Find the coordinates of the centroid of the triangle with the given vertices. X(5,7), Y(9,-3), Z(13,2)

Answer:

Slope-intercept form: y=3x-5

Step-by-step explanation:

The slope is 3 and the y-intercept is -5. We plug those in for m and b, respectively.

Answer:

|Least percentage = |32% - 5%| = 27%

Greatest percentage = |32% + 5%| = 37%

Step-by-step explanation:

|Percentage who favor ± error

Answer:

Cadence had gotten 7 refills.

Step-by-step explanation:

$14.25 + $1.25r = 23$

23 - 14.25 = 8.75

8.75/1.25 = 7

r = 7

Per year price drop is -41.50$

The cost of an MP3 player in the year 2003 is = $ 499

The cost of an MP3 player in the year 2009 is = $ 249.99

The price drop per year will be –

We need to subtract the base year price from that of the current year price  and divide that by the difference between the base year and the current year

The year that serves as the standard against which subsequent values are measured is referred to as the base year.

The term "current year" refers to the fiscal year that has already begun but has not yet completed its cycle.

So,

(499-249.99) / (2003-2009)

249.01 / -6 = -41.50 $

Hence per year price drop is -41.50$

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The formula for the given cosine function is:

g(x) = 6cos(0.8(x - 0.75π)) - 8

Hence the coefficients are:

a = 6, b = 0.8, c = -0.75π, d = -8.

The cosine function is defined as follows:

g(x) = acos(bx+c)+d.

The coefficients have these following roles:

In this problem, we have that the maximum value is of -2 and the minimum value is of -14(difference of 12), hence the amplitude is given as follows:

2a = 12.

a = 6.

A standard cosine function with amplitude would vary the between -6 and 6, while this one varies between -14 and -2, hence the vertical shift is of d = -8.

The minimum and maximum values form half the period, hence:

[tex]\frac{2\pi}{B} = 2\pi - \frac{3\pi}{4}[/tex]

[tex]\frac{\pi}{B} = \frac{5\pi}{4}[/tex]

B = 4π/5

b = 0.8π.

The minimum value in the standard function is at x = 0, while at this function is at x = 3π/4, hence the phase shift is of 3π/4 = 0.75π units to the right, that is, c = -0.75π.

Hence the formula for the given cosine function is:

g(x) = 6cos(0.8(x - 0.75π)) - 8

The graph of the function is given at the end of the answer.

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The next two terms of the given sequence are 20 and 23. And the the formula for finding the nth term of the given sequence is [tex]T_{n+1} = T_{n} + 3[/tex].

According to the given question.

We have a sequence 5, 8, 11, 14, 17...

Since, the first term of the given sequence is 5.

The second term of the given sequence is 8.

The third term of the given sequence is 11.

Here, we can see that each term is 3 more tahn the previous term.

So, the next two terms i.e.

Fifth term = 17 + 3 = 20

Sixth term = 20 + 3 = 23

Therefore, the formula for finding the nth term of the given sequence is given by

[tex]T_{n+1} = T_{n} + 3[/tex]

Hence, the next two terms of the given sequence are 20 and 23. And the the formula for finding the nth term of the given sequence is [tex]T_{n+1} = T_{n} + 3[/tex].

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Answer: 6

Step-by-step explanation:

3x ÷ x = 3

27 ÷ 3 = 9

9 = x + 3
x = 6

I don't which one is the width so I just assume the smaller badge side x cm is the width

Answer:

C

Step-by-step explanation:

hope this works for you :)

Marco ran 4 plays for a total of 60 yards throughout the first half of the football season. Marco committed 6 penalties that cost his team 80 yards in the second half of the season. His total 160 yardage for his football season.

Given that,

Marco ran 4 plays for a total of 60 yards throughout the first half of the football season.

Marco committed 6 penalties that cost his team 80 yards in the second half of the season.

We have to calculate his total season yardage in football.

In the 1st half of the football season, Marco ran 4 plays for a total of 60 yards.

4[tex]\times[/tex]60=240

In the 2nd half of football season, Marco committed 6 penalties that cost his team 80 yards.

That is.

240-80=160

Therefore, his total 160 yardage for his football season.

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The factor of the expression will be (x + 1) and (x + 1). Then the product of two binomials will be (x + 1) and (x + 1).

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The expression is given below.

⇒ x² + 2x + 1

Factorize the expression, then the factor of the expression will be

⇒ x² + x +  x + 1

⇒ x(x + 1)x + 1(x + 1)

⇒ (x + 1)(x + 1)

⇒ (x + 1)²

The product of two binomials will be (x + 1) and (x + 1).

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Out of these equations and inequalities, -2/3 > -3/4 is the true statement.

Briefly, A mathematical statement is a sentence that is either true or false. It may include words and symbols. "The square root of 4 is 5" is an example of a mathematical statement (which is, of course, false).

We use language in mathematics in a very precise way that is sometimes slightly different from everyday use. We'll start by talking about some common disagreements.

In everyday language, we say "either A or B" to mean that one of the two options is correct but not both.

And therefore out of these equations and inequalities

-2/3 = -3/4

-2/3 > -3/4

-2/3 < -3/4

The true statement is -2/3 > -3/4

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Answer:

Step-by-step explanation:

Givens

Let the angle = x

Let it's supplement = 180 - x

Equation

x + 9 = 2*(180 - x)                  Remove the brackets

Solution

x + 9 = 360 - 2x                     Add 2x to both sides

x + 2x + 9 = 360 - 2x + 2x     Combine

3x + 9 = 360                          Subtract 9 from both sides

3x + 9-9 = 360-9                   Combine

3x = 351                                 Divide both sides by 3

3x/3=351/3

x = 117

Answer

Given angle = 117

Supplement = 180 - 117 = 63

Answer: 6

Step-by-step explanation: 2=24 4=48 6=72

a. the equation of the formula in terms of x is: x = (c - b)/a

b. x = 4 and x = 6

Where we have a, b, and c as constants of the equation, ax + b = c, and the variable is x, we can solve for the value of x as shown below:

ax + b = c

Subtract b from both sides

ax - b = c - b

ax = c - b

Divide both sides by a

ax/a = c/a - b/a

x = c/a - b/a

x = (c - b)/a

b. 3x + 7 = 19

a = 3, b = 7, and c = 19

Substitute a = 3, b = 7, and c = 19 into x = (c - b)/a

x = (19 - 7)/3

x = (12)/3

x = 4

x - 1 = 5

a = 1, b = -1, and c = 5

Substitute a = 1, b = -1, and c = 5 into x = (c - b)/a

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

x = 6/1

x = 6

In summary, we have:

a. the equation of the formula in terms of x is: x = (c - b)/a

b. x = 4 and x = 6

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The area inside of the home is [tex]452.16 ft^2[/tex]

It is given that circular dwelling has a diameter of 24 feet then , radius will be [tex]r=\frac{24}{2} =12 \ feet[/tex]

Putting r = 12 feet in equation (1) , we get

       [tex]A=3.14\times( 12) ^2\\A=3.14\times144\\A= 452.16 ft^2[/tex]

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Using the definition of slope, the points (-2 , 6), (0 , 2), and (1 , 0) are collinear.

Three or more points are said to be collinear if they lie on a single straight line.

To determine whether the given points are collinear, use the definition of slope. The slope, m, determines the steepness of a line. It can be measured by the vertical distance from one point to another divided by the horizontal distance of the same points.

m = (y2 - y1)/(x2 - x1)

Getting the slope of each pair of points:

(-2 , 6) and (0 , 2)

m = (y2 - y1)/(x2 - x1)

m = (2 - 6)/(0 - -2)

m = -4/2

m = -2

(0 , 2), and (1 , 0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 2)/(1 - 0)

m = -2/1

m = -2

(-2 , 6) and (1 , 0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 6)/(1 - -2)

m = -6/3

m = -2

Since collinear points lies on the same line, the slope of any pair of points should be the same. Since the slopes of each pair of points is equal with each other, then they are collinear.

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Answer:

His calories go down 50 calories every day. Hope it helps!

Step-by-step explanation:

Byron agrega una cantidad de 17 / 80 kilogramos por cada pimentero. (Opción correcta: D)

En este problema debemos interpretar y emplear fracciones para encontrar una cantidad determinada, así como saber utilizar operaciones para obtener el resultado deseado y elegir la opción correcta entre las cuatro disponibles.

Byron tiene 17 / 10 kilogramos de pimienta negra y distribuye equitativamente siete octavas partes de esa pimienta en siete pimenteros. En consecuencia, la cantidad por pimentero es igual a siete octavas partes de la cantidad dispuesta por Byron y dividida a su vez por la cantidad de pimenteros:

x = [(7 / 8) × (17 / 10 kg)] / 7

x = (119 / 80 kg) / 7

x = 17 / 80 kg

Byron agrega una cantidad de 17 / 80 kilogramos por cada pimentero. (Opción correcta: D)

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Answer:

Step-by-step explanation:

This number would be between 3,300 and 3,400.  Which number would 3387 be closer to?  3350 would be right in the middle and 3387would be larger than 3350 so 3387 is closer to 3400.

The exterior angle (∠ 5) is larger than either remote interior angle

( ∠ 7 and ∠ 8) then m ∠ 2 > m ∠ 8 and m ∠ 5 > m ∠ 8.

According to the exterior angle inequality theorem, the measure of any exterior angle of a triangle is greater than the measure of either of the opposite interior angles.

The adjacent interior angle and the exterior angle are supplementary. A triangle's exterior angles add up to 360º.

A triangle's exterior angle is always greater than its two remote interior angles.

By the Exterior Angle Inequality Theorem, the exterior angle (∠ 2) is larger than either remote interior angle (∠ 6 and ∠ 8).

Similarly, the exterior angle (∠ 5) is larger than either remote interior angle (∠ 7 and ∠ 8).

m ∠ 2 > m ∠ 8 and m ∠ 5 > m ∠ 8 .

Therefore, the correct answer is ∠ 2 and ∠ 5.

The complete question is:

Use the Exterior Angle Inequality Theorem to list all of the angles that satisfy the stated condition

Measures greater than m ∠ 8

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The equation of the line in standard form passing through the point (-4 , 2) with slope equal to 3 is 3x - y = -14.

The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.

The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).

Using the point slope form, plug in the values of the slope and the point to set up the equation.

(y - y1) = m(x - x1)

where m = 3 and (x1 , y1) = (-4 , 2)

(y - 2) = 3(x - -4)

y - 2 = 3(x + 4)

y - 2 = 3x + 12

To write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.

y - 2 = 3x + 12

3x - y = -2 -12

3x - y = -14

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Answer:

"The poison arrow frog... has enough toxicity in its skin that a dart rubbed on the surface can kill a small mammal.

Step-by-step explanation:

An ellipsis is a punctuation mark that indicates the interruption of thought and has great power of suggestion. They are also used, for example, in interrupting a character's speech.

The sentence which uses ellipsis correctly is: "The poison arrow frog ... has enough toxicity on its skin ... ".

As per the passage, which defines the ellipsis, that the poison arrow frog who resides in the tropical forest of the South America has enough toxicity on its skin that a dart rubbed across the surface of the body which can kill a small mammals.

The given passage is a missing punctuation marks which defines the ellipsis. In this the thoughts are in the interruption face as well as in the power of suggestion. In this, the suggestions are very important because it is killing the mammals which are resided at the surface.

What is ellipsis?

Ellipsis has number of dots in a sentences or a phrase which define the intention of a passage as well as author. It is also called as punctuation marks with three dots.

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The simpler form of given fraction 2/x -5 / 6/x - 3 is (2 - 5x)/(6 - 3x)

The correct answer is an option (A)

In this question,

we have been given a rational function  2/x -5 / 6/x - 3

We need to simplify given fraction.

2/x -5 / 6/x - 3

=  [(2/x) - 5] / [(6/x) - 3]

= [(2 - 5x) / x] / [(6 - 3x) / x]

= (2 - 5x) / (6 - 3x)

Therefore, the simpler form of given fraction 2/x -5 / 6/x - 3 is:                 (2 - 5x) / (6 - 3x)

The correct answer is an option (A)

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Hence , on factorization given equation 2x² + 5xy/3 - 2y² gives ( 2x + 3y)(3x -2y) .

We have given an equation 2x² + 5xy/3 - 2y² .

On simplification , we get

  2x² + 5xy/3 - 2y² = 0

 6x² + 5xy - 6y² = 0

By splitting in the middle term , we can write 5xy as ( 9 - 4 ) xy

6x² + (9xy - 4xy ) - 6y² = 0

( 6x² + 9xy ) - (4xy + 6y²) = 0

3x ( 2x + 3y) - 2y (2x + 3y ) = 0

( 2x + 3y)(3x -2y) = 0

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The circumference is the perimeter of a circle or ellipse in geometry.  

If the diameter of the circle be 16 feet then the circumference of circle is 50.24

A circle's circumference is defined as the straight line distance around it. In other words, if you open a circle and draw a straight line through it, the length of that line is the circumference of the circle.

The circumference is the perimeter of a circle or ellipse in geometry. That is, the circumference would be the circle's arc length if it were opened up and straightened out to a line segment.

Let the diameter of the circle, d = 16 feet

Circumference of circle, c = πd

Circumference of circle = 2 (3.14)(16)

Circumference of circle = 9.42 × 16

Circumference of circle = 50.24

Therefore, the Circumference of circle be 50.24

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