Mathematics High School

## Answers

**Answer 1**

The properties of the **graph **of a function include domain, range, symmetry, asymptotes, intercepts, increasing or decreasing, continuity, smoothness, behaviour at infinity and shape.

1) **Domain**: The set of all input values (x-values) that produce a valid output (y-value) for the function.

2) **Range**: The set of all output values (y-values) that can be produced by the function for any valid input value in the domain.

3) **Symmetry**: A graph may be symmetric with respect to the x-axis, y-axis, or origin.

4) **Asymptotes**: A line that the **graph** of a function gets arbitrarily close to, but never touches.

5) **Intercepts**: The points where the **graph** of a function crosses the x- and y-axes.

6) **Increasing or Decreasing**: A function can be increasing over a certain interval, decreasing over a certain interval, or both.

7) **Continuity**: A function is continuous if its **graph** has no breaks or gaps.

8) **Smoothness**: A function is smooth if its **graph** has no sharp corners or links.

9) **Behavior at Infinity**: The behavior of a function at positive or negative infinity can be determined by analyzing the degree and leading coefficient of its equation.

10) **Shape**: The shape of a **graph** can be used to classify functions as linear, quadratic, exponential, logarithmic, etc.

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## Related Questions

The red line on this graph is y=-2x-1

The dotted line is y=x.

Write the equation of the inverse of this function

### Answers

Answer:

Step-by-step explanation:

A jar contains $1.70 in ckels, dimes and quarter. There are twenty coins in all with twice as amny nickels as dimes. How many nickels are there in the jar

### Answers

**American nickels** are issued as currency. A value of $1.70 is equal to 10 nickels and 12 dimes ($0.50 + $1.20).

How to find the calculation?

A dime is worth** ten cents** and a nickel five cents. In other words, one dime is equivalent to two nickels.

In light of this, we might state that a nickel is worth half what a dime is worth.

Despite having a **higher value** than a nickel, the dime is smaller.

n + d = 22 <— d = 22-n

Amount in pennies: 5n + 10d = 170

5n + 10(22 - n) = 170

5n + 220 - 10n = 170

220 - 5n = 170

220 - 170 - 5n = 0

50 - 5n = 0

50 = 5n

n = 10

A value of $1.70 is equal to 10 nickels and 12 dimes ($0.50 + $1.20).

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Select the values that make the inequality 5u> -80 true. Then write an equivalent

inequality, in terms of u.

(Numbers written in order from least to greatest going across.)

-26

0 -17

0-13

0 -21

☐ -16

Submit Answer

0 -11

Equivalent Inequality: u

□ -19

0-15

-6

### Answers

The **value **u > -16 that makes the inequality 5u > -80 is true.

What is an inequality?

In mathematics, "**inequality**" refers to a relationship between two expressions or values that are not equal to each other. To solve the inequality, you may multiply or divide each side by the same positive number, add the same amount to each side, take the same amount away from each side, and more. You must flip the **inequality **sign if you multiply or divide either side by a negative number.

Given:

We have the **inequality**,

5u > -80

To find the solution set of the **inequality**;

**Divide **by 5 to both sides,

5u/5 > -80/5

u > -16.

That means, the inequality is **true **for u > -16.

Therefore, the **inequality **is true for u > -16.

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Draw a quadrilateral aBCD whose vertices are A (0,0) B(5,0), C(3,2) and D (0,2)

### Answers

A **graph** of quadrilateral ABCD whose **vertices** are A (0, 0) B(5, 0), C(3, 2) and D (0, 2) is shown in the image attached below.

What are the types of quadrilateral?

In Geometry, there are different types of **quadrilateral** and these include the following:

ParallelogramSquaresRectangleRhombus**Trapezium**

Next, we would use an online graphing calculator to construct (plot) **quadrilateral **ABCD on a cartesian coordinate based on the given vertices. Also, you should enter the value for each vertices of **quadrilateral **ABCD on the x-coordinate and y-coordinate respectively as shown in the table.

By critically observing the graph of **quadrilateral **ABCD, we can reasonably infer and logically deduce that it represents a **trapezium**.

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We take a sample of 80 observations from a large population with a mean of 1460 and a standard deviation of 270. The probability that the sample mean is between 1300 and 1400 is:

### Answers

The **probability **that the sample **mean **is between 1300 and 1400 is approximately 1.34%.

We can use the **Central Limit Theorem **and the **standard normal distribution **to calculate the probability that the sample mean is between 1300 and 1400. The Central Limit Theorem states that as the sample size increases, the distribution of the sample **means **will approach a normal distribution, regardless of the distribution of the population.

Since we have a sample of 80 observations, we can assume that the sample mean follows a normal **distribution **with a mean of 1460 (the population mean) and a standard deviation of:

Standard deviation of the sample mean

= population standard deviation ÷ [tex]\sqrt {sample size[/tex]

[tex]= 270 \div \sqrt{80} = 27[/tex]

So the standard **deviation **of the sample mean is 27.

We can now standardize the **interval** between 1300 and 1400 by subtracting the **mean **and dividing it by the standard deviation of the sample mean.

[tex]Z_1[/tex] = (1300 - 1460) / 27 = -2.59

[tex]Z_2[/tex] = (1400 - 1460) / 27 = -2.22

We need to find the **area **under the standard normal distribution **curve **between Z1 and Z2.

Using a standard normal table or a calculator with the standard normal distribution function, we can find the **probability **that a random variable from the standard normal distribution is between -2.59 and -2.22. This **probability **is approximately 0.0134 or 1.34%.

Therefore, the **probability** that the sample mean is between 1300 and 1400 is approximately 1.34%.

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How many ways can the train be made up?

### Answers

**Answer:**

16c9

**Step-by-step explanation:**

First, we will add up the number of different car possibilities. This is:

6 + 7 + 3 = 16.

Then, we need to take 9 of these 16 cars, giving us **16c9**.

Hope this helped!

**Answer:**

4,151,347,200

**Step-by-step explanation:**

what number is in the same ratio to 64 as 5 is to 8

### Answers

**Answer: 102.4**

**Given ratio 5:8**

**Let's assume the answer to be x**

**5÷8 should be equal to 64÷x**

**∴ x= (64×8) ÷ 5**

**=102.4**

The number that has the same ratio to 64 as 5:8 is gotten as; 40

**How to Calculate Ratio?**

We have the **ratio** 5:8.

Now, we want to find the number that has the **same ratio **to 64 as 5:8. Thus, we will use **proportion** to get this;

x/64 = 5/8

**Cross multiply** to get;

x = 64 * 5/8

x = 40

The following dotplot shows the centuries during which the 111111 castles whose ruins remain in Somerset, England were constructed. Each dot represents a different castle. According to the 1.5.IQR rule for outliers, how many high outliers are there in the data set?

### Answers

The conclusion which we get after **analyzing **the data given is that there aren't **outliers **in the displayed **data set**.

We will calculate the interquartile range and us the rule 1.5 .

The formula to calculate interquartile range is to subtract the value of first quartile by the value of second quartile.

IQR = Q3 - Q1

Therefore, **interquartile **range becomes,

IQR = 17 - 13

IQR = 4

Now , we will apply rule 1.5 and for that we will **multiply **4 by 1.5 first

4 * 1.5 = 6

and then,

17 + 6 = 23

on applying the rue we will get ,

13 - 6 = 7 .

This value means that there is no **outlier **in the displayed **data set.**

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Write the coordinates of the vertices after a translation 1 unit down.

### Answers

**Answer:**

M(4,0)

K(0,5)

L(6,5)

go down one

5 1/4 divided by 1/4?

### Answers

let's convert the mixed fraction to **improper fraction** first.

[tex]\stackrel{mixed}{5\frac{1}{4}}\implies \cfrac{5\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{21}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{21}{4}\div \cfrac{1}{4}\implies \cfrac{21}{4}\cdot \cfrac{4}{1}\implies \cfrac{21}{1}\cdot \cfrac{4}{4}\implies \text{\LARGE 21}[/tex]

**Answer: 5 1/4 ÷ 1/4 = 21**

**Step-by-step explanation: Because the denominator is four, you would combine and create a mixed fraction. 5 × 4 = 20 and 20 + 1 = 21. So 5 1/4 equals 21 fourths which is why 5 1/4 ÷ 1/4 = 21**

solve the inequality and explain how

thank you :)

### Answers

**Answer:**

the answer is A

*[tex]x + 7 > 3[/tex]*

A lost tourist arrives at a point with 2 roads A and B. Road A leads to the city and takes either 4 or 8 hours, depending on traffic, with equal probability. Road B brings him to the city after 7 hours on average. Since there are no signs on the road, the tourist chooses a road with equal probability; what is the expected time until the tourist arrives to the city

### Answers

The expected **time **until the tourist **arrives **in the city is 4.75 hours.

The expected time until the **tourist **arrives at the city can be calculated by using the **formula **for the expected value:

Expected value = (**probability **of outcome 1) x (value of outcome 1) + (probability of outcome 2) x (value of outcome 2) + ...

In this case, there are two **possible** **outcomes**: the tourist takes road A or road B.

If the **tourist **takes road A, the expected **time **until he arrives in the city is the average of the two possible **travel** times (4 hours and 8 hours). The **probability **of this outcome is 0.5 (the tourist has an **equal **chance of choosing either road). So, the expected value for this outcome is (0.5) x (4 + 8)/2 = 6 hours.

If the tourist takes **road **B, the expected time until he arrives in the city is 7 hours. The probability of this outcome is also 0.5. So, the expected value for this **outcome **is (0.5) x 7 = 3.5 hours.

To find the overall expected **time** until the tourist arrives in the **city**, we add up the expected values for each outcome:

Expected time = (0.5) x 6 + (0.5) x 3.5 = 4.75 hours

So the expected time until the tourist **arrives **in the city is 4.75 hours.

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What are logarithms used for?

### Answers

Logarithms are used for a variety of purposes in **mathematics**, science, engineering, and other fields. Some common uses of logarithms are mentioned below:

What are functions?

A function in mathematics from a **set **X to a set Y allocates precisely one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

What are exponential function?

The mathematical expression f(x)=exp or ex denotes the exponential function. The word, unless specifically stated differently, normally refers to the positive-valued function of a real variable, however it can be extended to the complex numbers or adapted to other mathematical objects like matrices or Lie algebras.

They are used for:

Solving exponential equationsCompressing dataMeasuring the Richness of a signalComparing quantitiesSolving problems in physics and engineeringIn finance, it is used for financial modelings, such as the Black-Scholes model for pricing optionsIn computer science, it is used for information theory in the analysis of algorithms, complexity theory, and data compression.

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Someone please help! Picture attached

### Answers

**Answer:**

third side = 3

**Step-by-step explanation:**

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides.

let the third side be x , then

x² + 4² = 5²

x² + 16 = 25 ( subtract 16 from both sides )

x² = 9 ( take square root of both sides )

x = [tex]\sqrt{9}[/tex] = 3

At what point does the graph of the linear equation 2x 3y =- 15?

### Answers

The **graph **of the **linear equation** 2x - 3y = -15 is a line that passes through the point (-5, 5), and has a slope of 2/3.

The** linear equation**

2x - 3y = -15

can be written in the form

y = mx + b,

where m is the slope and b is the **y-intercept**. To find the slope of this equation, we can rearrange the equation to be in the form y = mx + b, which gives us

y = (2/3)x - 5.

This means that the slope of the line is 2/3. To find the y-intercept, we can plug in 0 for x and solve for y. This gives us

y = -5.

Therefore, the graph of this **equation **is a line that passes through the **point **(-5, 5) and has a slope of 2/3.

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Find the value of xx in the equation below.

11=

11=

\,\,x -6

x−6

### Answers

**Answer:**

Find the value of xx in the equation below.

11=

11=

\,\,x -6

x−6

**Step-by-step explanation:**

Determine which branch of statistics was used to make the following statement. In an online survey of 500 Virginia Tech students between spring 2010 and spring 2011, 3190 said that they had missed class because of alcohol consumption. A) differential statistics C) inferential statistics B) time series statistics D) descriptive statistics

### Answers

The branch of **statistics** used to make the given statement is **Option(D) Descriptive Statistics.**

**Which are the different branches of statistics?**

The **area** of mathematics that deals with **data** is **statistics**. **Data collection, descriptive statistics, and inferential statistics** are the three main **subfields** of statistics.

The **process** of **gathering data** is what **data collection** is all about.The area of **statistics** known as **descriptive statistics** deals with how we **present the data** we have. Basically, this can be done in one of two ways: either **visually** (using graphs, charts, etc.) or **quantitatively** (via averages and so on).The part of **statistics** that deals with** drawing inferences** from the data is called **inferential statistics**.

For the given question, we are **presented** with data **quantitatively**. The data shows out of **500 **students, **31%** missed class due to **alcohol consumption.**

Therefore the branch of **statistics** that was used to make the above statement is **descriptive statistics**.

Hence **Option(d)** is **correct.**

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Is y 4 a horizontal asymptote?

### Answers

**Yes**, the **horizontal asymptote** is at y = 4.

The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any **infinite **distance.

Here we have given the expression y = 4.

In order to find whether it is an horizontal asymptote or not, we have to plot it on the graph,

The first process is to label the graph with x and y **axis**.

And then we have to defines the scale for the for the graph.

Now, we have to input the **expression **y = 4 on the graph then we get the graph like the following.

While we looking into the given graph we have identified that the expression y = 4 makes the horizontal asymptote on the **graph**.

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You need to study the satisfaction of customers of a specific restaurant. You decide to order food and talk to those customers sitting next to you. This would most closely describe which type of sampling technique

### Answers

This is how the **Cluster **of sampling technique is best described.

Describe cluster sampling.Cluster sampling divides a **population **into clusters, which are more compact groupings. From these clusters, they next randomly select a sample. Cluster sampling is a **probability sampling** approach that is frequently used to explore large populations, especially those that are widely geographically dispersed.Large, dispersed populations should be investigated using cluster sampling. This is because interviewing each individual is expensive, time-consuming, and in some cases impossible.Building more compact, comparable representations of the population under study is made possible by cluster sampling.For instance, if you wanted to investigate the consumption of soda in a certain city, you could use area sampling to divide the city into several regions, or clusters, and then choose out specific clusters to study.

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Six toilet rolls cost $1.99. Nine toilet rolls cost $2.69. Is cost directly proportional to number of toilet rolls? Explain your reason!

### Answers

**Answer:**

not directly proportional

**Step-by-step explanation:**

if the cost is directly proportional to number of rolls , then the unit cost for both will be equal.

first

one roll costs $1.99 ÷ 6 = $0.33 ( to 2 decimal places )

second

one roll costs $2.69 ÷ 9 = $0.30 ( to 2 decimal places )

since the unit costs are different there is not a directly proportional relationship.

**Answer:**

No because to buy nine rolls would be $2.69 but to buy six and then three to make nine then it would be $2.985 which is more expensive.

**Step-by-step explanation:**

$1.99 divided by 2 = 0.995

$1.99 + 0.995 = $2.985

$2.985 > $2.69

**Hope this helps!!! :)**

Triangle ABC was rotated to form triangle A'B'C'. Triangle A'B'C' was reflected across the x-axis to form Triangle A"B"C".

Which of the following statements correctly describes the relationship between Triangle ABC, Triangle A'B'C', and Triangle A"B"C"? Select all that apply.

Group of answer choices

Triangle ABC has greater angle measurements than Triangle A"B"C".

Triangle ABC is congruent to Triangle A"B"C".

Triangle A'B'C' has greater angle measurements than Triangle A"B"C".

Triangle ABC has greater side lengths than Triangle A"B"C".

Triangle A'B'C' is congruent to Triangle A"B"C".

### Answers

Therefore , the solution of the given problem of **triangle** comes out to be ΔA"B"C "≅ ΔABC is congruent.

Explain the triangle.

The fact that a triangle has sides or vertices qualifies it as a **polygon.** It is an elementary geometric form. The name given to a triangle with vertices A, B, & C is Triangle ABC. A singular planes and triangle are obtained in Euclidean geometry when the vertices are not **collinear**. Any triangle that has three sides and three corners is a polygon.

Here,

Triangle A'B'C' is created by reflecting triangle ABC across the y-axis.

Afterward, it was dilated by a ratio of 1/3 to create triangle A "B"C".

Find the right answer for the triangles ABC and A"B"C."

So,

We are aware that reflection undergoes a rigorous transformation, meaning the shape and size of the original object do not change.

As a result, after reflection, figures always match their pictures.

"ABC," "A'B'C," etc (i)

The process of dilation is flexible. Although the size is changed, the shape is still the same.

Figures after dilatation therefore always resemble their photographs.

ΔA'B'C' ≅ ΔA "B"C" ... (ii)

With I and (ii), we obtain

ΔA"B"C "≅ ΔABC

Similar triangles include ABC and ABC.

As a result, choice A is the right one.

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=Round each number to five decimal places: a. 23.54 b. 0.916?

### Answers

Therefore the **rounded numbers **are 23.54 and 0.9160.

Define rounded numbers.

An** integer** containing one or more "0"s at the end in a certain base is said to be round. In this way, 590 is more rounded than 592 but less rounded than 600. A round number is **frequently** understood to stand for a value or values close to the nominal value given in both formal and informal language.

What is integer?

Zero, a positive natural number, or a negative integer denoted by a minus sign are all examples of integers. The inverse additives of the equivalent positive numbers are the negative numbers. The set of integers is frequently represented in mathematical notation by the boldface Z or blackboard bold mathbb Z.

a. To round 23.54 to five decimal places, we look at the sixth decimal place, which is 4. Since 4 is less than 5, we leave the fifth decimal place as is, and the number rounded to five decimal places is 23.54.

b. To round 0.916 to five decimal places, we look at the sixth decimal place, which is 1. Since 1 is greater than or equal to 5, we increase the fifth decimal place by one, and the number rounded to five decimal places is 0.9160.

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Is 2x 3 5 is a linear equation?

### Answers

yes, 2x + 3 = 5 is a **linear equation**.

What is a linear equation?

A linear equation is an algebraic equation of the form y=mx+b, where m is the slope and b is the **y-intercept**, and only a constant and a first-order (linear) component are included. The variables in the preceding equation are y and x, and it is occasionally referred to as a "linear equation of **two variables**." If a linear equation contains two variables, it is referred to as a linear equation in two variables, and so on.

Non-linear equations are those that do not produce a straight line. It has a changeable slope value and resembles a graphed curve.

Given that,

2x + 3 = 5

or, 2x = 5 - 3

or, 2x = 2

or, x = 2/2

x = 1

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The wind force f on a sail varies jointly as the area a of the sail and the square of the wind speed w. The force on a sail with an area of 500 ft^2 is 64. 8 pounds when the wind speed is 18 mph. What would be the force for a sail with an area of 250 ft^2 with a wind speed of 35 mph

### Answers

**Answer:**

**122.5 pounds.**

**Step-by-step explanation:**

f = kaw^2

So, k = f/aw^2

From the given data:

k = 64.8/(500*18)

= 0.0004

When a = 250 and w = 35:

f = 0.0004*250*35^2

= 122.5

Each side of a square is increasing at a rate of 7 cm/s. At what rate (in cm2/s) is the area of the square increasing when the area of the square is 81 cm2

### Answers

At the **rate** of 126cm/s is the **area** of the square increasing when the area of the **square** is 81cm2.

If each **side** of a square is increasing at a rate of 7 cm/s.

The **area** of the square increasing rate,

Area, **A = s2**

each side of the square is increasing at the rate of 7cm / s (= dx / dt).

s is the side length

=> dA/dt = 2s. ds/ dt

ds/dt = 7cm/s

Area of the square = 81 cm2

81 cm2 = s2

s = 9 cm

so, dA /dt = 2. 9. 7

= 126 cm2/s

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What is the value of aaa when we rewrite 6^{x}6 x 6, start superscript, x, end superscript as ax4 ?

### Answers

The **equation **can be rewritten as: [tex]ax^4 = (log(6))(2^4)[/tex]

Therefore, [tex]a = log(6) \ and\ x=2[/tex]

What is logarithm?

A **logarithm **is a mathematical function that describes the relationship between a number and its **exponent**. It is the inverse operation of exponentiation. Logarithms are typically written as log base b, where b is the base of the logarithm and is a positive number.

The logarithm of a number x to base b is denoted as [tex]logb(x)[/tex] and it is the exponent to which we need to raise the base b in order to get the number x.

For example, if we are given [tex]log10(100) = 2[/tex], this means that [tex]10^2 = 100[/tex].

The equation [tex]6^x * 6 * 6[/tex] can be rewritten as [tex]6^x * 6^2[/tex].

To convert 6^x to ax form, we need to take the logarithm of both sides of the equation:

[tex]log(6^x) = log(6^2)[/tex]

And we can simplify the equation as:

[tex]xlog(6) = 2log(6)[/tex]

So, the value of a is log(6) and the value of x is 2.

Therefore, the equation can be rewritten as:

[tex]ax^4 = (log(6))(2^4)[/tex]

Therefore, [tex]a = log(6)\ and\ x=2[/tex]

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How do you solve a 45 45 90 and 30 60 90 triangle?

### Answers

All** 45-45-90-degree triangles** have sides that are in a unique **ratio**. The two legs are exactly the same length.

This triangle is important because any time we're given one side of a 45-er triangle, we can figure out the other two** sides**.

If one leg is given, the** hypotenuse** is calculated by multiplying this length by the square root of 2.The hypotenuse is given, and the** leg** is calculated by dividing the hypotenuse by the square root of 2.

The **30-60-90 degree triangle** is half of an equilateral triangle, cut straight down the middle along its altitude. This triangle has** angles** of 30°, 60°, and 90°.

The shortest leg is over from the 30-degree angle, the length of the hypotenuse is always **double** the length of the shortest leg,If the hypotenuse is given, the long leg is calculated by **dividing** the hypotenuse by 2.If the long leg is given, the hypotenuse is calculated by dividing this side by the square root of 3.

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What is the domain and range of √ X 2?

### Answers

The **domain **of √ X 2 is** X ≥ 4**. The **range** is all **real numbers**.

Here is the proof, In order for the **square root **to be defined, the radicand (the value inside the square root symbol) must be greater than or equal to zero. In this case, the **radicand **is X - 2, so we must have X - 2 ≥ 0, which is equivalent to X ≥ 4. Therefore, the domain of √ X - 2 is all **values **of X that are **greater** than or equal to 4. The range of √ X - 2 is all real numbers because the square root of any **non-negative **value is a real number.

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What are the 4 ways to solve a quadratic equation?

### Answers

The **four **ways are 1) Factoring 2) Completing the Square 3) Quadratic Formula and 4) Graphing

1. **Factoring**: Factoring is the process of breaking down an expression into its simplest components. To solve a quadratic equation using factoring, you must start by writing the equation in standard form (ax² + bx + c = 0). Then, you must factor the equation into two binomials (x + a)(x + b) = 0. Once this is done, you can solve for x by setting each factor equal to zero and solving for x.

2. **Completing **the Square: Completing the square is another method of solving a quadratic equation by rewriting it in the form of (x + a)² = b. To do this, you first start by writing the equation in standard form (ax² + bx + c = 0). Then, you must rearrange it so that all the terms are on one side of the equation and the constant is on the other side. Next, divide the coefficient of x² by two and then square this number. Finally, add this number to both sides of the equation, which will then allow you to solve for x.

3. **Quadratic **Formula: The quadratic formula is a useful tool for solving quadratic equations.

4. **Graphing **: is another method useful for solving quadratic equation.

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Are 3x-2 and 3x2 reciprocals? Explain.

### Answers

**Answer: No, 3x-2 and 3x^2 are not reciprocals.**

**Step-by-step explanation: The reciprocal of a number is defined as the multiplicative inverse of that number, which means that when a number is multiplied by its reciprocal, the result is 1. For example, the reciprocal of 2 is 1/2, because 2 * (1/2) = 1.**

**In contrast, 3x-2 and 3x^2 are not numbers, they are expressions that contain variables. It is not possible to determine their reciprocals without knowing the values of the variables.**

**For example, if x=1, then the reciprocal of 3x-2 would be (1/3)/(1-2) = -1/3, and the reciprocal of 3x^2 would be (1/3)/(1^2) = 1/3. However, if x=2, then the reciprocal of 3x-2 would be (1/3)/(2-2) = undefined, and the reciprocal of 3x^2 would be (1/3)/(2^2) = 1/12.**

**So it is not accurate to say that 3x-2 and 3x^2 are reciprocals.**

No

The only thing stopping these from being reciprocals is the -2. Say x becomes 3

First we get 3(9)-2.

Next, we'd get 3(3)(2)