Find the following for the given functions.
f(x): =
X/X + 9 ,
g(x) = x³

Answer:

To find the ordered pairs that are solutions to the equation X+2y=8, we need to isolate the variable y on one side of the equation.

We can start by subtracting X from both sides:

X+2y = 8

X+2y-X = 8-X

2y = 8-X

Now we can divide both sides by 2:

y = (8-X)/2

So the ordered pairs (X, y) that are solutions to the equation X+2y=8 are the ones that satisfy the equation y = (8-X)/2.

We can substitute any value of x into the equation and find the corresponding y value.

For example, if we take X= 4, we can find the corresponding y value:

y = (8-4)/2 = 4/2 = 2.

so (4,2) is a solution to the equation X+2y=8.

We can also plot the equation on a Cartesian plane and find the points where the equation is true, those are the solutions.

Alternatively, we can solve the equation for X and find the solutions for y.

X = 8-2y

So the ordered pairs (X, y) that are solutions to the equation X+2y=8 are the ones that satisfy the equation X = 8-2y

We can substitute any value of y into the equation and find the corresponding X value.

For example, if we take y= 2, we can find the corresponding X value:

X = 8-2(2) = 8-4 = 4.

so (4,2) is a solution to the equation X+2y=8.

In this case, any value of X and y that satisfies the equations y = (8-X)/2 or X = 8-2y are solutions to the equation X+2y=8

The simple random sample of 200 eggs

Statistic=Proportion of eggs in the sample that contain salmonella.

p = 0.045

The population is the individuals that are being studied.

population=All eggs in one day

A sample is the part of the population of which information was actually collected.

Sample=The simple random sample of 200 eggs

A parameter is a descriptive measure for a population.

Parameter=Proportion of eggs shipped that day that contain salmonella.

p = 0.1 % =0.001

A statistic is a descriptive measure for a sample.

STATISTIC=Proportion of eggs in the sample that contain salmonella.

p=9÷200 = 0.045

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The work done by stretching the spring to the given distance is:

[tex]W=\frac{kx_{0} }{3}[/tex]

The given parameters:

Applied force on the spring = F

Extension of the spring, = x₀

The work done by stretching the spring to the given distance is calculated as follows:

[tex]W=\int\limits^b_a {F} \, dx[/tex]

Where:

F - Force.

W- Work.

x- Distance.

If we know that F=k.x², then the work of the nonlinear spring is:

[tex]W=\int\limits^b_a {F} \, dx \\W=\int\limits^b_a {kx^2} \, dx \\W=k\int\limits^b_a {x^2} \, dx \\\\W=k[\frac{x^3}{3}]\\\\W=k[\frac{x_b-x_a}{3} ]\\\\W=k[\frac{x_o-0}{3} ][/tex]      

W=kx₀/3

Thus, the work done by stretching the spring to the given distance is: W=kx₀/3

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When two pairs of corresponding angles and the included pair of sides are likewise congruent, a triangle is said to be congruent.

When two triangles can be superimposed, have identical side lengths, and equal angles, they are said to be congruent.

Triangles with the same angle measurements and side lengths are said to be congruent. SSS (Side-Side-Side) SAS are the triangle congruence criteria (Side-Angle-Side). When they have, triangles are congruent. There are precisely the same three sides and three angles.

Triangles are said to be congruent if two pairs of corresponding angles and the included pair of sides are also congruent. The triangles are congruent if a pair of sides that are not included and two pairs of comparable angles are congruent.

When the coordinates of XYZ are converted to produce its congruent image, X'Y'Z.

The triangle XYZ's translated picture is X'Y'Z'.

The triangle XYZ's reflected image becomes X'Y'Z'.

The triangle XYZ does not turn into its rotated counterpart, X'Y'Z'.

Therefore, Option I and II are true statements. so D is the correct answer.

The complete question is:

XYZ is transformed on a coordinate plane to obtain its congruent image X'Y'Z. Which of the following statements could be true?

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Mario can mail the books in the box, as the weight of the books is less than the weight of the box.

The total weight is obtained applying proportions, converting the fractions to decimal, dividing the numerator by the denominator.

The weights of each book are given as follows:

Hence the total weight for the books is given as follows:

0.625 + 0.4375 + 0.75 = 1.8125 pounds.

The weight of the box is given as follows:

2 + 0.5 = 2.5 pounds.

Hence Mario can mail the books in the box, as the weight of the books is less than the weight of the box.

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Answer:

307,8

Step-by-step explanation:

The area of a circle is 3.14 times the radius squared, and the radius is the diameter divided by 2. Hence the area is 307.8

The following congruence theorems can be applied to every triangle in the provided pair:

1) SSS

2) SAS

3)SAS

4) SSS

5) SAS

6) SAS

1) We can observe from the that;

FY ≅ CW

FP ≅ CM

YP ≅ MW

This proves the Side-Side-Side (SSS) congruency theorem, which states that the three corresponding sides of the two triangles are congruent.

2) We can observe from the picture that;

CBD and BCA are congruent because they both have alternate interior angles. Thus;

CBD and BCA

We can also see that

EB ≅ EC

DB ≅ CA

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

Using the Side-Angle-Side (SAS) congruency theorem, construct BED and AEC.

3) The image demonstrates that;

SVU and SVT

The shared sides provide using the reflexive property;

SV ≅ SV

VT ≅ VU

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

Side-Angle-Side (SAS) congruency theory is used by VSU and VST.

4) The picture shows what;

MN ≅ QP

MQ ≅ NP

The shared sides provide using the reflexive property;

NQ ≅ NQ

This implies that the three corresponding sides of the two triangles are congruent, which, according to the Side-Side-Side (SSS) congruency theorem, means that QNM QNP.

5) The image demonstrates that;

GL ≅ HL

GJ ≅ HK

JLG and HLK are incongruent angles in the vertical direction;

JLG and HLK

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

employing the Side-Angle-Side (SAS) congruency theorem, QNM and QNP.

6) From the triangles provided, we note that;

XZY and XZW (They both form a straight angle of 90 degrees.)

The shared side is congruent to itself using reflexive property, therefore;

XZ ≅ XZ

Also;

ZW ≅ ZY

Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent

Using the Side-Angle-Side (SAS) congruency theorem, XYZ = XWZ.

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Complete question:

Step-by-step explanation:

what is missing is the definition that QS is the height and therefore standing at a right angle (90°) at PR.

then this can be solved.

we use Pythagoras

c² = a² + b²

c being the Hypotenuse (the side opposite of the 90° angle), a and b are the legs.

let's start with the triangle PQS.

21² = 15² + QS²

441 = 225 + QS²

QS² = 216

QS = sqrt(216) = sqrt(36×6) = 6×sqrt(6) = 14.69693846...

now for triangle QSR

(5x - 16)² = (3x - 4)² + QS²

25x² - 160x + 256 = 9x² - 24x + 16 + 216

16x² - 136x + 24 = 0

2x² - 17x + 3 = 0

the solution to a quadratic equation

ax² + bx + c = 0

is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

x = (17 ± sqrt(17² - 4×2×3))/(2×2) =

= (17 ± sqrt(289 - 24))/4 = (17 ± sqrt(265))/4

x1 = (17 + 16.2788206...)/4 = 8.319705149...

x2 = (17 - 16.2788206...)/4 = 0.180294851...

but using x2 in side lengths 3x - 4 or 5x - 16 gives us negative side lengths. that does not make any sense for actual side lengths.

so, x1 is our solution :

x = 8.319705149...

The coordinates of the fourth vertex is (1,-8).

As three of a parallelogram's vertices, we were given:

(3,-2), (-1,-4), (5,-6). (5,-6).

We see that (3,-2) and (-1,-4) form a diagonal after charting the points as in the attachment.

The midpoint formula determines what point on this diagonal is in the middle.

Keep in mind that both diagonals' midpoints are identical.

Specify the coordinates of the fourth point (x,y).

As a result of once more applying the midpoint formula to (3, -2), we get:

x=1 and y=-8

The fourth point's locational details are as follows:

(1,-8).

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The complete question is,

A good can be produced for a total cost of 600 or 850 when making 100 units and 150 units, respectively. Discover an equation for TC in terms of Q, the number of generated units, presuming that the total cost function is linear.

Answer:

y = 5.25 [tex](8)^{x}[/tex]

Step-by-step explanation:

the general form of an exponential function is

y = a [tex](b)^{x}[/tex]

to find a and b , substitute the coordinates of the given points into the equation.

using (2, 336 )

336 = a b² → (1)

using (3, 2688 )

2688 = a b³ → (2)

divide (2) by (1)

[tex]\frac{ab^3}{ab^2}[/tex] = [tex]\frac{2688}{336}[/tex] ( cancel ab on numerator/denominator of left side )

b = 8

substitute b = 8 into (1) and solve for a

336 = a × 8² = 64a ( divide both sides by 64 )

5.25 = a

then exponential function is

y = 5.25 [tex](8)^{x}[/tex]

We can see here that the people of ages 18-29 that have tried vaping or e-cigarettes is: 25,803,450.

Population refers to the number of individuals of a particular species living in a particular area or region. In the context of human populations, it refers to the number of people living in a particular geographic area or country.

To find out the number of people ages 18-29 who said they have tried vaping or e-cigarettes, you can use the following calculation:

30,357,000 (the number of people ages 18-29) x 0.85 (the percentage of people who have tried vaping or e-cigarettes) = 25,803,450.

So, approximately 25,743,950 people ages 18-29 said that they have tried vaping or e-cigarettes.

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Answer:

6 votes

Step-by-step explanation:

The shingles are in the 6th row is 110 using arithmetic process.

A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.

The study of numbers and the operations on those numbers, which are relevant to all other branches of mathematics, is the focus of a branch of mathematics known as arithmetic operations. It includes addition, subtraction, multiplication, and division as its fundamental operations.

Given that A = 75 and d = 7, n = 6

A₆ = A + (n-1)d

A₆ = 75 + (6-1)7

A₆ = 75 + 5 * 7

A₆ = 75 + 35

A₆ = 110

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Answer:

33

Step-by-step explanation:

it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!

STARTS AT 75

row one: 68

row two: 61

row three:54

row four: 47

row five: 40

row six: 33

Answer:

To add or subtract fractions, they must have a common denominator. In this case, the denominators of the fractions are 2 and 8, which are not the same. To find the least common multiple of 2 and 8, we can list the multiples of each number and find the smallest one that is common to both:

2: 2, 4, 6, 8, 10, 12, 14, ...

8: 8, 16, 24, 32, ...

The least common multiple of 2 and 8 is 8. Therefore, to add or subtract the fractions, we must convert them to have a denominator of 8.

-3/2 = -12/8 and 3/8 = 3/8

So, -3/2 - 3/8 = -12/8 - 3/8

Now we can subtract the fractions directly:

-12/8 - 3/8 = -12 - 3 / 8

= -15/8

Therefore, the simplified form of -3/2 - 3/8 is -15/8

The average income per household that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.

The correlation of variables is the statistical relationship between two variables.

A correlation is positive if both variables move in the same direction and negative if the variables move in different directions - as one variable increases, the other decreases.

Correlation does not imply causation: This means that one can not legitimately associate a cause-and-effect relationship between the two variables.

In this example, it cannot be legitimately shown that increasing the number of cars per household would cause members of the community members to purchase health insurance, but when we bring in the lurking variable.

which is the increase in average income per household, we can see that this possibility might cause more people to buy more health insurance even after they have purchased cars, because they have more money to spend.

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The probabilities of adults who drinks only coffee , both/ coffee ,soda and doesn't drink any are 5% , 65% and 35%.

Let A be the event that an adult consumes coffee.

Let B be the event that an adult consumes carbonated soda.

Given probabilities of the events.

P (A) = 0.4

P (B) = 0.6

P(A∩B) = 0.35

(a). P(A)  - P(A∩B) = 0.4 - 0.35

                             = 0.05 OR 5 %

(b). P(AUB) = P (A) + P (B) - P(A∩B)

                   = 0.4 + 0.6 - 0.35

                   = 0.65 OR 65%

(c). The given case represents compliment of the event when the adult consumes at least one of the drink. According to probability axiom, the probability is given by:

P ((AUB)') = 1 - P (AUB) = 1-0.65 = 0.35

Therefore,

P ((AUB)') = 0.35 or 35 %.

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The margin of error, given the percentage who replied that Newton ate the apple, is 3.5%.

The margin of error is a measure of how much the sample results are likely to vary from the true population value.

To calculate the margin of error, you need to know the sample size, the proportion of the sample that gave a particular response, and the level of confidence.

The formula for the margin of error is:

Margin of Error = z x √(p x ( 1 - p) / n)

where:

z = the critical value from the standard normal distribution table

p = the proportion of the sample that gave a particular response

n = the sample size

The margin of error for Newton eating the apple is therefore:

Margin of Error = 1.96 x √(0.28 x (1 - 0.28) / 581)

Margin of Error = 1.96 * √(0.00035)

Margin of Error = 1.96 * 0.018

Margin of Error = 0.035

The margin of error is therefore 3.5%.

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If f(x) = x⁴ + 2, g(x) = x-6 and h(x) = √x , then the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.

What is the polynomial expression?

Any expression which consists of variables, constants, and exponents, and is combined using mathematical operators like addition, subtraction, multiplication, and division is a polynomial expression.

We can simplify f(g(h(x))) by first evaluating h(x), then substituting the result into g(x), and finally substituting the result into f(x).

Starting with h(x) = √x, we can substitute this into g(x) to get:

g(h(x)) = g(√x) = √x - 6

Next, we can substitute g(h(x)) = √x - 6 into f(x) to get:

f(g(h(x))) = f(√x - 6) = (√x - 6)⁴ + 2

Simplifying this expression requires some algebraic manipulation, but we can expand (√x - 6)⁴ using the binomial theorem or by using the method of FOIL (first, outer, inner, last) repeatedly. Either way, we will end up with a polynomial expression in x with terms of various degrees.

Therefore, the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.

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Answer:

The slope of a line is represented by the coefficient of the x-term in the equation, which is also known as the "rise over run" or change in y over change in x.

In this equation y = 29/8x - 2/3

The coefficient of the x-term is 29/8, so the slope of the line is 29/8.

Answer:

y ≥ -x -7

Step-by-step explanation:

The inequality is greater than or equal to because it is above the line and it is a solid line.

The slope is -1.  If you select a point on the line, you go down one unit and one unit to the right to get back on the line.  The slope is the rise over the run.  -1/1 = -1

The y intercept is where the graph crosses the y axis (0,-7) So the y intercept is -7

50 breaks do they make.

An equation is a mathematical statement that shows the relationship between two values, or variables. It is formed by using an equal sign between two expressions that have the same value. Equations are used to solve for unknown values, or to describe a relationship between two or more variables. Equations can be used to solve for a single variable or multiple variables, and can be used to solve problems in both mathematics and science.
To find the answer to this question we must use the formula V = L x W x H. In this case, V = 10 x 9 x 4 = 360. We now know that there is 360 cubic inches in each brick. To find the total number of bricks that can be made from 18,000 cubic inches of concrete, we must divide 18,000 by 360. The answer is 50, which means that the company can make 50 concrete bricks from 18,000 cubic inches of concrete.

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The correct answer is d.  The standard form of the equation of f(x) is −x2 + 6x + 16.

A downward opening parabola is a curve in the shape of a parabola that opens downward and is symmetrical about the x-axis. The equation of a downward opening parabola is y = ax^2 + bx + c, where a is a negative number, and b and c are constants.

The focus of a downward opening parabola is the point on the parabola where the curvature is greatest and is located at the vertex of the parabola.

The directrix of a downward opening parabola is a line parallel to the x-axis and the distance from the focus to the directrix is equal to the length of the latus rectum of the parabola. The equation of the directrix is y = -a(x - h)^2 + k, where h and k are constants.

Downward opening parabolas can be used to graphically represent any type of data that follows a parabolic shape. This includes physical phenomena such as the path of a projectile or the vibration of a string.

Downward opening parabolas can also be used to model economic or financial data, such as the demand for a product or the price of a commodity. They may also be used to describe relationships between two variables in a mathematical equation.

The standard form of a parabola equation is f(x) = ax2 + bx + c, where a, b, and c are real numbers. In this case, the vertex of the parabola is at (3, 25), so the equation is in the form f(x) = a(x - 3)2 + 25. Putting in the other points on the graph to solve for a, b, and c yields the equation f(x) = -x2 + 6x + 16.

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[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +7= -\cfrac{4}{3} (x -3) \\\\\\ y+7=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x-3 \end{array}}[/tex]

To reach the speed of light, the spaceship will take 3.1 × 10⁷ seconds. The result is obtained by using the formula for acceleration.

Acceleration is the rate of change in velocity of an object with respect to time. It can be expressed as

[tex]a = \frac{\Delta v}{\Delta t}[/tex]

Where

If we were in a spaceship with an acceleration of g, determine the time we reach the speed of light!

We have

To find the time so that we can reach the speed of light, we use the formula for acceleration.

[tex]a = \frac{\Delta v}{\Delta t}[/tex]

[tex]g = \frac{c - 0}{\Delta t}[/tex]

[tex]9.8 = \frac{3 \times 10^{8}}{\Delta t}[/tex]

[tex]\Delta t = \frac{3 \times 10^{8}}{9.8}[/tex]

Δt = 0.306 × 10⁸

Δt = 3.1 × 10⁷ s

Hence, the spaceship will take 3.1 × 10⁷ seconds to reach the speed of light.

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Answer: 7

Step-by-step explanation:

First, we need to prime factorize the number 189,

189 = 3 × 3 × 3 × 7 × m

From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.

Hence the answer is 7

Answer: <3, 1>

Step-by-step explanation: A translation of a vector is simply moving it a certain distance in a certain direction. In this case, the first translation of  <6, -4> moves the vector 6 units to the right and 4 units down. The second translation of <-3, -5> then moves the vector an additional 3 units left and 5 units down. The net result of these two translations is to move the vector 3 units to the right and 1 unit up, which is equivalent to a single translation of <3, 1>.

Answer: Net (of a shape)

Step-by-step explanation:

Answer:

Step-by-step explanation:

no need for step by step its called a net

Answer:

5 (less than sign) 2

Step-by-step explanation:

Answer:

5n-20

Step-by-step explanation:

Product means multiply and so the product of 5 and n is 5n. To decrease this value by 20 , means to subtract 20 from it hence: 5n - 20 is algebraic expression for the statement

The coordinate of the point that partitions the given line in the ratio 2:1 is; (-8, 0)

If the coordinates are given as;

P (x₁ , y₁) and Q (x₂ , y₂) and the partition of the line segment is divided internally in the ratio m : n, then its coordinate ( x, y) given by :

( x ,y ) = [(mx₂ + nx₁)/ ( m + n), (my₂ + ny₁)/ ( m + n)]

We are given the coordinates as  ( − 8 , 10 )to ( − 8 , − 5 ) and if it is partitioned in the ratio 2: 1, the coordinates of the points of partition are;

(x, y) =  [(2(-8) + 1(-8))/ (2 + 1), (2(-5) + 1(10))/ (2 + 1)]

(x, y) = (-24/3), (0/3)

(x, y) = (-8, 0)

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The constant of proportionality is equal to 6.

In Mathematics, a proportional relationship is a type of relationship that generates equivalent ratios and it can be modeled or represented by the following mathematical expression:

y = kx

Where:

Next, we would determine the constant of proportionality (k) for the relationship between correct answers and points on this graph as follows:

Constant of proportionality, k = y/x

Constant of proportionality, k = 30/5 = 72/12 = 108/18 = 120/20

Constant of proportionality, k = 6

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Answer:

6

Step-by-step explanation:

120/20 = 6

108/18 = 6

72/12 = 6

30/5 = 6

See the pattern? :)