Estimate the measure of

The quotient is x²+x+1 - 14/(x-1) after divide x³-15 by x-1.

What is synthetic division?

In algebra, synthetic division is a technique for manually dividing polynomials according to Euclid, requiring less writing and calculation than long division. Although the approach can be applied to division by any polynomial, it is often taught for division by linear monic polynomials.

The divisor is x - 1.The dividend is (x³-15).

Step 1:Take the constant term of the divisor with the opposite sign and write it to the left.

Write the coefficients of the dividend to the right (missed terms are written with zero coefficients).

Step 2:Write down the first coefficient without changes:

Step 3:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).

Add the obtained result to the next coefficient of the dividend, and write down the sum.

Step 4:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum

Step 5:Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).Add the obtained result to the next coefficient of the dividend, and write down the sum.

We have completed the table and have obtained the following resulting coefficients: 1,1,1,−14.

All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.

The quotient is x²+x+1 and the remainder is -14.Therefore (x³-15)÷(x-1) = x²+x+1 - 14/(x-1)

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The equivalent fraction for 2/3 and 8/11 is 22/33 and 24/33.

What is least common denominator?

The least common denominator (LCD) is the smallest number that can be a common denominator for a set of fractions. Also known as the lowest common denominator, it is the lowest number you can use in the denominator to create a set of equivalent fractions that all have the same denominator.

Given fractions are

2/3 and 8/11

L.C.M of 3 and 11 is 33.

We get,

2/3 ×11/11 = 22/33

and

8/11×3/3 = 24/33

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Numerous other sorts of numbers exist, including natural, whole, rational, real, and integers. Positive and negative numbers, but not decimals or fractions, make up the category of integers.

Q      What are integers in mathematics?
ANS An integer is a whole number without any fraction or decimal part.

The traits of each group of numbers are as follows:

Answer: [tex]x=7[/tex]

Step-by-step explanation:

[tex]3^x=2187\\\\x=\log_{3} (2187)\\\\x=7[/tex]

Answer:

Consider the right triangle below: State the Pythagorean Theorem as it relates to the above triangle. List the trig identities as they relate to the triangle above. Now suppose hypotenuse C represents a vector R, while sides B and A represent vector components Rx and Ry respectively. Redraw the triangle with the new labels below. Using Pythagorean Theorem, derive the equation for R.

Considering the expression of a line, the equation of the line that passes through the pair of points (-5,-4) and (0,4) is y=8/5x + 4.

A linear equation o line can be expressed in the form y = mx + b

where

Knowing two points (x₁, y₁) and (x₂, y₂) of a line, the slope m of said line can be calculated using the following expression:

m= (y₂ - y₁)÷ (x₂ - x₁)

Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, the value of the ordinate to the origin b can be obtained.

Being (x₁, y₁)= (-5, -4) and (x₂, y₂)= (0,4), the slope m can be calculated as:

m= (4 - (-4))÷ (0 - (-5))

m= (4 + 4)÷ (0 +5)

m= 8÷ 5

m= 8/5

Considering point 2 and the slope m, you obtain:

4= 8/5×0 + b

4= 0 +b

4= b

Finally, the equation of the line is y=8/5x + 4.

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Answer:

A.

Step-by-step explanation:

76263

Step-by-step explanation:

[tex] \: \: \: 20005[/tex]

[tex] + 56258[/tex]

___________

[tex] = 76263[/tex]

The two values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)

What is a Quadratic equation ?

A second-degree equation of the form ax² + bx + c = 0 is known as a quadratic equation in mathematics. Here, x is the variable, c is the constant term, and a and b are the coefficients. Since x is a second-degree variable, this quadratic equation has two roots, or solutions.

The given expression is ,

2x²– 11x + 15 = 0

Solve the equation and find roots

2x² - 6x - 5x + 15 = 0

Take common elements out

2x(x - 3) - 5(x - 3) = 0

we get the brackets same that means we're on right way,

(2x - 5) (x - 3) = 0

split the values into two and find values,

2x - 5 = 0            and        x - 3 = 0

2x = 5                               x = 3

x = 5 / 2

Hence, the  values of x is x = 3 and x = 5/2 of the equation 2x²– 11x + 15 = 0 i.e, the option(a) and option(d)

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If a₁ = 9 and aₙ = 4 + (aₙ - 1) in an arithmetic sequence, then the value of fifth term a₅ is equal to 25.

Mathematically, the nth term of an arithmetic sequence can be calculated by using this expression:

aₙ =  a₁ + (n - 1)d

Where:

From the information provided, we know that the common difference is equal to 4.

Substituting the given parameters into the formula, we have;

a₅ =  9 + (5 - 1)4

a₅ =  9 + 4(4)

a₅ =  9 + 16

a₅ =  25

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Complete Question:

If a₁ = 9 and aₙ = 4 + (aₙ - 1), then find the value of a₅.

Answer:

Step-by-step explanation: step 5
they have not proved the ASA postulate i.e. they the are missing a step to proove angle BEF = angle CED (Verticle angles)
so, correct answer is step number 5 and reason 'missing prior step'

The equation for the function of the ordered pair is y =10x+2.

What is equation for the function?

 An equation that has one solution for y for each value of x is referred to be a function. For each input of a particular type, a function assigns precisely one output. The names f(x) or g(x) are frequently used in place of y when naming functions. If our function's value is f(2), then we should calculate its value when x=2. Each functional equation contains some information about a function or several functions. An illustration of a functional equation is f (x) f (y) = x y, f(x) f(y) = x y.

Here in given order pair , let us take any two points,

[tex](x_1,y_1)=(0,2)\\(x_2,y_2)=(1,12)[/tex]

Now using slope formula,

=> slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

=> slope m =10/1 = 10

Now using equation formula,

=> [tex]y-y_1=m(x-x_1)[/tex]

=> y-2 =10(x-0)

=> y-2 = 10x

=> y=10x+2.

Therefore equation of the following order pair is y = 10x+2.

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The fractions of sixth graders that reached their goal after each day are given as follows:

A fraction is a numerical representation of the division of the two terms x and y that composed the fraction, as follows:

Fraction = x/y.

In which the technical terms related to x and y are as follows:

The fraction can be represented by bars, in which:

As shown by the image at the end of the answer, the fractions are given as follows:

The image is given at the end of the answer.

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Answer:

136-5x

Step-by-step explanation:

Answer:

2+4K

Step-by-step explanation:

distribute the 2

2(1+2k)

2(1)+2(2k)

2+4K

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The statements that are a result of corresponding parts of congruent triangles being congruent are:

An isosceles triangle is a type of triangle with two equal sides and angles. The other types of triangle includes;

From the figure;

Sides EFGH are congruent, that is, equal

Since Sides EFGH are congruent, it can not be a rectangle, it is a square.

Triangle FGH and FEH are both isosceles triangle.

Diagonal FH bisects triangle FGH and FEH

So therefore, the isosceles triangle FGH and FEH are congruent and bisected by diagonal FH.

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The number of shares he buy is $615.

Given that Barney just bought stock in Purple Dinosaur Industries and he paid a total of $7,380 and the price of the stock is $12 for one share.

We want to find the number of shares Barney buys.

The total amount barney should pay is $7380.

The price of the stock for one share is $12.

The total number of shares barney buy is 7380/12=615.

Hence, the number of shares barney should buy when he paid a total $7380 and the price of stock for one share is $12 is $615.

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The scale factor in the simplest form of a fraction of the triangles will be 43/78.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

The triangle on the right is a scaled duplicate of the triangle on the left.

The ratio of the side of a big triangle to the side of a small triangle. Then we have

Scale factor = 43 / 78

The scale factor in the simplest form of a fraction of the triangles will be 43/78.

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The correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.

What is property of similar triangle?

If the corresponding sides of two triangles have the same ratio and the corresponding angles are equal, then the triangles are similar.

They have parallel corresponding sides, and they have angles with the same measure.

hence, the correct statement is their corresponding sides have equal lengths, and the angle measures of triangle 2 are 0.25 times the corresponding angle measures of triangle 1.

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Answer:

6 pizzas

Step-by-step explanation:

12.99 times 3 which is the 3 pitchers of soda is 38.97

38.97 subtracted from 75 which is our total amount is 36.03

36.03 which is what we have left divided by 6 since each pizza is 6$ is 6.

Answer:

Vertex: (-2, 3) Axis of symmetry: x = -2 The parabola opens downward.

Step-by-step explanation:

Answer: A

Step-by-step explanation:

The number of revolutions taken by a wheel will be 353.68 millimeters.

The Circumference of a circle is defined as the product of the diameter of the circle and pi.

C = πd

where 'd' is the diameter of the circle

Given data as:

The radius of the wheel r = 45 millimeters

Circumference of wheel = Circumference of a circle

Circumference of wheel = 2πr =2π(45) = 282.74 millimeters

The distance traveled by wheel = 100,000 millimeters

Now, the number of revolutions taken by a wheel will be

⇒ distance traveled by wheel / Circumference of wheel

⇒ 100,000 / 282.74

⇒ 353.68

Thus, the number of revolutions taken by a wheel will be 353.68 millimeters.

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The first step Charlie should use to solve the equation will be to open the bracket on the left side of the equation.

Equations are mathematical statements containing two algebraic expressions on both sides of an 'equal to (=)' sign.

The equation Charlie wants to solve can be calculated as follows:

-1/4(x - 1) =2/3 x +2

The first step would be to open the parenthesis on the left side of the equation as follows:

-1/4(x - 1) =2/3 x +2

- 1 / 4 x + 1 / 4 = 2 / 3 x + 2

Let's subtract 1 / 4 from both sides of the equation

- 1 / 4 x + 1 / 4 = 2 / 3 x + 2

- 1 / 4 x + 1 / 4 - 1 / 4  = 2 / 3 x + 2 - 1 / 4

- 1 / 4 x = 2 / 3 x + 7  /4

subtract 2 / 3 x from both sides of the equation.

- 1 / 4 x = 2 / 3 x + 7  /4

- 1 / 4 x - 2 / 3 x = 2 / 3 x - 2 / 3 x + 7  /4

- 11 / 12 x = 7 / 4

cross multiply

-44x = 84

divide both sides by - 44

x = 84 / -44

x = - 21 / 11

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Answer:

H = 30 ft

Step-by-step explanation:

Since the triangle is 90 degrees and we have to find out how tall the streetlight is we have to subtract 90 and 40 degrees. Which we get 50 degrees, after we subtract 20 from the 50 degrees. So we get 30 ft or 30 degrees.

Answer:

first angle =35

second angle=63

third angle=82