What is the slope of the line that passes through the points (-5, 6) and (-9, -6)?
Write your answer in simplest form.

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.

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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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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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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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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Dalisay hits the Target more than Kendra hits the target.

Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.

Given that;

Kendra hits the target 3 times for every 5 misses,

And, Dalisay hits the target 5 times for every 7 misses.

Hence, The rate of hits the target by Kendra is,

⇒ 3/5

⇒ 0.6 times per misses

And, The rate of hits the target by Dalisay is,

⇒ 5/7

⇒ 0.7 times per misses

Hence, Dalisay hits the Target More.

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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 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?

For the given rectangle the length of the base, altitude , and the diagonals is given by 12, 9 , and 15 units respectively.

As given in the question,

In the given rectangle,

Base length of the rectangle = x  + 7

Altitude length of the rectangle = x + 4

length of diagonals = 3x

As diagonal , base , and altitude forms a right angled triangle,

Diagonal represents the hypotenuse.

Using Pythagoras theorem

(Diagonal length)² = ( Base length)² + ( altitude length)²

⇒(3x)² = ( x + 7 )² + ( x + 4 )²

⇒ 9x² = x² + 14x + 49 + x² + 8x + 16

⇒7x² - 22x - 65 = 0

⇒7x² - 35x + 13x - 65 = 0

⇒ 7x ( x - 5 ) + 13 ( x - 5 ) = 0

⇒ ( 7x + 13 ) ( x - 5 ) = 0

⇒ x = -13/7 or x = 5

Negative value unacceptable.

⇒x = 5

Base length = 12

Altitude length = 9

Diagonal length = 15

Therefore, for the given rectangle base length, altitude length, and the diagonal length is equal to 12, 9 , and 15 units respectively.

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Working with a sample rather than an entire population is often more practical and cost-effective. It can also be more accurate since it reduces the chances of sampling bias.

Additionally, it can be faster and more efficient since it requires less data and can be done in a shorter period. Furthermore, a sample can provide more insight into the population as a whole since it is representative of the population, and the results of a sample can be generalized to the entire population. Finally, working with a sample is more manageable and easier to analyze than working with an entire population. This is because a sample has fewer data points, which can make it easier to identify patterns and draw conclusions.

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Answer:

$1020 for 30 books

Step-by-step explanation:

We know

$1020 = 30 books

$34 = 1 book

$1725 = 50 books

$34.50 = 1 books

So, $1020 for 30 books is better

Answer: 1020 for 30 books is a better value

Step-by-step explanation: 1020 divided by 30 is 34 and 1725 divided by 50 is 34.5. When doing these kind of division questions, remember that money always goes on the numerator (top)

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

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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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

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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An angle of measure 360 degrees is called a full angle.

If after one whole rotation, the final ray coincides with the incident or initial ray, then the angle so formed is known as the complete angle.

A full angle is one that measures 360 degrees. An angle is generated when two lines intersect at a place and the distance between these two lines is measured. Angles are classified into several types, including right angles, acute angles, obtuse angles, and so on. A whole angle is one complete revolution of 360°.

Thus, An angle of measure 360 degrees is called a full angle.

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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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[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]

Therefore , the solution of the given problem of prime factor comes out to be 30 is the smallest integer for the three different prime number.

A prime factor is any non-zero natural integer that has just itself and 1 as its divisors. The first real numbers include 1,2,5,3,7  among others. a quantity that has been repeated to yield a different quantity. For example, we obtain (3) 5 = 15 when we divide 15 by Three and 5. primary components All elements that seem to be prime but aren't composite are referred to be prime factors. 2, 3, and 5 are some prime factors of 30.

Here,

Given :

The lowest three prime numbers can be calculated by

adding them together.

The answer is

=> 2 x 3 x 5 = 30,

since the first 3 prime numbers being 2, 3, and 5.

Thus , 30 is the smallest integer for the three different prime number

Therefore , the solution of the given problem of prime factor comes out to be 30 is the smallest integer for the three different prime number.

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The linear equations derived are:

y= 2x-4 ..................................1)

y=5x+3......................................2)

The slope and y-intercept of a linear equation in two variables are two important characteristics of the equation that can be used to graph the equation on a two-dimensional coordinate system.

The slope of a linear equation in the form of y = mx + b is represented by the coefficient of x, which is m. The slope tells us the steepness of the line and the direction it is moving. If m is positive, the line slopes upward to the right, if m is negative, the line slopes downward to the right.

The y-intercept of a linear equation in the form of y = mx + b is represented by the constant term b. The y-intercept is the point where the line crosses the y-axis. It can be found by setting x=0 and solving for y.

On comparing the equations with the general equation of linear equation in two variables we get:

m1=2 and b1=-4

m2=5 and b2=3

Therefore, The linear equations derived are:

y= 2x-4 ..................................1)

y=5x+3......................................2)

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2² is a mathematical expression that means "2 to the power of 2" or "2 multiplied by itself 2 times". The answer is 4.

2² is a mathematical expression that can be used to calculate the result of multiplying a number by itself a certain number of times. In this case, the expression 2² means to multiply 2 by itself 2 times. This can be written as 2 x 2, or 2 raised to the second power, which is represented by the small superscript 2 after the number 2. The result of this calculation is 4, which can be written as 2² = 4. This expression can be used to calculate the result of any number multiplied by itself a certain number of times, by replacing the number 2 with any other number and the superscript 2 with the number of times it should be multiplied. For example, 3² means 3 multiplied by itself 2 times, or 3 x 3, and the result is 9, which can be written as 3² = 9.

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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

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.

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%

Answer: Simplified answer: 14x 2−28x    Factor the expresion: 14x(x−2)

Step-by-step explanation: Simplified answer: Evaluate

(2x−4)(7x ′−6g−6)

Remove the parentheses

(2x−4)×7x

Multiply the terms

7x(2x−4)

Apply the distributive property

7x×2x−7x×4

Multiply the terms

14x 2−7x×4

Solution

14x2−28x

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

Answer: Kevin drew an obtuse scalene triangle.

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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4 sides, 4 corners(corners are called vertices).

Formula for area

The area of any rectangle may be calculated by multiplying the length by the width.

Let’s give it a go!

This rectangle has a length of 7 units. This rectangle has a width of 6 units.

Divide the length by the width.

So, the area of the rectangle is 42 square units.

a)8.x=8x m square

5×8=40 m square

b)as a sum of two areas

8x+40m square

As a product of the Length and width

(X+5).8m square

So the area is 8+40 or (x+5).8 m square

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