(a) Complete this synthetic division table.
-2√-1 2 12 0 -16

(b) Write your answer in the following form: Quotient + Remainder / x+2
-x⁴+2 x³+12 x²-16 / x+2= ____+ _____ / x+2

Step-by-step explanation:

4_/12=4_/3*4=4*2_/3=8_/3

5_/3+8_/3=13_/3

The result is irrational number because it cannot be written as the ratio of two integers. and its decimal extention is neither terminating nor repeting.

Answer:

The result of the calculation is approximately 22535940185.17

Step-by-step explanation:

To solve this problem, we can use the order of operations. First, we perform the multiplication:

122222 * 2222221 = 2704312822242

Then, we perform the division:

2704312822242 / 12 = 22535940185.17

The combination of radical 5√27 - 17√3 is -2 √3, so option D is correct.

The opposite of an exponent, denoted by the symbol "√" and also known as the root, is a radical. The number before the symbol or radical is regarded as an index number or degree.

Given:

5√27 - 17√3

Simplify the value under roots,

5√(3 × 3 × 3) - 17√3

5 × 3 √3 - 17√3

√3 (15 - 17)

-2 √3

Therefore, the combination of radical 5√27 - 17√3 is -2 √3.

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The value of p, using the exterior angle property is 53°.

What is the exterior angle property of a triangle?

The exterior angle property of a triangle states that the sum of the measures of the two non-adjacent angles of a triangle is equal to the measure of the exterior angle of the triangle. This means that if a triangle has three interior angles, the measure of any non-adjacent angle of the triangle must be equal to the measure of the exterior angle of the triangle. This property is useful in solving for unknown angles when the measures of two angles are known. For example, if two angles of a triangle measure 30° and 45°, then the measure of the third angle must be 105°, which is the same measure of the exterior angle.

The Exterior angle is = Sum of the Interior opposite angles.

By using the exterior angle property, we can get the following:

p+p-13°=p+40°

=>p=40°+13°

=>p=53°

The value of p is 53°

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Step-by-step explanation:

This is a Taylor series because our center is non-zero.

The goal of Taylor series is to approximate non polynomial functions using Calculus.

So let's be intuitive.

In order to be accurate, we need to match the center value at some center a.

We know that cos(pi/2)=0, so our first constant should be 0.

[tex]q(x) = 0[/tex]

Next, we must be spot on with the linear approximation

at x=pi/2

we know that

[tex] \frac{d}{dx} \cos(x) = - \sin(x) = - \sin( \frac{\pi}{2} ) = - 1[/tex]

We also want to divide this by 1! , which is just one so our constant there is

-1, since we want to use this as an linear approximation and we want to be general, and we have a center to stay in respect to,

our next term is

[tex] 0 - 1(x - \frac{\pi}{2} ) {}^{1} [/tex]

Next, up, we must be similar in concavity.

So we take the second derivative of cosine which is just

[tex] - \cos(x) = - \cos( \frac{\pi}{2} ) = 0[/tex]

Since our constant is 0, we can skip this, even if we divide by 2!

Our fourth term is the third derivative of cosine

which is

[tex] \sin(x) = \sin( \frac{\pi}{2} ) = 1[/tex]

We then divide that by 3!, which becomes

[tex] \frac{1}{6} [/tex]

since we want to use this as an cubic approximation and we want to be general, and we have a center to stay in respect to,

our next term is

[tex] - (x - \frac{\pi}{2} ) {}^{} + \frac{1}{6} (x - \frac{\pi}{2} ) {}^{3} [/tex]

Let do one more term,

we know the 5th term is the fourth derivative of cosine evaluated at x=pi/2, which is just 0 so we can skip it.

The 6th term is the fifth derivative of cosine evaluated at x=pi/2, which is -1, then we divide by 5!, so we get

[tex]q(x) = - (x - \frac{\pi}{2} ) + \frac{1}{6} (x - \frac{\pi}{2} ) {}^{3} - \frac{1}{120} ( x - \frac{\pi}{2} ) {}^{5} [/tex]

Using the approximations, plug in 1.5 for x and we get approximately

0.0707

Therefore by solving the equations we get to know that 196 children and  200 adults were present on that day.

equation, a declaration of equivalence between two expressions with variable- and/or number-filled expressions. In essence, equations are questions, and efforts to discover a method for answering them have fueled the growth of mathematics. Equations range in complexity from straightforward addition-and-multiplication equations in mathematics through differential equations, exponential equations that use exponential expressions, and integral equations.

Let's initially configure our system by giving the letters x and y meanings. Assume x is the number of kids and y is the number of adults.

Children are priced at $1.50, while adults are priced at $4.00. We multiply the total number of children, x, by 1.5 to get how much each child will cost. 1.5x is used to indicate this. We will use 4y for adults, whose entry fee is $4. On the specified day, $1094 in total revenue was earned. This sum requires the addition of 1.5x and 4y.

1.5x + 4y = 1094 works for the money equation involved.

Second equation: The total number of individuals present on the day is 283. X and Y, or the number of children and adults, must be added together to arrive at this figure.

x + y = 396

System of equations:

1.5x + 4y = 1094

x +   y = 396

Thus,

x + y = 396  

y = 396- x

Substitute y = 396 - x into the first equation.

1.5x + 4 (396 - x) = 1094

1.5x + 1584 - 4x = 1094  

1584 - 2.5x = 1094      

-2.5x = -490                  

x = 196

Substitute x =196 back into y = 396 - x

y = 396 - 196 = 200

Therefore by solving the equations we get to know that 196 children and  200 adults were present on that day.

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The missing terms are 34t and 0.

Finding the solution to linear equations in one, two, three, or more variables is referred to as solving a linear equation. In simple words, finding the values that satisfy a Linear equation.

Here we have

Equation 3(18t +1) = 20t +3  

Let's solve the given expression to get the missing step

=> 3(18t +1) = 20t +3

Multiply (18t + 1) by 3

=> 54t + 3 = 20t + 3

Subtract 3 from both sides

=> 54t + 3 - 3 = 20t + 3 - 3

=> 54t = 20t

Subtract 20t from both sides  

=> 54t - 20t = 20t - 20t    

=>  34t = 0

Divide by 34 into both sides

=> 34t/34 = 0/34  

=>  t = 0  

Therefore,

The missing terms are 34t and 0.

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Answer:

x = 8

Step-by-step explanation:

a rhombus has all equal sides so this means that you must set them equal to each other

8x - 5 = 5x + 19

now subtract 5x to both sides

3x = 24

x = 8

that is your answer

Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.

What is the half-life of a substance?

Half-life is the time required for the amount of something to fall to half its initial value. The converse of half-life is doubling time.

The half-life of a substance is the time it takes for half of the initial mass of the substance to decay.

Since the half-life of Palladium-100 is 4 days, after 4 days, the mass of the sample will be reduced to half of its initial value. After 8 days, it will be reduced to a quarter of its initial value, and after 12 days it will be reduced to an eighth of its initial value.

We are given that after 12 days, the mass of the sample is 6 mg. This means that the initial mass of the sample was 8 * 6 mg = 48 mg.

After 7 weeks (7 * 7 = 49 days), the mass of the sample will be reduced by a factor of

              =  [tex]8^{(49/4) }[/tex]

             = [tex]8^{12.5}[/tex] =

approximately [tex]2.6 * 10^6[/tex]. The mass of the sample after 7 weeks will be approximately [tex]\frac{6 mg }{2.6 * 10^6}[/tex] = approximately [tex]2.3 * 10^{-6}[/tex] mg.

Rounded to 5 decimal places, the initial mass of the sample was 48.00000 mg, and the mass 7 weeks after the start was 0.00002 mg.

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Answer:

1st darw

[tex] p(purple)= \frac{5}{20} \\ = \frac{1}{4} [/tex]

[tex]p(green) = \frac{1}{20} [/tex]

2nd draw

[tex]p(purple) = \frac{4}{18} \\ = \frac{2}{9} [/tex]

[tex]p(green) = 0[/tex]

When boys and girls are equally likely, the likelihood that at least 50 of 125 infants born will be females is 0.40.

Probability is an area of mathematics that deals with numerical representations of how probable an event is to occur or how likely a statement is to be true. The probability of an occurrence is a number between 0 and 1, where 0 denotes the event's impossibility and 1 represents certainty. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

total number of sample=125

number of girls=50

Probability that out of 125 babies born, at least 50 will be girls,

=50/125

=0.40

The probability that out of 125 babies born, at least 50 will be girls is 0.40 when boys and girls are equally probable.

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Therefore ,the radius of the given cylinder is 10 inches

A three-dimensional space's occupied volume is measured. It is frequently expressed as a numerical value using SI-derived units, other imperial units, or US customary units. Volume definition and length definition are connected.

Here,

The volume of the cylinder is 1570 cubic inches

Volume of the cylinder = 1570 cubic inches

Volume of cylinder = π[tex]r^{2}[/tex]h

Where r is the radius of cylinder

h is the height of cylinder

So,

Volume of the cylinder = 1570 cubic inches

=> 1570 = π[tex]r^{2}[/tex]h

=> 1570 = 3.14*[tex]r^{2}[/tex]*5

=> 1570/3.14 = [tex]r^{2}[/tex]*5

=> 500=[tex]r^{2}[/tex]  *5

=> 500/5 =[tex]r^{2}[/tex]

=>100 =[tex]r^{2}[/tex]

=>r=10 inches

Therefore the radius of the given cylinder is 10 inches.

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Answer: The diameter of a pizza is 20 inches.

Answer: 8 weeks

Step-by-step explanation: It would take John 8 weeks to collect more basketball cards than Frank with 67 cards for John and 66 for Frank.

Answer: 18

Step-by-step explanation:

[tex]\triangle HJK \cong \triangle HLK[/tex] by HL. Therefore, [tex]JK=2[/tex] by CPCTC.

Using the segment addition postulate, [tex]GK=9[/tex].

Furthermore, [tex]\triangle HGK \cong \triangle HMK[/tex] by HL. This means that [tex]MK=9[/tex] by CPCTC.

Using the segment addition postulate again, [tex]GM=9+9=18[/tex].

55 I think if I'm wrong sorry

The net signed area of f(x) = 2x - 6 on the interval [-8, 5] is - 21 units.

The definite integral can be used to calculate the net signed area, which is the area above the x-axis less the area below the x-axis.

Given, f(x) = 2x - 6 and the x-axis over the interval [-8 , 5].

∴ The net signed area is,[tex]\[ \int_{-8}^{5} 2x -6 \,dx \][/tex].

[tex]= \[ \int_{-8}^{5} 2x \,dx \ - \ \int_{-8}^{5} 6 \,dx \][/tex].

= (5)² - (-8)² - {(5×6) - (-8×6)}.

= 25 - 64 - 30 + 48.

= - 21 units.

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Answer:

A Hooe that helps. Brainliest

Answer:

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

Find the combination of 4 of 12 and 5 of 12:

Answer: B

Step-by-step explanation:

Answer:

B. (3, 2)

Step-by-step explanation:

When looking for a solution to an inequality you have to look for a point that is located in the shaded part of the inequality when graphed. B.) (3,2) is the only point that is located in the shaded part meaning that, that is a solution to the inequality

By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations.

There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.

The equation must be constrained with some constraints.

As per the given system of equations,

2x + 7y = 32 and 2x + y = 8

Subtract both equations from each other,

(2x + 7y) - (2x + y) = 32 - 8

2x + 7y - 2x - y = 24

2x - 2x + 7y - y = 24

6y = 24

y = 4

Hence "By subtraction, the variable x will eliminate and we will find out the value of y in the given system of equations".

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Let f:X→Ybe a function. Then the function  f  is a bijection if the relation   {(y ,x)∈Y×X∣ (x ,y)∈f}  is a function.  

Assume that X→Y is a bijective function.  

i.e. f:X→Y is one-one and onto function.

so different elements in X have different images in Y

and b ∈ Y there exists a ∈ X such that f(a)=b.

R= {(y ,x)∈Y×X∣(x ,y)∈f}  is a relation

we wish to prove R is a function.

R is a relation from Y to X  

let  Y∈Y by assumption f is bijection function from X to Y

for all y ∈ Y there exists X∈ X   such that f(x)=y.

so for every element in Y there is mapping element in X.
if (x ,y) ∈  f then (y ,x) ∈ R

therefore R is a function.        

   

let X1, X2, ∈ X then there exists some y1, y2,∈ y such that

take f ( x1 )= y1 and f( x2)=y2

by assumption R is a function from Y to X that is inverse of f is existing means f is bijection.

for bijective functions only inverse exists.

If f:X→Y is a function. Then the function f is a bijection if the relation

{(y ,x)∈Y×X∣(x, y)∈f}  is a function.

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Answer:

Below

Step-by-step explanation:

a) they won 120 games out of 369 played  = 40/23=.325

b) they lost 248 out of 369 played = 248/369 = .672

c) Home games are 185 out of 369 = .501

d ) at home they won 72 out of (72+112+1) = 72/ 185 = .389

The volume of the can of campbell's chicken Noodles Soup in cubic millimeters is 89,725.5 cubic millimeters

Volume of a cylinder = πr²h

Convert inch to millimeters:

Height of the cylinder = 5 inches = 127 millimeters

Radius = diameter / 2

= 30 millimeters / 2

= 15 millimeters

Volume of a cylinder = πr²h

= 3.14 × 15² × 127

= 3.14 × 225 × 127

= 89,725.5 cubic millimeters

Consequently, the can of campbell's chicken Noodles Soup has a volume of 89,725.5 cubic millimeters

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Hello,

I hope you and your family are doing well!

To solve for V, we can start by subtracting 13 from both sides of the equation:

|v-8| = 16

Since the absolute value of a number is always nonnegative, we know that the value inside the absolute value must be either positive or zero. This means that we have two possible cases to consider:

Case 1: v-8 > 0

In this case, we can drop the absolute value symbols and solve the equation:

v-8 = 16

v = 24

Case 2: v-8 = 0

In this case, we can drop the absolute value symbols and solve the equation:

v-8 = 0

v = 8

So the possible values of V are 8 and 24.

-----

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Happy Holidays!

Step-by-step explanation:

|v-8| + 13 = 29

subtract 13 from both sides

|v-8| = 16

form two equations:

v-8 = 16 -(v-8) = 16

v-8 = 16

add 8 to both sides

v = 24

-(v-8) = 16

-v+8 = 16

subtract 8 from both sides

-v = 8

divide both sides by a -1

v = -8

check work:

|v-8| + 13 = 29

|24-8| + 13 = 29

|16| + 13 = 29

29 = 29

|v-8| + 13 = 29

|-8-8| + 13 = 29

|-16| + 13 = 29

|-29| = 29

29 = 29

The domain of the graph is {-5,-4,-3,-1}.

How can I determine a graph's domain?

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The time required to match the record is 41.37 seconds. The correct option is (c).

The arithmetic operations are the fundamentals of all mathematical operations. The example of these operators are addition, subtraction, multiplication and division.

The given problem can be solved as follows,

The remaining time for matching the record is given by,

73.4 - (20(¹/₄) + 11.78)

= 73.4 - (81/4 + 11.78)

= 73.4 - (20.25 + 11.78)

= 73.4 - 32.03

= 41.37

Hence, the time Julie have left to match the record is 41.37.

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Answer:

Volume of a cuboid = length x width x height

8 x 8 x 32 = 2048

Volume of a cylinder = πr^2h

r = diameter/2 = 8/2 = 4

π(4)^2(32) = π(16)(32) = 1607.68

Volume of the shaded solid:

2048 - 1607.68 = 440.32

The correct answer would be C) 440.32 m^3