Find the value of x.
13)
O
(2x+8)
62°
20 22 Kuta Software LLC.
14)
A
(x-4) (2x+1)
All rights reserve d-1-Made with Infinite Geometry.

The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other.

The inverse of a function is a second function that "undoes" the effect of the first function. More specifically, if f is a function that maps elements from a set A to a set B, then its inverse function, denoted as f^(-1), maps elements from B back to A.

(a) To find f(g(x)), we need to substitute the expression for g(x) into f(x):

f(g(x)) = g(x) / (6 + g(x))

Substituting the expression for g(x) yields:

f(g(x)) = (6x / (1 - x)) / (6 + (6x / (1 - x)))

This equation can be made simpler by first locating a common denominator:

f(g(x)) = (6x / (1 - x)) / ((6(1 - x) / (1 - x)) + (6x / (1 - x)))

f(g(x)) = (6x / (1 - x)) / ((6 - 6x + 6x) / (1 - x))

f(g(x)) = (6x / (1 - x)) / (6 / (1 - x))

f(g(x)) = 6x / 6

f(g(x)) = x

To find g(f(x)), we need to substitute the expression for f(x) into g(x):

g(f(x)) = 6f(x) / (1 - f(x))

Substituting the expression for f(x) yields:

g(f(x)) = 6(x / (6 + x)) / (1 - (x / (6 + x)))

To simplify this expression, we can first find a common denominator:

g(f(x)) = 6(x / (6 + x)) / (((6 + x) / (6 + x)) - (x / (6 + x)))

g(f(x)) = 6(x / (6 + x)) / ((6 + x - x) / (6 + x))

g(f(x)) = 6(x / (6 + x)) / (6 / (6 + x))

g(f(x)) = x

(b) The answers f(g(x)) = x and g(f(x)) = x tell us that the two functions f(x) and g(x) are inverses of each other. This means that when we apply one function and then the other, we get back to the original input value. Specifically, if we apply f(x) to x and then apply g(x) to the result, we get x back, and if we apply g(x) to x and then apply f(x) to the result, we also get x back. This is a useful property when analyzing functions and their relationships.

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Answer:

To find the volume of Leah's new planter, we need to multiply the length, width, and height of the container:

V = 15 m x 4 m x 8 m x 11 m x 3 m

V = 11,880 cubic meters

Therefore, the total volume of Leah's new planter is 11,880 cubic meters.

Let's represent the volume of the large box as x cubic inches. Since the total volume of both boxes is 212 cubic inches, we can set up the following equation:

8 x 4 x 2 + x = 212

Simplifying the left side, we get:

64 + x = 212

Subtracting 64 from both sides, we get:

x = 148

Therefore, the volume of the large box is 148 cubic inches.

Para preparar un pastel, Anita tenía un paquete de harina de 1 1/3 kg:  0.83 kg

Primero, debemos convertir 1 1/3 kg a una fracción común. 1 1/3 kg es igual a 4/3 kg o 1.33 kg. Luego, podemos simplificar 3/6 a 1/2.
Ahora podemos restar 1/2 de 1.33 kg para encontrar la cantidad de harina que sobró.
1.33 kg - 1/2 kg = 1.33 kg - 0.5 kg = 0.83 kg
Entonces, Anita le sobró aproximadamente 0.83 kg de harina después de preparar su pastel.
Es importante recordar que la medición y las cantidades de los ingredientes son cruciales al preparar cualquier receta de cocina. Es importante seguir las instrucciones cuidadosamente para obtener resultados exitosos en la cocina.

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We can now prove that ∆GFE≈∆GCD by using the Transitive Property of Equality and Substitution. Since GF=EF and GC=DC, then ∆GFE≈∆GCD.

The transitive property of equality states that if two numbers are equal to the same number, then they are equal to each other. This property is written mathematically as a = b and b = c, then a = c. This property is based on the idea of transitivity, which is the concept that if a thing is true of a first element, and the same thing is true of a second element, then it must be true of the combination of the two elements.

We will use the Transitive Property of Equality and Substitution to prove that ∆GFE≈∆GCD.

Step 1: Transitive Property of Equality

GF/GC=GE/GD (Given)

GE/GD=EF/DC (Given)

GF/GC=EF/DC

Step 2: Substitution

GF=1/2GC (Given)

GE=1/2GD (Given)

EF=1/2DC (Given)

GF=EF (Substituting the given values)

GC=DC (Substituting the given values)

Step 3: Prove

We can now prove that ∆GFE≈∆GCD by using the Transitive Property of Equality and Substitution.

Since GF=EF and GC=DC, then ∆GFE≈∆GCD.

Therefore, ∆GFE≈∆GCD is true.

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The balance of the savings plan after 4 years with an APR of 8% and monthly payments of $150 is approximately $7,456.76.

As a result, the savings plan formula for such challenges is as follows: final saving = number of periods * (first and last period savings) / 2.

To calculate the balance of the savings plan after four years, we can use the formula for the future value of an annuity with regular payments:

P * ((1 + r/n)(n*t) - 1) / (r/n)

Where P is the monthly payment amount, which is $150.

r = 8% annual interest rate

n = the number of times annual interest is compounded = 12 (since we have monthly payments)

4 t = the number of years

We get the following results when we plug these values into the formula:

FV = 150 * ((1 + 0.08/12)^(12*4) - 1) / (0.08/12) ≈ $7,456.76

As a result, the savings plan balance after four years with an APR of 8% and monthly payments of $150 is approximately $7,456.76.

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Answer:

3/10 = 0.3

19/50 = 0.38

5/10 = 0.5

1/5 = 0.2

14/25 = 0.56

3/25 = 0.12

The solutions to the quadratic equations are as follows

4a. The rocket was launched from an initial height of 10 meters.

b. The maximum height of the rocket was 55 meters.

c. The rocket reaches its maximum height at 3 seconds

d. the rocket is in the air for t = 6.316 seconds

5. when the horizontal distance is 1 foot, the height of the balloon is 8.875 feet

b. when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet.

The function is a quadratic equation, and here is how we solve each problem;

a. The initial height of the rocket is the value of h when t=0. So we substitute t=0 into the equation to find:

h = -5(0)² + 30(0) + 10 = 10 meters

b. & c. The maximum height of a projectile launched upward occurs at the vertex of the parabola represented by the quadratic function. For a quadratic function in the form y = ax² + bx + c, the time at which the maximum (or minimum) occurs is -b/2a. In this case, a = -5 and b = 30. So:

t = -b/2a = -30 / (2×-5) = 3 seconds

So, the rocket reaches its maximum height at t=3 seconds. We can find this maximum height by substituting t=3 into the equation:

h = -5(3)² + 30(3) + 10 = -5×9 + 90 + 10 = 45 meters

The rocket is in the air from the time it was launched until it hits the ground. The time when it hits the ground is when h = 0. So we can set the equation to 0 and solve for t:

0 = -5t² + 30t + 10

This is a quadratic equation and can be solved using the quadratic formula: t = [-b ± √(b² - 4ac)] / (2a)

Let's calculate the roots:

t = [-30 ± √((30)² - 4×-5×10)] / (2×-5)

= [-30 ± √(900 + 200)] / -10

= [-30 ± √(1100)] / -10

= 6.316 or -0.32

5. a. To find the height of the balloon when d=1, we substitute d=1 into the equation:

h = -1/8(1)²+ 4(1) + 5 = -1/8 + 4 + 5 = 8.875 feet

b. To determine whether the balloon hits your enemy, we need to see if the balloon's height (h) is above ground level (h > 0) when d=33. So, we substitute d=33 into the equation:

h = -1/8(33)² + 4(33) + 5

h = -1/8×1089 + 132 + 5

h = -136.125 + 132 + 5

h = 0.875 feet

when the horizontal distance is 33 feet, the height of the balloon is 0.875 feet. This means the balloon is above ground level and therefore would indeed hit your nemesis standing 33 feet away.

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The value οf the variable y is 9 when k is -3 in the given question.

In mathematics and statistics, a variable is a quantity οr a characteristic that can take οn different values οr attributes. Variables can be classified as either quantitative οr categοrical, depending οn the type οf data they represent.

A quantitative variable is a variable that represents a numerical measurement οr quantity. Examples οf quantitative variables include height, weight, temperature, and incοme.

A categοrical variable is a variable that represents a grοup οr categοry. Examples οf categοrical variables include gender, race, and type οf car.

Given: y=k x

where, x= -3 and k= -3

we can find the value of y by multiplying k with x,

so, y=k x

now, putting values as follows:

we get, y = -3 × -3

               = 9

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Answer: The running club can buy 25 uniforms

Step-by-step explanation: If the running club has $1,328 to spend on new uniforms and each uniform costs $52, we can find the number of uniforms they can buy by dividing the total amount of money by the cost of each uniform:

$1,328 ÷ $52 = 25.54

Therefore, the running club can buy 25 uniforms with $1,328.

I hope this helps, and have a great day!

Peter is 1.68 meters tall.

What is height?

Height is a measure of the distance between the base and the top of an object, or the distance between the bottom and the top of a vertical structure. It is often used to describe the vertical dimension of an object or structure, such as the height of a building, the height of a person, or the height of a mountain. In mathematics, height can also refer to the vertical distance between two points on a coordinate plane or the vertical dimension of a three-dimensional shape. The height of a triangle, for example, is the perpendicular distance from the base to the highest point of the triangle.

Peter's height is Thandi's height plus the additional 0.45 m. Therefore:

Peter's height = Thandi's height + 0.45 m

Peter's height = 1.23 m + 0.45 m

Peter's height = 1.68 m

Therefore, Peter is 1.68 meters tall.

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Answer:

f(-x) = 8^-x

Step-by-step explanation:

Answer:

9 seconds

Step-by-step explanation:

right side of the graph touches the x axis at 9

Answer:

$16

Step-by-step explanation:

12C + 28 = 22012C = 220 - 2812C = 192C = 192÷12C = 16

sincerely, answered by luhvlii ♡ :: as an A+ student, I want to make sure other students can succeed as well, so in my free time: i answer questions like yours on Brainly! if you could click the thanks heart, give me brainliest by clicking the crown, and rate my answer 5 stars, it would be appreciated! have a luhvlii day (ᵔᴥᵔ)

Answer: how many places are you looking for? because it would be around 599.696332...(and more decimal numbers)

you get this from dividing 1884 by 3.14159 (pi)

We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

The mean is a measure of central tendency that represents the average value of a set of numbers. It is also called the arithmetic mean or simply the average.

We cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

The mean and the median are two different measures of central tendency, and they can have different values depending on the distribution of the data. In general, if a data set is symmetric and bell-shaped, the mean and the median are close to each other. However, if the data set is skewed, the mean and the median may be different.

For example, consider the following two data sets:

Set 1 data: 1, 2, 3, 4, and 5.

The median is 3.

The mean is (1 + 2 + 3 + 4 + 5) / 5 = 15 / 5 = 3.

Data set 2: 1, 2, 3, 4, 10

The median is 3.

The mean is (1 + 2 + 3 + 4 + 10) / 5 = 20 / 5 = 4.

In data set 1, the mean is the same as the median. In data set 2, the mean is greater than the median because the value 10 is an outlier that pulls the mean up.

Therefore, without additional information about the distribution of the data, we cannot make a general assumption about whether the mean is greater or less than 3.5 based solely on the fact that the median is 3.5.

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Answer:

a) To find the probability that a randomly chosen student completes the activity in less than 30.1 seconds, we need to standardize the value using the formula z = (x - mu) / sigma, where x is the time taken, mu is the mean, sigma is the standard deviation, and z is the standard normal variable.

z = (30.1 - 34.7) / 7.6 = -0.6053

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being less than -0.6053 is 0.2739.

Therefore, the probability that a randomly chosen student completes the activity in less than 30.1 seconds is 0.2739.

b) To find the probability that a randomly chosen student completes the activity in more than 38.1 seconds, we need to standardize the value using the same formula.

z = (38.1 - 34.7) / 7.6 = 0.4474

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being greater than 0.4474 is 0.3274.

Therefore, the probability that a randomly chosen student completes the activity in more than 38.1 seconds is 0.3274.

c) To find the proportion of students taking between 30.9 and 38.5 seconds, we need to standardize both values and then find the area between them in the standard normal distribution.

z1 = (30.9 - 34.7) / 7.6 = -0.5

z2 = (38.5 - 34.7) / 7.6 = 0.5

Using a standard normal distribution table or calculator, we find that the probability of a standard normal variable being between -0.5 and 0.5 is 0.3830.

Therefore, the proportion of students taking between 30.9 and 38.5 seconds to complete the activity is 0.3830.

d) To find the time taken by 90% of all students to finish the activity, we need to find the z-value corresponding to the 90th percentile of the standard normal distribution using a standard normal distribution table or calculator.

The z-value corresponding to the 90th percentile is approximately 1.28.

Now, we can use the formula z = (x - mu) / sigma to find the corresponding time value.

1.28 = (x - 34.7) / 7.6

x - 34.7 = 1.28 * 7.6

x - 34.7 = 9.728

x = 44.428

Therefore, 90% of all students finish the activity in less than 44.428 seconds.

the correct option for this question is  (a) e < 53.

Why it is?

The inequality that represents Natasha's earnings, e, from any of the companies she interviewed with is:

e < 53.5

This is because her projected earnings per hour range from $25.13 to $53.5, and the maximum value is $53.5. So, her earnings from any of the companies cannot be greater than $53.5 per hour. Therefore, the correct answer is option (a) e < 53.

Earnings are the amount of money that a person earns from their work, business, investments, or other sources of income. This can include salaries, wages, commissions, bonuses, and profits, among others.

Earnings are typically reported as gross income, which is the total amount earned before taxes and other deductions are taken out. It is an important measure of a person's financial well-being and is often used to determine eligibility for credit or loans. Earnings can vary widely depending on a person's job, level of experience, education, and industry, among other factors.

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Answer:

Step-by-step explanation:

We can solve this question by applying the Pythagorean theorem to the triangle (a^2+b^2=c^2). The Pythagorean theorem states that if the two shorter lengths are both squared and added the sum of those two numbers should be equal to the longest side squared. So 6 and 8 are the shorter sides of this triangle so we can plug either one in for either a or b, 6^2+8^2=9^2. Once you do that you have to square each individual number. You should get 36+64=81

36+64 is 100 and 100 does not equal 81 therefore this triangle is not a right triangle.

Answer:

Step-by-step explanation:

If a² + b² > c² , the triangle is acute,  

If a² + b² = c² , the triangle is a right triangle,

If a² + b² > c² , the triangle is obtuse,  

where "a" and "b" are the lengths of the 2 shorter sides of the triangle and "c" is the length of the longest side.

~~~~~~~~~~~~~

6² + 8² > 9² ⇒ given triangle is acute

The mathematical expression to be evaluated is:

[tex]2 \frac{3}{6} - \frac{1}{3}[/tex]

To simplify the expression, we first convert the mixed fraction to an improper fraction:

[tex]2 \frac{3}{6} = \frac{(2 \times 6) + 3}{6} = \frac{15}{6}[/tex]

Substituting this value back into the original expression, we get:

[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{15}{6} - \frac{1}{3}[/tex]

Now we need to find a common denominator for the two fractions:

[tex]\frac{15}{6} - \frac{1}{3} = \frac{15}{6} \times \frac{2}{2} - \frac{1}{3} \times \frac{2}{2} = \frac{30}{12} - \frac{2}{6}[/tex]

We can simplify the second fraction:

[tex]\frac{30}{12} - \frac{2}{6} = \frac{30}{12} - \frac{4}{12} = \frac{26}{12}[/tex]

Finally, we can simplify the fraction by dividing both the numerator and denominator by their greatest common factor, which is 2:

[tex]\frac{26}{12} = \frac{13}{6}[/tex]

Therefore, the simplified value of the mathematical expression is:

[tex]2 \frac{3}{6} - \frac{1}{3} = \frac{13}{6}[/tex]

Answer:

[tex]2\frac{1}{6}[/tex]

Step-by-step explanation:

First, write the fractions as improper fractions.

[tex]\sf2\frac{3}{6} -\frac{1}{3} \\\\\sf\frac{15}{6} -\frac{1}{3}[/tex]

To, subtract the fractions make the denominators the same.

For that, multiply both sides of 1/3 by 2.

[tex]\sf\frac{15}{6} -\frac{1*2}{3*2} \\\\\sf\frac{15}{6} -\frac{2}{6}[/tex]

Subtract.

[tex]\frac{13}{6}[/tex]

Write it as a mixed number.

[tex]2\frac{1}{6}[/tex]

Answer: 1.2 pounds of raisins

Step-by-step explanation:

If six pounds of raisins are distributed equally into five bags, then each bag will have an equal amount of raisins. To find out how many pounds of raisins are in each bag, we can divide the total amount of raisins by the number of bags:

6 pounds ÷ 5 bags = 1.2 pounds per bag

Therefore, each bag will have 1.2 pounds of raisins.

Answer:

we will do TanA = perpendicular / Base

A = 35°

Tan 35° = 217 / W

value of Tan 35° is approx = 0.7

0.7 = 217/ W

W = 217 / 0.7

W = 310

Answer:

9 Boys

Step-by-step explanation:

As we Know, 12 ÷ 4 is 3

3 x 3 is 9

therefore, it's 9

the other two angles of the triangle must also be equal, which means that the other two sides of the triangle must be equal as well. the length of the shorter sides is [tex]y = 16 feet[/tex] .

Let's start by using the information given to write equations for the perimeter of the heptagon in terms of the length of the sides:

Let x be the length of the four equal sides, and y be the length of the remaining three sides, which are half as long. Then, we have:

Perimeter  [tex]= 4x + 3y[/tex]

We also know that the perimeter is 88 feet, so we can set up the equation:

[tex]4x + 3y = 88[/tex]

Now we need to solve for y, which represents the length of the shorter sides.

We can simplify the equation by substituting y = (1/2)x:

[tex]4x + 3(1/2)x = 88[/tex]

Simplifying this expression, we get:

[tex]7x/2 = 88[/tex]

Multiplying both sides by 2/7, we get:

[tex]x = 32[/tex]

Now that we know x, we can find y by substituting it into the equation y   [tex]= (1/2)x[/tex]:

[tex]y = (1/2)(32) = 16[/tex]

Therefore, the length of the shorter sides is  [tex]y = 16[/tex] feet.

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The maximum height οf the rοcket is 16 feet.

A system οf equatiοns in algebra is made up οf twο οr mοre equatiοns that are sοlved tοgether. "A grοup οf equatiοns satisfied by the same set οf variables are called a system οf linear equatiοns. Finding the values οf the variables emplοyed in the system οf equatiοns is the first step tοwards sοlving it.

While maintaining the balance οf the equatiοns οn bοth sides, we cοmpute the values οf the unknοwn variables. Finding a variable whοse value makes the cοnditiοn οf all the given equatiοns true is the primary gοal οf sοlving an equatiοn system.

(x - 2)(x - 5) = 0

Sο x = 2 οr x = 5.

If x = 2, then frοm the equatiοn οf the flare, we have y = -2 + 14 = 12.

If x = 5, then frοm the equatiοn οf the flare, we have y = -5 + 14 = 9.

Sο the twο οbjects intersect at the pοints (2, 12) and (5, 9).

Tο find the maximum height οf the rοcket, we can use the fοrmula fοr the x-cοοrdinate οf the vertex οf a parabοla:

x = -b/2a

In this case, a = -1 and b = 8, sο we have:

x = -8/-2 = 4

Sο the rοcket reaches its maximum height at x = 4. Tο find the maximum height, we can substitute x = 4 intο the equatiοn fοr the rοcket:

[tex]y = -4^2 + 8(4) = 16[/tex]

Sο the maximum height οf the rοcket is 16 feet.

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The formula for the future value of an annuity is FV = Pmt * (((1 + r)n - 1) / r) to calculate the balance of the IRA at age 65. To compare this amount to the total deposits made over the time period, Total Deposits = Pmt * n = $45,600.

To calculate the balance of the IRA at age 65, we need to use the formula for the future value of an annuity:

FV = Pmt * (([tex](1 + r)^n[/tex] - 1) / r)

Where:

Pmt = $95 (the monthly deposit amount)

r = 4% / 12 = 0.003333 (the monthly interest rate)

n = (65 - 25) * 12 = 480 (the total number of months, assuming retirement at age 65)

Plugging in these values, we get:

FV = 95 * (([tex](1 + 0.003333)^480[/tex] - 1) / 0.003333)

FV = $98,052.52

Therefore, the IRA will contain $98,052.52 at age 65.

Part 2

To compare this amount to the total deposits made over the time period, we can calculate the total deposits as:

Total Deposits = Pmt * n

Plugging in the values, we get:

Total Deposits = 95 * 480

Total Deposits = $45,600

Therefore, the IRA will contain significantly more than the total deposits made over the time period, due to the power of compounding interest.

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The estimated value of cos(48) by using tangent line is found to be

0.99989.

A straight line which thus touches a function only once is called a tangent line.

The first step is to calculate y when x=π/4. We will receive that target coordinate point as a result.

The required coordinate point is ( π/ 4, √(2) / 2)

The derivative of such function y is then discovered.

y ' = -sin(x)

Input the derivative with the value of x. This corresponds to the tangent line's slope.

y' = -sin(π/4)

y' = - √(2) / 2

The slope plus coordinate point are now entered into the gradient intercept form of the formula to obtain b.

y = mx + b

√(2) / 2 = (-√(2) / 2)(π / 4) + b

√(2) / 2 = (-π√(2) / 8) + b

(√(2) / 2) + (π√(2) / 8) = b

[4√(2) + π√(2)] / 8 = b

[(4 + π)√(2)] / 8 = b

The tangent line comes out to be:

y = (-√(2) / 2)x + [(4 + π)√(2) / 8]

Now , for cos(48).

48° = π/180 * 48 radians

48° = 3.14/180 * 48  radians

48° = 0.01744*48 radians

48° = 0.83712 radians

So,  cos(48) =  cos(  0.83712 )

Using scientific calculator:

cos(48) =  cos(  0.83712 )  = 0.99989

Thus, the estimated value of cos(48) by using tangent line is found to be

0.99989.

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Answer:

4/9

Step-by-step explanation:

4 sandwiches in between 9 friends

4 sandwiches must be divided in between 9 people

- > [tex]\frac{4 sandwiches}{9 people}[/tex] = [tex]\frac{4}{9}[/tex]

Answer:

Step-by-step explanation:

2/3

Answer:

12.29 I thin

Step-by-step explanation:

The monthly periodic interest rate is 0.01%.

Simple interest is a method of calculating the interest charge. Simple interest can be calculated as the product of principal amount, rate and time period.

Simple Interest = (Principal × Rate × Time) / 100

We are given that;

APR=14.75%

Now,

The monthly periodic interest rate is the annual interest rate divided by 12 months. According to 1, the formula is:

r = (1 + i/m)^(m/n) - 1

Where:

r = periodic interest rate

i = nominal annual rate

m = number of compounding periods per year

n = number of payments per year

In this case, i = 14.75%, m = 12 and n = 12. Plugging these values into the formula, we get:

r = (1 + 0.1475/12)^(12/12) - 1

r = (1 + 0.012292) - 1

r = 0.012292 or 1.23%

Therefore, by the given APR the interest rate will be 0.01%, rounded to the nearest hundredth of a percent.

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The survey results, it can be estimated that approximately 17.93% of adult Americans have seen a ghost at some point in their lives[tex] (718/4,005 = 0.1793)[/tex].

However, it is important to note that this estimate is based on a sample and there may be some degree of error or variability.

Additionally, the term "supernatural experiences" may encompass a wide range of phenomena beyond just seeing ghosts, so the estimate may not accurately reflect the prevalence of all types of supernatural experiences in the population.

In the given survey on supernatural experiences, 718 out of 4,005 adult Americans reported having seen a ghost. Assuming this sample is representative of the adult American population, you can calculate the proportion of adults who have seen a ghost.

for such more questions on variability.

https://brainly.com/question/3321375

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