1/7 * 3/5
1/3 * 1 1/7 * 1/4

The equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1) is (x - 1)^2 + (y - 1)^2 = 13.

The endpoints are (2, -5) and (-3,1).

The standard form equation for a circle is known as

\((x-a)^2+(y-b)^2=r^2\)

where (a, b) are the center's coordinates and (r) is the radius.

Taking into account the stated endpoints of the diameter. The center will then be at the midpoint, and the radius will be the distance between the center and either of the two endpoints.

Calculating the midpoint is as follows:

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)\)

where, \((x_{1},y_{1})\) and \((x_{2},y_{2})\) are two points.

Now putting the values

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{-2+4}{2}, \frac{3-1}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(\frac{2}{2}, \frac{2}{2}\right)\)

\(\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)=\left(2, 1)\)

Now we determine the equation of circle.

The center (2, 1) and the terminal are the two points (-2, 3).

r = \(\sqrt{(-2-1)^2+(3-1)^2}\)

r =\(\sqrt{(-3)^2+(2)^2}\)

r = \(\sqrt{9+4}\)

r = √13

Now we can write the equation of circle as:

(x - 1)^2 + (y - 1)^2 = (√13)^2

(x - 1)^2 + (y - 1)^2 = 13

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The complete question is:

Find the equation for the circle with a diameter whose endpoints are (2, -5) and (-3, 1).

Write the standard equation for the circle.

Answer:

Any choice that has a slope of -1/2

Step-by-step explanation:

-2x - 4y = 3

-4y = 2x + 3

4y = -2x - 3

y = -1/2x -3/4

y = mx + b

m = slope

Answer:

To solve a pair of equations using substitution, first solve one of the equations for one of the variables. Then substitute the result for that variable in the other equation.

-2x+2y=6,4x+2y=-5

Choose one of the equations and solve it for x by isolating x on the left hand side of the equal sign.

-2x+2y=6

-2x=-2y+6

x=-\frac{1}{2}\left(-2y+6\right)

x=y-3

4\left(y-3\right)+2y=-5

4y-12+2y=-5

6y-12=-5

6y=7

y=\frac{7}{6}

Step-by-step explanation:

x=\frac{7}{6}-3

x=-\frac{11}{6}

x=-\frac{11}{6},y=\frac{7}{6} the answer

Use Socratic

Step-by-step explanation:

Use Socratic

Answer:

Carlos=1.5041

Mykala=2.6991

William=4.1350

Emily=4.1773

Answer:

The measure of ∠R = 60°

Step-by-step explanation:

The given parameters are;

Triangle XYZ is reflected across the y-axis to create triangle PQR

The measure of ∠Y = 30°

Triangle XYZ = A right triangle

The measure of ∠X = 90°

Where we have;

The image of the preimage of vertex X = P

The image of the preimage of vertex Y = Q

The image of the preimage of vertex Z = R

Therefore, given that a reflection is a rigid transformation, we have;

The measure of ∠X = The measure of ∠P

The measure of ∠Y = The measure of ∠Q

The measure of ∠Z = The measure of ∠R

Given that the measure of ∠Y = 30° and the measure of ∠X = 90°

∠X +∠Y + ∠Z = 180° (angle summation of a triangle property

∴ The measure of ∠Z = 180° - (∠X + ∠Y)  = 180° - (90° + 30°) = 60°

Therefore;

The measure of ∠Z = 60° = The measure of ∠R

The measure of ∠R = 60°.

Hello! I'm happy to help you with your question. Here's the notation for each sequence:

(a) 2 + 4 + 6 + 8 + ... + 2n can be rewritten as:
∑(2i) where i goes from 1 to n.

(b) 1 + 5 + 9 + 13 + ... + 425 can be rewritten as:
∑(4j-3) where j goes from 1 to 106. (Note: 425 is the 106th term in this sequence)

(c) 1 + 12 + 13 + 14 + ... + 150 can be rewritten as:
1 + ∑(k) ,where k goes from 12 to 150

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Therefore , the solution of the given problem of angle comes out to be the angle at point B is therefore a right angle.

An angle is a shape in Euclidean geometry composed of two rays, referred to as the sides of circle, that diverge at the angle's tip and the peak, which is situated in the middle. Within the plane they are located in, two rays can join to form an angle. Angle is another outcome of two objects interacting. They are known as dihedral angles. Two line beams with ends can be arranged in a variety of ways to create an angle in 2 dimensions.

Here,

We can determine whether this triangle is a right triangle by using the Pythagoras theorem:

=> AC² = AB² + BC²

=> 13² = 5² + 12²

=> 169 = 25 + 144

=> 169 = 169

It is a right triangle because the Pythagorean formula holds true for this triangle. The angle at point B is therefore a right angle.

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Answer:

Step-by-step explanation:

The alternating series test can be used to show convergence of the alternating series I, II, and III given in the options and the correct answer to this question is Option A. I only.

The alternating series test is a method used to determine the convergence or divergence of alternating series. According to the alternating series test, an alternating series converges if the absolute value of its terms decreases monotonically to zero. In other words, if the absolute value of the terms in an alternating series eventually becomes smaller and smaller until it is less than or equal to a certain positive number, then the series converges.

In conclusion, the alternating series test can be used to show the convergence of series I and III, but not for series II. Therefore, the answer is (A) I only.

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Answer:

8 percent

Step-by-step explanation:

p=rs1460

t=30month

=30÷12(1year=12months)

=2.5 years

interest=rs292

rate of interest=?

we know that

I=ptr/100

rs292=rs1460×2.5×R/100

rs2920=365R(subtracting 0 from both and multiplying remaining with 292)

2920/365=r

8 percent=R

Question:

You are running a fuel economy study. One of the cars you find is blue. It can travel \(44\frac{1}{2}\) miles on \(1\frac{1}{4}\) gallons of gasoline.

Another car is red. It can travel \(25\frac{3}{5}\) on \(\frac{4}{5}\) gallon of gasoline.

What is the unit rate for miles per gallon for each​ car?

Which car could travel the greater distance on 1 gallon of​ gasoline?

Answer:

(a)

\(Rate = 35\frac{3}{5}\ miles\ per\ gallon\)

\(Rate = 32\ miles\ per\ gallon\)

(b)

The blue car will travel faster

Step-by-step explanation:

Given

Blue Car:

\(Distance = 44\frac{1}{2}\ miles\)

\(Gasoline = 1\frac{1}{4}\ gallons\)

Red Car

\(Distance = 25\frac{3}{5}\ miles\)

\(Gasoline = \frac{4}{5}\ gallons\)

Solving (a):

This is solved by dividing the distance travelled by the amount of gasoline.

i.e.

\(Rate = Distance/Gasoline\)

Blue Car:

\(Rate = 44\frac{1}{2} / 1\frac{1}{4}\)

\(Rate = \frac{89}{2} / \frac{5}{4}\)

\(Rate = \frac{89}{2} * \frac{4}{5}\)

\(Rate = \frac{89}{1} * \frac{2}{5}\)

\(Rate = \frac{89 * 2}{1 * 5}\)

\(Rate = \frac{178}{5}\)

\(Rate = 35\frac{3}{5}\ miles\ per\ gallon\)

Red Car:

\(Rate = 25\frac{3}{5}/\frac{4}{5}\)

\(Rate = \frac{128}{5}/\frac{4}{5}\)

\(Rate = \frac{128}{5} * \frac{5}{4}\)

\(Rate = \frac{128 * 5}{5 * 4}\)

\(Rate = \frac{128}{4}\)

\(Rate = 32\ miles\ per\ gallon\)

(b)

In (a), we have:

\(Rate = 35\frac{3}{5}\ miles\ per\ gallon\) --- Blue Car

\(Rate = 32\ miles\ per\ gallon\) --- Red Car

By comparison:

The rate of the blue car is greater than that of the red

Hence, the blue car will travel faster

Quadrilateral HIJK is a kite because it has two pairs of adjacent congruent sides.

A kite is a quadrilateral with two pairs of adjacent congruent sides. In quadrilateral HIJK, we can see that sides HI and IJ are congruent, and sides IJ and JK are also congruent. This satisfies the definition of a kite. Additionally, the diagonals of a kite are perpendicular. If we examine the diagonals of HIJK, we can observe that segment HK is perpendicular to segment IJ. Hence, based on the congruent sides and perpendicular diagonals, we can conclude that quadrilateral HIJK is indeed a kite.

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"Which statement provides evidence or conditions that prove quadrilateral HIJK is a kite, considering all necessary properties and characteristics of a kite?"

Answer:

x=2

y=3

Step-by-step explanation:

9x2= 18, 6x3=18. 18+18=36

Answer:

The answer is that the ball was in the air for 0.56 seconds when it was 54 feet above the ground. This was determined by using the Quadratic Formula to solve the equation 54 = -16s^2 + 96s for the variable s.

Step-by-step explanation:

To solve this equation, we can use the Quadratic Formula, which states that for a quadratic equation in the form ax^2 + bx + c = 0, the solutions are given by:

x = (-b +/- sqrt(b^2 - 4ac)) / (2a)

In this case, a = -16, b = 96, and c = -54. Plugging these values into the Quadratic Formula, we get:

s = (-96 +/- sqrt(96^2 - 4 * -16 * -54)) / (2 * -16)

= (96 +/- sqrt(9216 + 4352)) / -32

= (96 +/- sqrt(13,568)) / -32

Since we want the time (in seconds) that the ball was in the air, we need to find the positive solution to this equation. Thus, we have:

s = (96 + sqrt(13,568)) / -32

= (96 + 120) / -32

= 0.5625 seconds

Rounding this value to the nearest hundredth of a second, we get 0.56 seconds. This means that the ball was in the air for 0.56 seconds when it was 54 feet above the ground.

To solve this equation, we used the Quadratic Formula. This method allowed us to find the time (in seconds) that the ball was in the air by solving for the value of the variable s in the given equation. This helped Vue answer his question by providing a numerical value for the amount of time that the ball was in the air when it was 54 feet above the ground.

To compare the two quantities, divide the number of giraffes by the number of penguins There are 5 times as many giraffes as penguins at the zoo.

To compare the two quantities, you need to divide the number of giraffes by the number of penguins.

30 giraffes / 6 penguins = 5

This means that there are 5 times as many giraffes as penguins at the zoo.

There are 5 times as many giraffes as penguins at the zoo. To compare the two quantities, divide the number of giraffes by the number of penguins (30/6 = 5). This means that there are 5 times more giraffes than penguins at the zoo.

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A scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.

Therefore, a scale that allows us to rank individuals or objects, but not say anything about the meaning of the differences between the ranks, is an ordinal scale.

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Answer:

$34.10

Step-by-step explanation:

55 Divided by 5 is 11, multiply 3.10 by 11, and you get your answer.

Step-by-step explanation:

a) 4x 12+n = There are no like terms )

b) (4x12) +n = There are no like terms )

c) 4x (12+ n)  = 4nx+48x

d) 4+ (12 x n) =12nx+4

( I hope this was helpful ) >;D

Answer:

3/10

Step-by-step explanation:

Answer:

Im pretty sure its D i had a problem like this as well.

Step-by-step explanation:

Sorry for bad handwriting

if i was helpful Brainliests my answer ^_^

Step-by-step explanation:

Using Pythagoras' Theorem, hypotenuse squared is equal to adjacent squared plus opposite squared.

The hypotenuse here is line PQ, the adjacent is line PR and the opposite is line QR.

Therefore, PQ^2 = PR^2 + QR^2

(2x + 7)^2 = (3x + 3)^2 + (x + 2)^2

{4x}^{2} + 28x + 49 = {9x}^{2} + 18x + 9 + {x}^{2} + 4x + 4

collecting like terms

{4x}^{2} - {9x}^{2} - {x}^{2} + 28x - 18x - 4x + 49 - 9 - 4 = 0

- {6x}^{2} + 6x + 36 = 0

Multiplying through by -1 to match the given equation

{6x}^{2} - 6x - 36 = 0

dividing through by 6

{x}^{2} - x - 6 = 0 (the final equation)

Answer:

3 OR 8  hope this helps!

Step-by-step explanation:

a) The depicted cross-section of the log represents the diameter of the log.

b) Given a diameter of 15 inches, the circumference of the log is 47.14 inches.

The circumference of a circular log or object is the total distance around the log or object.

The circumference can be determined using either of the following formulas:

Formula 1: C = πd

Formula 2: C = 2πr

Where π = pi or 22/7

d = diameter

r =radius

Thus, given the diameter as 15 inches, the circumference of the represented log is 47.14 inches.

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Answer:

I see what's happening here

You're face to face with greatness

And it's strange

You don't even know how you feel

It's adorable

It's nice to see that humans never change

Open your eyes, let's begin

Yes it's really me, breathe it in

I know it's a lot, the hair, the bod

When you're staring at a demigod

So what can I say except

You're welcome

For the tide, the sun, the sky

Hey, it's okay, it's okay

You're welcome

I'm just an ordinary demiguy

What can I say except

You're welcome

For the tide, the sun, the sky

Hey, it's okay, it's okay

You're welcome

I'm just an ordinary demiguy

Honestly, I can go on and on

I could explain every natural phenomenon

The tide, the grass, the ground

Oh, that was me I was messing around

I killed a snake, I buried its guts

Sprouted a tree, now you've got coconuts

What's the lesson?

What is the takeaway?

Don't mess with Maui when he's on a breakaway

And the tapestry here in my skin

Is a map of the victories I win

Look where I've been, I make everything happen

Look at that mean mini Maui just tikkity tappin'

Singing and scratchin'

Flipping and snappin'

People are clappin', hearing me rappin'

And bring the chorus back in

Well anyway, let me say you're welcome

For the wonderful world you know

Hey, it's okay, it's okay

You're welcome

Well, come to think of it, I gotta go

Hey, it's your day to say

You're welcome

'Cause I'm gonna need that boat

I'm sailing away, away

You're welcome

'Cause Maui's the ultimate guy

You're welcome!

You're welcome!

Step-by-step explanation:

Answer:

Y=-2x-3

Step-by-step explanation:

Y=mx+b

it goes down by 2

Answer:

Alvin's Age is 81 and Elga's age is 27

Step-by-step explanation:

let A be Alvin's age and E be Elga's age

A = 3 E (alvin's age is three times elga's age)

A + E = 108 ( the sum of their ages is 108)

3E + E = 108

4 E = 108

E= 108/4 = 27

A = 3E = 27*3 = 81

⭐ Let the Alvin's age be "a" and the Elga's age be "e".

⭐ If we carefully identify the question, we can get two hints provided in the question which can be framed into equations. They are,

(Alvin's age is 3 times the age of Elga's age)

(The sum of Alvin's and Elga's age is 108)

Substituting value of A i.e (A = 3E) in eqn (2) so as to get same variable and solve the eqn.

\(\Rrightarrow\bf{a + e = 108}\)

\(\Rrightarrow\bf{3e + e = 108}\)

\(\Rrightarrow\bf{4e = 108}\)

\(\Rrightarrow\bf{e = \frac{108}{4} }\)

\(\Rrightarrow\bf{e = 27}\)

Substituting value of (e = 27) in eqn (1),

\(\Rrightarrow\bf{a = 3e}\)

\(\Rrightarrow\bf{a = 3 \times 27}\)

\(\Rrightarrow\bf{a = 81}\)