Help if you know how to do this! I’d really appreciate it!

The polynomial x⁴ + 3x³ - x - 2 will have a remainder of 1 when divided by x + 1 and the result can be written in the form (x³ + 2x² + 2x - 3) + 1/(x + 1).

Using the long division method will require us to; divide, multiply, subtract, bring down the next number and repeat the process to end at zero or arrive at a remainder

We shall divide the polynomial x⁴ + 3x³ - x - 2 by x + 1. as follows;

x⁴ divided by x equals x³

x + 1 multiplied by x³ equals x⁴ + x³

subtract x⁴ + x³ from x⁴ + 3x³ - x - 2 will result to 2x³ - x - 2

2x³ divided by x equals 2x²

x + 1 multiplied by 2x² equals 2x³ + 2x²

subtract 2x³ + 2x² from 2x³ - x - 2 will result to 2x² - x - 2

2x² divided by x equals 2x

x + 1 multiplied by 2x equals 2x² + 2x

subtract 2x² + 2x from 2x² - x - 2 will result to -3x - 2

-3x divided by x equals -3

x + 1 multiplied by -3 equals -3x - 3

subtract -3x - 3 from -3x - 2 will result to a remainder of 1.

Therefore, the polynomial x⁴ + 3x³ - x - 2 divided by x + 1 gives a quotient x³ + 2x² + 2x - 3 and a remainder of 1 and can be written as (x³ + 2x² + 2x - 3) + 1/(x + 1).

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Answer:

well, both the domain, and the range can have a positive and/or negative infinity, but as long as the 2nd factor is an opposite symbol then you will have a correct answer, for instance, -infinity, and 2 could work, but if the 2 was negative then there would be a problem

Step-by-step explanation:

The building in the drawing is 700 centimeters or 7 meters.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

An ordered pair of integers a and b, represented as a / b, is a ratio if b is not equal to 0. A proportion is an equation that sets two ratios at the same value. For instance, you might express the ratio as follows: 1: 3 if there is 1 boy and 3 girls (for every one boy there are 3 girls) There are 1 in 4 boys and 3 in 4 girls.

Given 3 meters on real is equal to 7 centimeters on drawing

i.e. 3 meters=7 centimeters

or, 1 meter = 7/3 centimeters

We need to find reading for 300 meters so,

or, 300 meters=7/3*300 centimeters

                        =700 centimeters or 7  meters

Therefore the building in the drawing is 700 centimeters or 7 meters.

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The sample space when choosing one marble will be B s=(purple, pink, red, blue, green, orange, yellow}

A sample space is a set of potential results from a random experiment. The letter "S" is used to denote the sample space. Events are the subset of possible experiment results. Depending on the experiment, a sample space may contain a variety of outcomes.

A paper bag has seven colored marbles. The marbles are pink, red, green, blue, purple, yellow, and orange. The sample space when choosing one marble will be all the colors. The correct option is B.

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The maximum allowable pipe diameter is given as : 0.501. Option B

From the question the interior diameter of the pipe is said to be 0.49

The pipe is said to have the thickness of 0.005 inches.

The exterior diameter of the pipe would be solved as 0.49 + 2 * 0.005

= 0.49 + 0.01

= 0.5

The questions said the variance in the diameter of this pipe is 0.001

Then the maximum allowable pipe diameter would be solved as: 0.001 + 0.5 = 0.501

The diameter of the pipe that is allowable is 0.501

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Elena swaps her cookies for a friend's doughnut is the examples of voluntary exchange. Hence,

A voluntary exchange occurs when two parties freely exchange products or services without the use of coercion or other restrictive measures. Both parties will gain from the deal and both parties want to make the exchanged items. The idea of voluntary exchange is crucial to a free market economy.

Customers also willingly swap money to buy his strawberries. They can choose to buy strawberries somewhere else if they see that some of his strawberries have flaws. This is a voluntary exchange because both sides gain from it.

One of the most crucial principles of economics is voluntary exchange. In a market economy, where producers and consumers freely exchange products and services, this transaction is taking place. In the end, both sides benefit from the process.

Thus, option A is correct.

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The graph of the linear equation is attached below. After 11 months, the total savings will be $237.50.

What is a saving account?

An account in a retail bank is a savings account. Common characteristics include having a finite number of withdrawals allowed, not having check or connected debit card facilities, having few transfer choices, and not being able to become overdrawn.

Given equation is

y = 12.5x + 100

To find points on the linear equation, putting x = 0, 1 and 2 in the given equation:

y(0) = (12.5 × 0) + 100

y(0) = 100

y(1) = (12.5 × (1)) + 100

y(1) = 12.5 + 100

y(1) = 112.5

y(2) = (12.5 × 2) + 100

y(2) = 25 + 100

y(2) = 125.

The points on the linear equation are (0,100), (1, 112.5), (2,125).

Plot the points and join the points to draw the line to get graph the linear equation.

Putting y = 237.50 in the given equation y = 12.5x + 100:

237.50 = 12.5x + 100

Subtract 100 from both sides:

237.50 - 100 = 12.5x + 100 - 100

137.50 = 12.5x

Divide both sides by 12.5:

x = 137.50/12.5

x = 11

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Answer:

1) Let D be the number of dimes and Q be the number of quarters. We can set up the following system of equations to represent the given information:

D + Q = 65

0.1D + 0.25Q = 10.70

The first equation represents the total number of coins Victoria has, and the second equation represents the total value of those coins in dollars. Solving this system of equations will give us the number of dimes and quarters Victoria has.

2) Let M be the number of hours Max spends mowing lawns and T be the number of hours he spends tutoring. We can set up the following system of equations to represent the given information:

M + T = 14

12M + 15T = 192

The first equation represents the total number of hours Max worked over the weekend, and the second equation represents the total amount of money he made during that time. Solving this system of equations will give us the number of hours Max spent on each job.

Gross pay is $360, Health insurance is $50.40, Pension deduction is $21.60, Total deductions is $173.85 and net pay is $186.15.

Gross pay or gross earnings is the amount of money an employer earn before all the tax and other deductions and benefits.

Employee works for 40 hours at a rate of $9.00 per hour.

Gross pay = 40 × 9 = $360

Health insurance = 14% of gross earnings

                             = 14% × 360

                             = 0.14 × 360

                             = $50.40

Pension deduction = 6% of gross earnings

                                = 0.06 × 360

                                = $21.60

Total deductions = $55.00 + $21.80 + $25.05 + $50.40 + $21.60

                            = $173.85

Net pay = Gross earnings - Total deductions

             = $360 - $173.85

             = $186.15

Hence the amount of gross pay is $360, and net pay is $186.15.

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Answer: 72 square units

Step-by-step explanation: It is 72 square units because if you count the sides p and q you get 9 and the same with sides q and r you get 8 and if you multiply them together you get 72.

The three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4  and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.

What is ratio?

A ratio in mathematics demonstrates how many times one number is present in another. For instance, if a bowl of fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six. The ratio of oranges to the total amount of fruit is 8:14, and the ratio of lemons to oranges is 6:8.

First we have to write the equivalent ratios for 75%.

Since, 75% can be written as,

75/100

Simplifying this, 15/20

Again simplifying this, 3/4

Hence, the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4.

Now to write the equivalent ratios for 100%.

Since, 100% can be written as,

100/100

Simplifying this, 20/20

Again simplifying this, 4/4

Hence, the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.

Therefore,  the three ratios that are equivalent to 75% are 75/100, 15/20 and 3/4  and the three ratios that are equivalent to 100% are 100/100, 20/20, and 4/4.

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The reason why the cousin's procedure for getting the x and y intercepts work is because they represent the definition of those points on a graph.

The x-intercept of a graph or function simply refers to the point at which the graph crosses the graph crosses the x-axis or the point at which y = 0. In a similar manner, the y-intercept simply refers to the point at which the graph crosses the y-axis or simply the point at which x = 0.

Now, we are given the equation of the line as;

5x + 4y = 14

The general form of equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Rewriting the equation of the line in slope intercept form is;

y = -⁵/₄x + ⁷/₂

Now, the reason why we plug in 0 for x to get the y-intercept is because when x = 0, that is only where we can get the y-intercept as the corresponding value of x will be traced to 0.

Similarly,  the reason why we plug in 0 for y to get the x-intercept is because when y = 0, that is only where we can get the x-intercept as the corresponding value of y will be traced to 0.

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The trigonometric functions are sin A = 12/13, sin B = 5/13, cos A = 5/13, cos B = 12/13, tan A = 12/5, and tan B = 5/12 as fractions.

Trigonometric functions are defined as the functions which show the relationship between the angle and sides of a right-angled triangle.

The trigonometric functions are given in the question

Apply the sine ratio on the given right triangle

⇒ sin(θ) = Perpendicular/hypotenuse

sin A = BC/AB

sin A = 12/13

sin B = AC/AB

sin B = 5/13

Apply the cosine ratio on the given right triangle

⇒ cos(θ) = Base/hypotenuse

cos A = AC/AB

cos A = 5/13

cos B = BC/AB

cos B = 12/13

Apply the tangent ratio on the given right triangle

⇒ sin(θ) = Perpendicular/Base

tan A = BC/AC

tan A = 12/5

tan B = AC/BC

tan B = 5/12

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Answer:

- 2x +29

Step-by-step explanation:

Open up the parenthesis, then simplify

14 + 5x + 15 - 7x

5x - 7x + 14 + 15

-2x + 29

[tex]14+5(x+3) - 7x[/tex]

Distribute:

[tex]14+(5)(x)+(5)(3)-7x[/tex]

[tex]14+5x+15-7x[/tex]

Combine Like Terms:

[tex](5x-7x)+(14+15)[/tex]

[tex]\fbox{-2x + 29}[/tex]

Percentage of chocolates Jim given to his family is 11.11%.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Given that, Jim made 45 treats for his birthday. He gave 5 away to his family before taking the rest to school.

Now, percentage of chocolates Jim given to his family

= 5/45 ×100

= 0.1111 ×100

= 11.11%

Therefore, percentage of chocolates Jim given to his family is 11.11%.

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Answer: y=(x+3)2−17

Step-by-step explanation:

For both pizzas A and B to cost the same, there must be 5 toppings. Equations can be categorized as identities or conditional equations.

The number is said to be in its simplest form when divided into its smallest equivalent fraction. What should be done to find the most basic form. Look for common factors in the numerator and denominator. Verify a fractional integer to verify if it qualifies as a prime number. A statement having two equilateral triangles and an equivalent sign in the middle is called an equation in mathematics. The general form of any equation contains the degrees of all the variables in descending order. The conventional form of a linear model is an x + b = 0. The general form of a linear equation with two variables is an x + b y + c = 0. (or something similar). Equations can be categorized as identities or conditional equations. An identity holds true regardless of the value given to the variables.

given

number of toppings be x

number of toppings for pizza A = $10 + x*$1.5

number of toppings for pizza B = $12.5 + x*$1

10 +1.5x = 12.5 + x

10 -12.5 = x- 1.5x

-2.5 = - 0.5x

x = 5

For both pizzas A and B to cost the same, there must be 5 toppings.

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The current value of property is 4000

The capitalization rate (also known as cap rate) is used in the world of commercial real estate to indicate the rate of return that is expected to be generated on a real estate investment property. Formula: Capitalization Rate = Net Operating Income / Current Market Value

Given here cap rate as 10% and income as 40000, Thus Current market value of property is = 40000/10

                                 =4000

Hence, The current value of property is 4000

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The rate of growth or decay, r, is equal to 0.10.

Population in math refers to the set of all items of interest in a given context. It is the target or focus of a statistical study, and the objects described by the population's characteristics are known as population elements. It is important to define the population in detail before analyzing data and drawing conclusions. Examples of populations can include all students at a school, all people living in a particular country, or all people who bought a particular product.

So each year the number of residents in the town is 1.10 times the number in the previous year.

There were around 14,641 residents in the town 14 years after 2005.

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Answer:

A) Technically he/she can, but they shouldn't really.

B) Yes

C) Yes

D) Yes he/she can but is not necessary to solve the equation

E) Yes

Answer:

11.1 and 38.9

Step-by-step explanation:

16x + 18 (1-x) = 16.89

2x = 1.11

x = 0.222

0.222 x 50 = 11.1

50-11.1 = 38.9

There was 4 dollar of discount on the total amount.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

We are given that Adrian bought a jacket that costs 11 dollars and a scarf that costs 15 dollars.

At the counter, he received a discount. If he only paid 22 dollars total, then

Total cost 11 + 15 = 26

But 26 - 22 = 4

Therefore, the discount was 4 dollar.

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Answer:

The scale of the model is (21 ft / 3 in) = 7 ft / 1 in. So an 84 foot building would be (84 ft / 7 ft) * 1 in = 12 inches tall in the model.

Step-by-step explanation:

hope it helps

Answer:

588 inches

Step-by-step explanation:

First, find the scale factor of the model by dividing the height of the real building by the height of the model: 21 ft / 3 inches = 21/3 = 7

7 inches/ft

Then, multiply the scale factor by the height of the 84 foot building to find the height of the model: 7 inches/ft * 84 ft = 7*84 = 588

588 inches

7/100% can be written as a fraction as 7/100, and as a decimal as 0.07.

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{\dfrac{7}{100}\%}[/tex]

[tex]\mathsf{= \dfrac{7}{100} \div 100}[/tex]

[tex]\mathsf{= \dfrac{7}{100}\times \dfrac{1}{100}}[/tex]

[tex]\mathsf{= \dfrac{7(1)}{100(100)}}[/tex]

[tex]\mathsf{= \dfrac{7}{1,000}}[/tex]

[tex]\mathsf{= 0.0007}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{\dfrac{7}{1,000} \ \& \ 0.0007}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Therefore , the solution of the given problem of square comes out to be the ABCD  square is 18 inches

The side length of a square ABCD is 18 inches Each side of square ABCD is 18 inches The midpoints of ABCD are joined to form a square MNOP The figure is attached below

Here,

We need to find the side length of square MNOP

AMN form a Right angle triangle

We know AM =9  and AN= 9

To find MN , use Pythagoreans theorem

MN2=AM2+AN2

MN2=9square+9 square

MN2=162

Take square root on both sides

MN=9 root 2

so the side of the square MNOP is  9 square root 2 inches

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Considering the definition of a line, the linear function that represents the total cost when x tickets are ordered is c= 20.5x + 5.50.

A linear equation o line can be expressed in the form y = mx + b

where

In this case, you know:

Being Total cost= set price per ticket× amount of tickets + 5.50, then:

108=set price per ticket× 5 + 5.50

108 - 5.50= set price per ticket× 5

102.5= set price per ticket× 5

102.5÷5= set price per ticket

20.5= set price per ticket

Finally, the total cost is Total cost= 20.5× amount of tickets + 5.50.

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Answer:

Its letter A

Step-by-step explanation:

There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

The function f(x) = x³ +7x² - 5x + 19 is a polynomial function of degree 3, which means it has 3 roots (also known as zeros or solutions) that could be real or complex.

To determine the number of negative real roots, we can use the fact that a cubic function has at least one real root.

x³ +7x² - 5x + 19

the first coefficient is positive, the second is positive, the third is negative, and the fourth is positive.

There are two sign changes in the coefficients, which means that there could be 2 or 0 negative roots. So the answer is "2 or 0 negative real roots"

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On solving the provided question we cans ay that -  order when writing it on the number line: = -1.25, -0.75, 0.25, 1.5, 2

A number line is a visual representation of real numbers used in introductory mathematics. It is an image of a magnitude line. On the number line, each point represents a real number, and each real number is taken to represent a point. Increments on a number line are separated by equal distances. You can only respond to the numbers on a line in the manner indicated by those numbers. How the number is utilized is determined by the question that goes with it. B: Make a point.

The numbers on the number line must be

[tex]6/3 = 2\\-3/4 = -0.75\\1.5 = 1.5\\0.25 = 0.25\\-5.4 = -1.25\\[/tex]

In ascending order, t

[tex]-1.25 = -5/4\\-0.75 = -3/4\\0.25\\1.5\\2 = 6/3[/tex]

order when writing it on the number line:

-1.25, -0.75, 0.25, 1.5, 2

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Answer:

Step-by-step explanation:

1. (4x5) is 20

2. (4x 2) is 8

3. 20 plus 8 is 28

4. 28= 4x (5+n)

5. isolate n by dividing 4 on both sides= 28/4= 4+n

6. subtract 4 on both sides to get 7-4=n

7. n=3