**Answer:**

**Step-by-step explanation:**

The distance between two points is represented by the following equation;

[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]Therefore, if the endpoints of WX are (-5,-1) and X(2,6):

[tex]\begin{gathered} d=\sqrt{(2+5)^2+(6+1)^2} \\ d=7\sqrt{2} \end{gathered}[/tex]A car has 15 gallons of gas in its tank. The car travels 35 miles per gallon of gas. It uses 1/35 of a gallon of gas to go 1 mile

Answer:

525 miles is that was what was being asked

Step-by-step explanation:

sorry I don't know the quest but the car can travel a total of 525 miles with 15 gallons in the tank

15 times 35=525

what is the height of the candle after 7 hours

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

y=21.5 cmafter paying 5.12 salad , kamauri has 27.10

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?

R obery and dora need to write 4,300,000,000 using scentific notation robert wrote 4,300,000,000=4.3 10 9 whick descrbes. Whose number is correct and the reason it is

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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I REALLY NEED HELP PLEASE THIS WORK IS FOR MONDAY.can y’all please help me:(

**Answer: 5.13 **

**Step-by-step explanation:**

**1) Set up the equation**

3.8(1.35)

**2) Solve**

**5.13 **

How many seconds does it take for lighting to strike 7250

**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.

You bring 1.5 dozen bagels to school.

A dozen bagels cost $5.98.

You used a coupon that took $1.00 off the total.

$7.97

Because you do 5.98 plus half of 5.98 and then minus a dollar

Because you do 5.98 plus half of 5.98 and then minus a dollar

1. Multiply.

0.7 times 100 equals what number?

A. 7

B. 70

C. 700

D. 7,000

2.Multiply.

0.13 times 10,000 equals what number?

A. 13

B. 130

C. 1,300

D. 13,000

3. Multiply.

0.63 times 0.01 equals what number?

A. 0.0063

B. 0.063

C. 0.63

D. 6.3

4. Divide.

0.37 divided by 100 equals what number?

A. 0.00037

B. 0.0037

C. 0.037

D. 0.37

5. Divide.

0.8 divided by 0.01 equals what number?

A. 8

B. 80

C. 800

D. 8,000

The various values using **mathematical operations** are;

1) B: 70

2) C: 1300

3) A: 0.0063

4) B: 0.0037

5) B: 80

How to use mathematical operations?

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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Which expression is equivalent to 2x^ 2 -2x+7^ prime ?

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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which is closest to 8? 7.5 , 7 6/10 , 7 2/5 , 7.02?

**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]

Simplify the expression (2 − 5i)(3 + 7i) − (4 + 3i) and please be sure to explain your steps!

**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!**

Find the values of the constant p q and r in such that when the polynomial f(x)=x^3 +px^2+ qx+ r is divided by (x+2),(x-1),and (x-3) the remainders are respectively -48,0 and 2 hence actoreise f(x) completely

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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Select all sequence(s) of translations and reflections that were performed to show the two figures in each pair are

congruent. Image is shown with dashed lines.

*Remember to map the pre-image to the image. Select all that apply.

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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7/6 x 3 how to slove

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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450 x 670 - 80 x 500 = ?

Answer:

261 500

Step-by-step explanation:

450x670-80x500

301500-80x500

301500-40000

261500

Which of the following is the center and radius of the circle?

x² + y2 + 10x-6y + 15 = 0

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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14.2 cm correct 1 decimal place

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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Find the measure of the exterior angle.

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 front suspension system of a passenger car typically has coiled springs attached to the front wheels. a typical spring has a spring constant k of about 82,000 k/m

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 weight of items produced by a machine is normally distributed with a mean of 7 ounces and a standard deviation of 3 ounces. what percentage of items will weigh between 4.3 and 8.65 ounces? a. 47.52%

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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The right arrow symbol used to show the transition from a point to its image after a transformation is not contained within the Equation Editor. If such a symbol is needed, type "RightArrow." For example: P(0, 0) RightArrow P′(1, 2).

Write a translation rule that maps point D(7,-3) onto point D'(2,5)

PLLS HELP if you do it in simple words and step by step i will give brainliest

**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:

help me wwqưqưeqưeqưeqưeqưeqư

**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

Given g (x) = 3x+5 determine x for g (-2)

**Answer:**

-1

**Step-by-step explanation:**

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

There are integers that are not rational

numbers. (True or false)

There are whole numbers that are not rational

numbers. (True or false

There are integers that are not whole numbers.(true or false)

All rational numbers are integers. (True or false)

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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c) Suppose that you take a random sample of 5,000 people from the U.S. population.Make a table that shows the expected number of people in your sample who come fromeach of the four age groups

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.

[tex]\begin{gathered} Proportion:74,181,467\div308,745,538=0.240267333 \\ Number\text{ }of\text{ }Samples:0.240267333\times5,000=1,201.33\approx1,201 \end{gathered}[/tex]**Hence, we are expected to have 1,201 people aged under 18 in the sample.**

For those aged 18 - 44,

[tex]\begin{gathered} Proport\imaginaryI on:112,806,642\div308,745,538=0.3653709224 \\ Number\text{ }of\text{ }Samples:0.3653709224\times5,000=1,826.85\approx1,827 \end{gathered}[/tex]**Hence, we are expected to have 1,827 people aged 18-44 in the sample.**

For those aged 45 - 64,

[tex]\begin{gathered} Proportion:81,489,445\div308,745,538=0.2639372395 \\ Number\text{ }of\text{ }Samples:0.2639372395\times5,000=1,319.68\approx1,320 \end{gathered}[/tex]**The expected number of samples for people aged 45-64 is 1,320.**

Lastly, for aged 65 and over,

[tex]\begin{gathered} Proportion:40,267,984\div308,745,538=0.1304245051 \\ Number\text{ }of\text{ }Samples:0.1304245051\times5,000=652.12\approx652 \end{gathered}[/tex]**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**

.

Given f(x)= -6x+7, what are f(3) and f(-5). show your work please!!

f (3)=

f (-5)=

**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**

What dose 10x+9-6x=-19 mean

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

a vehicle covers a distance of 524/25 kilometers on 7/8 liters of petrol. How much distance will it cover 2 liters of petrol

**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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HELP PLS! How does the graph of g(x) = (x + 2)3 − 6 compare to the parent function of f(x) = x3?

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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Raj has put soup into the freezer to cool down. The soups tempature started at

170 °f and decreased at a rate of 30 °f per hour.

what’s the question

**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?

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