What is the remainder and quotient of 23 divided by 861

Answer:

  (2)  (-2, 4), (3, 9)

  (3)  (-2, 4), (1, 1)

Step-by-step explanation:

My favorite way to answer questions like this is to use a graphing calculator to find the points of intersection. The attached shows the points of interest.

If you want to solve this by hand, equate the expressions for y, then solve the resulting quadratic using any of the methods you know. Once you find the x-values, put those in either equation to find the y-value.

__

(2) x^2 = y = x+6

  x^2 -x -6 = 0 . . . . put in standard form

  (x -3)(x +2) = 0 . . . . factor

  x = 3 or -2 . . . . . find the x-values that make the factors zero

  y = x^2 = 9 or 4

The points are (3, 9) and (-2, 4).

__

(3) x^2 = -x +2

  x^2 +x -2 = 0 . . . . standard form

  (x +2)(x -1) = 0 . . . factored

  x = -2 or 1 . . . . . . .zeros

  y = x^2 = 4 or 1

The points are (-2, 4) and (1, 1).

_____

Comment on factoring

When you consider the factored form and its expanded equivalent, ...

  (x +a)(x +b) = x^2 +(a+b)x +ab

you see that the coefficient of the linear term (a+b) is the sum of factors of the constant term (ab). Your knowledge of multiplication tables will often help you factor equations easily. You need to pay attention to signs.

In problem 2, we want factors of -6 that have a sum of -1:

  -6 = (-1)(6) = (-2)(3) = (-3)(2) = (-6)(1)

These factor pairs have sums of 5, 1, -1, -5. The pair whose sum is -1 is the one we're looking for: -3 and 2. So, the factors in problem 2 are (x-3)(x+2).

__

In problem 3, we want factors of -2 that have a sum of +1:

  -2 = (-1)(2) = (-2)(1)

These factor pairs have sums of 1, -1. So, the second pair is the one of interest: -2 and 1. That makes the factors be (x-2)(x+1).

Answer:

[tex]0+6\sqrt{2}i[/tex]

or just [tex]6\sqrt{2}i[/tex]

Step-by-step explanation:

[tex]\sqrt{-72}[/tex] does not have a real part, it is a pure imaginary number.

Let's simplify.

First step:

[tex]\sqrt{-1}=i[/tex] is the imaginary unit.

So we have that we can write [tex]\sqrt{-72}=i \sqrt{72}[/tex].

Second step:

Let's simplify the factor [tex]\sqrt{72}[/tex] by looking for perfect squares of [tex]72[/tex].

[tex]72=2(36)=2(6^2)[/tex]

So [tex]36[/tex] is a perfect square because it can be written as [tex]6^2[/tex].

[tex]\sqrt{-72}[/tex]

[tex]i \sqrt{72}[/tex]

[tex]i \sqrt{2 \cdot 6^2}[/tex]

[tex]i \sqrt{2} \sqrt{6^2}[/tex]

[tex]i \sqrt{2} 6[/tex]

[tex]6 \sqrt{2}i[/tex]

We could write this as [tex]0+6\sqrt{2}i[/tex].

Greetings from Brasil...

Using sine, we will be able to find the value of X

SEN 17 = X/47

X = 47 · SEN 17

X = 47 · 0,29237

X = 13,741

Answer:

Option C: Do free market economies create problems for workers?

Step-by-step explanation:

There was a law called Say's law which states that capitalist production generates its own markets, and therefore, there can't possibly be any gluts or overproduction of goods in relation to market demand.

Now, keynes and marx rejected this say's law because they both believed that gluts or overproduction may likely occur.

They believed that this law would make capitalists own nothing but the right to sell their labor in exchange for wages.

That due to the capitalists competition with themselves for profits, it would squeeze as much work as possible out of the working class people at the lowest possible price and that this competition would cause some capitalist firms to fail, and thereby increasing unemployment among the working class.

Thus, it's clear this was an answer to the question on whether free market economies create problems for workers.

Answer:

A.Should government take total control over economies

Step-by-step explanation:

This is equivalent to x = z/8 + h or x = (1/8)z + h

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

Work Shown:

z = 8(x-h)

z = 8x-8h ... distribute

8x-8h = z

8x = z+8h .... adding 8h to both sides

x = (z+8h)/8 .... dividing both sides by 8

x = z/8 + 8h/8

x = z/8 + h

x = (1/8)z + h

Answer:  [tex]-\dfrac{1}{2}[/tex]

Step-by-step explanation:

The coordinate at -30° (-30° = 330°) = [tex]\bigg(\dfrac{\sqrt3}{2},-\dfrac{1}{2}\bigg)\\[/tex]

the x-value is  [tex]\dfrac{\sqrt3}{2}[/tex]

the y-value is  [tex]-\dfrac{1}{2}\\[/tex]

Answer:

-0.5

Step-by-step explanation:

Answer:

(a) The sample space is {00, 0, 1, 2, . . . , 30}.

(b) If the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3.

(c) If the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.

Step-by-step explanation:

We are given that in the game of roulette, a wheel consists of 32 slots numbered 00, 0, 1, 2, . . . , 30.

To play the game, a metal ball is spun around the wheel and is allowed to fall into one of the numbered slots.

(a) The sample space is {00, 0, 1, 2, . . . , 30} which means the metal ball can land on any of these numbers.

(b) As we know that there is an equal probability of the metal ball landing on any of the slots marked in the sample space.

Total number of slots = 32

Number of slots marked with 3 = 1

So, the probability that the metal ball falls into the slot marked 3 is given by =  [tex]\frac{1}{32}[/tex]  = 0.031 or 3.1%

This means that if the wheel is spun 100 times, it is expected about 3.1 of those times to result in the ball landing in slot 3.

So, if the wheel is spun 1,000 times, it is expected about 31 of those times to result in the ball landing in slot 3 because (0.031 [tex]\times[/tex] 1000) = 31.

(c) As we know that the odd slot in the given sample space is {1, 3, 5,......, 29}.

Total number of slots = 32

Number of odd slots = 15

So, the probability that the metal ball lands in an odd slot is given by =  [tex]\frac{15}{32}[/tex]  = 0.47 or 47%.

This means that if the wheel is spun 100 times, it is expected about 47 of those times to result in the ball landing in an odd number.

Answer:

1. agricultural inspecter

2. food-cooking machine operator

3. grader or sorter

4. food-baking machine operator

5. food batchmaker

Step-by-step explanation:

i got this correct on ED2021

The correct order is agricultural inspector, food-cooking machine operator, grader, or sorter. food-baking machine operator, food matchmaker.

The process of turning agricultural materials into food or transforming one type of food into the next is referred to as transformation.

It is given that:

For the descriptions:

Makes sure products meet safety regulations - agricultural inspector.

Operates equipment to cook meat for packaging in soup cans - food-cooking machine operator.

Classifies eggs based on size and quality - grader or sorter.

Operates a large oven in a factory to bake bread before packaging - food-baking machine operator.

Operates equipment that mixes ingredients together to make candy - food matchmaker.

Thus, the correct order is agricultural inspector, food-cooking machine operator, grader, or sorter. food-baking machine operator, food matchmaker.

Learn more about food processing here:

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Answer:

[tex]\huge \boxed{ \mathrm{D.} \ \ a^2 +b^2 =c^2}}[/tex]

Step-by-step explanation:

The correct equation for the Pythagorean theorem is:

[tex]\Rightarrow \ \ a^2 +b^2 =c^2[/tex]

c is the length of the hypotenuse of the right triangle

a and b are the side lengths of the right triangle

Answer: 2y + 5x + 16 = 0

Step-by-step explanation:

To solve this you need to understand the principle/ conditions for parallelism and perpendicularity.

for two lines to be parallel to each other, their gradients or slopes (m) must be equal, that is  m₁ = m₂

Now from the given equation,

5x + 2y = 14 , we need to rearrange it to conform to the equation of a straight line so that the gradient could be established. ie

y = mx + c where m is the gradient

 2y = -5x  + 14

   y = -5x/2  + 14/2

   y = ⁻⁵ˣ/₂  + 7 , therefore , m₁ = ⁻⁵/₂ and m₂ = ⁻⁵/₂ ( parallelism Rule )

The next step is to find the value of C using the coordinate ( -2, -3 )

  -3 = ⁻⁵/₂ ˣ ⁻² + C,

  -3 =  ¹⁰/₂  + C

  -3 =  5 + C

   C = -8.

Now to find the equation of the line that passed through the coordinate

  y = mx + c

  y = ⁻⁵ˣ/₂  - 8

  2y = -5x - 16

  2y + 5x + 16 = 0.

Answer:

A' (2, 1)

B' (1, 2)

C' (3, 2)

Step-by-step explanation:

Scale factor = 0.5

A(⁴₂ ) → A'([tex]\frac{1}{2} * 4\\\frac{1}{2} * 2[/tex]) = (²₁ )  ∴ A'(2, 1)

B(²₄ ) → B'([tex]\frac{1}{2} * 2\\\frac{1}{2} * 4[/tex]) = (¹₂ ) ∴ B'(1, 2)

C(⁶₄ ) → C'([tex]\frac{1}{2} * 6\\\frac{1}{2} * 4[/tex]) = (³₂ ) ∴ C'(3, 2)

Answer:

Step-by-step explanation:

Using the rules of indices

That's

So we have

So we have

Let

We have

4y = 9y - 2

4y - 9y = - 2

- 5y = - 2

Divide both sides by - 5

But

Take logarithm to base 2 to both sides

That's

So we have

Using the rules of logarithms

That's

Rewrite the expression

That's

But

So we have the final answer as

Hope this helps you

Answer:

the answer is D I hope this helps

Answer:

11.3 miles

Step-by-step explanation:

We can use the pythagorean theorem to find the distance from his home to work, since the 3 roads form a right triangle where the new road is the hypotenuse.

a² + b² = c²

8² + 8² = c²

128 = c²

= approx. 11.3 miles

The distance between his home and his work of place is 11.31 miles.

Given,

A man drove 8 miles directly east from his home, made a left turn at an intersection, and then traveled 8 miles due north to his place of work.

A road was made directly from his home to his place of work.

We need to find what would its distance be in miles,

We have,

                 North

West   <----- ⇅ ------->           East

                 South

In a right triangle,

The square of the hypotenuse is equal to the sum of the square of the other two sides.

Find the direction of the given statement.

A man drove 8 miles directly east from his home:

              8 miles

Home ------------------->East

Made a left turn at an intersection, and then traveled 8 miles due north to his place of work:

             North         Work

                 ⇅              Left

                                ⇅ 8 miles

Home ------------------->East

                                ⇅

                               Right

If a road was made directly from his home to his place of work:

                                                        Work

Home                       North          

West   <------------------⇅ --------------->East

                               South

                                          A  (Work)

                                     /   ║

                              /          ║                              

                       /                 ║ 8 miles

                  /                      ║  

(Home) B /___________║C

                      8 miles

Find the distance between home and place of work.

AB = distance between home from work

Applying the Pythagorean theorem.

AB² = BC² + AC²

AB² = 8² + 8²

AB² = 64 + 64

AB² = 128

AB = ±√128

The distance can never be negative here so,

√128 = 11.31

AB = 11.31 miles.

Thus the distance between his home and his work of place is 11.31 miles.

Learn more about justifying the distance Formula using the Pythagorean Theorem here:

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Answer:

b and c

Step-by-step explanation:

both are just greater than or less than

Responder:

c. x menos 25 menos estilo en línea fracción 4 entre 19 fin estilo paréntesis izquierdo x menos 25 paréntesis derecho igual 3

Explicación paso a paso:

Dado lo siguiente:

Cantidad original de gasolina en el tanque de combustible = x

Gasolina consumida en el primer viaje = 25 litros

Gasolina restante después del primer viaje = (x - 25) litros

Gasolina consumida en el segundo viaje = 4/19 de lo que queda, es decir;

(4/19) * (x - 25)

Gasolina restante después del segundo viaje = 3 litros

Cantidad inicial - cantidad consumida en el primer viaje - 4/19 de la cantidad restante después del primer viaje = 3

La gasolina que queda después del segundo viaje se puede modelar mediante la ecuación:

x - 25 - 4/19 (x - 25) = 3

Answer:

5 Games

Step-by-step explanation:

Step 1: State what is known

We know for every 5 games the win they lose 1 game

They won 5 games

Step 2: Define your variables

Let x represent how many games the Basketball team lost

Step 3: Create equation

[tex]\frac{5}{1}=\frac{25}{x}[/tex]

Step 4: Solve for 'x'

Cross multiply to solve for 'x'

[tex]5x=25[/tex]

[tex]x=\frac{25}{5}[/tex]

x = 5

Therefore the will have lost 5 games

Answer:

88

Step-by-step explanation:

We are given the expression:

x+43x

and asked to evaluate when x=2. Therefore, we must substitute 2 in for x.

x + 43 x (plug 2 in for each x )

2+43(2)

Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.

Multiply 43 and 2 first.

2+ (43*2)

2+ 86

Add 2 and 86.

88

The expression x+43x when evaluated for x=2 is 88.

Answer:

1

Step-by-step explanation:

Answer:

(x - 3)mph * > 2x

Step-by-step explanation:

KC's total rides in hours = 2x

KC's average speed = x

David's average speed :

3 mph less than KC's average speed = (x - 3)mph

David's total ride in hours in a month is more than KC's, that is ( >2x)

From the equation:

Speed = distance / time

Distance = speed * time

Total distance of miles David rides each month:

(x - 3)mph * > 2x

[tex] \huge{ \underline{ \underline{ \bf{ \orange{Solution:}}}}}[/tex]

Let the first term of the AP be a and the common difference of the AP be d

We know the formula for finding the nth term,

[tex] \large{ \boxed{ \rm{a_n = a + (n - 1)d}}}[/tex]

Here,

By using formula,

According to given condition,

⇛ a4 = 2a2 - 1

⇛ a + 3d = 2(a + d) - 1

⇛ a + 3d = 2a + 2d - 1

⇛ a - 2a + 3d - 2d = -1

⇛ -a + d = -1

⇛ a - d = 1

Then,

⇛ a = d + 1-----------(1)

It is given that, a6 = 7

⇛ a + 5d = 7

Putting a from eq.(1),

⇛ d + 1 + 5d = 7

⇛ 6d + 1 = 7

⇛ 6d = 6

⇛ d = 6/6 = 1

Putting value of d in eq.(1),

⇛ a = 1 + 1 = 2

⛈ First term of the AP(a) = 2

━━━━━━━━━━━━━━━━━━━━

Answer:

The temperature difference relative to the high temperature is -2°F.

Step-by-step explanation:

We are given that the temperature started at 35°F. The temperature went down 4°F and then up 2°F.

Firstly, the original temperature = 35°F

Now, it is stated that the temperature went down 4°F, this means that the temperature decreases by this amount.

So, the new temperature = 35°F - 4°F = 31°F

Now, the temperature went up by 2°F, this means that the temperature increases by this amount.

So, the final temperature = 31°F + 2°F = 33°F

Now, the final temperature difference relative to the high temperature is given by = 33°F - 35°F = -2°F.

{Here, the maximum temperature is 35°F}

Answer:

it has a 1% chance.

Step-by-step explanation:

Because of the whole there is one chip in it that has a 2 on it so it has a 1% chance out of 100%

Answer:

Option A and Option E

Step-by-step explanation:

Option A.

x + 3 = 5

(x + 3) - 3 = 5 - 3

x = 2

Option B.

x + 2 = 8

(x + 2) - 2 = 8 - 2

x = 6

Option C.

x + 1 = 1

(x + 1) - 1 = 1 - 1

x = 0

Option D.

x - 2 = 4

(x - 2) + 2 = 4 - 2

x = 2

Option E.

x - 7 = -5

(x - 7) + 7 = -5 + 7

x = 2

Therefore, Option (A) and Option (E) are the correct options.

The eigenvalues of the 5 x 5 matrix are 0 (multiplicity: 2), 6 (multiplicity: 1), 9 (multiplicity: 1) y 1 (multiplicity: 1).

The eigenvalues of the 5 x 5 matrix are represented by the roots of the characteristic polynomial. The multiplicity of a eigenvalue is the number of times that a root is repeated.

Now we proceed to determine the roots of the characteristic polynomial by algebraic means:

[tex]p = \lambda^{5}-24\cdot \lambda^{4}+189\cdot \lambda^{3}-486\cdot \lambda^{2}[/tex]

[tex]p = \lambda^{2}\cdot (\lambda^{3}-24\cdot \lambda^{2}+189\cdot \lambda -486)[/tex]

[tex]p = \lambda^{2}\cdot (\lambda -6)\cdot (\lambda - 9)\cdot (\lambda - 1)[/tex]

The eigenvalues of the 5 x 5 matrix are 0 (multiplicity: 2), 6 (multiplicity: 1), 9 (multiplicity: 1) y 1 (multiplicity: 1).

To learn more on eigenvalues, we kindly invite to check this verified question: https://brainly.com/question/5596684

Answer:

1. 12 pieces of wood

2. How to determine the number of pieces of wood Dean cut is by dividing the total length of wood by length of each piece of wood

Step-by-step explanation:

Total length of wood=3/4 of a foot

He needs to cut pieces of the wood into 1/16 of a foot long

How many pieces can Dean cut

Let x= number of pieces of wood Dean needs to cut

x=Total length of wood / length of each piece

=3/4 ÷ 1/16

=3/4 × 16/1

=48/4

=12 pieces

Number of pieces of the wood Dean can cut =12 pieces

How to determine the number of pieces of wood Dean cut is by dividing the total length of wood by length of each piece of wood

That is,

3/4 ÷ 1/6

Then follow the procedures in question 1

Answer:

12√3 inches or 20.785 inches.

Step-by-step explanation:

A regular hexagon can be defined as a polygon with 6 sides.

The formula for the perimeter of a regular hexagon =

6 × the length of the sides of the hexagon.

From the above question, we are told that there is an inscribed circle I'm the hexagon with a diameter of 4√3 inches long

Step 1

Find the radius of the circle

Radius of the circle = 4√3/2 = 2√3 inches

Step 2

The radius of the inscribed circle = Length of one of the sides of a regular hexagon.

Hence, the perimeter of the regular hexagon = 6 × 2√3

= 12√3 inches

= 20.784609691 inches.

Approximately 20.785 inches

Answer: A=276.52 cm²

Step-by-step explanation:

To find the surface area of the figure, we can find the surface area of the rectangular prism and hemisphere. Then we would add them together.

Rectangular Prism

A=2(lw+hl+hw)

Since we are given the length, width, and height, we can directly plug them into the equation and solve.

[tex]A=2((10*5)+(4*10)+(4*5))[/tex]

[tex]A=2(50+40+20)[/tex]

[tex]A=2(110)[/tex]

[tex]A=220 cm^2[/tex]

The surface area for the rectangular prism is 220 cm².

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

Hemisphere

A=2πr²

This formula above is derived from the formula for surface area of a sphere.

The surface area of a sphere is A=4πr². Since the picture displays half of a sphere, we divide that by 2. This gives us A=2πr².

Since we have the radius, all we have to do is plug it in.

[tex]A=2\pi (3)^2[/tex]

[tex]A=2\pi (9)[/tex]

[tex]A=18\pi[/tex]

[tex]A=56.52 cm^2[/tex]                             *Note I used 3.14 instead of π.

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

Now that we have the surface area of the hemisphere and rectangular prism, we add them together to find the surface area of the entire prism.

A=220+56.52=276.52 cm²

Answer:

(x² + 6)(3x² - 4)

Step-by-step explanation:

factor out (x² + 6)

(x² + 6)(3x² - 4)

Answer:

The coordinates of A would be (-1, 2)

Step-by-step explanation:

In order to find this, use the mid-point formula.

(xA + xB)/2 = xM

In this, the xA is the x value of point A, xB is the x value of point B, and xM is the x value of M. Now we plug in the known information and solve for xA.

(xA + 5)/2 = 2

xA + 5 = 4

xA = -1

Now we can do the same using the midpoint formula and the y values.

(yA + yB)/2 = yM

(yA + 10)/2 = 6

yA + 10 = 12

yA = 2

This gives us the midpoint of (-1, 2)

Answer:

hello your question has some missing parts below is the missing part

Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean.

Identify the p-value.

Source DF SS MS F p

Factor 3 13.500 4.500 5.17 0.011

Error 16 13.925 0.870

Total 19 27.425

A) 0.011 B) 4.500 C) 5.17 D) 0.870

answer :  p-value = 0.011 ( A )

Step-by-step explanation:

using this information

Source DF SS MS F P

Factor 3 13.500 4.500 5.17 0.011

Error 16 13.925 0.870

Total 19 27.425

significance level = 0.05

given that the significance level = 0.05

and

F statistics are given as :  F = 5.17 , F critical = 3.25

hence the p-value = 0.011

from the analysis the p-value is less than the significance level is lower than the significance level