Please help me finish this problem

The result of dividing 2x^3 + x^2 - 2x + 8 by x + 2 is:

Quotient: 2x^2 - 3x + 4

Remainder: 0

The given polynomial is 2x^3 + x^2 - 2x + 8.

First we choose a term to multiply with the first term of the divisor such that we get the first term of the polynomial.

(x)(2x^2) = 2x^3

Thus, we multiply the divisor (x + 2) by 2x^2 which gives 2x^3 + 4x^2.

Now we subtract this from the polynomial which gives -3x^2 - 2x +8.

Next we multiply the divisor by -3x which gives -3x^2 - 6x. Again we subtract the same from the remaining polynomial -3x^2 - 2x +8 and get 4x + 8.

Repeating the same we multiply the divisor by 4 which gives 4x + 8. Subtracting the same from the remaining polynomial 4x + 8 we get the remainder 0.

Thus, the quotient is 2x^2 - 3x + 4.

The question is incomplete, the complete question is:

What is the result of dividing 2x^3 + x^2 - 2x + 8 by x+2?

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Answer:

Below

Step-by-step explanation:

It is just the angles that are next to GHI  

  this would be IHJ   and  FHG  

At Nation Office Supply, Marley purchased 9 dozen notepads.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

At Nation Office Supply, pens are $1.69 per dozen and notepads are $4.59 per dozen.

Here, Marley purchases 9 dozen pens, and spend total $56.52.

Let number of notepads can she purchase = x

So, We can formulate;

⇒ 9 × $1.69 + $4.59x = $56.52

⇒ 15.21 + 4.59x = 56.52

⇒ 4.59x = 56.52 - 15.21

⇒ 4.59x = 41.31

⇒ x = 41.31 / 4.59

⇒ x = 9

Thus, Marley purchased 9 dozen notepads.

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The length of arc COD is approximately 12.56 units.

To find the radius of the circle, we can use the area of sector COD and the angle COD.

We know that the area of a sector is (angle/360) * pi * r^2, and we know that the area of sector COD is 50.24 square units. We also know that the angle COD is 90 degrees.

So we can set up the following equation:

50.24 = (90/360) * 3.14 * r^2

Solving for r, we get:

r = sqrt(50.24 / (90/360) * 3.14) = sqrt(50.24 / (0.25 * 3.14)) = sqrt(50.24 / 0.785) = sqrt(64.28) = 8 (approximately)

So the radius of the circle is approximately 8 units.

To find the length of the arc, we can use the formula of arc length which is Arc Length = (Angle/360) * 2πr

So the length of the arc COD is (90/360) * 23.148 = 4*3.14 = 12.56 (approximately).

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Answer:

3

Step-by-step explanation:

x = the third side

x² + ([tex]\sqrt{55}[/tex])²= 8²

x² = 64 - 55 = 9

x = [tex]\sqrt{9}[/tex] = 3

The equation for the horizontal asymptote of the function f is y=Lim x→∞ f(x).

In algebra and calculus, a horizontal asymptote is a horizontal line that the graph of a function approaches as the x-values or input values increase or decrease without bound.

The equation for the horizontal asymptote of a function f is:

Lim f(x) → ∞ = c

Where c is the horizontal asymptote.

Example:

f(x) = x2 + 3x + 2

Horizontal Asymptote:

Lim f(x) → ∞ = ∞

numeric value in equation

For example, if x = 5:

f(5) = 5^2 + 3*5 + 2 = 32

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In the given expression, 7^x=28, as there is variable in one side while in other side there is constant, also there is no logarithmic value, so it is not possible to  solve the equation by changing the base of both sides

The basic formula has been changed to logb b a = [logc c a] / [logc c b]. It simply implies that to alter the base of a logarithm logb b a, we divide [log a] / [log b], where these logarithms might have any (same) positive number as a basis.

The change of base formula gives you the answer of a log with a different base by utilizing only log computations with a base of 10. The formula instructs you to divide the log of the number in parentheses by the log of your base.

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The absolute value of the number plotted on the number line is 1.25

Answer: i believe its -3x+9

Step-by-step explanation:

it is important to recognize that the minus sign in front of −(x−3) applies to both x and −3.

remove the parentheses by distributing the minus sign to the terms inside them: −2x+6−(x−3)

⇒−2x+6−x−(−3)

⇒−2x+6−x+3

combine similar terms: ⇒(−2x−x)+(6+3)

⇒−3x+9

Answer:

Step-by-step explanation:

using the rise over run method:

1 up and three to the right

the slope is 1/3
m = 1/3

Formula used to calculate the y-intercept when coordinates of two points are given is as follow: y = mx + c where 'm' represents the slope and 'c' represents the y-intercept.

As given in the question,

Let us consider points of two coordinates be equal to

( x₁ , y₁ ) =  ( 2, 3 )

( x₂ , y₂ ) = ( 4, 7 )

Equation of the line is equal to :

( y - y₁ ) / ( x - x₁ )  = ( y₂ - y₁ ) / ( x₂ - x₁ )

⇒ ( y - 3 ) / ( x - 2 ) = ( 7 - 3 ) / ( 4 - 2 )

⇒ ( y - 3 ) / ( x - 2 ) = 2

⇒ y - 3 = 2x - 4

⇒ y = 2x - 1

Same as y = mx + c

Here c = -1

Here y-intercept is equal to -1 by substituting x = 0 we can get                 y - intercept.

Therefore, the value of y-intercept can be calculated with the coordinates of the given points using formula given by :

y = mx + c where 'c' represent y-intercept.

The given question is incomplete, I answer the question in general according to my knowledge:

If you're given coordinates of 2 points, how do you find the y-intercept?

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Yes, George can be claimed as a dependent by his parents.

A dependent is a person who qualifies for a dependency exemption but is not the taxpayer or the taxpayer's spouse. Every exemption for a dependent reduces the amount of taxable income by the exemption amount.

If a full-time student, your child must be younger than 24 or younger than 19 years old. If your child is totally and permanently incapacitated, there is no upper age restriction. Are these your roommates? There are a few situations where your child does not need to live with you for more than half the year.

Your child must be younger than you and either be a "student" younger than 24 years of age as of the end of the calendar year, or be younger than 19 years old.

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The value of x is 2 and NM = OL = 7

Now, According to the question:

What is a parallelogram?

A parallelogram is a special type of quadrilateral that has both pairs of opposite sides parallel and equal.

Given that, LMNO is a parallelogram and NM = x + 5 and OL = 2x + 3,

Since, we know that, opposite sides of a parallelogram are equal,

Therefore,

NM = OL

x+5 = 2x+3

x = 2

Therefore, NM = OL = 7

Hence, the value of x is 2 and NM = OL = 7

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By the definition of the mode, we can say the mode of this data is 33.

What is the mode?

The mode in statistics refers to a number in a set of numbers that appears the most often. For example, if a set of numbers contained the following digits, 1, 1, 3, 5, 6, 6, 7, 7, 7, 8, the mode would be 7, as it appears the most out of all the numbers in the set.

We have given,

Data set 18 16 11 45 33 16 33 14 18 33.

To find what is the mode for this data set.

Solution: We have given

Data set 18 16 11 45 33 16 33 14 18 33.

Mode: The mode of a set of data values is the value that appears most often.

So,

We can see the most repeated number is 33. ( 3 times)

Hence, by the definition of the mode, we can say the mode of this data is 33.

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Answer:

roots are real and rational

Step-by-step explanation:

given a quadratic equation in standard form

ax² + bx + c = 0 ( a ≠ 0 ) , then the discriminant is

b² - 4ac

the discriminant informs on the nature of the roots

• if b² - 4ac > 0 then roots are real and irrational

• if b² - 4ac > 0 and a perfect square, then roots are real and rational

• if b² - 4ac = 0 , then roots are real and equal

• if b² - 4ac < 0 , then the roots are not real

for 2x² + 7x + 6 = 0 , in standard form

with a= 2, b = 7 , c = 6 , then

b² - 4ac = 7² - (4 × 2 × 6) = 49 - 48 = 1

since b² - 4ac > 0 and a perfect square, then the roots are real and rational

A inverse example is when two variables are inversely related, meaning that as one increases, the other decreases. For example, as the temperature outside rises, the amount of ice cream sold decreases.

Inverse relationship means that the two variables are directly proportional to each other; if one increases, the other decreases. An example of an inverse relationship is the relationship between the temperature outside and the amount of ice cream sold. As the temperature outside rises, the amount of ice cream sold decreases. This is because people are less likely to buy ice cream when it is hot outside.

A inverse example is when two variables are inversely related, meaning that as one increases, the other decreases. For example, as the temperature outside rises, the amount of ice cream sold decreases.

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The number of gallons of gasoline pumped by a filling station during a day represents a B: "quantitative " type of variable.

Quantitative variables are data about numeric values such as how much; how often; or how many.  In other words, quantitative variables are referred to as any variables that represent amounts, such as age, height, or weight.

In the given case, it is talked about the number of gallons of gasoline filled during a day; since it represents the quantity or number of gallons so it is a type of quantitative variable, representing the number of gallons of gasoline to be pumped.

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The equation of equilibrium states that the sum of the forces in the x-direction must be zero.

Equation of equilibrium:

F_x = 0 = mgsinθ - mgsinϕ

mgsinθ = mgsinϕ

sinθ = sinϕ

θ = ϕ

The equation of equilibrium states that the sum of the forces in the x-direction must be zero. This means that the force due to gravity in the x-direction, mgsinθ, must be equal to the force due to gravity in the x-direction, mgsinϕ. This can be rearranged to sinθ = sinϕ, which means that the angles θ and ϕ must be equal. Thus, the relationship between angles θ and ϕ is that they are equal.

The equation of equilibrium states that the sum of the forces in the x-direction must be zero.

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No matter how far they reach, parallel lines are those that do not have a shared meeting point in the same plane.

If two lines cannot collide when extended in both directions to infinity, they are said to be parallel in a plane. Throughout the entire length, there remains a constant gap between two lines.

|| is the symbol used to represent the parallel lines. Assuming that lines "a" and "b" are parallel to one another, we may indicate this using the symbol "a||b," which means "a is parallel to b."

We need a ruler and a compass to create a line parallel to the other line starting from an outside point. The diagram of parallel line is given below:

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The value of y after solving the given equation is -8.

We can calculate the value of y through the following method,

We have been provided with an exponential equation [tex]8^{y} = 16^{y+2}[/tex]

As we know, an exponential equation is an equation whose exponent or part of the exponent is a variable.

For solving an exponential equation, we need to use logarithms and their properties.

We can write [tex]8^{y}[/tex] also as [tex]2^{3y}[/tex] since we know that 2³ = 8

Similarly, we can write [tex]16^{y+2}[/tex] also as [tex]2^{4(y+2)}[/tex] since we know that [tex]2^{4}[/tex] = 16

Therefore we get the new equation as,

[tex]2^{3y}[/tex] = [tex]2^{4(y+2)}[/tex]

Now we will add log with base 10 on both the sides

Therefore the equation will become,

log₁₀ [tex]2^{3y}[/tex] = log₁₀ [tex]2^{4(y+2)}[/tex]

Since, according to the property of logarithm,

log₁₀ aᵇ = b log₁₀ a

Therefore,

3y log₁₀ 2 = 4(y + 2) log₁₀ 2

We can cancel out log₁₀ 2 on both sides

We get the equation as,

3y = 4(y + 2)

3y = 4y + 8

y = -8

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We have a translation of 4 units downwards, so the correct graph is the first one (the one you answered).

Here we start with the parent function:

f(x) = |x|

And the translated function is:

g(x) = |x| - 4

Remember that a general vertical translation of N units of a function f(x) can be written as:

g(x) = f(x) + N

if N > 0 the translation is upwards.

if N < 0 the translation is downwards.

Here N = -4, so the translation is 4 units downwards.

Then the correct graph is exactly the one that you marked.

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Karen adds up 4 consecutive odd integers ,the sum if the smallest one is 2m-1 is 8m + 8.

Since they are odd numbers, each time it must be +2 (since +1 goes odd, even, odd, even, etc.), therefore the result will be:

(2m - 1) + (2m + 1) + (2m + 3) + (2m +5) = 8m + 8

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Althea volunteers 10.25 hours a week.

Given that Althea volunteers in the school library for 2 1/4 hours on Mondays, Wednesdays, and Fridays.

She volunteers 2 1/4 hours a day.

First we convert the improper fraction 2 1/4 to a proper fraction.

2 1/4 = 9/4

So by unitary method for three days the number of hours she volunteer:

3 × 9/4 = 27/4

Also, she volunteers for 1 3/4 hours on Tuesday and Thursday.

She volunteers 1 3/4 hours a day.

First we convert the improper fraction 1 3/4 to a proper fraction.

1 3/4 = 7/4

So by unitary method for two days the number of hours she volunteer:

2 × 7/4 = 14/4

So, the total number of hours Althea volunteers for a week,

27/4 + 14/4

= 41/4

= 10.25 hours

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Answer:

192.5 miles

Step-by-step explanation:

let h be number of hours Anne takes to drive to her friend's house

[tex](55mph)(h) = (35mph)(h+2)[/tex]

Both sides of this equation represent the miles to her friend's home. (speed * time = distance)

We add 2 to h on the right side because the way back takes 2 hours longer than the way to her friend's home.

Now we can solve.

[tex](55)(h) = (35)(h+2)\\55h = 35h+70\\20h = 70\\h = \frac{7}{2} = 3.5[/tex]

Now that we have how long the trip to her friend's house takes, we can solve for the distance to her friend's house by using either side of our equation. I will use the left side because it is simpler.

[tex](55)(h)\\(55)(3.5)\\\boxed{192.5}[/tex]

That is the answer

- Kan Academy Advance

The 30, 60, and 90 are special right triangles. the perimeter of the triangle is = [tex]a+b+c[/tex] =[tex]x+2x+x\sqrt{3}[/tex]

30,60,90 special right triangles because there is a relation between height, base, and the hypotenuse.

Point to be noted

the opposite side of [tex]30^o[/tex] is height, the opposite side of [tex]60^o[/tex] is base, and the opposite side of [tex]90^o[/tex] is the hypotenuse.

Assume the height of the triangle = [tex]x[/tex]

In this type of triangle, the hypotenuse is double of height,

so, hypotenuse = [tex]2x[/tex]

and the base of the triangle is [tex]\sqrt{3}[/tex] of the height.

Therefore, base = [tex]x\sqrt{3}[/tex]

so that, The perimeter of the triangle = [tex]x+2x+x\sqrt{3}[/tex]

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Answer:

The diameter of the circle is 7/2.

Step-by-step explanation:

⭐What is the radius of a circle?

⭐What is the diameter of a circle?

Thus, the diameter of said circle is twice the radius of said circle.

diameter = 2(radius)

diameter = 2(7/4)                   . . . . substitute known values

diameter = 14/4                      . . . . multiply the numerator & denominator

diameter = 7/2                       . . . . simplify

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Use the section formula to get the coordinates of a point that separates a line segment outside or internally in a specific ratio.

By building two right triangles and applying AA similarity, the section formula can be obtained. After determining the ratio of the triangle's side lengths in terms of the supplied ratios, we may solve for x and y to determine the coordinates of the point that divides the line segment.

To determine the coordinates of a point that splits a line segment externally or internally in a certain ratio, apply the section formula. A line segment's midpoint can be determined using this technique as well.

By section formula, we have, if (x, y) divides the line segments joining [tex]$\left(x_1, y_1\right)$[/tex] and [tex]$\left(x_2, y_2\right)$[/tex] internally in the ratio m: n then,

[tex]$x=\frac{m x_2+n x_1}{m+n}$[/tex] and [tex]$y=\frac{m y_2+n y_1}{m+n}$[/tex]

Here,

[tex]\left(x_1, y_1\right)=(8,-1) \\\\ \left(x_2, y_2\right)=(2,5) \\\\ (x, y)=(4, 3) \\[/tex]

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A perpendicular bisector of a triangle is a segment that is perpendicular to the side of a triangle at its midpoint. So option A is the correct answer.

Specifically, it is a line which passes through the midpoint of a side of the triangle, and is perpendicular to that side. It crosses the side at a 90 degree angle, and divides the side into two equal parts.

It can also be thought of as a line which connects the vertex and the opposite side at 90 degrees. In order for a triangle to be equilateral, the three perpendicular bisectors must all intersect at the same point, which is the center of the triangle.

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The inverse meaning in math is a function or operation which reverses the order or operation of another function or operation.

Let us take an inverse math example, The inverse operation of addition is subtraction, and the inverse operation of multiplication is division.

For example, The multiplication of two numbers 3 and 6 is 3 × 6 = 18. The inverse operation of this is a division which is as follows: 18/6 = 3.

The Inverse of a Number

Consider a number y where y is not equal to zero. Then the inverse of a number y is the reciprocal of the number that is 1/y.

For example, The inverse of the number 200 is 1/200, and the inverse of the number 32 is 1/32.

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