Use synthetic division to find the quotient and remainder. Express your answer as a polynomial.

1. 2x^3-11x^2+13x-21*x-3

2. 3x^3+7x^2-13x+10*x+2

3. 2x^3+13x^2-21x+9*x-1

4. 7x^3-8x+16/x-2

5. 8x^4-14x^3-71x^2-10x+24/x-4

The expression 8³ / 8 in the simplified form will be 8².

Algebra is the study of abstract symbols, while logic is the manipulation of all those ideas.

The acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

Exponentiation is a numerical activity, composed as bⁿ, including two numbers, the base b, and the type of power n, and articulated as "b to the n".

The expression is given below.

⇒ 8³ / 8

We know that 1/aⁿ will be written as a⁻ⁿ. Then the expression is written as,

⇒ 8³ / 8

⇒ 8³ × 8⁻¹

⇒ 8⁽³ ⁻ ¹⁾

⇒ 8²

The expression 8³ / 8 in the simplified form will be 8².

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Answer is (1, 2, -6)

x + 3y + z = 1   -------> first equation

2x – y – z = 6  -------> second equation

5x + y + z = 1 -------> third equation

Add second and third equation

2x – y – z = 6  -------> second equation

5x + y + z = 1 -------> third equation

-------------------------------------------------

7x = 7 (divide by 7 on both sides)

So x= 1

Now we add first and second equations

x + 3y + z = 1   -------> first equation

2x – y – z = 6  -------> second equation

-------------------------------------

3x +2y = 7

We already got x=1, replace it in the above equation

3(1) + 2y = 7

3 + 2y = 7 (subtract 3)

2y = 4 (divide both sides by 2)

So y =2

Now plug in the values in first equation

x + 3y + z = 1   -------> first equation

1 + 3(2) + z = 1

7 + z = 1 (subtract 7 from both sides)

z = -6

Answer is (1, 2, -6)

Answer: x < 0

There is no underline under the "less than" sign

===================================================

How I got this answer:

We have an open hole at 0, and shading to the left. The shading represents all the possible solutions. For example, x = -1 is a solution since it is in the blue shaded region. We can list out the numbers -7, -6, -5, -4, -3, -2, -1 as values in the solution set, but we'd be working forever since there are infinitely many numbers in this set. Also, we'd be excluding fractional and decimal values using this slow method.

As a shortcut, we can just say "any number less than 0 is a solution" which we write as x < 0 or "x is less than zero". We do not include x = 0 itself due to the open hole at 0 on the number line.

The inequality that represents a graph where the line slopes upward to the right is when b > 0.

The inequality that represents a graph where the line slopes upward to the right is when b > 0. This means that the coefficient of x is positive, causing the line to have a positive slope. The inequality can be written as y > a + bx.

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To find the missing measures in a figure, utilize the properties or formulas associated with that specific shape. For example, use the Pythagorean theorem for right triangles.

To find the missing measures in each figure, you would typically use the properties of the specific geometrical shape presented.

For example, triangles have properties that are different from squares, rectangles, or circles. So, if you have a right triangle where you know the lengths of two sides, you can use the Pythagorean theorem to find the missing side.

This theorem states that a² + b² = c², where c is the length of the hypotenuse and a and b are the lengths of the other two sides. For other shapes, you may use different formulas or identities based on their properties.

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The equivalent of 10095 m/s is 6.2728 mi/s.

Further Explanation

To get the answer to this problem we use the conversion factor for meters to miles: 1609.34 m = 1 mi.

Setting up the dimensional analysis:

[tex]speed \ = 10095 \frac{m}{s} \times \frac{1 \ mi}{1609.34 \ m}\\[/tex]

We put the number of meters in the numerator so that the unit (meter) may be cancelled.

By multiplying the given by the number of meters in mile, we arrive at the answer:

[tex]\boxed {\boxed {speed = 6.2728 \ \frac{mi}{s}}}[/tex]

Since the given has 5 significant figures, the final answer must also have five significant figures.

Additional Example:

Sometimes the problem requires the conversion of both numerator and denominator. Below is a worked example for these kinds of question.

The conversion factor relating miles to meters is 1mile=1610m. The speed of light is 3.00×108 m/s. How fast is this in miles per hour (miles/h)?

The problem gives the conversion factor for miles to meter:

1 mi =1610 m

To convert the speed of light into the desired unit the following steps must be carried out:

These conversion may be done individually or simultaneously in a single dimensional analysis equation. The equation below shows the simultaneous conversion in one equation:

[tex]speed \ of \ light = 3.00 \times 10^8 \ \frac{m}{s} \times \frac{1 \ mi}{1610 \ m} \times \frac{60 \ s}{1 \ min} \times \frac{60 \ min}{1 \ h}\\\\\boxed {speed \ of \ light = 6.71 \times 10^8 \ \frac{mi}{h}}[/tex]

Since the answer must be expressed with only 3 significant figures, the final answer is:

Learn More

Keywords: miles, meters, conversion

How to get answer:

[tex]\mathrm{Remove\:parentheses}:\quad \left(a\right)=a\\=3x^4-8x^3+9x+5+x-2\\Group\:like\:terms\\=3x^4-8x^3+9x+x+5-2\\\mathrm{Add\:similar\:elements:}\:9x+x=10x\\=3x^4-8x^3+10x+5-2\\\mathrm{Add/Subtract\:the\:numbers:}\:5-2=3\\=3x^4-8x^3+10x+3[/tex]

For this case we have a polynomial division.

A term of the quotient must be found step by step to eliminate the terms of the dividend.

The final result must comply with:

[tex]P (x) = Q (x) * D (x) + R (x)\\[/tex]

Where:

P (x) is the dividend

Q (x) is the quotient

D (x) is the divisor

R (x) is the remainder

Answer:

See attached image

Answer:

It IS balanced.  There are 4 Hydrogen atoms on the left and the right and 2 Oxygen atoms on the left and the right.  

Step-by-step explanation:

The given reaction follows the law of conservation of mass and is balanced. Thus, the correct option is C.

The balanced chemical equation for the reaction has been:

[tex]\rm 2\;H_2\;+\;O_2\;\rightarrow\;2\;H_2O[/tex]

The law of conservation of mass states that the mass of each element on the product and the reactant side has been equal. The mass has been proportional to the number of atoms, thus the atoms have been equal on both sides of the reaction.

In the given reaction:

Reactant = 4

Product = 4

Reactant = 2

Product = 2

Since there has been the same number of atoms of each element on both sides of the reaction, the reaction has been termed a balanced reaction. The law of conservation of mass has been followed in the equation.

Thus, option C is correct.

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x > 7                     x < 10

7 o---------------------o 10

This is not an empty set.  x contains all of the values between 7 and 10.

[tex]2-3(x+4)=8\qquad|\text{use distributive property}\\\\2+(-3)(x)+(-3)(4)=8\\\\2-3x-12=8\\\\-3x+(2-12)=8\\\\-3x-10=8\qquad|\text{add 10 to both sides}\\\\-3x=18\qquad|\text{divide both sides by (-3)}\\\\\boxed{x=-6}}\to\boxed{a.}[/tex]

All you have to do is simplify the equation, then isolate x to find its value:

2 - 3 ( x + 4 ) = 8

- 3 ( x + 4 ) + 2 = 8

- ( 3x + 12 ) = 2 = 8

-3x - 12 + 2 = 8

-3x - 10 = 8

-3x = 18

x = [tex]\frac{18}{-3}[/tex]

x = -6

The answer is A= -6

Hope that helps!

Given

He earns a commission of 5 percent on the first 10 suits.

he sells more than 10, he earns an additional 3 percent on the additional suits

Last weekend Juan sold 13 suits at a price of $250 each.

Find out Juan Ramirez commission

To proof

As given in the question

Juan sold 13 suits at a price of $250 each

13 suit selling price = 13 × 250

                               = $ 3250

As given

He earns a commission of 5 percent on the first 10 suits.

and for more than 10, he earns an additional 3 percent on the additional suits

Juan Ramirez sells 13 suit which are more than the 10 suits

Hence  

commission percent for the 13 suits = 8 %

First write 8% in the decimal form

[tex]= \frac{8}{100}[/tex]

=0.08

Than commission on the 13 suits = 0.08 × 3250  

                                                       = $260.

Therefore option ( D) is correct.

Hence proved

First we can calculate how many seconds there are in an hour:​

Since 1 hour has 60 minutes and each minute has 60 seconds.​

Then 1 hour = 60 minutes * 60 seconds/1minute = 3,600 seconds.​

Now we have to multiply x 40 to calculate how many seconds there are in 40 hours.​

In a 40-hour work week = 40 hours * 3,600 seconds/1hour = 144,000 seconds​

Answer : 144,000 seconds there are in a 40-hour work week​

​Hope this helps!

[tex]\textit{\textbf{Spymore}}[/tex]​​​​​​​

The correct formula to calculate the number of seconds in a 40-hour work week is 40 hours * 60 minutes/hour * 60 seconds/minute (option a). This method accurately converts hours to minutes and then minutes to seconds.

The correct formula for calculating the number of seconds in a 40-hour work week is as follows:

a. 40 hours * 60 minutes/hour * 60 seconds/minute

Here's the breakdown:

1. Start with the number of hours, which is 40 hours.

2. Convert hours to minutes using the conversion factor of 60 minutes per hour.

3. Convert minutes to seconds using the conversion factor of 60 seconds per minute.

By multiplying these three factors together, you obtain the total number of seconds in a 40-hour work week.

The other options (b, c, d) do not correctly set up the conversion factors and units, leading to incorrect results.

So, the correct answer is (a), as it correctly converts 40 hours into seconds using the appropriate conversion factors.

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Answer:

Phase angle is 50.527°

Step-by-step explanation:

Given that in a parallel circuit [tex]E_{T}=277V[/tex], R=56kΩ and [tex]X_{L} =[/tex]68kΩ.

And we are asked to find phase angle.

In any circuit, phase angle[tex]\theta=tan^{-1}(\frac{X_L-X_C} {R})[/tex]

Since we don't have any capacitor,[tex]X_{C}=0[/tex]

Hence phase angle,[tex]\theta=tan^{-1}(\frac{68000}{56000})[/tex]

                                                  [tex]=tan^{-1}(1.2143)[/tex]=50.527°≈50.53°

The radical √60 can be expressed as 2√15.

A radical is a mathematical symbol (√) used to represent the square root or other roots of a number. It indicates finding the value that, when squared, equals the given number.

The square root of 60 can be rewritten as the square root of (4 * 15). This allows us to express it as the square root of 4 times the square root of 15.

So, √60 = √(4 * 15)

= √4 * √15

= 2√15.

Therefore, the square root of 60 can be expressed as 2√15.

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Number #2 is D, number #3 i am not sure

The correctly identified hypothesis and conclusion is 'If it is raining, then the humidity level is 100%'. The biconditional form of the statement about complementary angles is 'Angles are complementary if and only if their sum measures to 90°.'

In the given scenarios, the true conditional with a correctly identified hypothesis and conclusion is 'If it is raining, then the humidity level is 100%'. The hypothesis is 'It is raining' and the conclusion is 'The humidity level is 100%'.

In relation to the second question about complementary angles, the definition is indeed reversible. We can write it as a biconditional statement: 'Angles are complementary if and only if their sum measures to 90°.' The biconditional statement holds true in both directions, showing that both conditions are necessary and sufficient for each other.

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The answer is 9,850 if you are adding the numbers together.

Answer:

9,000 + 800 + 50 = 9,850

Step-by-step explanation:

Hope it helped!

Answer:

20-7=13

Step-by-step explanation:

They gained 20 but it looks like they lost 7 so you would have to subtract.

Answer:

2.61 pounds of apples are left.

Step-by-step explanation:

Amount of green apples is 3.42 pounds and amount of red apples is 2.19 pounds.

So, the total amount of the two types apples will be:  [tex](3.42+2.19)pounds = 5.61[/tex] pounds.

Simone uses 3 pounds of apples to make a pie.

Thus, the amount of of apples left will be:  [tex](5.61-3)pounds= 2.61[/tex] pounds.

The solutions to the equation 4z² − z − 7 = 0 will be negative 1.2 and 1.45.

The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2. Then we have

The quadratic equation is given below.

4z² − z − 7 = 0

Then we have

a = 4, b = -1, and c = -7

Then solutions to the equation will be

[tex]\rm x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}\\\\x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4* 4 * (-7)}}{2 * 4}\\\\x = \dfrac{1 \pm \sqrt{1 + 112}}{8}\\\\x = \dfrac{1 \pm \sqrt{113}}{8}[/tex]

On further solving we have

x = (1 ± 10.63) / (8)

x = 1 - 10.63 / 8 , 1 + 10.63 / 8

x = - 1.2, 1.45

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Answer:

For the temperature to be below 32 F, following inequality must be met,

[tex]h\geq 9.333[/tex]

Step-by-step explanation:

Let "t" be the temperature at any time.

General format of a linear equation can be given as,

y= mx + c

Where,

y ⇒ dependent variable ( in this case temperature t)

m⇒ Gradient ( the rate at which the temperature drops)

x⇒ independent variable ( hours )

c⇒ intercept ( this is the starting temperature)

Now we can substitute the given values to the above format to arrive at the equation,

[tex]t=-3h+60[/tex]

We can re-arrange the equations as ,

[tex]3h=60-t[/tex]

=[tex]h=20-\frac{t}{3}[/tex]

We can write this as an inequality when t = 32 F

[tex]h\geq 20-\frac{32}{3}[/tex]

=[tex]h\geq \frac{28}{3}[/tex]

=[tex]h\geq 9.333[/tex]

[tex]70 = -5(-2 + x)\\\\70=10-5x\\\\5x=-60\\\\x=-12[/tex]

Final answer:

To find f(4x) for the function f(x) = x² + 2, you substitute 4x into the function and simplify to get f(4x) = 16x² + 2.

Explanation:

To find f(4x) for the function f(x) = x² + 2, we need to substitute 4x for every instance of x in the function. This gives us:

f(4x) = (4x)² + 2

Now we compute the square of 4x:

f(4x) = 16x² + 2

So, f(4x) for the given function is 16x² + 2.

you would need 7 eggs

Set up the proportion.  Then cross multiply and isolate the variable to solve.

[tex]\frac{2(eggs)}{10 (pancakes)} = \frac{x}{35 (pancakes)}[/tex]

2(35) = 10(x)

70 = 10x

[tex]\frac{70}{10} = \frac{10x}{10}[/tex]

7 = x

Answer: 7 eggs

[tex]\vec{u}=[5,\ 2],\ \vec{v}=[4,\ -3]\\\\2\vec{u}=2[5,\ 2]=[(2)(5),\ (2)(2)]=[10,\ 4]\\\\3\vec{v}=3[4,\ -3]=[(3)(4),\ (3)(-3)]=[12,\ -9]\\\\2\vec{u}+3\vec{v}=[10,\ 4]+[12,\ -9]=[10+12,\ 4+(-9)]=[22,\ -5][/tex]

The furniture company decreases its chair production by 66%, resulting in a reduction of 5214 chairs. The new production level is 2686 chairs per month.

A furniture company reduces its chair production by 66%. To find the amount of the decrease and the new number of chairs produced, we first calculate the decrease: 7900 chairs × 0.66 = 5214 chairs. Therefore, the reduction in the number of chairs produced is 5214. To find the new production amount, subtract the decrease from the original production: 7900 - 5214 = 2686 chairs.

The new number of chairs produced each month is then 2686 chairs. This calculation helps both the company and stakeholders understand the adjustment in production capacity and potentially adjust business strategies or resource allocation accordingly.

Let

x-----> the purchase price of the house

we know that

1) Marika paid [tex]80\%[/tex] of the purchase price of the house with a loan

2) Marika paid the remaining [tex]\$49,400[/tex] of the purchase price with her savings

3) [tex]\$49,400[/tex] represent the [tex]20\%[/tex] of the purchase price

so

[tex]0.20x=49,400[/tex]

Solve for x

Divide by [tex]0.20[/tex] both sides

[tex]0.20x/0.20=49,400/0.20[/tex]

[tex]x=247,000[/tex]

therefore

the answer is

the purchase price of the house is [tex]\$247,000[/tex]

Marika's house's total purchase price was $247,000, calculated by determining 1% of the purchase price from the known 20% and then multiplying it by 100.

To find the total purchase price of Marika's house, we can use the information that 80% of the purchase price was covered by a loan, while the remaining 20% (which is $49,400) was paid from Marika's savings. To find the full purchase price, we first find what 1% of the purchase price is by dividing the known 20% amount by 20.

1% of purchase price = $49,400 / 20

1% of purchase price = $2,470

To find the full 100% purchase price, we multiply the 1% value by 100.

Purchase price = 100 * (1% of purchase price)

Purchase price = 100 * $2,470

Purchase price = $247,000

Thus, the total purchase price of the house was $247,000.

Answer:

[tex]6/k[/tex]

Step-by-step explanation:

It's in the attachment!

I am pretty sure that the answer is x=6/k