10 POINTS!

What is the equation of the line in standard form?
(-3,2) and (2,-1)

Given the equation x² + y² + 4x - 8y + 11 = 0, the center of the circle is (-2, 4).

The standard form of the equation of circle is given by

(x - h)² + (y - k)² = r²

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x² + y² + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h² + k² - r².

If the equation of the circle in general form is x² + y² + 4x - 8y + 11 = 0, then the coefficients are:

D = 4

E = -8

F = 11

If D = -2h and D = 4, then

4 = -2h

h = -2

If E = -2k and E = -8, then

-8 = -2k

k = 4

Hence, the center of the circle is (h, k) = (-2, 4).

Learn more about equation of a circle here: brainly.com/question/1559324

#SPJ4

An inequality correctly compares One-half, Three-fourths, and Two-thirds is: One-half < Two-thirds < Three-fourths.

An inequality simply refers to a mathematical relation that can be used to compare two (2) or more numerical values (numbers) and variables in an algebraic equation, especially based on any of the following inequality symbols:

Translating the numbers in word to numerical values, we have:

One-half = 1/2 or 0.5

Three-fourths = 3/4 or 0.75

Two-thirds = 2/3 or 0.67

Next, we would compare the above numerical values by using the less than (<) inequality symbol as follows:

0.5 < 0.67 < 0.75

One-half < Two-thirds < Three-fourths.

Read more on inequality here: brainly.com/question/12996324

#SPJ1

The value e = 0.869 indicates that the ellipse is more elongated that circular.

Given,

x²/12+y²/49 = 1

We will compare with x²/a² + y²/b² = 1 where a<b

Coordinate of center = (0,0)

Here a²=12 and b²=49

We know that the formula of eccentricity(e)

e=√(1-(a²/b²))

= √(1-(12/49))

= √37/7

=0.869

Therefore e=√37/7 = 0.869

Therefore this value indicates that the ellipse is more elongated that circular.

In mathematics, an ellipse is a plane bend encompassing two central focuses, to such an extent that for all focuses on the bend, the amount of the two distances to the central focuses is a consistent. It sums up a circle, which is the extraordinary kind of oval wherein the two focal points are something similar.

To learn more about ellipse and circle,

https://brainly.com/question/18369410

#SPJ4

It is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

Given, a large number of MBA applicants are given an aptitude test. scores are normally distributed with a mean of 460 and standard deviation of 80.

We are asked the probability that an applicant scores below 552.

Now, using the formula of probability, we get

P(X < 552) = 0.8329

when the mean is given i.e. 460 and standard deviation is given i.e. 80.

Hence, it is true that when scores are normally distributed with a mean of 460 and standard deviation of 80, then the probability that an applicant scores below 552 is 0.8329.

Learn more about Probability here https://brainly.com/question/13604758

#SPJ4

The simplified expression is 2187.

Given expression:

expression 3 with the exponent 4 multiplying  3 with the exponent of 3.

= [tex]3^{4} *3^{3}[/tex]

we know that,

if base are equal exponents are added.

= [tex]3^{4+3}[/tex]

= [tex]3^{7}[/tex]

= 3*3*3*3*3*3*3

= 9*3*3*3*3*3

= 27*3*3*3*3

= 81*3*3*3

= 243*3*3

= 729*3

= 2187.

Therefore the simplified expression is 2187.

Learn more about the expression here:

https://brainly.com/question/14083225

#SPJ1

Using Combination formula, total 2,24,070 ways to make a math team of 14 selected students in which consist of 8 seniors and 6 juniors.

We have following information,

total number of seniors in math club = 15

total number of juniors in math club = 11

total number of students in math club = 26

A math team of 14 students be choosen from maths club such that it consists 8 seniors and 6 juniors .

Number of ways to choose 8 seniors out of 15 seniors = ¹⁵C₈ = 485

Number of ways to choose 6 juniors out of 11 juniors = ¹¹C₆ = 462

Number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors

= 485 × 462 = 2,24,070

Hence, the number of ways to select/choose a math team of 14 students consists 8 seniors and 6 juniors is 2,24,070..

To learn more about Combination formula, refer:

https://brainly.com/question/28065038

#SPJ4

Answer:

LCM of 90 and 225 = 450

I'm not too sure I understand

2 x 3 x 3 x 5 = 90, and 3 x 3 x 5 x 5 = 225

90: 90, 180, 270, 360, 450

225: 225, 450

LCM = 450

f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.

A sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given,

The sequence below shows a certain company's expected net worth in millions of dollars after 1, 2, 3, 4 years, etc....

8.3, 10.4, 12.5, 14.6,...

The given sequence is a arithmetic sequence.

The first term is 8.3

The common difference is 2.1

The nth term of arithmetic sequence aₙ=a+(n-1)d

the nth term of this sequence=8.3+(n-1)2.1

f(n)=8.3+(n-1)2.1

Hence, f(n) = 8.3 + 2.1(n−1) function models the nth term of the sequence 8.3, 10.4, 12.5, 14.6.

To learn more on Sequence click:

https://brainly.com/question/21961097

#SPJ1

The coordinate of image of P is (-6,-4)

What in math is a coordinate?

a pair of numbers that utilize the horizontal and vertical breakups from the two reference axes to define a point's location on a coordinate plane. generally expressed by the x-value and y-value pair (x,y).

P (-2,2)
Translation (x,y)=(x-4,y-6)
x= -2
y= 2
x-4= -6
y-6= -4
Hence the coordinate of image of p is (-6,-4)

Learn more about Coordinate of the image at
https://brainly.com/question/20935031
#SPJ1

Answer: it is not 27%

Step-by-step explanation:

The AGI and taxable income is $23,670 and $11,270

How to calculate AGI(Adjusted gross income) ?

The AGI calculation can be done as,

We have given that,

Gross income = $23670

1 Exemption = $12400

Adjustment = 0

Deduction = 0

Find AGI and Taxable income

AGI = Adjusted gross income

we know,

AGI = Total income - Any deduction or any adjustment  

AGI = ($23,670 + $12400)  - (0 + 0)

AGI = $36070

Now, Calculate taxable income

Taxable income = Gross income - 1 Exemption

                           = $23670 - $12400

                           = $11,270

Hence, the AGI and taxable income is $36,070 and $11,270

To read more about AGI

https://brainly.com/question/14059060

#SPJ13

Answer: D is the answer

Step-by-step explanation:

$23,670 and $11,270

The probability of of a random student having blue eyes and dark hair

 is 35% .

let consider the total students in the school be (U) = 100%

out of them ,

students having blue eyes (A) = 60%

students having  dark hair (B) = 55%

students with neither blue eyes nor dark hair (A∪B)' = 20%

let the students with blue eyes and dark hair be (A∩B) = x %

Then according to the set theorem

U = n(A∪B) + n(A∪B)'

U = n(A) + n(B) - n(A∩B) + n(A∪B)'

100 = 60 + 55 - x +20

∴ x = 60 + 55 +20 - 100

x = 35 %

So the probability of random student having blue eyes and dark hair is 35% .

learn more about probability here :

https://brainly.com/question/16484393

#SPJ4

Answer:

A $1.20

Step-by-step explanation:

Answer:   A) $1.20

Step-by-step explanation:   To get 10% of a number, you just need to divide by 10, so 12 ÷ 10 = 1.2.

Answer:

32.2222

Step-by-step explanation:

Answer: 32.22 degrees Celsius.

Based on the given ratio of modern and classical songs learned, the number of modern songs learned if 9 classicals have been learned is 15

If the choir has learned 9 classical songs;

Equate the ratio of the number of modern songs to the number of classical songs

5 : 3 = x : 9

5/3 = x/9

5 × 9 = 3 × x

45 = 3x

divide both sides by 3

x = 45/3

x = 15

In conclusion, the number of modern songs they have learned if they learn 9 classical songs is 15

Complete question:

Raymond sings in a choir called the Seaville Songbirds. For every 5 modern songs they learn, the choir leader teaches them 3 classical songs.

If the choir has learned 9 classical songs, how many modern songs have they learned?

Read more on ratio:

https://brainly.com/question/12024093

#SPJ1

Answer:

-2.475

Step-by-step explanation:

The measures of the each angle of the triangle is 84, 28 and 68 degrees.

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.  

The triangle has the sum of the measures of the angles as 180°.

Angle A is three times as large as angle B and also 16° larger than C.

Therefore,

let

angle A = x

Angle B = x / 3

Angle C = x - 16

Therefore,

x + x - 16 + x  /3  = 180

7 / 3 x - 16 = 180

7 / 3 x = 180 + 16

7 / 3 x = 196

cross multiply

7x = 196 × 3

7x = 588

divide both sides by 7

x = 588 / 7

x = 84

Therefore,

A = 84 degrees

B = 84 / 3 = 28 degrees

C = 84 - 16 = 68 degrees

learn more on triangle here: https://brainly.com/question/14773007

#SPJ1

Step-by-step explanation:

The graph of [tex]p(x)=2x^3[/tex] is less steep than [tex]f(x)=2.5x^3[/tex] because the coefficient 2 is less than the coefficient 2.5.  That makes points on the graph of p(x) lie closer to the x-axis than points on the graph of f.  For example, if  x = 2, the point (2, 20) is on the graph of  f  but the point (2, 16) is on the graph of  p (so it lies under the point (2, 20).

The graph of [tex]p(x)=-x^3[/tex] is less steep than the graph of  f  and it is reflected over the x-axis.  The negative coefficient -1 is doing that.  The values of the function  p(x)  are opposite sign to values of  f(x).

The graph of [tex]p(x)=3x^3[/tex] is steeper than the graph of f(x) because the coefficient 3 is larger than the coefficient 2.5, making the points on the graph of   p  lie farther away from the x-axis than points on the graph of  f(x).

the graph above is the graph of a Cubic function, namely a polynomial with a degree of "3", and the behaviour is that it comes from the bottom from -infinity goes up up get to a smooth flat or horizontal plateau then it keeps on going right back up, its slope is never negative.

now, Cubic functions do not have a "vertex" as in a U-turn sense or a peak-sense.

(a) The scatter plot and the line of fit are shown in the graph.

(b) The equation of the line of fit is y = -2.5x+18.3.

(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.

A scatter plot is a graph of the given points or given data.

(a)

To make a scatter plot of the data, plot the points (x,y) on a graph.

To draw the line of fit, draw a line such that the distance between the line and the plotted points is minimum.

(b) The line passes through points (7.3,0)and (0,18).

The equation of the line is given by:

[tex]y-y_1=\frac{(y_2-y_1)}{(x_2-x_1)}(x-x_1)[/tex]

Substitutes the points (x₁,y₁) = (7.3,0) and (x₂,y₂)=(0,18) into the above equation:

[tex]y-0=\frac{18-0}{0-7.3}(x-7.3)\\y=-2.5(x-7.3)\\y=-2.5x+18.3[/tex]

(c) The slope of a line of the form y=mx+c is m.

Therefore, the slope of the line y=-2.5x+18.3 is m = -2.5.

The slope indicates the change in y with respect to the change in x.

Therefore, the slope -2.5 indicates that the gamer losses 2.5 every week after getting a new game.

Hence,

(a) The scatter plot and the line of fit are shown in the graph.

(b) The equation of the line of fit is y = -2.5x+18.3.

(c) The slope is -2.5 which indicates that the gamer losses 2.5 every week after getting a new game.

Learn more about scatter plots here:

https://brainly.com/question/29231735

#SPJ1

The value of angle ∠5 will be equal to 120°.

Straight lines with little depth or width are present. You will learn about a variety of lines, including transversal, intersecting, and perpendicular lines.

A figure called an angle is one in which two rays originate from the same point. In this area, you might also encounter contrasting and related viewpoints.

Given that In the given figure, l ∥ m and n are transversal and the angles are ∠1=80° and ∠5=100°.

First, calculate angle 2,

∠1 = ∠2  = 80 ( By alternate interior angles)

Calculate the angle ∠4,

∠4 = 180 - 80 - 40

∠4 = 180 - 120

∠4 = 60°

Calculate the angle ∠5,

∠5 = 180 - 60

∠5 = 120

Therefore, the value of angle ∠5 will be equal to 120°.

To know more about lines and angles follow

https://brainly.com/question/25770607

#SPJ1

x = y = 48 , by using angle sum property of triangle.

What are the properties of triangle?

A triangle's characteristics are:

1. Three sides, three angles, and three vertices make up a triangle.

2. A triangle's total internal angles are always equal to 180 degrees. This is referred to as the triangle's angle sum property.

3. Any two triangle sides can add up to a length that is longer than the third side.

4. The greatest side of a triangle is the side that faces the largest angle.

5. The sum of the triangle's internal opposite angles is equal to any of its outer angles. This is referred to as the triangle's outside angle property.

In the given triangle , two sides of the triangle are equal and we know angle opposite to equal sides are equal therefore both angle x and y are equal.

Now, Using angle sum property of triangle

x + y + 84 = 180 degree

x + x + 84 = 180

2x + 84 = 180

2x = 180 - 84

2x = 96

x = 96/2  

x = 48

Similary , y = 48 as x and y are equal.

Therefore, x = y = 48

To learn more about the triangles from the given link.

https://brainly.com/question/1058720

#SPJ1

The strategy which would eliminate a variable in the system of equations is to multiply the top equation by -5 , then add the equation and is denoted as option B.

This is a mathematical term which is made up of two expressions and is connected by an equal sign.

In the example given below:

x - 2y = 11

5x + 3y = -11

We can multiply the top by -5 which will result in:

-5x + 10y = -55 after which it is added to the other to give:

-5x + 5x + 10y + 3y  = -55 + (-11)

13y = -66

y = -66/13.

From this we can notice that the variable x was eliminated which is why option B is the correct choice.

Read more about Equation here https://brainly.com/question/18831322

#SPJ1

The distance covered by second cyclist is, 9 + (3/4)b miles.

What is speed?

Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be meters per second (m/s) in this example since the distance is measured in meters (m) and the time is measured in seconds (s).

Given: Two cyclists are 7 miles apart when they begin biking away from each other in opposite directions.

The speed of the first cyclist is 12 miles per hour. The speed of the second cyclist is b miles per hour greater than the speed of the first cyclist.

Speed of first cyclist = 12 miles per hour.

Speed of second cyclist = 12 + b miles per hour.

Since, distance = speed x time

The distance covered by the second cyclist in 45 minutes is,

45 minutes = 45/60 = 3/4 hour.

Therefore, distance covered by second cyclist is,

=  (12 + b) x 3/4 = 9 + 3b/4 miles.

To know more about speed, click on the link

https://brainly.com/question/13943409

#SPJ13

Step-by-step explanation:

as the graph shows :

4x + 12x = 320

16x = 320

x = 20

Answer:

6x+97

Step-by-step explanation:

Hint: 3 sides of a triangle adds up to 180*.

((i know ur gonna clown on me for not giving the answer(i know the answer :d)but trust me the if u get da hint, ull solve it fine)