Amber wants to put a carpet on the floor of her bedroom. The floor is a square with an area of 7.29 square feet. How long should the piece of carpet on each side

In the polynomial expression f(x) = x³ + px² +  qx +r, the values of p is 1/5, q is -66/5 and r is 12.

Polynomial:

Polynomial means an expression which is composed of variables, constants and exponents, that are combined using mathematical operations such as addition, subtraction, multiplication and division.

Given,

Here we have the polynomial f(x) = x³ + px² +  qx +r

And it is divisible by (x+2),(x-1),and (x-3) the remainders are respectively -48,0 and 2.

Here we need to find the value of p, q and r.

Let us consider that the equations,

x + 2 = 0 then x = -2

x - 1 = 0 then x = 1

x - 3 = 0 then x = 3.

Now, apply these values on the polynomial expression then we get,

f(-2) = (-2)³ + p(-2)² +  q(-2) +r = -48

f(-2) = -8 + 4p - 2q +r = -48

f(-2) = 4p - 2q +r = -48 + 8

f(-2) = 4p - 2q + r = -40 ----------------------(1)

Apply the value of x as 1, then we get

f(1) = (1)³ + p(1)² +  q(1) +r = 0

f(1) = 1 + p + q + r = 0

f(1) = p + q + r = -1 ----------------------(2)

Apply the value of x as 3, then we get

f(3) = (3)³ + p(3)² +  q(3) + r = 2

f(3) = 27 + 9p + 3q + r = 2

f(3) = 9p + 3q + r = -25 ----------------------(3)

Now we have to solve the equation (2) and (1), then we get,

=> (4p -p) + (-2q - q) + (r - r) = -40 - (-1)

=> 3p -3p = -39

Divide it by 3, then we get

=> p - q = -13 ----------------------(4)

Similarly, solve equations (2) and (3), then we get,

=> (9p - p) + (3q - q) + (r - r) = -25 - (-1)

=> 8p + 2q = -24

Divide it by 2, then we get,

=> 4p + q = -12 ---------------------------(5)

Solve the equations (4) and (5), then we get,

=> (4p + p) + (q - q) = -12 - (-13)

=> 5p = 1

=> p = 1/5

Apply the value of p on equation (4), then we get the value of q as,

=> (1/5) - q = -13

=> -q = -13 -1/5

=> -q = -66/5

Apply the value of p and q on equation (2), then we get,

=> 1/5 + (-66/5) + r = -1

=> -65/5 + r = -1

=> -13 + r = -1

=> r = 12

Therefore, the value of p is 1/5, q is -66/5 and r is 12.

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The most appropriate form for equation of circle will be given by-

Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units

What is equation of circle?

A round figure whose all points on the boundary maintains a fixed distance from a point known as the centre of the circle and the fixed distance is called the radius of the circle.

If radius of a circle is doubled, we will obtain the diameter of the circle.

Equation of circle

[tex](x-a)^2 + (y-b)^2 = r ^2[/tex]

where (a, b) is the centre of the circle and r is the radius of the circle.

Here,

[tex]x^2 + y^2 + 10x-6y + 15 = 0[/tex]

[tex]x^2 + 2\times x\times 5 + 5^2 -5^2 +y^2 -2\times y\times 3 + 3^2 - 3^2 + 15 = 0\\(x+5)^2 + (y-3)^2-25-9+15=0\\(x+5)^2 + (y-3)^2-19=0\\(x+5)^2 + (y-3)^2=19\\ (x+5)^2 + (y-3)^2=\sqrt{19}^2\\[/tex]

Centre = (-5, 3) and radius is [tex]\sqrt{19}[/tex] units

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Answer:

it algebra

Step-by-step explanation:

10x-6x=4x

Then the equation becomes

4x+9=-19

Then you subtract the 9 from -19

4x=-28

Now you have to separate the 4 from x

4x/4 and -28/4

So now you get

X=-7

The sequence(s) of translations and reflections that were performed to show given two figures are congruent:

- Translate triangle ABC down and then reflect across vertical line.

- Reflect triangle ABC across vertical line and then translate down.

- ΔABC ≅ ΔDEF

In this question, we have been given a triangle and its image.

We need to select all sequence of translations and reflections that performed to show given figures in each pair are congruent.

From figure, we can see that the image of vertex A is vertex D, the image of vertex B is vertex E and the image of vertex C is vertex F.

In we translate the triangle ABC down and then reflect across vertical line then the image would be DEF.

We can do the same transformation by reflecting triangle ABC across the vertical line and then translating it down.

From above, we can conclude that, ΔABC ≅ ΔDEF

Therefore, the sequence(s) of translations and reflections that were performed to show given two figures are congruent:

- Translate triangle ABC down and then reflect across vertical line.

- Reflect triangle ABC across vertical line and then translate down.

- ΔABC ≅ ΔDEF

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Answer: 5.13

Step-by-step explanation:

1) Set up the equation

3.8(1.35)

2) Solve

5.13

The measure of the exterior angle is a = 54

Where is the exterior angle?

the exterior angle 2a = a + 10 + 44

                               2a  = a + 54

                                 2a - a = 54

                                      a = 54

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The number 4,300,000,000 in scientific notation is 4.3x10⁹.

What is a number?

A number is a quantitative entity that may be used to tally, measure, and name things. The natural numbers 1, 2, 3, 4, and so on are the original instances. Number words can be used to represent numbers in language. Individual numbers can be represented more generically by symbols known as numerals; for example, "5" is a numeral that represents the number five. Because only a small number of symbols can be memorized, fundamental numerals are often structured in a numeral system, which is a systematic method of representing any number. The most prevalent numeral system is the Hindu-Arabic numeral system, which allows any number to be represented using a combination of 10 fundamental numeric symbols known as digits.

The number 4,300,000,000 in scientific notation is 4.3x10⁹.

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Let

y -----> candle heigh in centimeters

x ----> burning time in hours

In this problem we have the ordered pairs

(5,22.5) and (17,16.5)

step 1

Find out the slope

m=(16.5-22.5)/(17-5)

m=-6/12

m=-1/2 -----> is negative because is a decreasing function

step 2

Find out the equation in slope-intercept form

y=mx+b

we have

m=-1/2

point (5,22.5)

substitute

22.5=-(1/2)(5)+b

solve for b

b=22.5+2.5

b=25

therefore

y=-(1/2)x+25

step 3

For x=7 hours

substitute in the equation

y=-(1/2)(7)+25

y=-3.5+25

The Solution:

Given the equation that modeled the population of fish after time (t) in years as below:

part 1:

We are to find the initial population of fish. This means we are to find the value of p when t = 0.

Part 2:

We are required to find the doubling time (t) for this population (Round the answer to the nearest tenth). This means we are to find t when P(t) = 500.

Note: double of 250 fish is 2x250 = 500 fish.

Dividing both sides by 3, we get

Taking the natural log of both sides, we get

Answer:

-1

Step-by-step explanation:

when you change g[×] to g[-2] , 3x+5 change to 3[-2] +5

8.32 Km is the distance of how much it would be covered

A unit rate means a quantity at a rate of one of something.

The distance traveled with 2 liters of petrol is 47.9 km.

A unit rate means a quantity at a rate of one of something.

It is written with a denominator of one. 

Example:

Man can walk 6km in 2 hours.

In one hour a man can walk 3 km.

We have,

A vehicle covers a distance of 524/25 kilometers on 7/8 liters of petrol.

This can be written as:

524/25 km = 7/8 liters

Multiply both sides by 8/7

8/7 x 524/25 km = 1 liter

23.95 km = 1 liter _____(1)

Now,

Multiply 2 on both sides of (1)

2 x 1 liter = 2 x 23.95 km

2 liter = 47.9 km

Thus,

The distance traveled with 2 liters of petrol is 47.9 km.

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It is to be noted that the graph of g(x) = (x+2)³ -6 compares to the parent function f(x) = x³ in that g(x) is shifted 2 units to the left and 6 units down. See the explanation below.

A parent function in mathematics is the simplest function in a family of functions that retains the concept of the whole family.

Here is how the transformation of a function can occur

Any change can occur during the transformation of a function.

Typically, they can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.

If the initial function is y = f(x), and the horizontal axis represents inputs and the vertical axis represents outputs, then:

Horizontal shift (also called phase shift):

Vertical shift

Stretching:

A function sets the value of one set's elements to the value of another set's specified element.

Given that the parent function is f(x)=x³, while the transformed function is g(x)=(x+2)³ - 6. Therefore, the transformation of the parent function that results in the transformed function is that g(x) is shifted 2 units to the left and 6 units down.

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The transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.

The function is a type of relation, or rule, that maps one input to a specific single output.

A change can be moved horizontally or vertically (by changing inputs or outputs), stretched (by multiplying outputs or inputs), and so on.

If the initial function is y = f(x), and the horizontal axis shows the inputs and the vertical axis shows outputs, then:

Horizontal shift would be Left shift by c units; y=f(x+c) and Right shift by c units; y=f(x-c)

Vertical shift would be Up by d units; y = f(x) + d and Down by d units; y = f(x) - d

Stretching would be as Vertical stretch by a factor k: y = k × f(x)

Horizontal stretch by a factor k: y = f(x/k)

Given that the parent function is; f(x)=x³,

And the transformed function is; g(x)=(x+2)³ - 6.

Hence, the transformation of the parent function results in the transformation which shows g(x) is shifted 2 units to the left and 6 units down.

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Answer:

Pues hablemos primero de lo que sucede antes de apagar la luz y usemos como ejemplo el viaje de un solo fotón.

Un fotón proveniente de un bombillo de luz blanca se dispara en línea recta hacia la pared. El material que cubre la pared, en este caso la pintura, tiene ciertas propiedades físicas y la energía del fotón es absorbida por un electrón de algún átomo de esa superficie. Ocurre una excitación del electrón, el cual ahora tiene más energía de la que normalmente tiene en su estado fundamental, y para regresar a su estado fundamental emite parte de esa energía como un nuevo fotón, este último de menor energía (frecuencia) que el anterior. La frecuencia dependerá del material y esa nueva frecuencia es la que da color a la pared. La luz blanca está compuesta por fotones de distintas frecuencias. Los de baja frecuencia son absorbidos y lo que se emite es en forma de calor, lo cual no puedes ver con tus ojos. Los de alta frecuencia tienen suficiente energía para que la energía que se re-emite sea visible y posiblemente sea re-emitida, cada vez con menos energía. Uno habla de que la luz “rebota” en el objeto. (Aunque “rebotar” no es necesariamente la acción correcta, voy a usar el término para simplificar).

Ahora digamos que ese fotón que “rebotó” en la pared rebota en otra pared y otra pared. Ese fotón es solo visible si en ese rebotar llega a tu ojo antes de que su energía sea demasiado baja. No podemos ver el calor ni las microondas que son fotones de baja energía. Al final la energía se va a convertir en calor, el cual es invisible al ojo humano.

Ese es el trayecto de un solo fotón. El bombillo produce un flujo de fotones en todas direcciones. Hay que recordar que esos fotones viajan a la velocidad de la luz. Cuando el bombillo se apaga, se interrumpe el flujo de fotones. Si se movieran a la velocidad del agua en una manguera, verías el flujo rebotando por varios segundos hasta que los fotones que más han rebotado desaparecen de tu vista por aquello de la baja frecuencia energética. Pero al viajar a la velocidad de la luz, el tamaño de la habitación se hace irrelevante y nuestra experiencia es prácticamente instantánea.

¿A donde va la luz? La luz no sale de la habitación sino que la calienta.

27.80% is percentage of items .

What percentage means?

Mean = 7

standard deviation = 3 ounces

Required % = p (5.6<x < 7.1 ) × 100 = ?

z = x - μ/σ = 5.6 - 7/2

 z = 7.1 - 7/2 = 0.05

∴ P(5.6 < x < 7.1 ) = p ( - 0.7 < z < 0.05 )

   p( z < 0.05 ) - p (  z < - 0.7)

= 0.51994 - 0.24196 ≅ 0.2780

So, required % =  0.2780 × 100

                         = 27.80%

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Answer:

2-33i

Step-by-step explanation:

(2 − 5i)(3 + 7i) − (4 + 3i)   |Set up equation|

6+14i-15i-35i-(4+3i)         |Multiply the numbers in the parentheses together using the distributive property|

6-1i-35i-(4+3i)                       Subtract like terms

6-36i-(4+3i)                           Subtract like terms

6-4-36i+31                          Open parentheses and put like terms together

2-33i                                    Answer

Hope this helped!

The expression which is equivalent to; 2x² - 2x + 7 as required in the task content is; 2 (x - 0.5)² + 6.5.

It follows from the task content that the expression which is equivalent to; 2x² - 2x + 7 is to be determined.

Therefore, since the expression whose equivalent is to be determined is; 2x² - 2x + 7; we have;

2x² - 2x + 7

By completing the square method; we have;

2(x² - x) + 7

2 {(x - 0.5)² - 0.25} + 7.

2 (x - 0.5)² - 0.5 + 7

2 (x - 0.5)² + 6.5

Therefore, the required expression which is equivalent to the given expression is; 2 (x - 0.5)² + 6.5.

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In order to determine the number of people in the sample for each age group, here are the steps:

1. Determine what proportion in the entire population the population of each group. To get the proportion, simply divide the population of each respective group by the entire population.

2. To get the number of samples for each group, multiply the proportion by 5,000 and round the answer to the nearest whole number.

Now, let's apply the steps above in each group.

Let's start with ages under 18.

Hence, we are expected to have 1,201 people aged under 18 in the sample.

For those aged 18 - 44,

Hence, we are expected to have 1,827 people aged 18-44 in the sample.

For those aged 45 - 64,

The expected number of samples for people aged 45-64 is 1,320.

Lastly, for aged 65 and over,

The expected number of samples for people aged 65 and over is 652.

To summarize, we have:

Age under 18 ⇒ 1,201 samples

18 - 44 ⇒ 1,827 samples

45 - 64 ⇒ 1,320 samples

65 and over ⇒ 652 samples

.

Answer:

translates up 8 and 5 left

Step-by-step explanation:

To find the distance (x) it translate up, -3 + x = 5 where x = 8

To find the distance (x) it translate left, 2 + x = 7 where x = 5

Answer:

(x, y) → (x-5, y+8)

Step-by-step explanation:

A translation is a type of transformation that moves a figure up, down, left or right.

Calculate the change in the coordinates by subtracting the coordinates of point D from the coordinates of point D':

[tex]\implies (x_{D'}-x_D, y_{D'}-y_D)[/tex]

[tex]\implies (2-7, 5-(-3))[/tex]

[tex]\implies (-5, 8)[/tex]

Therefore, to map point D onto point D', move 5 units left and 8 units up.

Therefore, the translation rule that maps point D(7, -3) onto point D'(2, 5) is:

If the front suspension system of a car has coiled springs of spring constant(k) of about 82,000N/m attached to the front wheels, then the force required to compress this spring by 1.2 cms will be  984N.

As per the question statement, the front suspension system of a passenger car has coiled springs attached to the front wheels and a typical spring has a spring constant "k" of about 82,000 k/m.

We are required to calculate the force required to compress this spring by 1.2 cms

To solve this question, we will need to apply the formula to calculate the force to compress a spring, which is known as the Hooke's Law. So, as per the Hooke's Law, the force (F) required to compress a spring of spring constant (k) by "x" units, can be represented as

[F = (k * x)]

Now comparing the RHS of the Hooke's Law equation with the data provided in the question statement, we get, (k = 82000 N/m) and

(x = 0.012 m), and using these values in the Hooke's law equation, we get, the force required to compress a spring of spring constant(k) of about 82,000N/m by 1.2 cms will be (82000 * 0.012)N = 984 N.

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The amount of money that Kamauri has at first will be 32.22.

From the information, it was stated that after paying 5.12 for salad, Kamauri has 27.10.

Based on the information given, the total amount of money that he had at first will be the addition of the cost of salad and the change left.

This will be illustrated as:

= 5.12 + 27.10

= 32.22

The amount is 32.22.

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After paying 5.12 for salad, Kamauri has 27.10. What was the total amount of money that he had at first?

A number that contains both positive and negative integers, including zero, is called an integer. There are no fractional or decimal parts in it. Here are a few instances of integers: -5, 0, 1, 5, 8, 97, and 3,043

Integers, as opposed to fractions or decimals, are all whole numbers plus their antipodes. For instance, numbers include -3, -2, -1, 0, 1, 2, 3,... On a number line, positive numbers are those to the right of zero. Negative numbers are those to the left of 0

An integer, pronounced "IN-tuh-jer," is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043.

False. An integer is a whole number.

False. For instance, 1/2 is not a whole number but is a rational number.

False. For instance, -3 is not a whole number but is an integer.

True. Rational numbers include all integers.

Answers:

False

False

False

True

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Answer:

Step-by-step explanation:

So, what you need to do is find out the formula for this question. And your answer will come out to be x=32

The various values using mathematical operations are;

1) B: 70

2) C:  1300

3) A: 0.0063

4) B: 0.0037

5) B:  80

1) We want to multiply 0.7 times 100.

Now, 0.7 can be expressed as 0.7 = 7/10. Thus;

0.7 * 100 = 7/10 * 100 = 70

2) We want to multiply 0.13 by 10000.

0.13 can be expressed as;

0.13 = 13/100. Thus;

0.13 * 10000 = 13/100 * 10000 = 1300

3) We want to multiply 0.63 times 0.01.

They can be expressed as;

63/100 * 1/100 = 63/10000 = 0.0063

4) Divide 0.37 by 100.

0.37 can be expressed as 37/100. Thus;

0.37/100 = 37/100 ÷ 100

= 37/100 * 1/100 = 37/10000 = 0.0037

5) Divide 0.8 divided by 0.01.

They can be expressed as;

8/10  ÷ 1/100

= 8/10 * 100/1

= 80

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Answer:7 6/10 is the answer if you turn a fraction into a decimal like so

7.5=7.5, 7 6/10=7.6, 7 2/5=7.4, 7.02=7.02 i hope i helped

Step-by-step explanation:

Answer:  [tex]7\frac{6}{10}[/tex] is closest to 8.

Step-by-step explanation:

[tex]7\frac{6}{10} =\frac{70}{10} +\frac{6}{10} = \frac{76}{10} = 7.6[/tex]

[tex]7\frac{2}{5} = \frac{35}{5} +\frac{2}{5} =\frac{37}{5} =7.4[/tex]

7.02 < 7.4 < 7.5 < 7.6

7.02 < [tex]7\frac{2}{5}[/tex] < 7.5 < [tex]7\frac{6}{10}[/tex]

The expression given: 7/6 x 3  can be calculated to get 7/2

This is a basic math operation that helps to determine the product of two or more numbers.

The numbers given here include a whole number and a fraction

A fraction refers  to classification of numbers to be represented as having a stroke dividing the two groups of numbers.

The numbers on top is referred to as numerators while the numbers below is referred to as the denominator

in the question the fraction is 7/6: The numerator is 7 while the denominator is 6

= 7/6 * 3

= 7/2

= 3.5

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Answer:

f(3) = -11

f(-5) = 37

Step-by-step explanation:

f(x) = -6x + 7

We want to find f(3) and f(-5)

To do so we substitute the input with any x in the equation and evaluate.

f(3) = -6x + 7

==> substitute all x's with the input, 3

f(3) = -6(3) + 7

==> multiply -6 and 3

f(3) = -18 + 7

==> add -18 and 7

f(3) = -11

f(-5) = -6x + 7

==> substitute all x's with the input -5

f(-5) = -6(-5) + 7

==> multiply -6 and -5

f(-5) = 30 + 7

==> add 30 and 7

f(-5) = 37

Answer:

261 500

Step-by-step explanation:

450x670-80x500
301500-80x500

301500-40000

261500

The 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.

Rounding is a technique to reduce a large number to a smaller, more approachable figure which is very similar to the actual. Rounding numbers can be achieved in a variety of ways.

It is given that:

14.2 cm correct 1 decimal place

14.2

Rounded to the nearest 0.1 or

the Tenths Place.

Rounded to the nearest tenth place. The 2 in the tenth place rounds down to 2 or stays the same because the digit to the right in the hundredth place is 14.2

Thus, the 14.2 cm correct 1 decimal place is 14.2 after rounding to the nearest 0.1 or the tenth place.

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Answer:

If the same cup of 190∘F soup is instead placed into a freezer set at 30∘F, what is the time required for the soup to cool from 190∘Fto135∘F in this situation?