Use synthetic division to find the quotient and remainder when -x^4+2 x^3+12 x^2-16 is divided by x+2 by completing the parts below.

Answer:

C) 20.72 (Question 1: Solve for Circumference)

Step-by-step explanation:

Question 1:

Using the formula:

[tex]C=2\pi r[/tex]

⇒ r = 3.3

[tex]C=2\pi r[/tex]

[tex]2\times\pi\times3.3[/tex]

≈ [tex]20.73451[/tex]

Rounding, 20.72.

Thanks.

By using the concept of growth and depreciation, it can be calculated that

1a) Amount of sample left after 15 years = 123.76 g

b) Time taken by the substance to reduce to half is 21.66 years

2) Amount is $1560.97

3) It took 11.94 years for $900 to get doubled

What is growth and depreciation?

Growth is the increase in the value of an asset or cost or population at a certain rate over a certain period of time

Depreciation is the decrease in the value of an asset or cost or population at a certain rate over a certain period of time

1) Original weight of the isotope = 200g

Function = [tex]200e^{-0.032t}[/tex]

a) Time  = 15 years

Amount of sample left after 15 years = [tex]200e^{-0.032 \times 15}[/tex] = 123.76 g

b) Amount left = 100g

100 = [tex]200e^{-0.032t}[/tex]

[tex]e^{-0.032t} = \frac{100}{200}[/tex]

[tex]e^{-0.032t} = \frac{1}{2}[/tex]

[tex]-0.032t = ln(\frac{1}{2})\\-0.032t = -0.693\\t = \frac{0.693}{0.032}\\[/tex]

t = 21.66 years

2) Principal = $1100

   Rate = 5%

    Time = 7 years

  Amount =  [tex]1100e^{\frac{5}{100} \times 7}\\[/tex]

                  = [tex]1100e^{0.35}[/tex]

                  = $1560.97

3) Principal = $900

   Amount = $900 [tex]\times[/tex] 2 = $1800

   1800 = [tex]900(1 + \frac{6}{1200})^{12n}[/tex]

    [tex]\frac{1800}{900} = (\frac{201}{200})^{12n}[/tex]

     [tex](\frac{201}{200})^{12n} = 2[/tex]

     [tex]12n \times log(1.005) = log 2\\12n \times 0.0021 = 0.3010\\n = \frac{0.3010}{12 \times 0.0021}\\[/tex]

     n = 11.94 years

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Answer: Neither

Step-by-step explanation:

The congruent pairs for the angles and sides of the given two congruent triangles are

∠A ≅ ∠D      

∠B ≅ ∠ E

∠C ≅ ∠F   and

AB ≅ DE

BC ≅ EF

AC ≅ FD

What is congruent triangles?

If and only if we can use rigid transformations to map one figure onto the other, then two figures are said to be congruent. All corresponding sides and angles are congruent because rigid transformations maintain distance and angle measure. Therefore, measuring all of the sides and angles of a pair of triangles would be one method of determining whether they are congruent.

Let the given two triangles, ΔABC and ΔDEF are congruent.

We have to find the congruent pairs from the given two congruent triangles.

First to find the congruent pairs for angles.

∠A ≅ ∠D

∠B ≅ ∠ E

∠C ≅ ∠F

Now to find the congruent pairs for sides,

AB ≅ DE

BC ≅ EF

AC ≅ FD

These are the congruent pairs for the angles and sides of the given two congruent triangles.

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Answer:

[tex] \dfrac{2}{x} - 9[/tex]

Step-by-step explanation:

the quotient of 2 and x:

[tex] \dfrac{2}{x} [/tex]

9 less than the quotient of 2 and x:

[tex] \dfrac{2}{x} - 9[/tex]

The point on the perpendicular bisector of the segment MN, M(7, 5), N(-1, 5), is (3, 9)

The perpendicular bisector of a segment, divides the segment into two segments that have the same length, and which forms an angle of 90° with the line.

The specified endpoints on the segment MN = M(7, 5), and N(-1, 5)

The y-coordinates of the points M and N are the same, therefore, the segment is an horizontal segment.

The midpoint of the line is therefore;

(7 + (-1 - 7)/2, 5 + (5 - 5)/2) = (3, 5)

The slope of the segment, MN, m = (5 - 5)/(-1 - 7) = 0

The slope of the perpendicular line is therefore;

-1/0 = ∞

The segment MN is parallel to the x-axis, therefore, the perpendicular bisector is parallel to the y-axis, and the x-values of points on the perpendicular bisector have the save value s the x-value of the midpoint of the segment MN, (3, 5), which is x = 3

The point that lies on the perpendicular bisector of the segment MN from the options is therefore; (3, 9)

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Answer:

  61 months, about 5.07 years

Step-by-step explanation:

You want the time it takes to pay off a loan of $11,000 at 4% compounded monthly when the payment is $200 per month.

The number of payments required can be found by solving the amortization formula, or using any spreadsheet, financial calculator, or suitable app.

The attachment shows the number of months required is about 60.9.

It will take 61 months, or about 5.07 years to pay off the loan.

__

Additional comment

The formula for the number of monthly payments on a loan amount of P at interest rate r with monthly payments of A is ...

  [tex]N = -\dfrac{\log{\left(1-\dfrac{Pr}{12A}\right)}}{\log{\left(1+\dfrac{\vphantom{R}r}{12}\right)}}[/tex]

Answer: 8^4

Step-by-step explanation: A 'base' is a number with an exponent.

The results of operations between the two functions f(x) = 2 · x + 1 and g(x) = 6 - x are listed below:

In this problem we have the definitions of two functions, linear equations on both cases. The procedure consists in using the definitions of operations between two functions and evaluate the resulting expression at a given value of x:

Addition

(f + g)(x) = f(x) + g(x)

Subtraction

(f - g)(x) = f(x) - g(x)

Multiplication

(f · g)(x) = f(x) · g(x)

Division

(f / g)(x) = f(x) / g(x)

Now we proceed to derive each expression and evaluate the resulting expression:

(f + g)(x) = (2 · x + 1) + (6 - x)

(f + g)(x) = x + 7

(f + g)(2) = 2 + 7

(f + g)(2) = 9

(f - g)(x) = (2 · x + 1) - (6 - x)

(f - g)(x) = 3 · x - 5

(f - g)(- 5) = 3 · (- 5) - 5

(f - g)(- 5) = - 20

(g - f)(x) = (6 - x) - (2 · x + 1)

(g - f)(x) = - 3 · x + 5

(g - f)(4) = - 3 · 4 + 5

(g - f)(4) = - 7

(f · g) (x) = (2 · x + 1) · (6 - x)

(f · g) (x) = 2 · x · (6 - x)  + 6 - x

(f · g) (x) = 12 · x - 2 · x² + 6 - x

(f · g) (x) = - 2 · x² + 11 · x + 6

(f · g)(1 / 2) = - 2 · (1 / 2)² + 11 · (1 / 2) + 6

(f · g)(1 / 2) = 11

(f / g) (x) = (2 · x + 1) / (6 - x)

(f / g)(- 1) = [2 · (- 1) + 1] / [6 - (- 1)]

(f / g)(- 1) = - 1 / 7

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Answer:  " x = [tex]-\frac{7}{3}[/tex] " ; or, write as: " x = [tex]-2\frac{1}{3}[/tex]  " .

Step-by-step explanation:

" Given h(x) =  -3x − 5 ;  solve for x  when h(x) = 2 " .

_________________
So, substitute 2  for h(x) ; and  rewrite:
     2 = -3x − 5 ;

Add 5  to Each Side of the equation;
   2 + 5 = -3x − 5 + 5 ;

To get:

   7 = -3x ;

Now divide Each Side of the equation by -3 ;

  to isolate x on one side of the equation;

    & to solve for x ;

    7 / -3  = -3x / -3 ;
to get:
 - 7/3 = x ;  

↔   x = - [tex]\frac{7}{3}[/tex]  ;

Or; to write as a mixed number:
_____________

Note:  -7/3  =  - (7/3) = - (7 ÷ 3) ;

We can use long division to obtain the mixed number ;

→  which is the "opposite value of the following:   " [7 ÷ 3]" ;

 First:  We shall solve for the value of [7 ÷ 3] ;
_____
        2

  3⟌ 7        ⇒   So we have " 2 R 1 " , or, "2 remainder 1" ;  
      - 6       ⇒    or:   2 and 1/3 ;  
        1        
⇒  Note:  The remainder; 1 , is the numerator ; and:
The divisor; 3, is the denominator ; and:

The number; 2, is the "whole number portion" of this mixed number.

[which we shall make, "- 2 "; as explained later.

_____

Second:  We shall write out the mixed number" by:
 A] writing the value from the information above' ; with our obtained values;  as:  " [tex]2\frac{1}{3}[/tex] " ;  and by:

 B]  writing the correct 'mixed number' by writing the 'oppositive value'

of that said number.  In our case, we take " [tex]2\frac{1}{3}[/tex] " ; and make the value "negative".  In our case, we write the correct value by adding a
'negative sign'—as follows:  " [tex]-2\frac{1}{3}[/tex] " .
_____

The answer is: " x = [tex]-\frac{7}{3}[/tex] " ; or, write as: " x = [tex]-2\frac{1}{3}[/tex]  " .
_____

Hope this is helpful to you!  Best wishes!
_____

The equivalent of the radical  expression √(100p⁴z⁸) is

10p²z⁴

The given expression √(100p⁴z⁸) is first rewritten in exponents form

Writing in exponents form

= √(100p⁴z⁸)

= (100p⁴z⁸)^1/2

multiplying through

= 100^1/2 * p^(4 * 1/2) * z^(8 * 1/2)

noting that √100 = 100^1/2 = 10

= 10 * p^(2) * z^(4)

= 10p²z⁴

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Answer:

B

Step-by-step explanation:

The volume of a box with dimensions a, b, and c is given by

V(a,b,c)=abc.

It follows that

dV(a,b,c)/V(a,b,c)=da/a + db/b + dc/c .

Therefore, "in first approximation", the relative error in volume is the sum of the relative errors in the side lengths.

In the given example the relative errors in the side lengths are 1%. As the case may be these add up, and we obtain a relative volume error of 3% or 1.5 cubic inches as a "first estimate".

The actual minimal volume of the box under the given constraints is

4.95*4.95*1.98=48.51495 cubic inches, which is <1.5 cubic inches off; and the maximal volume is 5.05*5.05*2.02=51.51505 cubic inches, which is 1.51505>1.5 off the intended value of 50 cubic inches. It follows that the worst-case analysis gives a larger error than the "first estimate".

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Arrays can be passed as parameters to a function by value, but it is faster to pass them by reference. The given statement is False.

An array is a collection of items of same data type stored at contiguous memory locations. This makes it easier to calculate the position of each element by simply adding an offset to a base value, i.e., the memory location of the first element of the array.

In Pass by value, function is called by directly passing the value of the variable as an argument. So any changes made inside the function does not affect the original value.

In Pass by Reference, Function is called by directly passing the reference/address of the variable as an argument. So changing the value inside the function also change the original value. In JavaScript array and Object follows pass by reference property. Parameters passed as an arguments does not create its own copy, it refers to the original value so changes made inside function affect the original value.

Thus, the statement that Arrays can be passed as parameters to a function by value, but it is faster to pass them by reference is False.

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The value of the equation A = 1/10 is 10 %

So , the 20 overseas investors owns 10 % of the business

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the percentage of business owned by the overseas investors be = A

Now , the equation will be

The number of overseas investors = 20

The fraction of business the overseas investors own = 1/10

Now , the percentage is always expressed in terms of 100

So ,

The percentage of business owned by the overseas investors = fraction of business the overseas investors own x 100

Substituting the values in the equation , we get

Percentage of business owned by the overseas investors = ( 1/10 ) x 100

Percentage of business owned by the overseas investors = 10 %

Therefore , the value of A is 10 %

Hence , the 20 overseas investors owns 10 % of the business

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The reflection rule for the given graph is Option A.

What is reflection?

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.

Given the graph of triangle ABC under reflection, we analyse each answer choice one by one

For Option A) Reflection across the origin, the y-coordinate is negated, as well as the x-coordinate (their signs are changed). The image of the point (x,y) is the point in a point reflected in the origin (-x,-y).

So, A(-3,-1) becomes A'(3,1) which is correct for the given coordinates of the reflected graph of the figure.

Hence, Option A is the correct choice and the remaining choices are eliminated.

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Answer:  $16,800

Step-by-step explanation:

Hence, the diagonals of parallelogram is not perpendicular to each other. They are equal in length and they bisect each other but diagonals are not perpendicular so it would be rectangle.

What is the parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

The congruence of opposite sides and opposite angles is a direct consequence of the Euclidean parallel postulate and neither condition can be proven without appealing to the Euclidean parallel postulate or one of its equivalent formulations.

Here given that,

[tex]DE=3y+7 \\DB=10y-6[/tex]

As we know the slope of a line is

[tex]y=mx+c[/tex]

where [tex]m[/tex] is the slope.

So,

[tex]DE=3y+7\\\\m_1=3\\\\\\DB=10y-6\\\\m_2=10[/tex]

Then,

[tex](m_1)(m_2)=(3)(10)\\\\(m_1)(m_2)\neq 30[/tex]

Draw the graph of given equations

Hence, the diagonals of parallelogram is not perpendicular to each other. They are equal in length and they bisect each other but diagonals are not perpendicular so it would be rectangle.

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The correct reason for Step 2 is the Vertical Angle Theorem

There are four angles created when two straight lines cross or intersect at a point, in which two sets of angles are not contiguous. These pair of non-adjacent angles are known as Vertical angles or Vertically opposite angles.

According to The theorem of vertical angles, two opposing vertical angles that are created when two straight lines intersect at a point, are always equal to one another.    

Here we have

3 three straight lines named SZ, TV, WY  

Where Line SZ and TV intersected at U,

Thus the formed pairs of Vertical angles are ∠SUV, ∠TUX;  ∠SUT, ∠VUX

As we know according to Vertical Angles Theorem the vertical angles are equal

=> ∠SUV = ∠TUX    

Therefore,

The correct reason for Step 2 is the Vertical Angle Theorem

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Answer:

The answers are A B and C

they could be whole numbers

Step-by-step explanation:

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The constant of proportionality is 5.

What is the constant of proportionality?

When two variables move in the same direction, this is known as direct variation. The other variable also rises when one rises. The points rise along with the number of goblins defeated. This is an exact alteration.

The equation used to represent direct variation is: y = kx

Where k is the constant of proportionality

5 = k

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Answer: 20.98

Step-by-step explanation: Pythagorean theorem to find a is the square root of c^2 - b^2 C is 27 and b is 17 so square root of 27^2 17^2 is 20.98

Distance between points is 7 units.

What are co-ordinate system?

In pure mathematics, a co-ordinate system could be a system that uses one or a lot of numbers, or coordinates, to unambiguously confirm the position of the points or alternative geometric components on a manifold like Euclidean space.

Main body;

points given = (4,2) and(-3,2).

Distance formula = √(x₁-x₂)² +(y₁ -y₂)²

so,

distance between points = √(4-(-3))² + (2-2)²

                                          =√ 7² +0²

distance between points = 7 units

Hence ,distance between points is 7 units.

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Answer:

B. 11/12

Step-by-step explanation:

Answer: B. 11/12

Step-by-step explanation:

.

The price should be higher than the AVC and ATC in order to make a profit in the short term. Therefore, in order to achieve the requisite profit, the MR curve must rise above cost = 7.

When businesses in a cutthroat sector start making money, it opens the door for more businesses to enter the market, which leads to a shift to the right in the supply curve, a drop in price, and the return of all businesses to a state of no economic profit.

If the market price is lower than the average total cost, a company will experience positive economic profit in the short term.

In the short run, a monopolistically competitive firm optimises profits or avoids losses by producing the amount where marginal revenue equals marginal cost. If the average total cost is less than the market price, the company will make a profit.

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Micha can choose her drink is 64 different ways.

A permutation is an arrangement of things where order matters, AB and BA are two different permutations.

The combination is a selection of things where order does not matter, AB and BA are the same combinations.

Given, She can pick from four cup sizes, eight different drink flavors, and two different straw colors.

∴ The no. of ways in which she can choose from is [tex]^4C_1 \times ^8C_1 \times ^2C_1[/tex] ways.

= 4!/(4-1)!1! + 8!/(8-1)!1! + 2!/(2-1)!1!.

= 4!/3! × 8!/7! × 2!/1!.

= 4 × 8 × 2.

= 64 ways.

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Answer:

X= 6+y/7

Step-by-step explanation: