Write the polynomial in standard form g(x) = 3(x + 2)(4x - 1)(x - 5)

The only equation that represents a piecewise defined function is;

Option A: f(x) = {-2, if x ≥ 4

        {x², if x < 4

A piecewise function is defined as a function that consists of multiple subfunctions, whereby each subfunction defined over a specific subset of the domain of the main function which is called a subdomain.

The equation of a piecewise function is usually written with a curly bracket that indicates the fact of being comprised of more than one subfunction. An example of a piecewise function is;

f(x) = {x, x < 0

        {x + 1, x ≥ 0

Let us look at each of the given functions;

Function in option A is clearly a piecewise function when compared to the definition given above

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The equation of the line with a slope of one third and passes through (-2, 1) is y = one-third x + five-thirds.

The equation of a line can be represented in a slope intercept form as follows:

y = mx + b

where

Therefore, the equation of the line has a slope of 1 / 3. Let's find the y-intercept using the coordinates (-2, 1)

y = 1 / 3 x + b

1 = 1 / 3 (-2) + b

1 + 2 / 3 = b

b = 3 + 2 / 3

b = 5 / 3

Therefore, the equation is y = 1 / 3 x + 5 / 3

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2.Under feudalism, landowners were granted plots of land (called fiefs) by nobles in exchange for their loyalty and military service. The landowner, or vassal, was required to provide the lord with soldiers when needed and give him a portion of the land's produce. In return, the lord provided the vassal with protection from invaders.

Manorialism (how did it work)

Manorialism was an economic system that developed in medieval Europe. It was based on the control of land and the produce of that land by a lord. The lord would grant land to peasants in exchange for their labor and a portion of the produce. This system allowed for the development of large estates and the growth of a class of landowners.

Justinian ( identify and achivements)

Justinian was the Byzantine emperor from 527 to 565. During his reign, Justinian sought to revive the empire's greatness and reconquer the lost western half of the historical Roman Empire.

One of Justinian's most famous achievements was the construction of the Hagia Sophia, which was completed in 537. The Hagia Sophia is a former Greek Orthodox cathedral that was turned into a mosque after the Ottoman conquest of Constantinople in 1453. It is now a museum in Istanbul, Turkey.

Another of Justinian's accomplishments was the compilation of the Justinian Code, a collection of laws that codified Roman law and is still used as a reference today. The Justinian Code was instrumental in the development of modern legal systems.

vassal

The social position and duties of a vassal during the Middle Ages was to provide military service to their lord in exchange for land that they could then cultivate. Vassals were also required to attend their lord's court and give him counsel

Knights

Serve as a military support system for the king

. Helped keep the peace within the kingdom

. Provided protection for the king and queen

. Guarded the king's castle

serf

The serfs were the lowest class of society in medieval Europe and were bound to the land that they worked on. They were required to work for their lord for a certain number of days each week and were given a plot of land to farm for themselves. They were also required to pay taxes and fees to their lord.

Answer:

C

Step-by-step explanation:

C is the input.  The input is the independent variable.  The output would be the dependent variable.

Answer:

Step-by-step explanation:

x=2.3

Answer:

The slope is 1/3, calculate the rest from there

Step-by-step explanation:

We can picture this as a graph with the x value being the shoe size and the y being the length of a foot in inches. If we visualize it that way, we have two points on the graph: (5,9) and (11,11). From this, we can calculate the slope. The formula for slope is change in y value/change in x value, or rise/run. The slope in this case would be 2/6, simplified to 1/3. From this, we know that every time the X value increases by 1, the Y value increases by 3. Using this, you can find the two points on the line yourself. The equation formula for slope is y = mx + b. M is the slope, and Y is the y intercept (the value of Y when X = 0). Since the slope is 1/3, the equation is y = 1/3x+(y intercept). I am not going to fully solve this problem for you because I have a feeling you need this answer for a test of sorts (because of the level of urgency) but with this information you can probably solve this yourself! Good luck :)

The graph of the transformation of f(x) to f(b·x), where f(1) in f(b·x) is equal to f(5) in f(x) indicates that the value of b is 5

The transformation of a function is represented by a function that changes one function into another function, such that the size, or position of the graph of the original function is modified

The given transformation of the function f is f(b·x)

A formula for the transformation of a function y = f(x) is the function;

y = a·f(b(x + c)) + d

Where;

The a indicates a vertical translation of the function

b indicates an horizontal dilation of f

c stands for a horizontal translation

d stands for a vertical translation

The translation in the question is f(b·x), which is a horizontal dilation, is expressed as follows;

When b > 1, the graph of f(x) shrinks horizontally

When 0 < b < 1, the graph of f(x) is stretched

At x = 1, f(x) = 1, and f(b·x) = 5

The graph of f(x) shrinks to obtain the graph of f(b·x), such that the value obtained at f(5) in f(x) is obtained at f(1) in f(b·x)

f(5) = f(b·1)

b×1 = 5

b = 5 ÷ 1 = 5

The value of b is 5

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The values of the variables associated ot translation operations are (w, x, y, z) = (3, 1, 0, 2 / 3).

Herein we find two translation cases of points set on Cartesian plane. Translations are rigid operations of the form:

P'(x, y) = P(x, y) + T(x, y)

Where:

Now we proceed to determine the values of the variables w, x, y, z behind each translation operation, substitute on each component and solve the resulting formula:

T(x, y) = A'(x, y) - A(x, y)

(2 · x + 1, 4) - (- 1, w) = (4, 1)

(2 · x + 2, 4 - w) = (4, 1)

(x, w) = (1, 3)

T(x, y) = B'(x, y) - B(x, y)

(3, 3 · z) - (8 · y - 1, 1) = (4, 1)

(4 - 8 · y, 3 · z - 1) = (4, 1)

(y, z) = (0, 2 / 3)

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8. -a+b-7

9. m=(y-b)/x

Answer:

first one: C

second one: A

Step-by-step explanation:

4a - 5 + 3b - 2 - 2b - 5a

combine a terms:

-a - 5 + 3b - 2 - 2b

combine b terms:

-a - 5 + b - 2

combine numbers:

-a  + b - 7 (this is option c)

_____________________

y = mx + b, solve for m

subtract b from both sides:

y - b = mx + b - b

y - b = mx

divide both sides by x:

(y - b)/x = mx/x

m = (y - b)/x (this is option a)

Answer:

He gets $7.50 per cap

Step-by-step explanation:

I took the test

Answer:

$17.50

Step-by-step explanation:

Answer:

Subtract 6 from both sides

Answer: (0,-13)

Step-by-step explanation:

The y intercept is x=0

Hence,

y=2(0²)-9*(0)-13

y=2(0)-0-13

y=0-13

y=-13

Thus, (0,-13)

Answer:

Step-by-step explanation:

Given functions,

→ f(x) = 4x + 5

Now the value of f(-3) will be,

→ f(x) = 4x + 5

→ f(-3) = 4(-3) + 5

→ f(-3) = -12 + 5

→ [ f(-3) = -7 ]

Then the value of f(3) will be,

→ f(x) = 4x + 5

→ f(3) = 4(3) + 5

→ f(3) = 12 + 5

→ [ f(3) = 17 ]

Hence, the answer of f(3) is 17.

Substitute [tex]x=-3[/tex] into [tex]f(x)=4x+5[/tex] :

[tex]f(-3)=4(-3)+5[/tex]

          [tex]=-12+5[/tex]

          [tex]=-7[/tex]

Substitute [tex]x=3[/tex] into[tex]f(x)=4x+5[/tex] :

[tex]f(3)=4(3)+5[/tex]

       [tex]=12+5[/tex]

       [tex]=17[/tex]

[tex]\text{Hence, } f(-3)=-7 \text{ and } f(x)=17.[/tex]

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The equation of the given values of x and y will be; y = 2x - 2

An equation represents equality of two or more mathematical expression.

Solutions to an equation are those values of the variables involved in that equation for which the equation is true.

We have been given the values of x and y. then we need to find the equations;

First slope

m = (4 +2)/(3 - 0)

m = 6/3 = 2

Now the standard form of the equation is;

y-y₁ = m(x-x₁)

y+ 2 = 2(x- 0)

y = 2x - 2

The graph of the given equation of line is attached below.

Hence, the equation of the given values of x and y will be; y = 2x - 2

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The equation of each line in slope-intercept form are:

1. y = 3/4x + 4.

2. y = -x - 2

To express the equation of a line in slope-intercept form, y = mx + b, substitute the value of the slope (m) and the value of the y-intercept (b) into the equation.

1. Slope (m) = 3/4

y-intercept (b) = 4

Substitute m = 3/4 and b = 4 into the equation y = mx + b:

y = 3/4x + 4.

2. Slope (m) = -1

y-intercept (b) = -2

Substitute m = -1 and b = -2 into the equation y = mx + b:

y = -x - 2

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Answer:

Her weekly allowance is $18

Step-by-step explanation:

We can use an algebraic equation to solve this problem.

x/2 + 6 = 15

x/2 + 6 ( - 6) = 15 ( - 6)

x/2 ( · 2)= 9 ( · 2)

x = 18

Her weekly allowance is $18

The population estimated minimum sample size will be 11 , and the critical value will be 1.28.

The average gorilla weight is being calculated as a range estimate by a researcher (in pounds).

She wants to be within 7.1 pounds of the actual average with 80% accuracy.

Previous research has shown that the standard deviation of the weights of gorillas is 18.2 pounds.

a)  Since the confidence is 0.80 or 80% then the value of α is 0.20 and  and we can calculate the critical value. Then the value of the z-score will be  z = 1.28.

b)  The margin of error is given as

M.E.= z*(standard deviation/√n)

We have,

Margin of error = 7.1

From the above formula we get;

n =  ((z* standard deviation )/marginal error)²

n =  ((1.28*18.2)/7.1)²

  =   10.76 ≈ 11

Therefore, the researcher should take 11 samples.

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Answer:

Step-by-step explanation:

You want the radius and water depth in a spherical bowl in which the water level is 10 cm above the center of the sphere, and the circular surface has a diameter of 30 cm.

The geometry of the diameter of the water surface can be modeled as shown in the attachment. The radius of that surface forms one leg of a right triangle with the other leg being 10 cm. The hypotenuse of the triangle is the radius of the sphere, so we have ...

  r² = 15² +10² = 325

  r = √325 = 5√13 ≈ 18.03 . . . . . cm

The water depth is 10 cm more than the radius, so is ...

  d = 10 +r = 10 +5√13 ≈ 28.03 . . . . . cm

The radius of the bowl is about 18.03 cm; the depth of water is about 28.03 cm.

Answer: Real and Rational

Step-by-step explanation:

2/3 is a fraction. ALL numbers are are considered real numbers. Rational numbers are typically fractions and decimals.

hello hope you are having a good day

the answer to your question would be A 6 miles i took the test and got an 100% also asked the teacher.

The first option Focus(2,-0.5); directrix x=0 of the parabola is the correct answer.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves. A parabola can be described using a point and a line.

The general equation of a parabola is as follows:

[tex](y-k)^2=4a(x-h)[/tex]

Now, consider the given equation.

[tex](y+0.5)^2=4(x-1)[/tex]

Now, compare with the standered equation.

a=1, k=-0.5 and h=1

Here, a is positive hence, the parbola opens right side.

Focus is given by the following coordinate:

[tex](h+a,k)=(1+1,-0.5)\\=(2,-0.5)[/tex]

Now, equation of diretrix is given by the following expression:

[tex]x=h-a\\x=1-1\\x=0[/tex]

Hence, the first option Focus(2,-0.5); directrix x=0 is the correct answer.

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The total number of water glasses on the shelf may be 39, 63 or 87.

Given, that there were more than 24 glasses, but less than 100 glasses.

If the glasses were in rows of 6, there would be 3 left over.

If the glasses were in rows of 8, there would be 7 left over.

Let the number of glasses be x,

So, x = 6k1 + 3

=> (x - 3) is a multiple of 6

x = 8k2 + 7

=> (x - 7) is a multiple of 8

Now, the numbers that can satisfy the given conditions are,

39 , 63 & 87.

So, the total number of glasses may be 39, 63 or 87.

Hence, the total number of water glasses on the shelf may be 39, 63 or 87.

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Answer:

23 boxes of pasta

Answer:

Rs 171.40

Step-by-step explanation:

For 1 apple we have to divide 120 by 14 which is 8.57 to 2d.p.

So 20 * 8.57 = 171.4

to 2d.p. = Rs 171.40

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