The foot of the perpendicular drawn from the point (2, 3) to a line is (3, -1). Find
the equation of the line. Also find the equation of the line parallel to the line and
passing through the origin.

Based on the relation between two numbers considering their difference and multiple, the numbers are 50 and 250.

Let the one number be x. So, the other number, according to the information in question, will be 5x. Now representing the equation depending on the stated details -

5x - x = 200

Performing subtraction on Left Hand Side of the equation

4x = 200

Writing the equation again to find the value of x

x = 200/4

Performing division on Right Hand Side of the equation

x = 50

First number = 50

Another number = 50×5

Performing multiplication on Right Hand Side of the equation

Second number = 250

The two numbers according to multiple and difference are 50 and 250.

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Answer: k=±`12

Step-by-step explanation:

[tex]ax^2-bx+c=0\\\\9x^2-kx+4=0\\\\D=b^2-4ac\\\\a=9\ \ \ \ b=-k\ \ \ \ c=4\\\\D=0\\\\Hence,\\\\D=(-k)^ 2-4(9)(4)=0\\\\k^2-144=0\\\\k^2=144\\\\k^2=12^2[/tex]

Extract the square root of both parts of the equation:

[tex]k=б\sqrt{12^2} \\\\k=б12[/tex]

Answer:

---------------------------------------------

A perfect square trinomial is:

Given trinomial:

Show this as:

Compare and find possible values of k:

The person who mows the lawn in less time is given as follows:

Daniel.

To obtain who mows the lawn in less time, we calculate the hourly rates for each person, applying the proportion, which is the division of the amount of area mowed by the time needed.

Daniel can mow 15,000 ft³ in 3/4 = 0.75 hours, hence his hourly rate is calculated as follows:

Daniel hourly rate = 15000/0.75 = 15000 x 4/3 = 20,000 ft² per hour.

Bronwyn can mow 12,000 ft² in hour, hence her rate is of:

12,000 ft² per hour.

20,000 > 12,000, hence Daniel can mow the law in less time, as he has a higher rate.

The missing sentence is of:

"Bronwyn can mow 12,000 ft² in hour".

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The radius of the sector of area 135π is 15.

A sector is a geometric figure bounded by two radii and the included arc of a circle.

To calculate the radius of the sector, we use the formula below

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the radius of the sector is 15.

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Answer:

215

Step-by-step explanation:

218+212/2

Answer:

The answer is B.

Step-by-step explanation:

Looking at the points gives you a x-axis and y-axis.

(x , y)

(-2 , 3) ,

(0 , 5) ,

(1 , 5) ,

(2 , 4) ,

(8 , -2)

Focus on the y-axis instead of the x-axis and list them.

{3 , 5 , 4 , -2}

Answer:

C. The graph of the function does not form a straight line

Answer:

b

Step-by-step explanation:

Infer from domain and range

The time it take until 2000 people know about the rumor is 16 days.

The square root of a variety of is described because the value, which offers the variety while it's miles increased with the aid of using itself. The radical symbol √ is used to suggest the square root.  Radical is any other call given to the square root symbol. It is likewise called the surds. While Radicand is the variety gift beneath neath the square root symbol.

Find t, when N=200

N=5OO t^1/2

2000=500 t^1/2

t^1/2=4

t=16 days

Thus, the time it take until 2000 people know about the rumor is 16 days.

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The airplane pilot should include and follow the relation y > [D][x] for his fuel estimates.

Function : In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function

Expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators

Equation : A mathematical equation is used to equate two expressions.

Given is that an airplane pilot is planning a flight to Hawaii. In his flight plan, he will include fuel estimates for the trip.

Assume that the distance of Hawaii from the initial location of pilot is [D] miles. If the amount of fuel burnt per miles is [x] liters/miles. Let the total amount of fuel needed to reach Hawaii is [y] liters. Than, his estimates should include and follow the given relation as -

y > [D][x]

Therefore, the airplane pilot should include and follow the relation y > [D][x] for his fuel estimates.

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Answer:

----------------------------------------

Simplify the expression in below steps:

Answer:

[tex]32-60i[/tex]

Step-by-step explanation:

Given expression:

[tex](2+\sqrt{-4})(3 +5i)(-4-i)[/tex]

[tex]\textsf{Rewrite $\sqrt{-4}$ as $\sqrt{4 \cdot -1}$}:[/tex]

[tex]\implies (2+\sqrt{4 \cdot -1})(3 +5i)(-4-i)[/tex]

[tex]\textsf{Apply radical rule} \quad \sqrt{ab}=\sqrt{a}\sqrt{b}:[/tex]

[tex]\implies (2+\sqrt{4}\sqrt{-1})(3 +5i)(-4-i)[/tex]

[tex]\implies (2+2\sqrt{-1})(3 +5i)(-4-i)[/tex]

[tex]\textsf{Apply imaginary number rule} \quad \sqrt{-1}=i:[/tex]

[tex]\implies (2+2i)(3 +5i)(-4-i)[/tex]

Multiply:

[tex]\implies (6+16i+10i^2)(-4-i)[/tex]

[tex]\implies -24-6i-64i-16i^2-40i^2-10i^3[/tex]

[tex]\implies -24-70i-56i^2-10i^3[/tex]

[tex]\textsf{Apply imaginary number rule} \quad i^2=-1:[/tex]

[tex]\implies -24-70i-56(-1)-10(-1)i[/tex]

Simplify:

[tex]\implies -24-70i+56+10i[/tex]

[tex]\implies 32-60i[/tex]

Step-by-step explanation:

It takes 73 pounds of seed to completely plant an 11 -acre field. How many pounds of seed are needed per acre?

73 / 11 = 6.6363636 pounds per acre

rounded to two decimal places: 6.64 pounds per acre

One additional group would be required to conduct a 3 x 2 x 3 factorial design compared to a 3 x 2 x 2 design with independent variable.

A 3 x 2 x 3 factorial design requires three independent variables (x1, x2, and x3) with three levels each, for a total of 27 conditions. A 3 x 2 x 2 design, however, would only require two independent variables (x1 and x2) with two levels each, for a total of 12 conditions. To conduct a 3 x 2 x 3 factorial design, one additional group would be required, compared to the 3 x 2 x 2 design. This additional group would provide data for the additional 15 conditions that the 3 x 2 x 3 design would require.

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The amount of taxes owed on a taxable income of $49,652 is $10,293.44.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, Are the tax percentages for various amounts of income.

Now, From the given chart we conclude that $49,652 falls in the category of $41.176-$89.075 is 22% tax.

So, the Tax owed is 22% of $49,652.

∴ (22/100)×$49,652.

= $10,293.44.

So, an income of $49,652 owed 22% tax of the income which is $10,293.44.

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Answer:THE ANSWER IS B)6,600.44

Step-by-step explanation:

I got it right :)

Answer:

Answer. it is -111 because it is greater than 112 and in positive form it is smaller and in negative it is bigger .

Answer:

y=1/3(x)+1/3

Step-by-step explanation:

x=3y-1

x+1=3y

(x+1)/3=(3y)/3

y=1/3x+1/3

The mean absolute deviation over three period of time is 200

The absolute value of error in period 1 = 300

The absolute value of error in period 2 = 200

The absolute value of error in period 3 = -100

Total absolute value of error = The absolute value of error in period 1 + The absolute value of error in period 2 + The absolute value of error in period 3

Substitute values in the equation

Total absolute value of error  = 300 + 200 + 100

= 600

The mean absolute deviation = Total absolute value of error / 3

Substitute the values in the equation

The mean absolute deviation  = 600 / 3

= 200

Therefore, the mean absolute deviation is 200

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The weighted mean of the mixture of recyclables would be (4 x $1 + 2 x $2) / 6 = $1.33.

To calculate the weighted mean of the mixture of recyclables, first identify the number of each material and their respective values. In this case, there are 4 items worth $1 each and 2 items worth $2 each. To calculate the weighted mean, multiply each item's value by the number of items and then divide by the total number of items

In this case,

4 x $1 + 2 x $2 = $6

and 6 items total, so the weighted mean is

$6 / 6 = $1.33.

This means that if compost is now worth twice as much, the weighted mean would be

(4 x $1 + 2 x $2) / 6 = $1.33.

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Answer:

Graph B

Step-by-step explanation:

First, simplify by subtracting 1 on both sides.

|x| + 1 - 1 < 3 - 1

|x| < 2

Using the absolute value definition, we know the inequalities are:

x < 2

-x < 2

Divide both sides by -1.

x < -2

If you multiply or divide both sides of an inequality by a negative number, you must flip the sign.

x > -2

x<2, x>-2

Graph B

Answer:

Graph A

Step-by-step explanation:

if x ≥ 0

x + 1 < 3

x < 3 - 1

x < 2

0≤ x < 2

if x < 0

-x + 1 < 3

-x < 3 - 1

-x < 2

x > -2

-2 < x < 0

Final solution

-2 < x < 2

IT is found that the value of x is 4 and value of y is 5.

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The given system of equations are

2x-6y=22

-5x+y=1

The matrix form is

[tex]\left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}22\\1\end{array}\right][/tex]

Let as assume

[tex]A = \left[\begin{array}{ccc}2&-6\\-5&1\end{array}\right]\\ \\X = \left[\begin{array}{ccc}x\\y\end{array}\right] \\B = \left[\begin{array}{ccc}22\\1\end{array}\right][/tex]

WE know that AX = B

Then we have;

[tex]\left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}4\\5\end{array}\right][/tex]

Therefore, the value of x is 4 and value of y is 5.

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Answer:

To find the new price after a discount, you can use the formula: new price = original price * (1 - discount rate). In this case, the new price would be $28 * (1 - 0.25) = $28 * 0.75 = $<<28*0.75=21>>21. So the new price, rounded to the nearest cent, would be $21.

Step-by-step explanation:

the Central Limit Theorem, which states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal.

The Central Limit Theorem states that as the sample size increases, the sampling distribution of the sample mean tends to become more normal. This means that the mean of the sample will be closer to the mean of the population, and the variability of the sample will be smaller. Since the sample proportion is just the mean of the sample, as the sample size increases, the distribution of the sample proportion will also become more normal. The larger the sample size, the more likely it is that the sample will accurately represent the population, and the more normal the distribution of the sample proportion will be. In other words, the sample proportion will be closer to the true population proportion, and the variability of the sample proportion will be smaller.

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P(n) = 1³ +2³ +···+n³ = (n(n+1)/2)²

P(1) = 1³ = 1

According to statement P(n) = (n(n+1)/2)²

Checking for n = 1,

(n(n+1)/ 2)² = (1(1+1)/ 2)²

P(1) = (1 × 2/ 2)²

P(1) = 1² = 1

P(1) = 1³ = 1

So P(n) holds for n = 1.

The inductive hypothesis is that the statement holds for P(n). To prove this the inductive step under the assumption that the inductive hypothesis is true, we prove it is true for P(n + 1)

Let us assume P(n) = 1³ + 2³ + ... + n³ = (n(n+1)/ 2)²

Then P(n + 1) = 1³ + 2³ + ... + n³ + (n + 1)³ = (n(n+1)/ 2)² + (n + 1)³

P(n + 1) = (n(n+1)/ 2)² + n³ + 3n² + 3n + 1

P(n + 1) = ((n + 1)((n + 1) + 1)/ 2)²

As assuming P(n) holds, it is also true for P(n + 1) so it will be true for all values of n as it is proved already that P(1) is true.

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Answer:

39.95m

Step-by-step explanation:

To find the side length of a regular 36-gon with a given area and apothem, we need to use the formula for the area of a regular polygon and the formula for the apothem of a regular polygon.

The formula for the area of a regular polygon is given by:

A = (1/2) * a * p

where A is the area of the polygon, a is the apothem of the polygon, and p is the perimeter of the polygon.

The formula for the apothem of a regular polygon is given by:

a = r * cos(180/n)

where a is the apothem of the polygon, r is the radius of the polygon, and n is the number of sides of the polygon.

In this case, we are given that the area of the 36-gon is 164,592 square meters, the apothem of the 36-gon is 228.6 m, and the number of sides of the 36-gon is 36.

We can use these values to solve for the side length of the 36-gon. First, we can use the formula for the area of a regular polygon to solve for the perimeter of the 36-gon:

A = (1/2) * a * p

164,592 = (1/2) * 228.6 * p

164,592 = 114.3 * p

p = 1438.3

Next, we can use the formula for the apothem of a regular polygon to solve for the radius of the 36-gon:

a = r * cos(180/n)

228.6 = r * cos(180/36)

r = 561.8

Finally, we can use the formula for the perimeter of a regular polygon to solve for the side length of the 36-gon:

p = n * s

1438.3 = 36 * s

s = 39.95

Therefore, the side length of the 36-gon is 39.95 meters.

The simple interest is $2160 and the amount after 30 years is $6160.

Given that, principal =$4000, rate of interest =1.8%, and time period =30 years.

Simple interest is a method to calculate the amount of interest charged on a sum at a given rate and for a given period of time.

Simple interest is calculated with the following formula: S.I. = (P × R × T)/100, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years.

a) Now, S.I =(4000×1.8×30)/100

= 40×1.8×30

= $2160

b) Amount = Principal + Interest

= 4000 + 2160

= $6160

Therefore, the simple interest is $2160 and the amount after 30 years is $6160.

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The area of the triangular dock is 19.5 square feet and the area of the rectangular box is 10 feet. The box will fit under the dock.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the rectangle in a two-dimensional plane is called the area of the rectangle. The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Calculate the area of the triangle first,

Area = 1 / 2 x B x H

Area = 1/2 x 12 x 3.25

Area = 19.5 square feet

Calculate the area of the rectangle,

Area = L x W

Area = 2 x 5

Area = 10 square feet

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To find the percentage of girls in class A, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:

14 / 20 * 100 = 70%

To find the percentage of girls in class B, we need to divide the number of girls by the total number of students and then multiply by 100. This gives us:

15 / 25 * 100 = 60%

Thus, the percentage of girls in class A is 70%, and the percentage of girls in class B is 60%.

The gradient value of the line 2x + y = 4 is 2. This can be found by rearranging the equation into slope-intercept form, which is y = -2x + 4. The coefficient of the x term, -2, is the slope of the line.

The result of executing the code segment is -2

The complete question is added at the end of this solution as an attachment

The code in the question is given as

IF X > Y

  DISPLAY X + Y

ELSE

  DISPLAY X - Y

Given that

X = 3 and Y = 5

When x and y are compared, we have the truth value to be

Y > X

This means that the executed segment is

DISPLAY X - Y

So, we have

DISPLAY 3 - 5

Evaluate

DISPLAY -2

Hence. the displayed result is -2

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