Find the exact value of x.

The inverse of the function f(x) = 3 · x / (8 + x) is f⁻¹(x) = 8 · x / (3 - x).

In this problem we must determine the inverse of a function, this can be done by means of algebra properties. First, write the entire function:

f(x) = 3 · x / (8 + x) (Step 0)

y = 3 · x / (8 + x) (Step 1)

Second, use the following substitutions:

x → y

y → x

x = 3 · y / (8 + y) (Step 2)

Third, clear y within the expression:

x · (8 + y) = 3 · y (Step 3)

8 · x + x · y = 3 · y

8 · x = 3 · y - x · y (Step 4)

8 · x = y · (3 - x)

y = 8 · x / (3 - x)

Fourth, use final notation:

f⁻¹(x) = 8 · x / (3 - x) (Step 5)

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Answer:  x = -3/2

Step-by-step explanation:

Answer:

A=60

B=27

Step-by-step explanation:

D x = 7.8

√7.82

E y = 11.1

√11.12

F x = 5.1

√5.12

G y = 24.3

√24.32

H x = 9.1

√9.12

I y = 15.4

√15.42

J x = 13.7

√13.72

K y = 20.2

√20.22

L x = 11.9

√11.92

M y = 18.3

√18.32

N x = 21

√21

O y = 17.5

√17.52

The system of linear equations has no solutions.

Here we want to solve the system of linear equations:

2x-  2y = 7

-x + y = -2

One could easily identify that the two lines are parallel, but let's prove it. To do so, we can multiply the second equation by -2.

Then we will get:

-2*(-x + y) = -2*-2

2x - 2y = 4

Then the system of equations is:

2x-  2y = 7

2x - 2y = 4

The coefficients in the left side are the same ones and the constants in the right side are different. Thus, the lines are parallel, and thus, the system has no solutions.

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well, let's first find out how much is 30% of 30000

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{30\% of 30000}}{\left( \cfrac{30}{100} \right)30000}\implies 9000[/tex]

ok, that means if we split that down the middle, each will get 4500.

so the remaining is 21000, and that's split on a 3:4 ratio, assuming from A to B, so let's simply divide the total 21000 by (3 + 4) and distribute accordingly.

[tex]\stackrel{A}{3}~~ : ~~\stackrel{B}{4} ~~ \implies ~~ \stackrel{A}{3\cdot \frac{21000}{3+4}}~~ : ~~\stackrel{B}{4\cdot \frac{21000}{3+4}}\implies \stackrel{A}{3\cdot 3000}~~ : ~~\stackrel{B}{4\cdot 3000} \\\\\\ \stackrel{A}{9000}~~ : ~~\stackrel{B}{12000}\hspace{9em}\underset{ \textit{share for A} }{\stackrel{ 4500~~ + ~~9000 }{\text{\LARGE 13500}}}[/tex]

The correct mathematical expression to find the number of tiles needed to surround a square pool would depend on how the tiles are arranged and how the dimensions of the pool and the tiles are related.

4(s+1): This expression appears to be correct if we assume that each side of the square pool is surrounded by a row of tiles, and each corner requires an additional tile.

So, the expression can be simplified to 4s+4. This is a valid expression for the number of tiles needed to surround the pool.

s²: This expression does not appear to be correct, as it only gives the area of the square pool, and does not take into account the dimensions of the tiles or the need to surround the pool.

4s+4: This expression is the same as the first expression, 4(s+1), and is a valid expression for the number of tiles needed to surround the pool.

2s+2(s+2): This expression appears to be incorrect, as it gives the total perimeter of the pool plus an additional 4 units, but does not take into account the size of the tiles or the need to surround the pool.

4s: This expression is incorrect, as it only gives the perimeter of the pool and does not take into account the need to surround the pool with tiles.

Thus, two of the given expressions (4(s+1) and 4s+4) are correct, one expression (s²) is incomplete, and two expressions (2s+2(s+2) and 4s) are incorrect.

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The equation of the ellipse is y² = 35 (1 - x²)

The given ellipse has vertices at ( 0, -6) and ( 0 , 6), which lie on the  y - axis.

The distance between the centr of the ellipse (which also lies on the y -  axis) and each vertex is 6 units. So since we hve

c = 6

and the eccentricity of the ellipse is also given as   e = 6

we can use the r elationship between e, a, and c to find the value of a....

e = c/a

6 = 6/a

a = 1

Using the value of A and C, we  find the equation of the ellipse, we can use the standard form

( x² / a²) + (y² / b²)    = 1

Since the center of the ellipse is at the origin,    know that

x / a² + y² / b  ² = 1

Substituting a and c, ......

x² / 1² + y² / b² = 1

y² / b² = 1 - x²

y² = b² (1 - x²)

We need to find the value of b. We know that the distance between the center and each co-vertex of the ellipse is 5 units. So we state this as

b² = c² - a²

 b² = 6² - 1 ²

b² = 35

Substituting the value of b² in the equation we got earlier, we get

y² = 35(  1 - x²)

Therefore, the equation of the ellipse is:

y² = 35 (1 - x² )

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a household with a credit score of 525 would pay $4,280.82 more than a household with a credit score of 675 for a principal balance of $8,000.

what is principal balance ?

Principal balance refers to the amount of money that you still owe on a loan or debt, not including any interest or fees that have accrued. When you make a payment towards your loan or debt, a portion of the payment goes towards paying down the principal balance,

In the given question,

To calculate the difference in payment between a household with a credit score of 525 and one with a score of 675, we need to compare the total amount paid for each score range.

For a principal balance of $8,000, based on the given information:

A household with a credit score of 525 would have a simple interest rate of 28%, and would make 60 payments of $249.08 each, for a total amount paid of $14,945.00.

A household with a credit score of 675 would have a simple interest rate of 18%, and would make 38 payments of $280.61 each, for a total amount paid of $10,664.18.

The difference in payment between these two scores would be:

$14,945.00 - $10,664.18 = $4,280.82

Therefore, a household with a credit score of 525 would pay $4,280.82 more than a household with a credit score of 675 for a principal balance of $8,000.

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The rectangle have length = 4, breath = 16, perimeter = 40, and area = 64.

The perimeter of a rectangle is the sum of length of its four sides or the sum of its length and breadth, multiplied by two. While the area is the length multiplied by the breadth.

Perimeter = 2(L + B)

Area = L × B

From the question;

2(L + B) = 2LB

32L = 2L(L²)...(1) {since B = L²}

from equation (1), L = 4 by solving for L

so;

B = 4² = 16

perimeter of the rectangle = 2(4 + 16) = 40

area of the rectangle = 4 × 16 = 64

Therefore, the rectangle have length = 4, breath = 16, perimeter = 40, and area = 64.

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The width of the path is approximately 7.45 meters.

What is meant by width?

The width refers to the measurement of something from side to side, typically in a direction perpendicular to its length or height, such as the width of a door or the width of a piece of paper.

What is meant by meters?

Meters are a unit of measurement used to measure the length in the metric system. One meter is equal to 100 centimetres or approximately 3.28 feet. It is commonly used to measure distances, heights, and lengths.

According to the given information

The area of the pool is given by the product of its length and width:

18 × 30 = 540 square meters

The area of the entire region, including the pool and the path, is given by the product of the length and width of the outer rectangle:

(18 + 2x) × (30 + 2x)

Expanding this expression, we get:

540 + 36x + 60x + 4x²

Simplifying, we get:

4x² + 96x + 540

We are given that the area of the entire region is 1900 square meters:

4x² + 96x + 540 = 1900

Subtracting 1900 from both sides, we get:

4x² + 96x - 1360 = 0

Dividing both sides by 4, we get:

x² + 24x - 340 = 0

We can use the quadratic formula to solve for x:

x = (-24 ± √(24² - 4 × 1 × (-340))) / (2 × 1)

Simplifying, we get:

x = (-24 ± √(1216)) / 2

x ≈ -17.45 or x ≈ 7.45

Since the width of the path cannot be negative, we can ignore the negative solution.

Therefore, the width of the path is approximately 7.45 meters.

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The angle that is supplementary to <DEA is DEC

To determine the angle that is supplementary to <DEA , we need to consider the following;

From the information given, we have that;

<DEA is supplementary to <DEC that is sum of angles on a straight line.

Then,

<DEA + <DEC = 180 degrees

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Sample Response: Bobby’s interquartile range is 113, while Amelia’s is 179. A lower interquartile range means Bobby’s scores are closer to the median.

I cannot agree or disagree with personal beliefs. However, based on statistical principles, if the range of Bobby's scores is narrower than Amelia's range, then it is likely that Bobby's scores are closer to his median. Alternatively, if Amelia's scores are spread out more, her median may not be a good representation of the typical score, and her scores may not cluster closely around it. Ultimately, without more information on the distribution of the scores, it is impossible to determine who has scores clustered closer to their median.

The angle of elevation from the player's eyes to the center of the rim is approximately 16.2 degrees.

A circle having a radius of 1 that is centred at the origin of a coordinate plane is known as the unit circle. The sine, cosine, and tangent values for every angle in the unit circle are frequently defined in trigonometry.

A radian-measured angle that begins at the positive x-axis and rotates anticlockwise around the circle can be used to represent each point on the unit circle. (Cos, Sin) are the coordinates of the point on the unit circle that corresponds to the angle.

For the given triangle first determine the value of the height from, the player to the top of the baseball pole as follows:

10 - 5.8 = 4.2 units

Now, using the trigonometric identity of tangent we have:

tan θ = opposite / adjacent

tan θ = 4.2 / 15

θ = tan⁻¹(4.2 / 15)

Hence, the angle of elevation from the player's eyes to the center of the rim is approximately 16.2 degrees.

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Answer:

The dimensions of the rectangle are approximately 8.54 units by 3.54 units.

Step-by-step explanation:

Let's start by using algebra to represent the information given in the problem.

Let L be the length of the rectangle.

Then, the width of the rectangle is 5 units less than the length, which means the width can be expressed as L - 5.

The area of a rectangle is given by the formula A = L * W, where A is the area, L is the length, and W is the width. In this case, we are given that the area is 36 square units. So we can write:

A = L * (L - 5)

36 = L * (L - 5)

Expanding the right-hand side of the equation, we get:

36 = L^2 - 5L

Moving all the terms to the left-hand side of the equation, we get:

L^2 - 5L - 36 = 0

Now we can use the quadratic formula to solve for L:

L = (-(-5) ± sqrt((-5)^2 - 4(1)(-36))) / (2(1))

Simplifying this expression, we get:

L = (5 ± sqrt(229)) / 2

We can discard the negative solution since the length of a rectangle cannot be negative.

So, the length of the rectangle is approximately 8.54 units (rounded to two decimal places).

To find the width, we can substitute this value of L into the expression we derived earlier for the width:

W = L - 5

W = 8.54 - 5

W ≈ 3.54 units (rounded to two decimal places)

Therefore, the dimensions of the rectangle are approximately 8.54 units by 3.54 units.

Answer:

We need to subtract 41/6 from 53/6 to get 8. Alternatively, we can say that 8 is 41/6 less than 53/6.

Step-by-step explanation:

To determine how much to subtract from 53/6 to make 8, we need to perform the following calculation:

53/6 - x = 8

where x is the amount we need to subtract.

To isolate x, we need to isolate it on one side of the equation. We can do this by subtracting 53/6 from both sides:

53/6 - x - 53/6 = 8 - 53/6

Simplifying the left-hand side gives:

-x = 8 - 53/6 + 53/6

Simplifying the right-hand side gives:

-x = 41/6

Multiplying both sides by -1 gives:

x = -41/6

Therefore, we need to subtract 41/6 from 53/6 to get 8. Alternatively, we can say that 8 is 41/6 less than 53/6.

The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

A. x² + (y - 3)² = 36.

D. x² + (y + 8)² = 36.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.

Based on the information provided above, we have the following parameters:

Radius, r = diameter/2 = 12/2 = 6 units.

Center, (h, k) = (0, 3).

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 3)² = 6²

x² + (y - 3)² = 36.

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The equations that represent circles that have a diameter of 12 units and a center that lies on the y-axis are:

A. x² + (y - 3)² = 36.

D. x² + (y + 8)² = 36.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

Note: A center that lies on the y-axis simply means the value of h on the x-axis is equal to 0.

Based on the information provided above, we have the following parameters:

Radius, r = diameter/2 = 12/2 = 6 units.

Center, (h, k) = (0, 3).

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 3)² = 6²

x² + (y - 3)² = 36.

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Answer:

1,-6

Step-by-step explanation:the vertex is the lowest/highest point, as you can see here it is at 1,-6

Using the information regarding the set, it should be noted that (D NE) UF will be {b, a, t, h, s, t}

D U E = {b, a, c, k} U {t, a, s, k}

     = {b, a, c, k, t, s}

Next, we need to find the complement of set D with respect to set E, which is denoted as D NE. This is the set of all elements in E that are not in D: D NE = E \ D = {t, s}

(D NE) UF = {t, s} U {b, a, t, h}

         = {b, a, t, h, s, t}

In conclusion, Using the information regarding the set, it should be noted that (D NE) UF will be {b, a, t, h, s, t}

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7:76 - This is not a valid time. There are only 60 minutes in an hour, so the minutes place cannot be 76.

Time is a measurable and non-spatial quantity used to describe or quantify the sequence, duration, or occurrence of events. It is a concept used to understand the order in which events occur and to measure the duration of those events.

10:44 - Yes, the statement is true. The time is 44 minutes after 10:00.

9:47 - No, the statement is false. The time is 13 minutes before 10:00.

12:13 - Yes, the statement is true. The time is 13 minutes after 12:00.

11:00 - Yes, the statement is true. The time is exactly 11:00.

7:76 - This is not a valid time. There are only 60 minutes in an hour, so the minutes place cannot be 76.

1:05 - Yes, the statement is true. The time is 5 minutes after 1:00.

5:02 - No information is provided about this time on the clock.

2:00 - Yes, the statement is true. The time is exactly 2:00.

4:00 - Yes, the statement is true. The time is exactly 4:00.

3:00 - Yes, the statement is true. The time is exactly 3:00.

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Answer: ∠EAI and/or ∠EDG (More listed below lol)

Step-by-step explanation:

Starting Angle: ∠ADE

Possible Supplements: ∠EAI, ∠EDG, ∠DAH, ∠DEC, ∠ADF, and ∠AEB

If the archaeologist found a fossil whose length is 489.44 inches, using the conversion table, the length in feet, to the nearest tenth, is 40.8 feet.

The conversion table refers to the tabulated standard units of measurement, showing temperature, length, area, volume, weight, and metric conversions

For instance, the conversion table shows that 12 inches equal 1 foot.

The length of the fossil = 489.44 inches

12 inches = 1 foot

489.44 inches = 40.8 feet (489.44 ÷ 12)

Thus, using the conversion table, which relies on multiplication or division operations using the conversion factors, the length in feet of the fossil is 40.8 feet.

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The cubic equation graphed have the functions as follows

Graph of cubic function

The equation of cubic function is

y = a(x - h)^3 + k

For horizontal inflection at (-5, -7)

y = a(x + 5)^3 - 7

passing through point (-1, -3.8)

-3.8 = a(-1 + 5)^3 - 7

4.8 = -64a

a = 4.8/64 = 3/40

hence the equation is: y = 3/40(x + 5)^3 - 7

Graph of cubic function

The equation of cubic function is

y = k - a(x - h)^3

For horizontal inflection at (-0.5, 2)

y = 2 - a(x + 0.5)^3

passing through point (-5, 38.45)

38.45 = 2 - a(-5 + 0.5)^3

38.45 -2 = -a(-4.5)^3

a = -36.45/(-4.5)^3 = 2/5

hence the equation is: y = 2 - 2/5(x + 0.5)^3

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Answer:C is your answer

Step-by-step explanation:This is not a 90 degree angle or 360 degree shape

The function f(x) = -0.05(x²-18x -40) represents the "height" of the projectile fired from the cannon at a "horizontal-distance" of x.

The function which represents the path, coming out of the cannon is f(x) = -0.05(x²-18x -40);

The term inside the bracket is : (x²-18x -40) is a quadratic expression that represents the shape of the projectile's path.

Now, let us consider the "negative-coefficient" (-0.05) in front of the quadratic expression.

This means that the function will be reflected about the x-axis, which  means that the height of the projectile will be measured downwards from a reference point.

Therefore, f(x) represents the height of the projectile.

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Answer: The length of the original side of the square is 22 units.

Step-by-step explanation:

Let x be the length of the original side of the square.

If the sides are increased by 11, the new side length is x + 11.

The area of the new square is given as 400, so we have:

(x + 11)^2 = 400

Expanding the left side: x^2 + 22x + 121 = 400

Subtracting 400 from both sides: x^2 + 22x - 279 = 0

Using the quadratic formula:

x = (-22 ± sqrt(22^2 - 41(-279))) / (2*1)

x = (-22 ± sqrt(12100)) / 2

x = (-22 ± 110) / 2

Taking the positive solution:

x = (-22 + 110) / 2

x = 44 / 2

x = 22

An equation to match the graph include the following: f(x) = |x + 1| + 1.

In Mathematics and Geometry, the translation a geometric figure or graph to the left simply means subtracting a digit from the value on the x-coordinate of the pre-image while the translation a geometric figure or graph upward simply means adding a digit to the value on the y-coordinate (y-axis) of the pre-image.

Since the parent function is f(x) = |x|, g(x) would be created by translating f(x) the parent function one unit to the left and one unit upward as follows;

f(x) = |x|

g(x) = |x + 1| + 1

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