

where Z is the standard normal variable, x is the sample mean, μ is the population mean, σ is the population standard deviation, and n is the sample size.

Substituting the values we obtained, we get:

Z = (14 - 12) / (0.237)

Z = 8.43

To find the probability that the sample mean is 14 or larger, we need to find the area under the standard normal distribution curve to the right of Z = 8.43.

This can be done using a standard normal distribution table or a calculator. The probability turns out to be practically 0.

To know more about average here

https://brainly.com/question/16956746

#SPJ4

We can conclude after answering the provided question that Therefore, expression the final answer is [tex]-2x^3 + x + 1.[/tex]

An expression in mathematics is a collection of representations, digits, and transnational corporations that depict a significant correlation or regimen. A real number, a mutable, or a combo of the two can be used as an expression. Mathematical operators include addition, subtraction, rapid spread, polarisation, and exponentiation. Arithmetic, arithmetic, and shape all make full use of manifestations. They are used in the representation of mathematical formulas, the solution of equations, and the simplification of mathematical relationships.

[tex]1/x - 1 = (1 - x)/x\\1/x + 1 = (1 + x)/x\\(x^2 - 1) [(1 - x)/x - (1 + x)/x + 1]\\(x^2 - 1) [(-2x)/x + 1]\\(x^2 - 1) (1 - 2x)\\x^2 - 2x^3 - 1 + 2x\\-2x^3 + x + 1\\[/tex]

Therefore, the final answer is [tex]-2x^3 + x + 1.[/tex]

To know more about expression visit :-

https://brainly.com/question/14083225

#SPJ1

Answer:

It earned $60 in interest

Step-by-step explanation:

The statements that describe the graph of f function are A) Asx → ∞, f(x) → -4 and C) The y-intercept is (0, -3).

Let's analyze the given function:

f(x) = 9(1/3)ˣ⁺² - 4

Now, let's analyze the properties of the graph:

A) As x → ∞, f(x) → -4.

As x → ∞, the exponential term ((1/3)ˣ⁺²) approaches 0, so f(x) = 9(0) - 4 = -4. This statement is correct.

B) As x → -∞, f(x) → -∞.

As x → -∞, the exponential term (1/3)ˣ⁺² approaches ∞, so f(x) = 9(∞) - 4 → ∞, not -∞. This statement is incorrect.

C) The y-intercept is (0, -3).

To find the y-intercept, we can plug x = 0 into the function:

f(0) = 9(1/3)ˣ⁺² - 4 = 9(1/9) - 4 = 1 - 4 = -3

The y-intercept is (0, -3), so this statement is correct.

D) The domain is {x | x > -2}

This is incorrect. The domain of the given function is all real numbers because there is no restriction on the value of x.

E) The range is the set of real numbers.

This is incorrect. The range of the given function is {y | y > -4} since the function approaches -4 as x goes to ∞, but never reaches -4, and it increases as x goes to -∞.

Learn more on graph functions here: https://brainly.com/question/29115560

#SPJ1

Image transcribed:

Identify the statements which describe the graph of f(x) = 9(1/3)ˣ⁺² - 4.

Select all that apply.

A) Asx → ∞, f(x) → -4.

B) Asx → -∞, f(x) →-∞.

C) The y-intercept is (0, -3).

D) The domain is {xlx > -2}

E) The range is the set of real numbers.

Answer: 1. 37.5%,

Step-by-step explanation:

1. we can solve this using a proportion, 10/13.75 = 100/x

a. using cross multiplication we get 10x = 1375

b. when you simplify you get x= 137.5, the percent it was of the whole

c. then subtract the original 137.5-100, and you get 37.5%

The rest of the problems follow a similar fashion

15 is the distance of the equation of a line passing through the points.

What is distance ?

Distance is the separation between two objects. Moreover, it serves as a gauge for the distance between two objects. It is measurable along any route. So even though his position does not change, a person who circles about has moved a certain amount of distance.

the points (4,-3) and (16, 6)

D = √(x₂ - x₁)² + (y₂ - y₁)²

     = √(16 - 4)² + (6 -(-3)²

     = √(12)² + (9)²

      = √144 + 81

       = √225

       = 15

Learn more about distance

brainly.com/question/15172156

#SPJ1

Answer:

tesla: y = 25x + 50

acdc: y = 50x

Step-by-step explanation:

(D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.

Dilation means changing the size of an object without changing its shape.

The size of the object can be increased or decreased based on the scaling factor.

In mathematics, a dilation is a function f from a metric space M to itself that satisfies the identity d = rd for every point x,y \ in M.

Where d is the distance from x to y and r is a positive real number. In Euclidean space, such extensions are spatial similarities.

So, stretching from the origin is the same as multiplying all coordinates by a number.

Only D satisfies this. We know that we multiply all the coordinates by 3 to create this set of points.

Therefore, (D) R’(3, 3), S’(9, 24), and T’(15, 3) set of points represents a dilation from the origin of triangle RST respectively.

Know more about dilation here:

https://brainly.com/question/3457976

#SPJ1

Complete question:

Triangle RST has the coordinates R(1, 1), S(3, 8), and T(5, 1). Which of the following sets of points represents a dilation from the origin of triangle RST?

A. R’(3, 1), S’(3, 24), T’(15, 1)

B. R’(4, 4), S’(6, 11), T’(8, 4)

C. R’(3, 1), S’(9, 8), T’(15, 1)

D. R’(3, 3), S’(9, 24), T’(15, 3)

The value of a₅ is 688. The problem provides us with a recursive formula that relates each term of the sequence to the previous term.

We can use this formula to find the value of any term in the sequence, given the value of the previous term.

The recursive formula is:

aₙ = -3aₙ₋₁ - 2

This formula tells us that to find the value of aₙ, we need to take the previous term aₙ₋₁, multiply it by -3, and then subtract 2.

The problem also provides us with the value of the first term a₁, which is 8. Using the recursive formula, we can find the value of the second term a₂:

a₂ = -3a₁ - 2 = -3(8) - 2 = -26

We can repeat this process to find the value of the third term a₃:

a₃ = -3a₂ - 2 = -3(-26) - 2 = 76

Continuing in this manner, we can find the values of a₄ and a₅:

a₄ = -3a₃ - 2 = -3(76) - 2 = -230

a₅ = -3a₄ - 2 = -3(-230) - 2 = 688

Therefore, the value of a₅ is 688.

To learn more about recursive please click on below link.

https://brainly.com/question/30027987

#SPJ1

If a₁ = 8 and aₙ = -3aₙ₋₁ - 2, then what is the value of a₅?

Unit rate of commercials per hour is 12 commercials per hour based on division in mathematics.

We must divide the number of ads by the number of hours in order to determine the unit rate of commercials per hour.

Wendy watched her favourite television programmes for an hour or an hour and a half. There were 18 advertisements running at this time.

So, the unit rate of commercials per hour can be calculated as:

18 commercials ÷ 1.5 hours = 12 commercials per hour

So, it is possible to compute the number of ads each hour as follows: 18 commercials divided by 1.5 hours equals 12 commercials every hour.

Consequently, 12 commercials are broadcast each hour as the unit rate of commercials.

This indicates that while viewing her favorite television programes, Wendy saw 12 adverts every hour on average.

It's crucial to remember that unit rate come in handy when comparing two quantities that are measured using various units. In this instance, we were comparing two different units of measurement: the quantity of advertising and the amount of time in hours. By providing the rate at which the quantity is changing per unit of time, the unit rate enables us to meaningfully compare them.

Learn more about unit rate here:

https://brainly.com/question/14607658

#SPJ4

The required perimeter of the given figure is 68 units.

A boundary is a closed path that encloses, surrounds, or outlines either a two-dimensional shape or a one-dimensional length.

The circumference of a circle or ellipse is called the perimeter.

Perimeter calculations have several practical applications.

Perimeter is the distance around the object.

For example, your house has a fenced garden.

The perimeter is the length of the fence.

If the yard is 50 feet by 50 feet, the fence length will be 200 feet.

So, the perimeter of the given figure:

= 10 + 4 + 2 + 12 + 6 + 6 + 6 + 2 + 12 + 4 + 4

= 68 units

Therefore, the required perimeter of the given figure is 68 units.

Know more about the perimeter here:
https://brainly.com/question/19819849

#SPJ1

Complete question:

Use the figure below to answer the following questions. NOT TO SCALE!

10

12

POSSIBLE POINTS A

Give the perimeter of the figure.

Answer: Correct me if I'm wrong but it should be about 1/4th of a meter

The value of x in the right triangle is  4√2 units.

Similar triangles are the triangles that have corresponding sides in ratio to each other and corresponding angles congruent to each other.

Therefore, the triangles are similar. Let's use this similarity to find the value of x in the triangles.

Hence, using proportion,

x / 8 = 4 / x

cross multiply

x² = 8 × 4

x² = 32

square root both sides of the equation

x = √32

x = √16 × 2

x = 4√2 units

learn more on similar triangles here: brainly.com/question/28966438

#SPJ1

James will be flying a total of 85,680 miles in the next year.

To find out how many miles James will be flying in the next year, we need to multiply the distance of one round trip by the number of round trips he will make in a year.

The distance of one round trip is twice the one-way distance, so:

2 x 2,856 miles = 5,712 miles per round trip

Since James will make 15 round trips in a year, we can multiply the distance of one round trip by 15:

5,712 miles/round trip x 15 round trips = 85,680 miles

Therefore, James will be flying a total of 85,680 miles in the next year.
To know more about miles go through:-
https://brainly.com/question/29806974
#SPJ9