Write the sentence two plus three equal five seven two

The two solutions of the equation:

(6x - 12)/3 + 4 = 18/x

Are x = 3 and x = -3

Here we have the following equation:

(6x - 12)/3 + 4 = 18/x

Notice that in the right side we have x on a denominator, then x can not be zero, so x ≠ 0.

Now, let's start by simplifying the left side:

(6x - 12)/3+  4 = 18/x

2x - 4 + 4 = 18/x

2x = 18/x

Now we can multiply both sides by x so we get:

2x^2 = 18

Now divide both sides by 2:

x^2 = 18/2

x^2 = 9

Finally, apply the square root in both sides:

√x^2 = ±√9

x = ±3

The two solutions are x = 3 and x = -3

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Answer: Half of them are even and half of them are odd.

Step-by-step explanation:

The even numbers are 6, 12, 18, 24, and 30. An even number is defined as a number that is divisible by 2, meaning it has no remainder when divided by 2. For example, 6 divided by 2 equals 3 with no remainder, so 6 is even.

The odd numbers are 3, 9, 15, 21, and 27. An odd number is defined as a number that is not divisible by 2, meaning it has a remainder of 1 when divided by 2. For example, 9 divided by 2 equals 4 with a remainder of 1, so 9 is odd.

Therefore, out of the given numbers, half of them are even and half of them are odd.

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Polynomial: 6x^3 + 12x^2 - 18x

Form 1: 6(x^3 + 2x^2 - 3x)

Explanation: This form was created by factoring out the GCF of 6 from each term in the polynomial.

Form 2: 6x(x^2 + 2x - 3)

Explanation: This form was created by factoring out the GCF of 6x from each term in the polynomial.

In both forms, the GCF of 6 allows us to factor out common factors and simplify the polynomial expression while preserving its original meaning.

To create a factorable polynomial with a greatest common factor (GCF) of 6, we can start by considering the common factors of the terms. Let's construct a polynomial:

Polynomial: 6x^3 + 12x^2 - 18x

To rewrite this polynomial in two other equivalent forms, we can factor out the GCF from each term and simplify.

Form 1: 6(x^3 + 2x^2 - 3x)

In this form, we factored out the GCF of 6 from each term: 6x^3/6 = x^3, 12x^2/6 = 2x^2, and -18x/6 = -3x.

Form 2: 6x(x^2 + 2x - 3)

In this form, we factored out the GCF of 6x from each term: 6x^3/6x = x^2, 12x^2/6x = 2x, and -18x/6x = -3.

We created each form by identifying the common factors in the polynomial and factoring them out. This process allows us to rewrite the polynomial in equivalent forms that emphasize different aspects.

In Form 1, we factored out the GCF of 6, leaving the remaining polynomial inside the parentheses. This form highlights the fact that the polynomial can be written as the product of the GCF and the remaining terms.

In Form 2, we factored out the GCF of 6x, again leaving the remaining polynomial inside the parentheses. This form emphasizes the fact that the polynomial can be written as the product of the GCF and another factor, in this case, x.

By rewriting the polynomial in these two forms, we have created equivalent expressions that emphasize the presence of the GCF and demonstrate the polynomial's factorability.

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The statement which best describes the data given is C) The data can be modeled by a quadratic function.

Given a data,

The numbers of customers that visited a store each hour for several hours after the store opened at 8 am are shown in the table.

It is clear that the number of customers increases to 18 for the first 4 hours and then decreases to 0 after 9 hours.

So this data cannot be modeled by a linear function or an exponential function.

Also since the number of customers arriving is not constant, this cannot be expressed as constant function.

So it is quadratic function.

Hence the correct option is c.

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Answer:

378,075

Explanation:

The population of Ashton in 2007 = 294876

The population increases at a constant rate of 2.8%.

Therefore, the population at any time, t after 2007 is:

Therefore, the population in 9 years time will be:

The predicted population in 9 years will be 378,075.

Using the Intersecting secants theorem, the length of JK in the given diagram is 17

From the question, we are to determine the length of JK in the given diagram.

The diagram shows a circle with intersecting secants.

From the Intersecting secants theorem which states that "if two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment".

Then,

We can write that

JK × KL = NM × ML

From the given diagram,

KL = 14

NM = 14

ML = 17

Substituting the values

JK × 14 = 14 × 17

JK = (14 × 17) / 14

JK = 17

Hence, the length of JK is 17

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Answer is D

I say this because I can't be a cause international numbers real

B every integers a real number

C every integers is also an interration number.

Answer:

Decrease of 63.5%.

Step-by-step explanation:

Exponential function:

An exponential function has the following format:

\(y = y(0)(1+r)^{x}\)

In which y(0) is the initial value and r is the rate of change, as a decimal. If r is positive, it is a increase. If it is negative, it is a decrease.

In this question:

We have that:

\(y = 3100(0.365)^x\)

So

\(1 - r = 0.365\)

\(r = 0.365 - 1 = -0.635\)

So a decrease of 63.5%.

Answer:

63.5

Step-by-step explanation:

Answer:

6.24 x \(10^{-7}\)

Step-by-step explanation:

0.000000624 in scientific notation is 6.24 x \(10^{-7}\)

Answer:

Step-by-step explanation:

The resulting number is in scientific notation. In this case, the number is 6.24 * 10^-7.

The volume of the given cylinder is 84.8 cm³.

Given: Radius of cylinder, r = 3cm Height of cylinder, h = 3cm

Formula used: Volume of cylinder = πr²hπ is a constant and is approximately equal to 3.14.

Volume of cylinder = πr²h= 3.14 x 3² x 3= 84.78 cm³ (rounded to the nearest tenth)= 84.8 cm³

Therefore, the volume of the given cylinder is 84.8 cm³.

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\(\qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}} ~\hspace{6em} \stackrel{\textit{constant of variation}}{y=\cfrac{\stackrel{\downarrow }{k}}{x}~\hfill } \\\\ \textit{\underline{x} varies inversely with }\underline{z^5} ~\hspace{5.5em} \stackrel{\textit{constant of variation}}{x=\cfrac{\stackrel{\downarrow }{k}}{z^5}~\hfill } \\\\[-0.35em] \rule{34em}{0.25pt}\)

\(\stackrel{\textit{"F" inversely proportional to }\sqrt{g}}{F=\cfrac{k}{\sqrt{g}}}\qquad \textit{we also know that} \begin{cases} F=18\\ g=9 \end{cases} \\\\\\ 18=\cfrac{k}{\sqrt{9}}\implies 18=\cfrac{k}{3}\implies 54=k~\hfill\boxed{ F=\cfrac{54}{\sqrt{g}}} \\\\\\ \textit{when g = 36, what is "F"?}\qquad F=\cfrac{54}{\sqrt{36}}\implies F=\cfrac{54}{6}\implies F=9\)

Answer:

f = 9

Step-by-step explanation:

f = k/square root of g (k is the constant) so 18 = k/square root of 9.

We can rearrange this to find k, so 18*square root of 9 = k

Consequently, k = 54

We can put k in our equation to now find f. f = 54/square root of 36

Therefore, f is 9

The volume of the cuboid is 58 cubic units.

A cuboid is a 3 dimensional figure that has six rectangular faces. So that the volume of a cuboid can be determined by;

volume of cuboid = length x width x height

From the given question, we have;

the volume of a cuboid that is 2.9 x 5 x 4 can be determined as follows;

volume of cuboid = length x width x height

                             = 2.9 x 5 x 4

                             = 58

The volume of the cuboid with the given dimension is 58 cubic units.

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The coordinates of the image after a dilation are (1, 1), (3, -3), and (-5, -5).

In Geometry, dilation can be defined as a type of transformation which typically changes the size of a geometric object, but not its shape. This ultimately implies that, the size of the geometric object would be increased or decreased based on the scale factor used.

Next, we would have to dilate the coordinates of the preimage by using a scale factor of 2 centered at the point (1, 1) by using this mathematical expression:

(x, y)  →  (k(x - a) + a, k(y - b) + b)

For coordinate A, we have;

Coordinate A = (1, 1)  →  (2(1 - 1) + 1, 2(1 - 1) + 1)

Coordinate A' = (1, 1)  →  (1, 1)

For coordinate B, we have;

Coordinate B = (2, -1)  →  (2(2 - 1) + 1, 2(-1 - 1) + 1))

Coordinate B' = (2, -1)  →  (3, -3)

For coordinate C, we have;

Coordinate C = (-2, -2)  →  2(-2 - 1) + 1, 2(-2 - 1) + 1))

Coordinate C' = (-2, -2)  →  (-5, -5)

In conclusion, the coordinates of the image of triangle A'B'C' are (1, 1), (3, -3), and (-5, -5).

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Total number of rabbits produced in 9 years will be 45.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

Given is a rabbit can produce 5 new rabbits per year

Total number of rabbits produced in 9 years will be -

n = 5y = 5 x 9 = 45 new rabbits

Therefore, total number of rabbits produced in 9 years will be 45.

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The onto functions (surjective functions) are:

c. f(m, n) = m + n + 1.

At first we have to identify onto (surjective) functions from Z x Z to Z, we need to check if each element in the codomain (Z) has at least one preimage in the domain (Z x Z).

a. f(m, n) = 2m - n

This function is not onto because for odd numbers in the codomain (Z), there is no pair of integers (m, n) in the domain that will map to them.

b. \(f(m, n) = m^2 - n^2\)

This function is not onto because for negative numbers in the codomain (Z), there is no pair of integers (m, n) in the domain that will map to them.

c. f(m, n) = m + n + 1

This function is onto. For any integer 'z' in the codomain (Z), we can find a pair of integers (m, n) in the domain such that m + n + 1 = z.

For example, if z = 0, we can choose m = 0 and n = -1, and then m + n + 1 = 0.

d. f(m, n) = |m| - |n|

This function is not onto because negative numbers in the codomain (Z) cannot be obtained from the domain (Z x Z).

For example, there is no pair of integers (m, n) in the domain that maps to -1.

Hence, The onto functions (surjective functions) are:

c. f(m, n) = m + n + 1.

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Answer:

y=x-5

Step-by-step explanation:

We need to first make these improper fractions. 5 = 40/8, so 40/8+6/8 = 46/8. Similarly, 4 = 20/5, so 20/5+4/5=24/5.

So we need to find the value of 46/8+24/5. Multiply the first fraction by 5/5 and second fraction by 8/8 to get the same denominator. We get (46*5+24*8)/8*5 = 422/40. This is equal to 400/40 + 22/40 = 10+22/40.

So the third answer choice is correct.

Hope that helped!

When matched, the prompts on asymptotes would be:

The presence of a vertical asymptote at x=0 signifies that the cost of producing pills can never reach a value of 0, remaining persistently positive. Simultaneously, the horizontal asymptote at y=0 serves as a reassuring indication that the cost of producing pills cannot be negative, as it steadfastly remains at or above zero.

This crucial constraint ensures that the cost incurred in the pill production process is always a non-negative quantity. Consequently, the prompt related to the impossibility of negative costs aligns with this notion.

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Answer:

(3+4)+5=12

Step-by-step explanation:

(3 + 4 ) = 7

7 + 5 =

12

Answer:

3x + x - 2x + 8 = 3x + x

2. 2 (2x + 4) - 2x = x + 18

3. If x = 5 , evaluate : 2 ( x + 3) + 3x

4. 3 (2x) - 3x + 4= 2x + 5

5. 3x +2x + x = x + 6

6. 2 ( x+ 4) + x = 16

Answer:

\(g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22\) in the factored form will be:

Step-by-step explanation:

Given the function

\(g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22\)

Use the rational root theorem.

\(a_0=22,\:\quad a_n=1\)

\(\mathrm{The\:dividers\:of\:}a_0:\quad 1,\:2,\:11,\:22,\:\quad \mathrm{The\:dividers\:of\:}a_n:\quad 1\)

\(\mathrm{Therefore,\:check\:the\:following\:rational\:numbers:\quad }\pm \frac{1,\:2,\:11,\:22}{1}\)

\(-\frac{2}{1}\mathrm{\:is\:a\:root\:of\:the\:expression,\:so\:factor\:out\:}x+2\)

\(=\left(x+2\right)\frac{x^3-4x^2-x+22}{x+2}\)

as

\(\frac{x^3-4x^2-x+22}{x+2}=x^2-6x+11\)        ∵ \(x^3-4x^2-x+22=\left(x+2\right)\left(x^2-6x+11\right)\)

so the expression becomes

\(x^3\:-\:4x^2\:-\:x\:+\:22=\left(x+2\right)\left(x^2-6x+11\right)\)

Therefore,

\(g\left(x\right)=x^3\:-\:4x^2\:-\:x\:+\:22\) in the factored form will be:

Answer:

6 fewer starfish

Step-by-step explanation:

16+4=20

20-14=6

6 fewer starfish are there.

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

The subject of mathematics includes quantities and their variations, equations and related structures, forms and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A relationship between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

h(x) = (x+1)²

h(-2) = 1

h(-1) = 0

h(3) = 8

In light of this, 1,0,8 is the value of the function h(x) = (x+1)2 where h is defined for all real integers.

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Answer:

42.25485 or 42.25

Btw is this your homework or a test.

Answer:

1=83.08

Step-by-step explanation:

mean=summation of number divided by number

To maximise profit, or $470, the corporation should create 40 pounds of Mixture A and 70 pounds of Mixture B.

Net profit, commonly referred to as the bottom line, is the amount of money that remains after all costs are deducted from total income. It displays the real profit that a business made during a given time frame, typically a fiscal year or a quarter. A company's net profit is determined by deducting all of its costs from its total revenue, including wages, rent, utilities, taxes, and interest payments. The resultant figure will be positive if a profit was made by the business. If it's negative, it means that the business has lost money.

given

The triangle in darkened text is the possible area. The three lines' intersections make up the triangle's vertices. To determine the highest value of P, we can examine the objective function P's value at each vertices.

P = 0 at position (0, 0).

P = 320 at location (80, 0).

P = 390 at point (60, 30).

P = 470 at point (40, 70).

To maximise profit, or $470, the corporation should create 40 pounds of Mixture A and 70 pounds of Mixture B.

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Answer:

Step-by-step explanation:

The angle of depression is the downward angle the air traffic controller

looks down from in the tower.  It also equals the angle of elevation which is the angle formed by the runway and the line of sight.

With this information you can find the remaining angle:

180 - (90 + 18)

180 - 108 = 72

Let Angle B = 72°

Angle A = 18°

Angle C =90°

We have one side - 140 feet - this is side a - it is across from angle A.

There is a right triangle formed by the runway (side b) the tower, side a, and the line of sight (side c)

Using the law of sines:

sin A/a = sinB/b

sin 18°/a = sin72°/b

.3090/140 = .9510/x

cross multiply and then divide

140 × .9510/.3090

133.14/.3090

430.873 ft

round to a tenth = 430.9 ft