Mathematics High School

## Answers

**Answer 1**

**Answer:**

x-intercept: (-56, 0)

y-intercept: (0, -14)

**Step-by-step explanation:**

The **x-intercept** is the point at which the line **crosses the x-axis**, so when y=0. To find the x-intercept, substitute y=0 into the given equation:

[tex]\begin{aligned}y=0\implies x+4(0)&=-56\\x+0&=-56\\x&=-56\end{aligned}[/tex]

Therefore, the **x-intercept **of the given **linear equation** is:

(-56, 0)

The **y-intercept** is the point at which the line **crosses the y-axis**, so when x=0. To find the y-intercept, substitute x=0 into the given equation:

[tex]\begin{aligned}x=0\implies 0+4y&=-56\\4y&=-56\\y&=\dfrac{-56}{4}\\y&=-14\end{aligned}[/tex]

Therefore, the** y-intercept** of the given** linear equation** is:

(0, -14)

## Related Questions

solve for the missing side length in this triangle

### Answers

**Answer:**

**1****0**** **and **2****4**units

**Step-by-step explanation:**

Pythagoras' Theorem

Pythagoras' Theorem applies to right angle triangles with the formula:

[tex] {c}^{2} = {a}^{2} + {b}^{2} [/tex]

where c is the longest side, with a and b the shorter ones (interchangable)

Solution

With the parameters given from the question and the formula given as well, we can find the value of x and therefore the side lengths.

By Pythagoras' Theorem,

[tex] {26}^{2} = ( {5x)}^{2} + ( {12x)}^{2} \\ 676 = 25 {x}^{2} + 144 {x}^{2} \\ 169 {x}^{2} = 676 \\ {x}^{2} = 676 \div 169 \\ {x}^{2} = 4 \\ x = \sqrt{4} \\ = 2[/tex]

Now we can find the side lengths.

[tex]5x = 5(2) = 10units \\ 12x = 12(2) = 24units[/tex]

Therefore the side lengths are **1****0**** **and **2****4** units.

What is the degree of polynomial 2 yÂ² YÂ³ 2y8?

### Answers

The **degree** of the **polynomial** [tex]2yA^2yA^32y^8[/tex] is 15

A **polynomial's degree** is the sum of the degrees of its monomials with non-zero coefficients. A term's degree is the sum of the exponents of the variables in it, and it is thus a **non-negative integer.**

The degree of a polynomial is the highest or largest power of a variable in a polynomial equation. The degree denotes the polynomial with the maximum exponential power (ignoring the coefficients).

Consider the following polynomial expression with two variables: [tex]x^3 + 6x^2y^4 + 3y^2+5[/tex]

The polynomial has a **degree** of 6.

This is because the exponent values of x and y in the second term of the **algebraic formula**, [tex]6x^2y^4[/tex], are 2 and 4, respectively. We get 6 when we sum the exponent values. As a result, the **multivariable polynomial** expression has a degree of 6.

As per question, polynomial is: [tex]2yA^2yA^32y^8[/tex]

The total sum of power is: 1+2+1+3+8=15

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What is the x-intercept of the line 4x y =- 4?

### Answers

The **x**-**intercept **of the line 4x-y =- 4 is (1,0).

At x-intercepts, y=0 and at

y-intercepts, x=0.

So, to find the,

x-**intercept**, set y=0

4x−0=4

4x=4

x=1.

The points at which the graph of a function or an **equation **crosses or "touches" the x-axis of the **Cartesian **Plane are referred to as the x-intercepts. This could be thought of as a point with a y-value of zero. Let y equal 0 and then solve for x to **determine **the equation's x-intercepts.

Because the line **crosses **the x-axis when y=0, the equation for x must be solved in order to determine the **x-intercept**. We can solve for the intercepts when an equation is not in the form y = mx + b by solving for the remaining **variable **and plugging in 0 as necessary. To locate the y-intercept: solve for y and set x to zero.

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1. Is the following a function?

2. Write a function that represents the following description:

“After 8 hours, a person earned $148 in wages”

3. Let f(x)=x and g(x)=x-13

Find (f+g)(9)

4. Paige is paying off her car loan. The function that models how much she has left to pay is P(m) = 6000 -300m where m is the number of months since Paige took out the loan. What was the original amount of her loan?

### Answers

a) The given **relation **is **function**.

b) The **function **is, $x = 18.5 y

c) The value of (f+ g)(9) is 5.

d) The he **original amount **of her loan is 6000.

What is Linear Function?

A **function **with one or **two variables **and **no exponents **is referred to as a **linear **function. It is a function with a straight line as its graph.

Given:

a) The given relation is function because is input have have output, **no two outputs **have **same input**.

b) After 8 hours, a person earned $148 in wages.

So, the **unit **rate **change **= 148/ 8

= 18.5

So, if y represents the number of **hour **and $x the **wages**, then the **function **is $x = 18.5 y.

c) Let f(x)=x and g(x)=x-13

(f+ g)(9)

= (x+ x-13) (9)

= 2x -13

= 2(9)- 13

= 5

d) The **modeled function**. P(m) = 6000 - 300m.

so, the **original** **amount **of her loan is 6000.

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y

Which of the following best represents R = A - B?

A)

B)

R

### Answers

The closing side of the** triangle** serves as the best representation of the resultant vector for the resultant R=A+B, so selecting option C would be the appropriate response.

what is vector ?

A vector in mathematics is a quantity that has both magnitude and direction but no specific location. Illustrations of such numbers include velocity and acceleration. The term "vector" refers to something that has both magnitude and direction. When viewed **geometrically**, a vector can be thought of as a directed reference line, the direction of which is indicated by an arrow and whose length corresponds to the vector's magnitude. A quantity or **phenomenon** known as a vector has two distinct qualities that are its size and direction. Also included in the term is a description of how these values are represented geometrically or mathematically. Vectors are present in electromagnetic fields, as well as in weight, velocity, force, and velocity.

given

As stated in the issue, we must determine the resultant vector by adding vectors A and B.

The triangle law of vector addition, which states that the total is supplied by the triangle's closing side, can be used to calculate the vector's outcome.

Option C is the proper response, thus.

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Find the missing length and area of each figure

### Answers

LM = √(8² + 6²) = √(64 + 36) = √100 = 10 yd

Area = 2 × (1/2) × 6 × 8 = 48 yd²

A sequence is represented by the recursive formula below:

### Answers

The value of the **sequence** is (c) 13, 25, 37, 49

How to determine the value of the sequence

The **definition** of the **sequence **is given as

a(1) = 13

a(n) = a(n - 1) + 12

The above definitions imply that we simply add 12 to the **previous term **to get the **current term**

Using the above as a guide,

So, we have the following representation

a(2) = 13 + 12 = 25

a(3) = 25 + 12 = 37

So, the **sequence **is 13, 25, 37

Hence, the value is (c)

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fill in the following statements with sometimes, always, or never in order to the statements true

### Answers

**Perfect squares** NEVER be irrational numbers.

Repeating decimals will ALWAYS be rational numbers.

**Irrational numbers** will NEVER be able to be written as fractions.

What is a perfect square?

A **square** number, also known as a perfect square, is an integer that is the square of another integer, or the result of multiplying another **integer** by itself. For instance, 9 is a square number since it equals 3² and is represented by the symbols 3 × 3.

A number whose **decimal** representation eventually becomes periodic is known as a repeating decimal, also known as a recurring decimal.

All real **numbers** that are not **rational** are considered irrational numbers. In other words, it is impossible to express an irrational number as the ratio of two integers.

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Complete question

Fill in the following statements with either "sometimes ", "always ", or "never " in order to make it a true statement.

Perfect squares _______be irrational numbers

Repeating decimals will_____be rational numbers

Irrational numbers will____ be able to be written as fractions

A high school statistics class wants to conduct a survey to determine what percentage of students in the school would be willing to pay a fee for participating in after-school activities. Twenty students are randomly selected from each of the freshman, sophom*ore, junior, and senior classes to complete the survey. This plan is an example of which type of sampling

### Answers

This method is used when the population has **distinct** subgroups.

The plan to conduct a survey by **randomly** selecting 20 students from each of the freshman, sophom*ore, junior, and senior classes is an example of **stratified** random sampling.

In stratified random sampling, the population is first divided into **subgroups** or strata based on some characteristic, such as class level (freshman, sophom*ore, junior, senior), and a random sample is then selected from each stratum.

This method is used when the population has **distinct** subgroups and it is important to ensure that the sample is **representative** of each subgroup. In this case, by taking **random** samples of 20 students from each class level, the statistics class can ensure that the survey results accurately reflect the views of each class level and not just one particular group.

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The KOT club has 5 pledges. They will send at least 2 and no more than 4 pledges to work at Goodwill on Helping-Out Day. In how many ways can this be done?

### Answers

**Answer:**

The KOT club has 5 pledges and can send between 2 and 4 pledges to work at Goodwill on Helping-Out Day. This can be done in 10 different ways

**Step-by-step explanation:**

Cory is hiking up a hill with a constant slope the double number line shows that after Cory hikes 3 km his elevation is 120 m

### Answers

Cory is **hiking** up a hill with a constant slope the double number line shows that after Cory hikes 3 km his elevation is 120 m. Select the double number line that correctly labels is option 'A'.

What do you meant by hiking?

From brief half-day programs to extensive itineraries lasting more than 20 days, the activity's duration varies. The majority of the time, it is an activity that accepts groups of various sizes.

A **long stroll**, especially one undertaken for the sake of **recreation** or exercise; see also hike; an **increase**, particularly in quantity or amount. While it is entirely up to each hiker to assign whatever classification they see fit to their experience, I have found that the vast majority of hikers fall into one of the three most common categories: peak-bagging, long-distance hiking, or day hiking.

Because it is a constant slope and Cory hikes 3 km his elevation is 120 m.

slpoe = 120m/3km = 40m/1km

So, Cory's elevation after he hikes 1 km, his elevation is 40 m.

Cory's elevation after he hikes 2 km, his elevation is (2*40 m) 80 m.

Cory's elevation after he hikes 4 km, his elevation is (4*40 m) 160 m.

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**The complete question is:**

Cory is hiking up a hill with a constant slope. The double number line shows that after Cory hikes 3 km his elevation is 120m. Select the double number line that correctly labels Cory's elevation after he hikes 1, 2, and 4 km. Choose 1 answer:

Given that $k$ is a positive integer less than 6, how many values can $k$ take on such that $3x \equiv k \pmod{6}$ has no solutions in $x$

### Answers

Supposing the value of x to be an **integer**, the values of k that donot

satisfy the given equation 3x = k mod 6 are 1,2,4,5.

What is an integer?

An integer, which can comprise both positive and negative integers, including zero, is a number **without a decimal **or fractional portion.

What is the difference between integers and whole numbers?

Integers are a set of numbers that include both positive and negative numbers, as well as zero. Whole numbers, on the other hand, only include the set of non-negative numbers starting from 0 (i.e., 0, 1, 2, 3, 4, ...). In other words, whole numbers are a subset of integers.

If 3x = k mod 6 has no solutions in x, then k must not be divisible by 3. The positive integers less than 6 that are not divisible by 3 are 1, 2, 4, and 5. Therefore, k can take on 4 values: 1, 2, 4, and 5.

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Write the equation in standard form with integer coefficients. 0.5x - 2y - 0.75 = 0, y = - 3 x - 5

### Answers

**Answer:**

50x - 200y = 75

3x + y = -5

**Step-by-step explanation:**

Standard form of a line

Ax + By = C

0.5x +-2y -0.75 Multiply through by 100

50x - 200 - 75 = 0 Add 75 to both sides

50x - 200y = 75

y = -3x - 5 Add 3x to both sides

3x + y = -5

Find the largest prime number that divides the quantity 0! + (1!) x 1 + (2!) x 2 + (3!) x 3 + ... + (50!) x 50

### Answers

The largest prime number that divides the quantity is the largest **prime number** less than 5.5e+22.

A **prime number** is a natural number greater than 1 that is not a product of two smaller natural numbers. A prime number that divides a quantity is a prime number that is a factor of that quantity.

We can start by computing the values of the factorials, and then use the property of modular arithmetic to find the prime divisors of the quantity.

0! = 1

1! = 1

2! = 2

3! = 6

...

50! = 30414093201713378043612608166064768844377641568960512000000000000

Now we can write the expression as

(0! + 1x1!) + (2x2!) + (3x3!) + ... + (50x50!)

We can notice that the number is very large, and it's impractical to **factorize **it using traditional methods.

We can use the property that if n is not divisible by a** prime number** p, then n! is not divisible by p^2. So we can eliminate all the powers of 2 and 5 from the expression, since 2 and 5 are the only prime factors of the factorials.

The next step would be to check if the remaining number is divisible by any **prime numbers**.

Since it's impractical to check for all the **prime numbers**, we can use the fact that the largest prime number is less than the square root of the number in question. Therefore, we can check for all primes less than √(50!) = √(30414093201713378043612608166064768844377641568960512000000000000)

Which is approximately 5.5e+22.

Therefore, the largest **prime number** that divides the quantity is the largest prime number less than 5.5e+22.

It's important to note that this is a very large number and checking for all prime numbers less than it would take a long time. And thus, answer cannot be given.

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A farm brings 15 tons of watermelon to market. Find a 90% confidence interval for the population mean cash value of this crop. What is the margin of error

### Answers

The **margin **of error is $148.89. The upper limit is $2215 and lower limit is $1914.

What is a confidence interval with an example?

In statistics, confidence is another word for probability. If you create a confidence interval, for instance, with a 95% level of confidence, you can be sure that 95 out of 100 times, the estimate will fall between the upper and lower **values **indicated by the confidence interval.

First we need to name some of the variables we are given:

n = 38 the sample size

x = 6.88 the sample mean

= 1.86 the population standard deviation

We need to find a 90% confidence interval for the mean price per 100 lbs of watermelon:

= 1-.90 = .10

/2 = .05

z(/2) = -1.64

-z(/2) = 1.64

This can give us a probability expression:

P(-1.645 < z < 1.645) = .90

The margin of error is calculated with the formula: E = z(/2)(/√n)

E = 1.645(1.86/√38) = $.4963(300) = $148.89

Then to calculate the upper and lower limit we add and subtract E from x:

lower limit = 6.88 - .4963 = $7.38(300) = $2214

upper limit = 6.88 + .4963 = $6.38(300) = $1914

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The function f(x) = 225(1.29)", represented in the table, shows the number of people (in thousands) who own a cell phone device in a certain country where x is the number of years after 2010.

Year

Number of Cell Phone Owners

(in thousands)

2010 2012 2014 2016 2018

225 375 623 1,037 1,725

Find the average rate of change from 2012 to 2018 and interpret its meaning in terms of the context. (1 point)

-225; represents the average depreciation in cell phone owners from 2012 to 2018

225; represents the average growth in cell phone owners from 2012 to 2018

-37.5, represents the average depreciation in cell phone owners from 2012 to 2018

37.5, represents the average growth in cell phone owners from 2012 to 2018

### Answers

Therefore , the solution of the given problem of **function** comes out to be f(x) = 2871 thousands.

What is meant by the word function?

A science called mathematics studies numbers, its variations, **arithmetic **and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of **inputs** that together produce a single, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x). The input has an x in it.

Here,

Given :

=> f(x) = 225(1.29)×

After 10 year number of years x =10

=> f(x) = 225(1.29)¹⁰

=> f(x) = 12.76 * 225

=> f(x) = 2871 thousands.

Therefore , the solution of the given problem of function comes out to be f(x) = 2871 thousands.

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Find the median of data 1/3 3/2 1/6 1/4 2/3

### Answers

**Answer:**

median= 1/3

**Step-by-step explanation:**

Help

1. 4 < 7 Multiply both sides by 3, then by 2, then by 4, then by 9

2. 11 > -2 Add 3 to both sides, then add 3, then add (-4)

3. -2 \leq -2 Subtract 6 from both sides, then 8, and then 2

4. -4 < 8 Divide both sides by -4, then by -2

5. Write a short explanation of the effects of the above operations. Did this affect the inequality sign? Was it still true? Why or why not?

### Answers

The **short explanation **of the effects of the above operations will not affect the **inequality**.

What is inequality?

**Inequality **is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's **relative size **and can be used to compare these **two claims**.

1. 4 < 7 **Multiply** both sides by 3, then by 2, then by 4, then by 9, then we have

4 x 3 x 2 x 4 x 9 < 7 x 3 x 2 x 4 x 9

864 < 1512

2. 11 > -2 **Add** 3 to both sides, then add 3, then add (-4)

11 + 3 + (-4) > - 2 + 3 + (-4)

10 > - 3

3. -2 ≤ -2 **Subtract** 6 from both sides, then 8, and then 2

-2 - 6 - 8 - 2 ≤ -2 - 6 - 8 - 2

- 18 ≤ - 18

4. -4 < 8 **Divide **both sides by -4, then by -2

- 4 / (-4) > 8 / (-4)

1 / (-2) > - 2 / (-2)

- 1/2 < 1

The **short explanation **of the effects of the above operations will not affect the **inequality**.

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A tudent council ell 48 badge for $432. Which equation repreent the relationhip of x badge to y dollar

### Answers

The **equation** that represents the **relationship** of **x** number of **badges** to **y** **dollars** is** y = 9x.**

**What is an equation?**

A mathematical statement called an **equation** displays the **equality **of **two **mathematical **expressions**. Variables, coefficients, exponents, arithmetic operators, equal signs, and constants are some of the **components **that make up an **equation**.

An **equation** is said to be **linea**r if the maximum **power **of the **variable** is consistently 1.

Let the** number** of **badges** be **x** and the **cost** of **x** number of **badges** be **y**.

From the question, we know that for 48 badges, the cost is $432.

So the **cost** of **one** **badge** = 432/48 = $9

Now the **cost** of **x** number of **badges** = $(**9x**)

We mentioned in the beginning that the **cost** of **x** number of **badges** is **y**

Therefore the **equation** that represent the **relationship** of **x badge** to **y dollars** is,

** y = 9x**

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Find the volume of the given solid.

Bounded by the coordinate planes and the plane

6x + 7y + z = 42

### Answers

The volume of the given solid is equal to the **triple integral of 1** over the region **bounded **by the **coordinate **planes and the plane 6x + 7y + z = 42. This can be written as:

[tex]$\iiint 1\, dV = \iiint 1\, dx\, dy\, dz$[/tex]

The region of **integration** is bounded by the coordinate planes x = 0, y = 0, and z = 0, and the plane 6x + 7y + z = 42. This is a right **triangular **prism with vertices (0,0,0), (6,0,0), and (0,6,42). To calculate the volume, we will use the triple integral in **cylindrical** coordinates, which can be written as:

[tex]$\iiint 1\, dV = \int0^{2\pi}\int0^6\int_0^{42/7} r\, dz\, dr\, d\theta$[/tex]

The **volume **of the given solid is given by:

[tex]$\frac{504\pi}{7}$[/tex]

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A telktronics dental X ray machine bears a label stating that the machine gives radiation dosages with a maximum of 5. 00 millorientgens. Sample data consist of 46 randomly selected observations with a mean of 4. 23 milliroentgens and a standard deviation of 1. 91 milliroentgens. Test the claim that the machine gives a radiation dose lower than the maximum on the label

### Answers

There is very strong evidence to reject the **null **hypothesis, and to conclude that the machine gives radiation doses lower than the maximum on the label.

What is hypothesis testing?

Hypothesis testing is a **statistical **method used to test a claim or a hypothesis about a population parameter, based on a sample of data. The goal of hypothesis testing is to determine whether there is enough evidence in the sample data to support or reject a claim about a population.

What is t-test?

A t-test is a type of statistical hypothesis test that compares the mean of a sample to a known population mean. There are different types of t-tests, depending on the design of the study and the number of samples being compared.

To test the claim that the machine gives a radiation dose lower than the maximum on the label (5.00 milliroentgens), we can use a one-sample t-test. A one-sample t-test compares the mean of a sample to a known population mean (in this case, the maximum on the label). The null hypothesis for this test is that the mean radiation dose given by the machine is equal to or greater than the maximum on the label (5.00 milliroentgens). The alternative hypothesis is that the mean radiation dose given by the machine is less than the maximum on the label.

The test statistic for a one-sample t-test is:

t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))

Plugging in the given values:

t = (4.23 - 5.00) / (1.91 / sqrt(46)) = -4.05

We can use a t-distribution table to find the p-value associated with this test statistic. With 45 degrees of freedom (sample size - 1), the p-value for t = -4.05 is extremely low, much less than 0.001, the significance level commonly used in hypothesis testing.

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Of the 6,960 balloons thrown in a water-ballon fight, 870 were red. At this rate, how many balloons out of 48 would be red? WRITE JUST THE ANSWER WITHOUT UNITS

### Answers

The number of *balloons* out of 48 that will be **red** would be = 3/**435**

How to calculate the number of red balloons?

The number of **balloons** thrown in a water-ballon fight = 6,960 balloons.

The number of **red balloons** =870 balloons.

The number of balloons out of 48 that would be red; **divide** through by two.

= 48/6,960

= 24/3,480

= 12/1740

= 6/870

= 3/435

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What is the value of 7 power 2?

### Answers

The correct answer to the given **question **is 49. To solve the given problem following steps are followed :

**Step **1: 7 power 2 means 7 multiplied by itself 2 times.

**Step **2: 7 times 7 is 49.

**Step **3: So, the answer is 49.

**Comparing **two quantities that generate the same result when one is multiplied by a certain amount is known as a multiplicative comparison. Sam, for instance, has twice as many balloons as Sid does. Sid's got three balloons. Sam has two times Sid's amount of balloons. Sam has a total of 6 balloons, which is equal to 2 + 3 + 1.

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Are polynomials closed under addition?

### Answers

**Polynomials** form a system like to that of integers hence they are closed under the operations of **addition** and **subtraction**.

**Exponents** of polynomials are whole numbers.

Hence the **resultant** exponents will be whole numbers , addition is closed for whole numbers. As a result, polynomials are closed under addition.

If an **operation** results in the production of another polynomial, the resulting polynomials will be closed.

The outcome of subtracting two polynomials is a polynomial. They are also **closed** under subtraction as a result.

The word polynomial is a Greek word. We can refer to a polynomial as having many terms because poly means many and **nominal** means terms. This article will teach us about **polynomial expressions**, polynomial types, polynomial degrees, and polynomial properties.

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Find the product of the factors 8.075*0.08

### Answers

**Answer: 8.075: gotta get somebody else to do this one...sorry. and 0.08 = 8**

**Step-by-step explanation:**

Did this with a classmate couple months ago. Hope this helps. :)

What are the 3 types of polynomials and how many terms does each one have?

### Answers

**Monomial**, binomial, and** trinomial **expressions are all categorized by the number of terms they include.

A **polynomial **is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

An expression that consists of **variables**, constants, and exponents that is combined using **mathematical operations** like addition, subtraction, multiplication, and division is referred to as a polynomial (No division operation by a variable).

A polynomial with one term is called a monomial. A polynomial having two dissimilar terms is called a **binomial**. An algebraic expression having three terms is called a **trinomial.**

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66. Mechanical Engineering A crossed belt connects

a 10-centimeter pulley on an electric motor with a

20-centimeter pulley on a saw arbor (see figure). The

electric motor runs at 1700 revolutions per minute.

(c) Let L be the total length of the belt. Write L as

a function of o, where is measured in radians.

What is the domain of the function? (Hint: Add the

lengths of the straight sections of the belt and the

length of the belt around each pulley.)

### Answers

On solving the provided question, we cans ay that - the value of the each unit in this time will be from **unitary method **is 85.

What is unitary method ?

The **unit technique **is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required **value**. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

value of the 20 unit is 1700

value of the each unit will be 1700/20 = 85

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Is the inverse of every linear function also a function?

### Answers

In most cases, the inverse of a **linear function **is also a linear function.

**What is a linear function?**

The term "linear function" in mathematics applies to two different but related ideas: A **polynomial **function of degree zero or one that has a straight line as its graph is referred to as a linear function in calculus and related fields.

A function with the formula f(x) = ax + b, where a and b are real values, is referred to as a linear function.

Here, stands for the line's gradient and b for the y-axis intercept (which is sometimes called the vertical intercept).

These functions' graphs are mirror images of one another when viewed along the line y=x.

As a result, the points on the graph of f(x) are the points on the graph of f(x) that have been turned around.

A linear function's inverse is typically also a linear function.

Therefore, in most cases, the inverse of a linear function is also a linear function.

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What is the greatest possible quotient of any two distinct members of the set $\left\{\frac{2}{5}, \frac{1}{2},5,10\right\}$? Specifically, we wish to maximize $\frac{x}{y}$, where $x$ and $y$ are chosen from the previous set.

### Answers

The **greatest** possible **quotient** of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required is; 25.

What is the maximum possible quotient of any pair of numbers from the set?

It follows from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Hence, in a bid to **maximize** the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Consequently, it follows that the **greatest** possible **quotient** as required is; 25.

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what is -7 divided by 3/4 ?

### Answers

**Answer:**

-9.333333333333333333333

**Step-by-step explanation:**

Answer-9 1/3

Step-by-step example

first, multiply 7x4 over 3 then next to that cross multiply that with 28 over 3

then simply that which’s gets to 28 over 3 then you get your answer 9.3333 then simplify that and you get 9 1/3