P is the point (0,-1) and Q is the point (5,9) find the equation of the line through P that is perpendicular to PQ

Step-by-step explanation:

4x - y = 5

You need to convert this equation to point intercept form: y = mx + b where m = slope and b = y-intercept.

4x - y = 5

subtract 4x from both sides:

4x - y - 4x = 5 - 4x

-y = 5 - 4x

divide both sides by -1:

(-y)/-1 = (5 - 4x)/-1

y = -5 + 4x

rearrange right side:

y =  4x - 5

Remembering that: y = mx + b where m = slope and b = y-intercept

slope = 4

y-intercept = -5 or (0 , -5)

Answer:

5

Step-by-step explanation:

-3x

2y

-6

12

-4y

The distance between the two points in simplest radical form is 5.

The length of the line segment connecting two points in a plane is the distance between them. The formula for calculating the distance between two places is typically d=((x₂ - x₁)² + (y₂ - y₁)²). This formula is used to calculate the distance between two locations on a coordinate plane or the x-y plane.

In geometry, distances are usually positive unless the points coincide.  Consider two points A(a, b) and B to obtain the formula for the distance between two points in the plane (c, d).

The linear distance between two points is equal to the square root of the sum of the squared x-axis and y-axis distances. To continue with the example, the distance between (3,2) and (7,8) is sqrt (52), or 7.21 units.

Given,

The two points are (7,1), (4,5)

Distance between two points

AB=√(x₂-x₁)²+(y₂-y₁)²

AB=√(4-7)²+(5-1)²

=√3²+4²

=√9+16

=√25

=5

Distance between two points=5

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Answer: x=1, y=2

Step-by-step explanIation:

I hope this is right  :)

A descriptive statement (also known as a positive statement) is meant to describe the world as it is a Normative Statement is meant to talk about the world as it should be.

Normative Statement: It expresses a value judgmental about the disability of a situation. For example:  samples of normative economic statements including " women should be provided higher school loan than men", etc.

Empirical Statement: It describes what is in the social world, without evaluating it. They are statements that can be measured empirically. Example of Empirical would be : it will rain tomorrow.

Normative statements are judgmental. They are ought statements and they poses question, they device and explicitly say how things should be. They are generalized and subjective in nature, they act as the necessary channels for out of the box thinking.

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Answer:

$693.80

Step-by-step explanation:

The volume of the right cone is 7 units.

The radius of a cone can be found as follows:

The volume of the right cone is 245π unit³. The height of the right cone is 15 units.

Therefore,

volume of a right cone = 1 / 3 πr²h

where

Hence,

volume of the right cone = 245π

h = 15 units

Hence,

245π = 1 / 3 × π × r²  × 15

divide both sides by π

245 = 15 / 3 r²

245 = 5r²

r² = 245 / 5

r = √49

r = 7 units

Therefore,

radius of the cone = 7 units

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The integral Value is [tex]\pi[/tex] or 22/7 or 3.14

Integral Value: It is a value which is obtained after integrating.

Triple Integral: Integral function of a three variable over a region in R³ ( real number 3D space) are called triple integral.

            For x = 2,

              x = 2y² + 2z²

equating those two functions, we get,

                         1 = y² + z²

that gives -1≤ y≤ 1 and -(√x/2 -y²) ≤ z≤ (√x/2 - z²) and  2y²≤ x ≤ 2

so after the integration, the form is quite complicated to solve so use the following form instead letting x = 2 and x = 2y² + 2x², so that the integral became

      ∫∫∫ 2y² + 2z² dx dA which becomes

     ff (2 - 2y² - 2z²) da now use polar coordinate where y= 1 cos Ф          and z = 1 sinФ

now, integral becomes

       2 ∫¹₀ (1- r²) r dr dФ

= 4[tex]\pi[/tex] ( r²/2 - r⁴ /4)¹ ₀

= 4[tex]\pi[/tex] ( 1/2 - 1/4)

= 4[tex]\pi[/tex] × 2 - 1/4

= [tex]\pi[/tex]

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The total amount of its donated funds is  43[tex]\frac{23}{29}[/tex].

Given,

In the question:

A charity received a donation of 12.7 million.

If this represents 29% of the charity's donated funds.

To find the total amount of its donated funds.

Now, According to the question:

Based on the given conditions:

Received donation is = 12.7 million

Charity Funds = 29%

Formulate;

12.7 ÷ 29%

12.7/29%

= 12.7/0.29

Multiply both the numerator and denominator with the same integer

= 1270/29

= 43[tex]\frac{23}{29}[/tex]

Hence,  The total amount of its donated funds is  43[tex]\frac{23}{29}[/tex].

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The long polynomial division of the given equation is [tex]\ 2x^2-5x+4-\frac{6}{5x+1}[/tex].

What is long polynomial division?

Polynomial long division is a generalized variant of the well-known arithmetic operation known as long division. It is an algorithm for dividing a polynomial by another polynomial of the same or lower degree.

We have,

            [tex]10x^{3} -23\pi x^{2} +15x - 2[/tex]   £ [tex]5x+1[/tex]

By taking long division

                        [tex]= \:\frac{10x^3-23x^2+15x-2}{5x+1} \[/tex]

                        [tex]= \quad 2x^2-5x+4-\frac{6}{5x+1}[/tex]

                        [tex]= \ 2x^2-5x+\frac{20x-2}{5x+1}[/tex]

                        [tex]= \ 2x^2-5x+4+\frac{-6}{5x+1}[/tex]

By simplifying we get,

                        [tex]= \ 2x^2-5x+4-\frac{6}{5x+1}[/tex]

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Answer:

1450 residents

Step-by-step explanation:

Number of residents who live in Harris

= 5800 pounds ÷ 4 pounds

= 1450 residents

Answer: 7/10

Step-by-step explanation:

Answer:

7/10 or 70/100

Step-by-step explanation:

The 7 is in the tens place!

The value of slope is 5 .

Write the first few terms of the sequence.

f₁ = 6

f₂ = f₁ + 5 = 11

f₃ = f₂ + 5 = 16

f₄ = f₃ + 5 = 21

and so on

The sequence is

6, 11, 16, 21, ...,

This is an arithmetic sequence with a common difference of 5.

In function notation, the sequence is

Fn+1 = 6+5n

n= 0,1,2......

The straight line equation with n as the independent variable and f as the dependent variable is shown here.

The slope is 5.

A graph of the line is shown below.

Answer:

The sequence is Fn+1 = 6+5n ,n= 0,1,2......

The slope is 5.

The complete question is : A recursive arithmetic sequence is defined ad f(1)=6, f(n+1)=f(n)+5 for n>1. The first four terms of the sequence are shown in the table. Write an explicit formula that represents the sequence using function notation. Find the slope of the line that passes through the points given in the table. The slope is

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For given equation x_(n+1) = ((x_n)^3 - 5)/10,

a) (i) x2 = -0.6

(ii) x3 = -0.5216

b)  the solution to 6 decimal places, x5 = -0.513594

Given equation, x_(n+1) = ((x_n)^3 - 5)/10

also, x1 = -1

a)

(i) we need to find the value of x2

Substitute n = 1 in given equation,

x_(1+1) = ((x1)^3 - 5)/10

x_2 = [(-1)^3 - 5]/10

x_2 = (-1 - 5)/10

x2 = -6/10

x2 = -0.6

(ii) we need to find the value of x3

Substitute n = 2 in given equation,

x_(2+1) = ((x2)^3 - 5)/10

x3 = [(-0.6)^3 - 5]/10

x3 = (-0.216 - 5)/10

x3 = -5.216/10

x3 = -0.5216

b)

We need to find the solution to 6 decimal places.

First we find the value of x4.

Substitute n = 3 in given equation,

x_(3+1) = ((x3)^3 - 5)/10

x4 = [(-0.5216)^3 - 5]/10

x4 = (-0.1419 - 5)/10

x4 = -5.1419/10

x4 = -0.51419

Substitute n = 4 in given equation,

x_(4+1) = ((x4)^3 - 5)/10

x5 = [(-0.51419)^3 - 5]/10

x5 = (-5.13595)/10

x5 = -0.513594

Therefore, for given equation x_(n+1) = ((x_n)^3 - 5)/10,

a) (i) x2 = -0.6

(ii) x3 = -0.5216

b)  the solution to 6 decimal places, x5 = -0.513594

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The quadrilateral above is a parallelogram.

A parallelogram is a quadrilateral with opposite sides equal to each other. Opposite sides of a parallelogram is parallel to each other.

The sum of angles in a parallelogram is 360 degrees.

Opposite angles of a parallelogram is congruent to each other.

Adjacent angles of a parallelogram sum up to 180 degrees. This means adjacent angles are supplementary.

Let's check if the Known adjacent angles of the quadrilateral is supplementary.

Therefore,

105 + 75 = 180 degrees.

Hence, the quadrilateral is a parallelogram.

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The likely error was that B. Your classmate multiplied the exponents

Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations.

In this case, your teacher asks the class to evaluate the expression (2^3)^1. This will be:

= 2³

= 8

The fact that the person got 16 means the person multiplied it and then joined 1.

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If Adam buys x stamps and Charlie buys 5 more stamps than Adam, then the expression in terms of x for the number of stamps Charlie buys is x + 5

The number of stamps that Adam buys = x

The expression is the mathematical statement that consist of different variable, numbers and arithmetic operators. The arithmetic operators are addition, subtraction, division and multiplication. The expression does not contains any equal signs or inequality signs

Charlie buys 5 more stamps than Adam.

Then the expression will be

The number of stamps that Charlie buys = x + 5

Hence, if Adam buys x stamps and Charlie buys 5 more stamps than Adam, then the expression in terms of x for the number of stamps Charlie buys is x + 5

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The measure of the angle x in the right triangle ABD is 38.06 degrees.

Points B, C and D lie on a straight line.

AC is perpendicular to BD.

BC = 4cm and BD = 24 cm.

Triangle ABC has area 36 [tex]cm^{2}[/tex]

To Calculate the size of angle x.

What is a right angle triangle?

A right angle triangle has one of its angles as 90 degrees. Therefore, the sides of the triangle can be found using trigonometric ratios.

area of a triangle = 1 / 2 bh

where

   b = base of triangle

   h = height of triangle

Hence,

area of a triangle =  1 / 2 × 4 × h

24 = 2h

h = 24 / 2

h = 12 cm

DC =  24 - 4 = 20 cm

AC = 12 cm

tan x = opposite / adjacent

tan x = 12 / 20

x = tan ⁻¹ 0.6

x = 38.06

x = 38.06 degrees.

Hence the answer is the measure of the angle x in the right triangle ABD is 38.06 degrees.

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Answer:

if there are at least 9 chairs at each table then yes

Step-by-step explanation:

this question might be something

so lets divide 145 by 18 to see how many seats at each table is required for everyone to fit

145/18

8.05555

and since we cant have 0.555 of a chair or person we round up to the nearest whole chair which is 9

hopes this helps please mark brainliest

The distance between the point (-3,3) and (a, b) is;

⇒ d = √(a + 3)² + (b - 3)²

What is an expression?

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

Given that;

Two points are,

(-3,3) and (a, b)

Now,

The distance between the point (-3,3) and (a, b) is;

d = √(a - (-3))² + (b - 3)²

d = √(a + 3)² + (b - 3)²

Thus, The distance between the point (-3,3) and (a, b) is;

⇒ d = √(a + 3)² + (b - 3)²

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Answer:

the answer is because u need trust me6

Answer:

Step-by-step explanation:

Where is the figure

Step-by-step explanation:

this has infinitely many solutions.

why, because both equations are actually representing the same function.

-x + 6y = -2

let's multiply both sides by -4, and the result is

4x - 24y = 8

exactly the same as the second equation.

as both are the same function, their curves are covering each other perfectly, so that every point on the curves is an intersection and therefore solution.

so : infinitely many solutions.

The result is 1.91 and the technique used is the decimal shifting.

It follows from the task content that the quotient of 5.73 and 3 is to be determined and the method of solving be explained according to the given task.

Therefore, since the given quotient is;

5.73 / 3

However, for ease of computation, the decimal in the numerator may be shifted two spaces right so that we have;

= 573 / 3. (which is a lot easier to evaluate)

= 191

However, the initial decimal shift needs to be reversed by shifting two spaces left so that we have;

= 1.91

Consequently, the quotient of 5.73 and 3 is; 1.91.

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Answer:

6 weeks = 42 days

Step-by-step explanation:

6 weeks = 42 days​​ Formula: multiply the value in weeks by the conversion factor '7'. So, 6 weeks = 6 × 7 = 42 days.

The total cost to the nearest cent = 2675 cents.

Given that:

The cost of backpack = $25

Tax = 7%

To calculate the total cost, we can also approach the problem in two ways:

1). Multiply the amount by 7% ($25 x 0.07 = $1.75, rounded up to the nearest cent at 175 cents or $1.75). This will tell us how much tax we will have to pay. Add this to the cost to get the total amount one has to pay (25 + 1.75 = $26.75 or 2675 cents).

2). Multiply the amount by 107%. This includes both steps from 1 in one step. ($25 x 1.07 = $26.75; $26.75 rounded to dollars).

We know that,

1 dollar ($) = 100 cents

Multiply both sides by 26.75

$ 26.75 = 2675 cents.

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Answer:

h

Step-by-step explanation:

p depends on h

h won't change according to p

p will change according to h

Answer:

Step-by-step explanation:

should be h

Hence in 1990 town a will have a population of 90518 and town B will have a population of 9051.85.

What is the arithmetic operation?

The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or more quantities. Included in them is the study of numbers, especially the order of operations, which is important for all other areas of mathematics, including algebra, data management, and geometry. The rules of arithmetic operations are required in order to answer the problem.

To calculate the size of town A in 1990, multiply the current population by 2000 + (200x40) and add 40 years to account for population growth.

To work out how big town B will be in 1990

We have to use the equation 2000 X 1.1^40 because to work out plus 10 percent you need to do 1.1 and do it to the power of 40 for how many years

So 2000* 45.259 = 90518. for 2000people of A Town

And 200* 45.259 = 9051.8 for 200people of B Town

Hence in 1990 town, a will have a population of 90518 and town B will have a population of 9051.85

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Answer:

15%

Step-by-step explanation:

180/1200 × 100% = 15%