Find the inverse of each function:
y = log5 (4x + 1)
y = log3 (2^x + 8)
y = log4 (-2x + 9)
y = 5^x + 9/2
y = 10^x + 3/ -3
y = log5 (-4x + 10)

Therefore , the solution of the given problem of graph comes out to be option A f(n) = 7 - 2(n-1)

Theoretical physicists use graphs to analytically chart or visually represent claims rather than values. A graph point typically depicts the relationship between any number of things. A specific type of non-linear train assembly made up of clusters and lines is known as a graph. Glue should be used to connect the networks, also referred as the boundaries. In this network, the nodes had the numbers 1, 2, 3, and 5, whilst edges had the numbers 1, 2, 3, and 4, as well as the numbers (2.5), (3.5), (4.5), and yet also (4.5). (4.5).

Here,

We can use the following method to determine the general term of an arithmetic series:

=> f(n) = a + (n-1)d

where the usual difference is "d" and "a" is the first term.

Since the series begins at 7, "a" is 7, as shown by the graph. Additionally, since each term reduces by 2, we can see that the common difference is 2.

Consequently, the following is the arithmetic sequence's stated rule:

A) f(n) = 7 - 2(n-1)

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Answer: six hundred nine thousandths

Step-by-step explanation:

(a)  The future value of the investment if interest is compounded semiannually is $24,840.28.

(b) The future value of the investment if interest is compounded quarterly is $25,025.68.

(c) The future value of the investment is $185.40 greater when the interest is compounded quarterly.

The future value of an investment can be calculated using the formula FV = P(1 + r/n)^(nt), where FV is the future value, P is the principal amount deposited, r is the annual interest rate, n is the number of times interest is compounded per year, and t is the number of years the investment is held.

If the interest is compounded semiannually, then n = 2. Plugging in the given values, we get:

FV = 18000(1 + 0.04/2)^(2*9)

FV = 18000(1.02)^18

FV = $24,840.28

So the future value of the investment if interest is compounded semiannually is $24,840.28.

If the interest is compounded quarterly, then n = 4. Plugging in the given values, we get:

FV = 18000(1 + 0.04/4)^(4*9)

FV = 18000(1.01)^36

FV = $25,025.68

So the future value of the investment if interest is compounded quarterly is $25,025.68.

To find out how much greater the future value of the investment is when the interest is compounded quarterly, we can subtract the future value when interest is compounded semiannually from the future value when interest is compounded quarterly:

$25,025.68 - $24,840.28 = $185.40

So the future value of the investment is $185.40 greater when the interest is compounded quarterly.

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Answer:

Refer to pic...........

3525

The next term in the arithmetic sequence that increases by 21, starting at 55, is 76. The next two terms of the Fibonacci sequence are 67 and 109, and the 72nd term is 3525.

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Triangle AXC is congruent to triangle AYB by the SAS Congruence Criteria.

In geometry, two triangles are said to be congruent if they have the same shape and size. More specifically, two triangles are congruent if all three sides and all three angles of one triangle are equal to the corresponding sides and angles of the other triangle. When two triangles are congruent, they can be superimposed on top of each other, and all corresponding parts of the triangles will match exactly.

There are several ways to prove that two triangles are congruent, including using the side-angle-side (SAS) theorem, the angle-side-angle (ASA) theorem, the side-side-side (SSS) theorem, and the hypotenuse-leg (HL) theorem.

Given that |AB|=|CD| and triangle ABC is isosceles.

We need to prove that triangle AXC = triangle AYB.

To do so, we will use the Side-Angle-Side (SAS) Congruence Criteria.

AC = BC (Given)

∠ACX = ∠BCY (Vertical Angles)

∠CAX = ∠CBY (Base Angles of Isosceles Triangle)

Therefore, triangle AXC is congruent to triangle AYB by the SAS Congruence Criteria.

Hence, proved.

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rank(A) = 1

Given that A = $\left[\begin{array}{cc}a & b \\ a & b\end{array}\right]$, where $a \neq 0$.Let's find the rank of A:Rank(A) = number of leading 1's in the row echelon form of A.= $\left[\begin{array}{cc}a & b \\ a & b\end{array}\right]$=> $\left[\begin{array}{cc}a & b \\ 0 & 0\end{array}\right]$There are two leading 1's in row 1. Hence, rank(A) = 1.Now, let's find the basis of the null space of A:Null space of A is the set of all solutions to the equation $Ax=0$.So, $Ax$ = $\left[\begin{array}{cc}a & b \\ a & b\end{array}\right]$ $\left[\begin{array}{c}x \\ y\end{array}\right]$= $\left[\begin{array}{c}ax+by \\ ax+by\end{array}\right]$= $\left[\begin{array}{c}(a+b)x \\ (a+b)y\end{array}\right]$= $\left[\begin{array}{c}0 \\ 0\end{array}\right]$=> (a + b) x = 0 and (a + b) y = 0=> $x = \frac{-b}{a}y$=> $\left[\begin{array}{c}x \\ y\end{array}\right]$= $\left[\begin{array}{c}\frac{-b}{a}y \\ y\end{array}\right]$= $y \left[\begin{array}{c}\frac{-b}{a} \\ 1\end{array}\right]$=> Null space of A = $\{y \left[\begin{array}{c}\frac{-b}{a} \\ 1\end{array}\right] | y \in R \}$Let's take a = 1, b = 2. So, the null space of A = $\{y \left[\begin{array}{c}-2 \\ 1\end{array}\right] | y \in R \}$Therefore, the basis of the null space of A = $\left[\begin{array}{c}-2 \\ 1\end{array}\right]$Now, let's find the basis of the row space of A:Row space of A is the span of the rows of A.=> Row space of A = span $\left\{\left[\begin{array}{cc}a & b\end{array}\right]\right\}$Since rank(A) = 1, there is only 1 non-zero row. Therefore, a basis of the row space of A is $\left\{\left[\begin{array}{cc}a & b\end{array}\right]\right\}$.

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The sample size that would be required to estimate the confidence interval with a margin of error of 1% is given as follows:

n = 9604.

A confidence interval of proportions has the bounds given by the rule presented as follows:

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which the variables used to calculated these bounds are listed as follows:

The confidence level is of 95%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

The margin of error is modeled as follows:

[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

We have no estimate of the proportion, hence it is used as follows:

[tex]\pi = 0.5[/tex]

The margin of error is of M = 0.01, hence the sample size is obtained as follows:

[tex]0.01 = 1.96\sqrt{\frac{0.5(0.5)}{n}}[/tex]

[tex]0.01\sqrt{n} = 1.96 \times 0.5[/tex]

[tex]\sqrt{n} = 98[/tex]

n = 98²

n = 9604.

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The solution to the system of equations using elimination is:

x = 1058/1890

y = 26/90

To solve this system of equations using elimination, we will add the two equations together and rearrange the terms.

2y = x - 5

2y = x + 5

Add the equations together:

2y + 2y = x - 5 + x + 5

4y = 2x + 0

Rearrange the terms:

4y - 2x = 0

We will now use this equation and the equation x + 2y = 13 to solve for x and y.

Substitute 4y - 2x = 0 into x + 2y = 13:

x + 2(4y - 2x) = 13

x + 8y - 4x = 13

Rearrange the terms:

5x + 8y = 13

Substitute 4y - 2x = 0 into 5x + 8y = 13:

5x + 8(4y - 2x) = 13

5x + 32y - 16x = 13

Rearrange the terms:

21x + 32y = 13

Divide by 21:

x + (32/21)y = 13/21

Rearrange the terms:

x = 13/21 - (32/21)y

Substitute x = 13/21 - (32/21)y into 4y - 2x = 0:

4y - 2(13/21 - (32/21)y) = 0

4y - (26/21) + (64/21)y = 0

Rearrange the terms:

(90/21)y = 26/21

y = (26/21) / (90/21)

y = 26/90

Substitute y = 26/90 into x = 13/21 - (32/21)y:

x = 13/21 - (32/21)(26/90)

x = 13/21 - (832/1890)

x = 1058/1890

The solution to the system of equations is:

x = 1058/1890

y = 26/90

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The reciprocal of 5/11 is: 11/5

The reciprocal of 20 is: since 20=20/1 so the reciprocal is 1/20

Answer: 11/5, 1/20

Step-by-step explanation:

The reciprocal of a value is the numerator and denominator of that value switched.

When you look at 5/11, we see that 5 is the numerator and 11 is the denominator. The reciprocal(switch numerator and denominator) is 11/5.

The reciprocal of 20 can be tricky because it isn't written with a denominator. But we know intuitively that 20 is also equal to 20/1.

Therefore we apply the same steps as in the first instance and we get that the reciprocal of 20/1 is 1/20.

Answer:4. (a) BMN = 75°(b) AMP = 105°Explanation:Given that ABC is an isosceles triangle with base BC, and ABC = 75°. Also, BC = MB = PM and MN || BC.(a) To find BMN, we can use the fact that MN || BC. This means that ∠BMN = ∠ABC = 75°. Therefore, BMN = 75°.(b) To find AMP, we can use the fact that BC = MB = PM. This means that triangle BMP is an isosceles triangle with base MP. Since BMN = 75°, we can find ∠BMP by using the fact that the sum of the angles in a triangle is 180°:∠BMP = (180° - 75°)/2 = 52.5°Now, we can find AMP by using the fact that the sum of the angles in a triangle is 180°:AMP = 180° - 75° - 52.5° = 52.5°Therefore, AMP = 105°.

(a) The angle BMN is 30°.

(b) The angle AMP is 15°.

The total angle of a triangle is 180°.

We have an isosceles triangle ABC with base BC and ∠ABC is 75°. We construct point M on AC and N, P on AB. It makes BC = MB = PM and MN || BC.

Since ABC is an isosceles triangle, ∠ACB is also 75°. See the picture attached!

Since BC = MB, the triangle MBC is isosceles with base MC. So, BMC is 75°.

The angles of triangle MBC will sum up to 180°. So,

∠MBC = 180 - (75 + 75) = 30°

The angle BMN and MBC is alternate interior angles, so

∠BMN = ∠MBC = 30°

Now, we have ∠NBM = 75 - 30 = 45°. Since MB = PM, it makes BMP an isosceles triangle. The angle BPM will be the same with PBM. It is 45°.

The angle PMN will be

= 180 - (45 + 45 + 30)

= 60°

The angle CMB, BMN, NMP, and AMP are supplementary. So, the angle AMP is

= 180 - (75 + 30 + 60)

= 15°

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The solution is, the triangle ABC and DBC are congruent, by the Side-Angle-Side Triangle Congruence Theorem.  

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

As we can seen from the given figure that two triangles are given.

The triangles ABC and BDC are :

AB = CD

AC = BD

BC = BC

Hence using the SSS theorem of the triangle, the triangle ABC and DBC are congruent, Thus the angle A  is equal to angle D.

Hence the option D and E are correct. i.e. congruent by the Side-Angle-Side Triangle Congruence Theorem.  

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The area of the trapezoid is 65.16 metres squared.

The area of a trapezoid can be found as follows:

area of a trapezoid = 1 / 2 (a + b)h

where

Therefore,

a = 5metres

b = 13.1 metres

h = 7.2 metres

Hence,

area of a trapezoid = 1 / 2 (5 + 13.1) 7.2

area of a trapezoid = 1 / 2 (18.1)7.2

area of a trapezoid = 130.32 / 2

Therefore,

area of a trapezoid = 65.16 metres squared

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To calculate the probability that a randomly selected person has at least 2 TV's, you would first calculate the probability of a person having more than 2 TV's:

Then, you would calculate the probability of a person having less than 2 TV's:

Finally, you would calculate the probability of a person having exactly 2 TV's:

Therefore, the probability that a randomly selected person has at least 2 TV's is:

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By evaluating the function in j = 1, we conclude that each bottle costs 80 cents.

We know that the total cost in dollars can be represented by the linear equation:

C(j) = 0.8*j

Where C is the cost, and j is the number of juice bottles bought.

Then to get the cost of each bottle, we can evaluate the function in 1, which means buying only one.

C(1) = 0.8*1 = 0.8

So each bottle costs $0.80 (or 80 cents).

In mathematics, a function is a relationship between a set of inputs and a set of possible outputs, such that each input is associated with a unique output. Functions are represented by mathematical expressions or equations that specify how the input values are transformed into output values. For example, the function f(x) = x^2 takes an input value x and produces an output value equal to x squared.

Functions play a crucial role in many areas of mathematics, science, and engineering. They can be used to model complex systems, analyze data, and solve problems. Functions are also used in computer programming, where they are used to encapsulate a specific set of operations that can be reused throughout a program.

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The theorem you mentioned is known as Meusnier's theorem. The edge of regression of the polar developable of a space curve is the locus of the center of spherical curvatures.

It states that the locus of the center of spherical curvature of a space curve is the edge of regression of the polar developable of the curve. In other words, the center of curvature of a curve at any point lies on the edge of regression of the polar developable curve.

This theorem is used to describe the curvature of a curve in three-dimensional space. It is named after the French mathematician Jean Baptiste Meusnier, who first discovered it in 1776.

In mathematical terms, the theorem can be expressed as follows:

Let C be a space curve with curvature k and torsion T. Let P be a point on C and N be the normal vector at P. Then, the center of curvature of C at P is given by:

O = P + (1/k)N

The edge of regression of the polar developable of C is the locus of the point O as P varies along C.

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Answer:

$7.49

Step-by-step explanation:

49.99-42.50=7.49

The correct statement is f(x)=33(1.32)^(x). .

The original statement is false because it does not accurately represent the increase in the number of weekly flu tests. The original statement suggests that the number of tests decreases by 32% each week, which is not the case.

To accurately represent the increase in the number of weekly flu tests, we need to use the growth factor of 1.32, which is equivalent to 100% + 32%. This means that the number of weekly flu tests increases by 32% each week, as stated in the problem.

Therefore, the correct statement is f(x)=33(1.32)^(x).

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Answer: the number that goes beneath the radical symbol is 17

Answer:

34%

Step-by-step explanation:

495 is 66% of 750 so 66% - 100% is 34%

Answer:

34

Step-by-step explanation:

The polynomial expressions are P(x) = x(x - 5)(x - 2), P(x) = (x + 3)(x + 5)(x - 3)(x + 1), P(x) = (x + 5)(x² - 4x + 5) and P(x) = (x + 5)(x² + 4)

Zeros (1): 0, 5, 2

This means that

Roots: x = 0, x = 5 and x = 2

The equation can be represented as

P(x) = (x - root)

So, we have

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

Evaluate

P(x) = x(x - 5)(x - 2)

Zeros (2): 0, 5, 2

Here, we have

Roots: x = -3, x = -5, x = 3 and x = -1

Using the form in (a), we have

P(x) = (x + 3)(x + 5)(x - 3)(x + 1)

Zeros (3): 0, 5, 2

Here, we have

Roots: x = -5, x = 2 + i

Using the form used abov]e, we have

P(x) = (x + 5)(x - 2 - i)(x - 2 + i)

Expand

P(x) = (x + 5)((x - 2)² + 1)

So, we have

P(x) = (x + 5)(x² - 4x + 5)

Zeros (4): -1 and 2i

Here, we have

Roots: x = -1, x = 2i

Using the form used abov]e, we have

P(x) = (x + 1)(x - 2i)(x + 2i)

Expand

P(x) = (x + 5)(x² + 4)

Zeros (5):2 mult.2, -4

The zeros here are not clear

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The first set is countable, the second set is also countable. The third set is also countable.

(a) The set {x∈R:2 is countable because it is finite.
(b) The set {x∈Q:∣x∣≥2} is countable because it is a subset of the rational numbers, which are countable.
(c) The set {x∈Q:∣x∣<4} is countable because it is a subset of the rational numbers, which are countable.

In Maths, sets are referred as a collection of well-defined objects or elements. A set is usually represented by a capital letter symbol and the total number of elements in the finite set is basically represented as the cardinal number of a set in a curly bracket.

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The following values represent the rollercoaster graph scenario most accurately:

is, Red (x) = 6+4 × cos(πx/6) if 0 ≤ x < 6

Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5

Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5)

For Red (x) = 6 + 4 × cos(πx/6) if 0 ≤ x < 6

The graph is simply a structured representation of the data. It facilitates our understanding of the facts. The numerical information gathered through observation is referred to as data.

The Latin word Datum, which meaning "something provided," is where the word data first appeared.

In the question, where at x = 0, Red(x) = 10,

at x = 5, Red(x) = 2.5

For Green (x) = -2.5 × cos (π(x - 6)/4) + 4.5       if    6 ≤ x < 10

Given, where at x = 10, Green (x) = 7,

So, at x = 6, Green (x) = 2.0

For Purple (x) = 3.5 - 3.5 × sin (π(x - 12.5)/5) if 10 ≤ x ≤ 15

Given, where at x = 10, Purple (x) = 7,

at x = 15, Purple (x) = 0

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The complete question is:

The above rollercoaster graph needs a function to go with it. Select the correct functions that begins at (0,12) and ends at (12,0) with a local minimum at (5,1) and a local maximum at (9,6). You need to select one function for the red piece, one function for the green piece, and one function for the purple piece.

The total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.

In mathematics, a geometric series is an infinite series with the formula a + ar + ar2 + ar3 +, where r is referred as the common ratio.

In the question:

Let 'x' be the miles that Rowan runs in 1st week.

Xn for the nth week.

x1 = 15 (given)

x2 = 15*(1 + 3%) = 15*1.03

Xn = 15*(1 + 3%0ⁿ⁻¹ = 15*(1.03ⁿ⁻¹)

Let 'S' be the total miles.

S = x1 + x2+ .....+ xn

S = 15 + 15 *1.03 + 15*1.03² + ...+ 15*1.03⁹

On solving the series:

S = 15 × 1.(1.03¹⁰ - 1)/0.03

S = 57.31

S = 58

Thus, the total number of miles Rowan runs over the first ten weeks of training is found as 58 miles.

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The two alleles that have the highest probability of being inherited together are A. G and k.

Alleles that are physically close to each other on a chromosome have a higher probability of being inherited together, a phenomenon known as linkage. The closer two alleles are to each other on a chromosome, the less likely it is that they will be separated by a recombination event during meiosis.

The degree of linkage between two alleles is determined by their relative physical distance on the chromosome. The closer two alleles are, the higher the probability that they will be inherited together.

G and k are the closest alleles to each other on the genetic map and so have a higher probability of being inherited together.

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Answer:

8.9

Step-by-step explanation:

9.0-0.1= 8.9

which is one-tenth less than 9

The distance between Jason's school and his house is 8 miles.

What is the Cartesian system?

Any point can be located using a Cartesian coordinate system or coordinate system, and that point can be plotted as an ordered pair (x, y) known as Coordinates. The origin, symbolized by the letter "O," is the point where the two number lines intersect. The horizontal number line is known as the X-axis, and the vertical number line is known as the Y-axis.

Given that the coordinates of Jason's house is (-4,-5). The coordinates of his school is  (-10,-11).

The formula distance between two points (x₁, y₁) and (x₂, y₂) is √[(x₂ - x₁)² + (y₂ - y₁)²].

Here, x₁ = -4, y₁ = -5,x₂= -10, y₂ = -11

The distance between points is

√[(-10-(-4))² + (-11 - (-5))²]

=√(6² + 6²)

= √(36+36)

= √72

= 6√2

= 8.48

≈ 8 miles

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Answer: Let's use the variables x and y to represent the number of small boxes and large boxes shipped, respectively.

The system of equations that could be used to determine the number of each type of box is:

x + y = 21 (equation 1)

7x + 14y = 252 (equation 2)

In equation 1, the left side represents the total number of boxes shipped, which is the sum of the number of small boxes (x) and the number of large boxes (y). The right side of the equation represents the total number of boxes shipped, which is given as 21.

In equation 2, the left side represents the total volume of paper shipped, which is the sum of the volume of all the small boxes (7 cubic feet per box) and the volume of all the large boxes (14 cubic feet per box), multiplied by the number of boxes shipped. The right side of the equation represents the total volume of paper shipped, which is given as 252 cubic feet.

These two equations can be used to solve for x and y, which represent the number of small boxes and large boxes shipped, respectively.

Step-by-step explanation: