describing motion verbally with speed and velocity

The quotient of (x^3 + 8)/(x + 2) is x^2 - 2x + 4.

To find the quotient of (x^3 + 8)/(x + 2) we can use polynomial long division method.

First, divide x^3 by x and write down the quotient (x^2) and the remainder (0)

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

So remainder is

(x^3 + 8) - (x^3 + 2x^2)

= -2x^2 + 8

Dividing -2x^2 by x gives -2x, so note down -2x

-2x(x + 2) = -2x^2 - 4x

So remainder is

(-2x^2 + 8) - (-2x^2 - 4x) = 4x + 8

Now dividing 4x by x gives a quotient of 4, so now the quotient all together is x^2 - 2x + 4

4(x + 2) = 4x + 8

So remainder is

(4x + 8) - (4x + 8) = 0

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Area of region A is equal to the sum of area of region B and area of region C when a right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C.

Let the diameters of semicircle A, B and C be a, b and c respectively.

We know area of a semi-circular region of diameter d is

A = (1/2)(πd²/4)

A = πd²/8

Thus,

area of region A is πa²/8

area of region B is πb²/8

area of region C is πc²/8

The triangle formed is a right angled triangle, with hypotenuse a and legs b and c. By Pythagoras theorem

a² = b² + c²

Multiplying both sides by π/8

(π/8)a² = (π/8)(b² + c²)

πa²/8 = πb²/8 + πc²/8

Area of region A = Area of region B + Area of region C

Hence proved.

--The question is incomplete, answering to the question below--

"A right-angled triangle is formed by the diameters of three semi-circular regions A, B, and C as shown in the diagram. Show that area of region A = area of region B + area of region C."

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Answer:

7 sides is the answer of regular polygon

To solve an algebra , Identify the problem and what you need to find (the variable).

What is algebra ?

Algebra is a branch of mathematics in which arithmetic operations and other formal manipulations are applied to abstract symbols rather than specific numbers.

To solve an algebraic equation, you can follow these steps:

1) Identify the problem and what you need to find (the variable).

2) Write the equation clearly and legibly.

3) Simplify both sides of the equation by combining like terms, if possible.

4) Isolate the variable on one side of the equation by using inverse operations (e.g. adding or subtracting the same value from both sides, or dividing or multiplying both sides by the same value).

5) Check your solution by substituting it back into the original equation and making sure both sides are equal.

To solve an algebra , Identify the problem and what you need to find (the variable).

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The line that passes through  (0, 15) and (5, -20) has an equation E = -7t + 15

An equation is an expression that shows the relationship between two or more numbers and variables. An equation can either be linear, quadratic, cubic and so on

The slope intercept form of a linear equation is:

y = mx + b

where m is the rate of change and b is the y intercept

Let us assume that the graph have E plotted on the y axis and t plotted on the x axis

If the graph passes through (0, 15) and (5, -20), hence:

[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\substituting:\\\\E-15=\frac{-20-15}{5-0} (t-0)\\\\E = -7t + 15[/tex]

The equation is E = -7t + 15

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Answer:

1. 1.25 [tex]g/cm^{3}[/tex]

2. 1.36 [tex]g/cm^{3}[/tex]

3. 1.04 [tex]g/cm^{3}[/tex]

4. 0.79 [tex]g/cm^{3}[/tex]

Step-by-step explanation:

Density = Mass/Volume

1. 15g/[tex]12cm^{3}[/tex] = 1.25 [tex]g/cm^{3}[/tex]

2. 7.5g/[tex]5.5cm^{3}[/tex] = 1.36 [tex]g/cm^{3}[/tex]

3. 26g/[tex]25cm^{3}[/tex] = 1.04 [tex]g/cm^{3}[/tex]

4.  1350g/[tex]1700cm^{3}[/tex] = 0.79 [tex]g/cm^{3}[/tex]

Answer:

1. 1.25

2. 1.36

3. 1.04

4. 0.79

Answer:

$3.60

Step-by-step explanation:

First lets find out what 1 ruler is.

If 2 rulers cost $1.20 divide it by 2 =

$ .60 .

Now we know that 1 ruler is $ .60 .

Lets multiply 6 x .60 .

What I like to do is to move the number by 1 decimal place ( to make easier ) :

.60 —> 6.0 .

Now lets multiply it 6 x 6 = 36.

Since, We moved the decimal place now lets move it back by 1 decimal place :

36 —> 3.6 .

Answer : 3.6

Answer:

x=5

Step-by-step explanation:

90+(6x+5)+11x=180

Add 90 and 5 to get 95.

95+6x+11x=180

Combine 6x and 11x to get 17x.

95+17x=180

Subtract 95 from both sides.

17x=180−95

Subtract 95 from 180 to get 85.

17x=85

Divide both sides by 17.

x=

17

85

​

Divide 85 by 17 to get 5.

x=5

HAVE A GREAT NIGHT!!

Answer:

x = 5

Step-by-step explanation:

We simply need to isolate x to solve:

[tex]90+(6x+5)+11x=180\\6x+5+11x=90\\17x+5=90\\17x=85\\x=17[/tex]

Answer:

Investment A:

Using the formula A = P(1 + r/n)^(nt) where A is the future value, P is the principal, r is the annual interest rate, t is the number of years and n is the number of times compounded per year.

A = $3,000(1 + 0.08/2)^(27) = $3,000(1.04)^14 = $3,0005.9812 = $17,943.60

Investment B:

A = $5,000(1 + 0.036/4)^(44) = $5,000(1.009)^16 = $5,0003.3375 = $16,687.50

Investment A results in a greater total amount of $17,943.60 compared to $16,687.50 in investment B.

The domain and range of y = 5^x is all real numbers.

The domain of y = 5^x is all real numbers, x. There are no restrictions on the input value for x, so any real number can be used as the exponent.

The range of y = 5^x is all positive real numbers, y. This is because the base of the exponential function, 5, is positive and the exponent, x, can be any real number. As the exponent increases, the value of the function will also increase and the function will approach positive infinity. Similarly, as the exponent decreases, the value of the function will also decrease and approach zero. Therefore, the range of y = 5^x is all positive real numbers, y.

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Answer:

x = -7, y = -1

Step-by-step explanation:

Solve the following system:

{12 y = x - 5 | (equation 1)

9 y - 2 x = 5 | (equation 2)

Express the system in standard form:

{-x + 12 y = -5 | (equation 1)

-(2 x) + 9 y = 5 | (equation 2)

Swap equation 1 with equation 2:

{-(2 x) + 9 y = 5 | (equation 1)

-x + 12 y = -5 | (equation 2)

Subtract 1/2 × (equation 1) from equation 2:

{-(2 x) + 9 y = 5 | (equation 1)

0 x + (15 y)/2 = -15/2 | (equation 2)

Multiply equation 2 by 2/15:

{-(2 x) + 9 y = 5 | (equation 1)

0 x + y = -1 | (equation 2)

Subtract 9 × (equation 2) from equation 1:

{-(2 x) + 0 y = 14 | (equation 1)

0 x + y = -1 | (equation 2)

Divide equation 1 by -2:

{x + 0 y = -7 | (equation 1)

0 x + y = -1 | (equation 2)

Collect results:

Answer:{x = -7, y = -1

Answer:

This is true because the order of operations applies. In this case, we have to divide the 1/5 by 2 first and then get the result.

Dividing 1/5 by 2 is the same as multiplying 1/5 by 1/2, which is equivalent to multiplying the numerator and denominator by 1/2.

(1/5) * (1/2) = (1 * 1)/(5 * 2) = 1/10

So, (1/5)/2 = 1/10

This is also true because dividing a fraction by another fraction is the same as multiplying the first fraction by the reciprocal of the second fraction. The reciprocal of 2 is 1/2, and so dividing 1/5 by 2 is the same as multiplying 1/5 by 1/2.

That's why the answer is 1/10.

The inequality equation is given by m > -1

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

In an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥.

Given data ,

Let the inequality equation be represented as A

Now , the value of A is

10 > -6m - ( -4 )   be equation (1)

On simplifying the equation , we get

10 > -6m + 4

Subtracting 4 on both sides of the equation , we get

6 > -6m

Divide by -6 on both sides of the equation , we get

m > -1

Therefore , the value of m is all numbers greater than -1

Hence , the inequality equation is m > -1

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The only logarithmic function of the given options is y = log 0.25x, which is a function that expresses the logarithm of 0.25 times x. Logarithmic functions are inverse of exponential functions, and are represented by an equation of the form y = log bx, where b is the base of the logarithm.

1. The logarithmic function y = log 0.25x can be written as y = log(0.25) + log(x).

2. To calculate the value of y, first calculate the logarithm of 0.25: log(0.25) = -2.

3. Then calculate the logarithm of x: log(x) = log(x).

4. Finally, add these two values together to get the value of y: y = -2 + log(x).

The logarithmic function y = log 0.25x is a function that expresses the logarithm of 0.25 times x. Logarithmic functions are inverse of exponential functions and are represented by an equation of the form y = log bx, where b is the base of the logarithm. To calculate the value of y, first calculate the logarithm of 0.25, which is equal to -2. Then calculate the logarithm of x, which is equal to log(x). Finally, add these two values together to get the value of y: y = -2 + log(x). This equation can be used to calculate the value of y for any value of x. Logarithmic functions can be used to solve equations and simplify calculations involving exponential functions. Logarithmic functions are also important for understanding concepts like exponential growth and decay, and for calculating compound interest.

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Answer:

y=log0.25^x or  C

Step-by-step explanation:

edge

Option B is Correct. A quadrilateral having precisely one pair of Parallel sides is referred to as a trapezoid.

A quadrilateral with one set of parallel opposite sides is referred to as a trapezoid. It can have congruent sides (isosceles) and right angles (a right trapezoid), but neither is necessary. A quadrilateral is a certain shape. It must have two parallel sides and four sides total.

A right trapezoid has two sides that are perpendicular to one another and two parallel sides. Isosceles trapezoids are a particular kind of trapezoid. Isosceles trapezoid features include congruent legs, base angles, and diagonals in addition to one pair of parallel sides.

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Correct Question:

A trapezoid is a quadrilateral with exactly one pair of:

A. Equal sides

B. Parallel sides

C. Perpendicular sides

D. Curved sides

The future value of investment in 10 years for Steve will be $3,257.79 and for Gretta will be $5,187.48.

To find out how much money Steve and Gretta will have in 10 years, we need to calculate the future value of their investments using the compound interest formula:

FV = PV× (1 + r)ⁿ

Where:

FV is the future value of the investment

PV is the present value of the investment (i.e. the initial investment)

r is the annual interest rate (expressed as a decimal)

n is the number of years

For Steve:

PV = $2,000

r = 0.05 (5% expressed as a decimal)

n = 10

So, the future value of Steve's investment in 10 years will be:

FV = $2,000(1 + 0.05)¹⁰

FV = $3,257.79

For Gretta:

PV = $2,000

r = 0.10 (10% expressed as a decimal)

n = 10

So, the future value of Gretta's investment in 10 years will be:

FV = $2,000(1 + 0.10)¹⁰

FV = $5,187.48

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[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Question \#1.}[/tex]

[tex]\mathsf{f(x) = -2x - 9}\\\mathsf{f(x) = -2(-11) - 9}\\\mathsf{f(x) = 22 - 9}\\\mathsf{f(x) = 13}\\\\\\\huge\text{Therefore, your answer should be:}\\\huge\boxed{\mathsf{f(x) = 13}}\huge\checkmark[/tex]

[tex]\huge\textbf{Question \#2.}[/tex]

[tex]\mathsf{y = 4x - 1}\\\mathsf{y = 4(\dfrac{7}{2}) - 1}\\\\\mathsf{y = \dfrac{4}{1}(\dfrac{7}{2}) - 1}\\\\\mathsf{y = \dfrac{4\times7}{1\times2} - 1}\\\\\mathsf{y = \dfrac{28}{2} - 1}\\\\\mathsf{y = 14 - 1}\\\\\mathsf{y = 13}\\\\\huge\text{Therefore, your answer should be:}\\\huge\\\boxed{\mathsf{y = 13}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex]\frac{HI}{JK}[/tex]

Step-by-step explanation:

Corresponding sides of similar triangles have proportional side lengths.

The value of power 7 can be calculated by multiplying 7 with itself the number of times indicated by the power. Therefore, the value of power 7 is 128

The value of power 7 is 128.

7^1 = 7

7^2 = 49

7^3 = 343

7^4 = 2401

7^5 = 16807

7^6 = 117649

7^7 = 823543

Therefore, the value of power 7 is 128.

The value of power 7 can be calculated by multiplying 7 with itself the number of times indicated by the power. For example, when the power is 7, then 7 needs to be multiplied by itself 7 times. 7 to the power of 1 is 7, 7 to the power of 2 is 49, 7 to the power of 3 is 343, 7 to the power of 4 is 2401, 7 to the power of 5 is 16807, 7 to the power of 6 is 117649, and 7 to the power of 7 is 823543. Therefore, the value of power 7 is 128.

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Answer:200

Step-by-step explanation: Since 30% of the sixth graders = 60, we can divide the equation by 30 to get 1% of the total number of sixth graders.

               30% = 60

                1% = 2

Multiplying this by 100 and we get 100% = 200.

Answer: 9 consecutive throws

Step-by-step explanation:

Here we will take 100x= be the the total attempts made

We want the result of success to be 68%

so equation be like

68x + 8 = 100x

so consecutive free throws required will be

32x = 8

x= 8/32 =1/4

so total success will be 68/4 = 17

hence he requires 17-8 = 9 consecutive free throws to raise percentage to 68%

The domain and range of the function are  (-3, ∞) and (-∞, ∞) respectively

The collection of all input values (also known as independent variables) for which a function is defined and yields a valid output is known as the domain of the function (also called dependent variable). Typically, a set of numbers or a range of numbers is used to represent the domain.

The collection of all possible output values (dependent variable) that a function can generate for the input values inside its domain is known as the function's range. Typically, the range is shown as a group of numbers or as a range of numbers.

In the logarithmic function given;

f(x) = log_(1/3) (x + 3) - 2

The domain values are (-3, ∞)

The range values are (-∞, ∞)

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The average monthly cost to commute to work will be $18.18.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

From the given information monthly cost of Les is,

= $(4×0.195 + 2.25)×24.

= $72.72.

Now,  Les joins a car pool with three other workers, Therefore including Les, there are 4 people, So the monthly cost of Les would be,

= $72.72/4.

= $18.18.

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The expression 12x + 8 can be Witten as product as 4(3x +2)

In this question we have to write the value into the product.

Firstly, we have to write it as twelve 'x' plus eight. Then we have to check in which table both numbers in common.

The common between both is four hence we multiply the common values from the two into 'x'  in order to find the product of the equation.  

12x + 8

3*4= 12 and 4*2 = 8

Hence, we take 4 as common

We just take the common value and write numbers as product form like multiplication,

Therefore, the answer is 4(3x+2).

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The slope of the line whose equation 3x + 7y = 9 is [tex]-\frac{3}{7}[/tex].

In the given question, we have to find the slope of the line whose equation 3x + 7y = 9.

The given equation is 3x + 7y = 9.

The slope-intercept version of the line's equation is what we need. In other words, we want y=mx+b in the form of ax+by=c. M is the slope and b is the y-intercept in the slope-intercept form.

To find the slope of the line convert the given equation in the general form of line by isolating the y.

Subtract 3x on both side, we get

7y = -3x + 9

Divide by 7 on both side, we get

y = [tex]-\frac{3}{7}x+\frac{9}{7}[/tex]

By comparing the equation y = mx + c

m = [tex]-\frac{3}{7}[/tex]

Hence, the slope of the line whose equation 3x + 7y = 9 is [tex]-\frac{3}{7}[/tex].

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The complete question is:

What is the slope of the line whose equation 3x + 7y = 9?

The tax department used Simple Random Sampling, as they have chosen four districts randomly and audited everyone from those districts.

Simple Random Sampling is a method of selecting a sample from a larger population where every member of the population has an equal chance of being selected. In this case, every individual in the four randomly selected districts had an equal chance of being audited by the tax department. It is considered as the most basic form of probability sampling, and it is easy to implement and understand.

The main advantage of Simple Random Sampling is that it is highly representative of the population, if the sample is large enough, and if the sample is selected independently and randomly.

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The statement is true that statistics uses methods that generalize results obtained from a sample to the population and measure the reliability of the results.

Statistics is a branch of mathematics used to analyze, interpret, and present data. It is used to generalize results and measure the reliability of results obtained from a sample to the population. This is done through the use of probability theory, which helps to develop models for predicting the likelihood of certain outcomes. Statistics also help to identify patterns in data and draw conclusions from them. It also provides information about the relationships between different variables, which can be used to draw conclusions and make decisions. Finally, it helps to test hypotheses and assess the reliability of results.

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