What is the magnitude and direction of RS with tail and head points R(4, -6) and S(-2, 1)?
9.2 units, 49.4° north of west
10.4 units, 40.6° north of west
9.2 units, 49.4° south of east
10.4 units, 40.6° south of east

Answer:

  17

Step-by-step explanation:

The geometry program that drew the circle through the three given points wrote this equation for the circle:

  (x -6)^2 +(y -11)^2 = 130

Compared to the standard form equation, ...

  (x -h)^2 +(y -k)^2 = r^2 . . . . . . circle with center (h, k) and radius r

we can see that the center is (h, k) = (6, 11).

The sum h+k is 6+11 = 17.

__

Additional comment

The center is at the point of intersection of the perpendicular bisectors of chords of the circle.

Here it is convenient to choose one of them as the horizontal segment with endpoints (3, 0) and (9, 0). The vertical line that bisects this segment is x=(3+9)/2 = 6. So, x=6 is the x-coordinate of the circle center.

We can use endpoints (-1, 2) and (3, 0) as another chord. Its midpoint is (-1+3, 2+0)/2 = (1, 1). The slope of this chord is (y2-y1)/(x2-x1) = (0-2)/(3-(-1)) = -1/2. So, the slope of the perpendicular bisector is -1/(-1/2) = 2, and the equation of that line is

  y -1 = 2(x -1)

For x=6, the point of intersection of the chord bisectors is ...

  y -1 = 2(6 -1) = 10

  y = 11

The coordinates of the circle center are (6, 11), so h+k = 6+11 = 17.

Answer:

Formula of Mean= Efx/n

Formula of Median=n+1/2

I think it will help you

Answer:

1/2

Step-by-step explanation:

It appears to be 1/2 because the areas labeled "parrots" and "sparrows" takes up half of the pie chart. hope this helped!

Answer: the answer is 1 over 2 as a fraction

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

49

Answer:

Rational:2.1,2.2

Irrational:[tex]\sqrt{5},\sqrt{6}[/tex]

Step-by-step explanation:

Trial and error

Answer:

7.8

Step-by-step explanation:

3.2 + 4.6 = 7.8 because 6+2 equals 8 and 4+3 equals 7 so 7.8

Answer:

When dissolved, bases release hydroxide ions, OH-(aq) into solution.

Step-by-step explanation:

Water is the product of an acid and base reacting. Chemists say that the acid and base cancel or neutralise each other, hence the reaction is known as "neutralisation"

Answer: It increases the concentration of OH- in solution.

Step-by-step explanation:

Answer: 432 sq ft.

Step-by-step explanation: I decomposed the figure above into halves where the dotted line is drawn. I multiplied 25 x 10 to find the area of the rectangle on the right, pretending for now that it is a complete rectangle, which equals 250. Then, I subtracted 15 from 25, which equals 10, to find the length of the right triangle that’s missing to make the right half of the decomposed figure a rectangle. Then I multiplied 10 x 10, or 10 to the second power divided by 2 because 10 x 10 would be the formula to find a rectangle, and a right triangle is half of a rectangle so you would divide by 2. 10 x 10 divided by 2 because equals 50. 250 - 50 = 200. Next, you do the same thing for the other half of the irregular figure. I subtracted 4 from 25 to get 21. Then, I multiplied 21 x 16 divided by 2 which equals 168. Now, you multiply 25 x 16 which equals 400. 400 - 168 = 232. 200, the answer for the area of the other half of the decomposed figure, must be added to 232 to find your answer for the total area.

yes it is true and second is false

Answer:

Length = 8+7 = 15

Width = 8

Step-by-step explanation:

                       New

Length = x+7 , x+4

Width = x ,x+2

(x+7) x = (x+4)( x+2)

expand and simplify x =8

The length of the shorter side length of original rectangle is 8 inches and of original rectangle longer side length is 15 inches.

Let l is the length and b is the breadth of the rectangle.

then the area of the rectangle is ab.

Given One side of a rectangle is 7 inches longer than another side.

then shorter side length is x and the large side length is 7+x.

then the area of the original rectangle is x(x+7)

Now calculate the sides of the new rectangle.

longer side of this rectangle decreases by 3 then new side is 7+x -3= 4+x

The shorter side increases by 2 inches then x+2.

So new rectangle area is (x+4)(x+2)

Both rectangle area is equal then

(x+4)(x+2) = x(x+7)

x² +2x+4x+8 = x²+7x

x²+6x+8 = x²+7x

x²-x²+7x-6x = 8

x = 8

Since a shorter side length is 8 inches and a longer side length is 8+7 =15 inches.

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Answer: 96

Step-by-step explanation: formula for volume is lwh. 2 times 8 times 12 equals 192. divide that by 2 because there is only half left.

The equation solved for w is:

w = A/l

The correct option is A.

A pair of algebraic equations with the equal symbol (=) in the center and the same value are referred to as an equation.

Starting with the equation:

A/l = lw/l

We can simplify it by multiplying both sides by l:

A = lw

To solve for w, we need to isolate it on one side of the equation.

We can do this by dividing both sides by l:

A/l = w

Therefore, the required equation is A/l = w.

To learn more about the equation;

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Answer:

Given:

< or > = open circle

≤ or ≥ = closed circle

So we are looking for:

Therefore, the attached is the correct answer.

Answer:

6x³ - 15x² - 1

3x divided by 3x is 1

So, here we are to simplify the polynomial :

[tex] \\ \longrightarrow \sf \qquad6x^3 - 15x^2 - \frac{3x}{ 3x}\\ \\[/tex]

We can simplify it as,

[tex]\\ \longrightarrow \sf \qquad6x^3 - 15x^2 - 1 \\ \\[/tex]

Some points to know :

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's use section formula ~

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{mx_2 + nx_1}{m + n} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{my_2 + ny_1}{m + n} [/tex]

And since mid point divides a line segment Into two equal parts, m : n = 1 : 1

so, take m = n = 1

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{(1 \times - 1)+(1 \times - 2)}{ 1+ 1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{- 1- 2}{ 2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:x = \dfrac{ - 3}{ 2} [/tex]

Now, let's find y - coordinate ~

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{(1 \times - 5) + (1 \times - 4)}{1 + 1} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{ - 5 - 4}{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \:y = \dfrac{ - 9}{2} [/tex]

So, coordinates of midpoint is ~

[tex]\qquad \sf  \dashrightarrow \:( - \dfrac{3}{2} ,- \dfrac{9}{2} )[/tex]

Answer:

we need more information

Answer: 100 grams

Step-by-step explanation:

Mass remains constant. So 100 grams of water will be 100 grams of water vapor

its b i know

Step-by-step explanation:

Answer:x=4 (0,0)

Step-by-step explanation:

Determine the zeros of function,factor the functions. Set the factored function equal to 0 and solve. Then find the y-y-intercept of the given function by setting x equal to 00and Solving for y.

Answer:

Look at the photo.

Step-by-step explanation:

The formula is y=mx+b. So, for the first one you start at the coordinate (0, 2) and then move down 2 and right one.

For the second one you start at the coordinate (0, -2) and then move down two and move right one.

Answer: 5/3

Step-by-step explanation:

1. 3/x = 5/y

2. Cross multiply

3y = 5x

3. Dividing the sides by 3

y = 5x/3

4. Dividing the sides by x

y/x = 5/3

Answer:

slope = 3x

Step-by-step explanation:

Equation is y = 3x - 6
3x is slope

It's a geometric sequence

Formula:&

[tex]\\ \sf\longrightarrow a(n)[/tex]

[tex]\\ \sf\longrightarrow ar^{n-1}[/tex]

[tex]\\ \sf\longrightarrow 1.3125(4)^{n-1}[/tex]

Answer:

The fully factored form of the function f(x) is : (x+5)(x-1)(x-3)

Step-by-step explanation:

Answer:

[tex]Hi, ~I'm ~beinggreat78,~ and~ am~ here~ to~ help~ you.[/tex]

The answer is D. Tanɵ. But why? Let's break it down. Tan pi + theta in the base equation should look like this...

[tex]\frac{tan\pi+ tanTheta}{1 - tan\pi * tanTheta}[/tex]

We now have to simplify this expression. Let's do that.

[tex]tan(\pi) = \frac{sin\pi }{cos\pi } = \frac{0}{-1} = 0[/tex]

Now that we have broken this problem into simpler fragments, we have to put it all together, The final equation should look like the one below!

[tex]tan(\pi + Theta) = \frac{0 + tanTheta}{1 - 0} = tanTheta[/tex]

With that information, we have solved the problem, your final answer is tanɵ

What have we learned?

Answer:

triangle D and F

Step-by-step explanation:

triangle D and F are the same as A, just angled differently.

God bless! hope i helped someone, somehow.

Answer:

D,F

Step-by-step explanation:

Answer:

Step-by-step explanation:

(i)

PQRS is a parallelogram (given)

      ∴ QT = TS (Diagonals of a parallelogram bisects each other)

also,   QT = RM (given)

      ∴TS = RM

PQRS is a parallelogram,

     ∴RT = PT (Diagonals of a parallelogram bisects each other)

also, SM = PT (given)

    ∴RT = SM

TS = RM

RT = SM

∴ RTSM is a parallelogram (both pairs of opposite sides are equal in length)

(ii)

QP // RS (Opposite sides of a parallelogram are parallel)

∴ ∡RQP = ∡NRS (Corresponding ∡s)

RTSM is a parallelogram(Proved above)

∴MS // RT (Opposite sides of a parallelogram are parallel)

∴NS//RP

∴∡RNS = ∡ QRP (Corresponding ∡s)

in ΔPQR and Δ NSR,

QP = RS (Opposite sides of a parallelogram are equal)

∡RQP = ∡NRS (Proved above)

∡RNS = ∡ QRP(Proved above)

∴ ΔPQR≡ΔSRN (AAS)

Corresponding sides of ≡ Δs are equal, ∴QR = RN