The diameter of a circle has endpoints P(-12, -4) and Q(6, 12).
Write an equation for the circle. Be sure to show and explain all work.

Answers

Answer 1

9514 1404 393

Answer:

  (x +3)² +(y -4)² = 145

Step-by-step explanation:

The center of the circle is the midpoint of the given segment PQ. If we call that point A, then ...

  A = (P +Q)/2

  A = ((-12, -4) +(6, 12))/2 = (-12+6, -4+12)/2 = (-6, 8)/2

  A = (-3, 4)

The equation of the circle for some radius r is ...

  (x -(-3))² +(y -4)² = r² . . . . . . where (-3, 4) is the center of the circle

The value of r² can be found by substituting either of the points on the circle. If we use Q, then we have ...

  (6 +3)² +(12 -4)² = r² = 9² +8²

  r² = 81 +64 = 145

Then the equation of the circle is ...

  (x +3)² +(y -4)² = 145

The Diameter Of A Circle Has Endpoints P(-12, -4) And Q(6, 12).Write An Equation For The Circle. Be Sure

Related Questions

Will give brainliest answer

Answers

It is A) Tamara’s work is correct

When graphed you can see that the function is even

substitute for A,P and T in the fomula A=P (1+r)^t,give that A=1 000 000,P=10 000 and T=2,and express as a quadratic equation​

Answers

A = 10,00,000

P = 10,000

T = 2

1000000 = 10000(1+r/100)^2

1000000 = 10000((100 + r)/100)^2

1000000 = 10000× 100 + r/100 × 100 + r/100

1000000 = 10000 + r^2

1000000 - 10000 = r^2

990000 = r^2

√99000 = r

Quadratic Equation

10000(1+r/100)^2

Which of the following rational functions is graphed below?
o
A. F(x) = 1/2x
B. AX) = 1/x-2
C. F(x) = 1/x+2

Answers

Answer:

Option B.

Step-by-step explanation:

We can see that we have an asymptote at x = 2

Remember that in a rational function, the asymptote is at the x-value such that the denominator is equal to zero.

So, the denominator is something like:

(x + a)

we have that the denominator is zero when x = 2

Then:

(2 + a) = 0

solving that for a, we get:

a = -2

Then the denominator of the rational function is:

(x - 2)

For the given options, the only one with this denominator is option B, then the correct option is B.

Answer:

B. f(x) = 1/x-2

Step-by-step explanation:

Math is ez bro.

What is the measure of m?

Answers

Answer:

√245

Step-by-step explanation:

altitude on hypotenuse theorem:

m^2=7*35

m^2=245

m=√245

could anyone help me solve this? I’ve had several questions like this and I don’t understand how to solve it. I’ll give brainliest:)

Answers

Answer:

-2, - 1, - 2 and - 3

Step-by-step explanation:

As the graph depicts an odd function, it will follow the rule f(-x) = - f(x)

the mode of 3,5,1,2,4,6,0,2,2,3 is
giving out brainliest ​

Answers

Mode is the number that occurs the most so the answer will be 2

Is u=−12 a solution of 8u−1=6u?

Answers

Answer:

No, -12 is not a solution.

Step-by-step explanation:

8u-1=6u

8(-12)-1=6(-12)

-96-1=-72

-97=-72

Untrue, to it’s not a solution

If a and b are positive numbers, find the maximum value of f(x) = x^a(2 − x)^b on the interval 0 ≤ x ≤ 2.

Answers

Answer:

The maximum value of f(x) occurs at:

[tex]\displaystyle x = \frac{2a}{a+b}[/tex]

And is given by:

[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Step-by-step explanation:

Answer:

Step-by-step explanation:

We are given the function:

[tex]\displaystyle f(x) = x^a (2-x)^b \text{ where } a, b >0[/tex]

And we want to find the maximum value of f(x) on the interval [0, 2].

First, let's evaluate the endpoints of the interval:

[tex]\displaystyle f(0) = (0)^a(2-(0))^b = 0[/tex]

And:

[tex]\displaystyle f(2) = (2)^a(2-(2))^b = 0[/tex]

Recall that extrema occurs at a function's critical points. The critical points of a function at the points where its derivative is either zero or undefined. Thus, find the derivative of the function:

[tex]\displaystyle f'(x) = \frac{d}{dx} \left[ x^a\left(2-x\right)^b\right][/tex]

By the Product Rule:

[tex]\displaystyle \begin{aligned} f'(x) &= \frac{d}{dx}\left[x^a\right] (2-x)^b + x^a\frac{d}{dx}\left[(2-x)^b\right]\\ \\ &=\left(ax^{a-1}\right)\left(2-x\right)^b + x^a\left(b(2-x)^{b-1}\cdot -1\right) \\ \\ &= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right] \end{aligned}[/tex]

Set the derivative equal to zero and solve for x:

[tex]\displaystyle 0= x^a\left(2-x\right)^b \left[\frac{a}{x} - \frac{b}{2-x}\right][/tex]

By the Zero Product Property:

[tex]\displaystyle x^a (2-x)^b = 0\text{ or } \frac{a}{x} - \frac{b}{2-x} = 0[/tex]

The solutions to the first equation are x = 0 and x = 2.

First, for the second equation, note that it is undefined when x = 0 and x = 2.

To solve for x, we can multiply both sides by the denominators.

[tex]\displaystyle\left( \frac{a}{x} - \frac{b}{2-x} \right)\left((x(2-x)\right) = 0(x(2-x))[/tex]

Simplify:

[tex]\displaystyle a(2-x) - b(x) = 0[/tex]

And solve for x:

[tex]\displaystyle \begin{aligned} 2a-ax-bx &= 0 \\ 2a &= ax+bx \\ 2a&= x(a+b) \\ \frac{2a}{a+b} &= x \end{aligned}[/tex]

So, our critical points are:

[tex]\displaystyle x = 0 , 2 , \text{ and } \frac{2a}{a+b}[/tex]

We already know that f(0) = f(2) = 0.

For the third point, we can see that:

[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(2- \frac{2a}{a+b}\right)^b[/tex]

This can be simplified to:

[tex]\displaystyle f\left(\frac{2a}{a+b}\right) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Since a and b > 0, both factors must be positive. Thus, f(2a / (a + b)) > 0. So, this must be the maximum value.

To confirm that this is indeed a maximum, we can select values to test. Let a = 2 and b = 3. Then:

[tex]\displaystyle f'(x) = x^2(2-x)^3\left(\frac{2}{x} - \frac{3}{2-x}\right)[/tex]

The critical point will be at:

[tex]\displaystyle x= \frac{2(2)}{(2)+(3)} = \frac{4}{5}=0.8[/tex]

Testing x = 0.5 and x = 1 yields that:

[tex]\displaystyle f'(0.5) >0\text{ and } f'(1) <0[/tex]

Since the derivative is positive and then negative, we can conclude that the point is indeed a maximum.

Therefore, the maximum value of f(x) occurs at:

[tex]\displaystyle x = \frac{2a}{a+b}[/tex]

And is given by:

[tex]\displaystyle f_{\text{max}}(x) = \left(\frac{2a}{a+b}\right)^a\left(\frac{2b}{a+b}\right)^b[/tex]

Hãy tìm hàm gốc f(t) có hàm ảnh Laplace như dưới đây:
F(p)=6/p(2p^2+4p +10)

Answers

It looks like we're given the Laplace transform of f(t),

[tex]F(p) = L_p\left\{f(t)\right\} = \dfrac6{p(2p^2+4p+10)} = \dfrac3{p(p^2+2p+5)}[/tex]

Start by splitting up F(p) into partial fractions:

[tex]\dfrac3{p(p^2+2p+5)} = \dfrac ap + \dfrac{bp+c}{p^2+2p+5} \\\\ 3 = a(p^2+2p+5) + (bp+c)p \\\\ 3 = (a+b)p^2 + (2a+c)p + 5a \\\\ \implies \begin{cases}a+b=0 \\ 2a+c=0 \\ 5a=3\end{cases} \implies a=\dfrac35,b=-\dfrac35, c=-\dfrac65[/tex]

[tex]F(p) = \dfrac3{5p} - \dfrac{3p+6}{5(p^2+2p+5)}[/tex]

Complete the square in the denominator,

[tex]p^2+2p+5 = p^2+2p+1+4 = (p+1)^2+4[/tex]

and rewrite the numerator in terms of p + 1,

[tex]3p+6 = 3(p+1) + 3[/tex]

Then splitting up the second term gives

[tex]F(p) = \dfrac3{5p} - \dfrac{3(p+1)}{5((p+1)^2+4)} - \dfrac3{5((p+1)^2+4)}[/tex]

Now take the inverse transform:

[tex]L^{-1}_t\left\{F(p)\right\} = \dfrac35 L^{-1}_t\left\{\dfrac1p\right\} - \dfrac35 L^{-1}_t\left\{\dfrac{p+1}{(p+1)^2+2^2}\right\} - \dfrac3{5\times2} L^{-1}_t\left\{\dfrac2{(p+1)^2+2^2}\right\} \\\\ L^{-1}_t\left\{F(p)\right\} = \dfrac35 - \dfrac35 e^{-t} L^{-1}_t\left\{\dfrac p{p^2+2^2}\right\} - \dfrac3{10} e^{-t} L^{-1}_t\left\{\dfrac2{p^2+2^2}\right\} \\\\ \implies \boxed{f(t) = \dfrac35 - \dfrac35 e^{-t} \cos(2t) - \dfrac3{10} e^{-t} \sin(2t)}[/tex]

Write the quadratic equation whose roots are 2 and -4 and whose leading coefficient is 2

Answers

Answer:

2x^2+4x-16

Step-by-step explanation:

The quadratic can be written as

f(x) = a(x-z1)(x-z2) where z1 and z2 are the roots

f(x) = a (x-2)(x- -4)

a is the leading coefficient

f(x) = 2(x-2)(x+4)

     = 2(x^2 -2x+4x-8)

     = 2(x^2 +2x-8)

     = 2x^2 +4x-16

Help please!??!!?!?

Answers

9514 1404 393

Answer:

  a) CP = SP/1.1

  b) CP = $59.50

  c) GST = $5.95

Step-by-step explanation:

a) Divide by the coefficient of CP.

  SP = 1.1×CP

  CP = SP/1.1

__

b) Use the formula with the given value.

  CP = $65.45/1.1 = $59.50

__

c) You can do this two ways: subtract CP from SP, or multiply CP by 0.1.

  GST = SP -CP = $65.45 -59.50 = $5.95

  GST = CP×0.10 = $59.50 × 0.10 = $5.95

Given two dependent random samples with the following results: Population 1 30 35 23 22 28 39 21 Population 2 45 49 15 34 20 49 36 Use this data to find the 90% confidence interval for the true difference between the population means. Assume that both populations are normally distributed. Step 1 of 4: Find the point estimate for the population mean of the paired differences. Let x1 be the value from Population 1 and x2 be the value from Population 2 and use the formula d=x2−x1 to calculate the paired differences. Round your answer to one decimal place.

Answers

Answer:

(-14.8504 ; 0.5644)

Step-by-step explanation:

Given the data:

Population 1 : 30 35 23 22 28 39 21

Population 2: 45 49 15 34 20 49 36

The difference, d = population 1 - population 2

d = -15, -14, 8, -12, 8, -10, -15

The confidence interval, C. I ;

C.I = dbar ± tα/2 * Sd/√n

n = 7

dbar = Σd/ n = - 7.143

Sd = standard deviation of d = 10.495 (using calculator)

tα/2 ; df = 7 - 1 = 6

t(0.10/2,6) = 1.943

Hence,

C.I = - 7.143 ± 1.943 * (10.495/√7)

C.I = - 7.143 ± 7.7074

(-14.8504 ; 0.5644)

What are the x-intercepts for the function ƒ(x) = -x(x − 4)?
A 0
B -1, 4
C 4
D 0, 4

What are the solutions to the quadratic equation 4x2 − x − 3 = 0?

Answers

Answer:

D

Step-by-step explanation:

f(x)=-x(x-4)

f(x)=-x²+4x

-x²+4x=0

x(-x+4)=0

x=0, x=4

(2)

4x²-x-3=0

(4x²+3x)-(4x-3)=0

x(4x+3)-1(4x+3)=0

x=1, x=-3/4

Please answer this and show the work/explain
2/7m - 1/7 = 3/14

Answers

(2/7)m - (1/7) = 3/14

2m/7 =(3/14) + (1/7)

2m/7 = (3/14) + 2(1/7)

here we are multiplying 2 with 1/7 to make the denominator same for addition.

2m/7 = (3/14) +(2/14)

2m/7 = (3 + 2)/14

2m/7 = 5/14

2m = (5 *7)/14

2m = 35/14

2m = 5/2

m = 5/4

m = 1.25

So the value of "m" is 1.25

find the maximum number of children to whom 30 sweaters and 45 trousers can be equally divided. also how many sweaters and trousers will each get?​

Answers

Answer:

five kids .each 6 sweaters and 9 trousers

Step-by-step explanation:

f

I need to know the answer please

Answers

Focusing on the center point of f(x) (0,0), we can see that it has moved to the left 4 units and up 3 units.

g(x) = [tex](\sqrt[3]{x + 4}) + 3[/tex]

Option C

Hope this helps!

A triangle has base of 7 1/8 feet and height 6 1/4 feet. Find the area of a triangle as a mixed number.

Answers

Answer: The area is 22 17/64.

Step-by-step explanation:

base = 7 1/8 = 57/8

height = 6 1/4 = 25/4

area = 1/2*b*h

= 1/2*57/8*25/4

= 1425/64

= 22 17/64

Given FE=23.5, find BD.

Answers

Answer:

11.75

Step-by-step explanation:

The required triangle is attached below :

The triangle AFE has it's by the mid segment as BD ;as B is the mid-point of line EA ; and D is the mid-point of line FA ;

HENCE, The Length of the midsegment BD = 1/2FE

Hence, BD =. 1/2 * 23.5

BD = 23.5 / 2 = 11.75

Scientists have steadily increased the amount of grain that farms can produce each year. The yield for farms in France is given by y=−2.73x2+11000x−11000000 where x is the year and y is the grain yield in kilograms per hectare (kg/ha).

What does the y-intercept of this function represent?

Answers

9514 1404 393

Answer:

  the yield in year 0

Step-by-step explanation:

The y-value is the yield for farms in France in year x. The y-value when x=0 is the yield for farms in France in year 0.

_____

Additional comment

The reasonable domain for this function is approximately 1843 ≤ x ≤ 2186. The function is effectively undefined for values of x outside this domain, so the y-intercept is meaningless by itself.

Solve the following formula for a.

Answers

Answer:

B is correct .trust me

Step-by-step explanation:

Help me out!! Anyone

Answers

Answer:

4:10

Step-by-step explanation:

if they have to wait for plane B and it arrives every 10 mins then 4:10 is the anser

find the value of the trigonometric ratio. make sure to simplify the fraction if needed

Answers

Answer:

Sin A = o/h

= 9/41

Step-by-step explanation:

since Sin is equal to opposite over hypotenuse, from the question, the opposite angle of A is 9 and hypotenuse angle of A is 41. Thus the answer for Sin A= 9/41

What is the image of -8 ,8 after a dilation by a scale factor of one fourth centered at the origin?

Answers

Answer:

(-2, 2)

Step-by-step explanation:

If you have a point (x, y) and you do a dilation by a scale factor K centered at the origin, the new point will just be (k*x, k*y)

So, if the original point is (-8, 8)

And we do a dilation by a scale factor k = 1/4

Then the image of the point will be:

(-8*(1/4), 8*(1/4))

(-8/4, 8/4)

(-2, 2)

A 10-ft ladder, whose base is sitting on level ground, is leaning at an angle against a vertical wall when its base starts to slide away from the vertical wall. When the base of the ladder is 6 ft away from the bottom of the vertical wall, the base is sliding away at a rate of 4 ft/sec. At what rate is the vertical distance from the top of the ladder to the ground changing at this moment?

Answers

Answer:

2.5/ft per sec

Step-by-step explanation:

its vertica.

The height of the ladder is decreasing at a rate of 24 ft/sec.

What is the Pythagorean theorem?

Pythagorean theorem states that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

We can apply this theorem only in a right triangle.

Example:

The hypotenuse side of a triangle with the two sides as 4 cm and 3 cm.

Hypotenuse side = √(4² + 3²) = √(16 + 9) = √25 = 5 cm

We have,

Let's denote the distance between the base of the ladder and the wall by x.

The length of the ladder = L.

Now,

L = 10 ft

dx/dt = 4 ft/sec

x = 6 ft.

The rate of change of the height of the ladder with respect to time.

Using the Pythagorean theorem, we have:

L² = x² + y²

Differentiating both sides with respect to time t, we get:

2L (dL/dt) = 2x(dx/dt) + 2y(dy/dt)

Substituting L = 10 ft, x = 6 ft, and dx/dt = 4 ft/sec.

20(dL/dt) = 12(4) + 2y(dy/dt)

Simplifying and solving for dy/dt.

dy/dt = (20/2y)(dL/dt) - 24

Now,

The height of the ladder.

Using the Pythagorean theorem again, we have:

y² = L² - x²

   = 100 - 36

   = 64

y = 8

Now,

Substituting y = 8 ft, dL/dt = 0

(since the length of the ladder is constant), and dx/dt = 4 ft/sec.

dy/dt

= (20/2(8))(0) - 24

= -24 ft/sec

Therefore,

The height of the ladder is decreasing at a rate of 24 ft/sec.

Learn more about the Pythagorean theorem here:

https://brainly.com/question/14930619

#SPJ2

Which of the following graphs represents a one-to-one function? On a coordinate plane, a function has two curves connected to a straight line. The first curve has a maximum of (negative 6, 4) and a minimum of (negative 4.5, negative 1). The second curve has a maximum of (negative 3.5, 2) and a minimum of (negative 2.5, 0.5). The straight line has a positive slope and starts at (negative 2, 1) and goes through (1, 2). On a coordinate plane, a circle intersects the x=axis at (negative 2, 0) and (2, 0) and intercepts the y-axis at (0, 4) and (0, negative 4). On a coordinate plane, a v-shaped graph is facing up. The vertex is at (0,0) and the function goes through (negative 4, 4) and (4, 4). A coordinate plane has 7 points. The points are (negative 4, 1), (negative 3, 4), (negative 1, 3), (1, negative 3), (3, negative 4), (4, negative 2), (5, 3). Mark this and return

Answers

Answer:

d. this graph

Step-by-step explanation:

4. Lynn can walk two miles intenta
24 minutes. At this rate, how long will
it take her to walk 6 miles?

Answers

Lynn will take 1 hour and 12 minutes to walk
6 miles.

Three numbers are in the ratio of 1:2:4. If 3 is added to the first and 8 is subtracted from the third, the new numbers will be the first and third terms of an A.P., whose second term is the second number. Find the original numbers.​

Answers

9514 1404 393

Answer:

  5, 10, 20

Step-by-step explanation:

Suppose the three numbers are x, 2x, and 4x. Then they have the required ratios. After the transformation, we have ...

  ((x+3) +(4x -8))/2 = 2x . . . . . 2nd term is average of 1st and 3rd

  5x -5 = 4x   ⇒   x = 5

The original numbers are 5, 10, 20.

_____

After the adjustment, the arithmetic sequence is 8, 10, 12.

Triangle DEF has sides of length x, x+3, and x−1. What are all the possible types of DEF?

Answers

Triangle DEF is scalene

Must click thanks and mark brainliest

The triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.

What is a scalene triangle?

A scalene triangle is a type of triangle which have all the sides to be unequal and similarly, all the angles will also be unequal to each other.

Given that:-

Triangle DEF has sides of length x, x+3, and x−1

it is given that all the sides of the triangle are x, x+3, and x−1 we can clearly see that for any value of x all the three sides will have different values. we can conclude from this that the triangle DEF is a scalene triangle.

Therefore triangle DEF will be a scalene triangle as all the sides of the triangle are unequal.

To know more about the scalene triangle follow

https://brainly.com/question/16589630

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Value of [(3/2)^(-2)] is *​

Answers

Answer:

[tex] { (\frac{3}{2} )}^{ - 2} \\ = { (\frac{2}{3}) }^{2} \\ = \frac{4}{9} \\ thank \: you[/tex]

what is an example of a quintic bionomial?

Answers

3x^5+2

quantic means with the degree of 5 and binomial means two terms.
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