Write the equation of the circle with center (−1, −3) and (−7, −5) a point on the circle.

Answers

Answer 1

so, we know the center is at -1, -3, hmmm what's the radius anyway?

well, the radius will be the distance from the center to any point on the circle, it just so happen that we know -7, -5 is on it, thus

[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &&(~ -1 &,& -3~) % (c,d) &&(~ -7 &,& -5~) \end{array} \\\\\\ d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ r=\sqrt{[-7-(-1)]^2+[-5-(-3)]^2}\implies r=\sqrt{(-7+1)^2+(-5+3)^2} \\\\\\ r=\sqrt{36+4}\implies r=\sqrt{40}\\\\ -------------------------------[/tex]

[tex]\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{-1}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{\sqrt{40}}{ r} \\\\\\\ [x-(-1)]^2+[y-(-3)]^2=(\sqrt{40})^2\implies (x+1)^2+(y+3)^2=40[/tex]

Related Questions

Use the diagram to complete the statement. Given JKL, sin(38) equals—
(Diagram is a right triangle. Angle K is 52 degrees and angle L is 38)

cos(38)
cos(52)
tan(38)
tan(52)

Answers

Cos(52) . Sine and Cosine are cofunctions so to convert from one to the other you subtract the value from 90 to get the other function. 90-38= 52. you can check this by putting both into a calculator. (in degree mode on calculator)
sin(38) = 0.61566......
cos(52) = 0.61566......

Answer:

Answer is b

Step-by-step explanation:

A pillow that usually costs $20 is marked down 45%. Table Use the table to find the new price of the pillow. $9 $11 $29 $33

Answers

It would now cost $11. 45% of 20 is 9, therefore, you would subtract 9 from 20 (since it is getting marked down).

Answer:

$11

Step-by-step explanation:

20-9=11

y+2=−2(x−3)

Slope from equation
Problem
What is the slope of the line?

Answers

y = -2x + 6 - 2
y = -2x + 4
The slope of the line is -2.

Please find below the given equation-

y + 2 = -2 ( x - 3 )

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

y + 2 = -2 x + 6

y = -2 x + 6 - 2

y = -2 x + 4

Let's compare this equation with the form y = mx +c

By comparing we get,

m = -2 and c = 4

We know, in y = mx + c , slope of the line is given by m

Here m = -2, as discussed above

Therefore the slope of the given line is -2

Hope it helps ..!!

A photographer enlarges a photo by using a scale of 5. The length of the original photo is 7 in. What is the length of the enlarged photo? Enter your answer in the box.

Answers

The answer is 35, i hope i helped if you have any questions just comment ill respond as soon as possible

Answer:

Step-by-step explanation:

NEED HELP PLEASE :) ONLY 100% ANSWERS
1) An Egyptian pyramid has a square base that measures 80 meters on each side. If the height of the pyramid is 30 meters, what is the slant height of the pyramid?

2) A room in a bank is shaped like the rectangular prism shown below. The room has a security system that is triggered by two laser beams which stretch from Point A to D and Point B to C. How many total feet of laser beams are there?

*A 3-D rectangle 15 ft. length the back rectangle 12 ft. width the side 35 ft. width front*

Answers

first answer is 81.39 but can't picture the second one without a figure

Answer:

1) the slant height of the pyramid is 50 meters.

2) there are (approximately) a total of 80 ft of laser beams.

Step-by-step explanation:

1) The height of the pyramid (30 m) and half of the length of its base (40 m) form a rectangular triangle, where the slant height is its hypotenuse (H). From Pythagorean theorem:

H^2 = 30^2 + 40^2

H = √2500

H = 50 m

2) In the figure attached the rectangular prism is shown (point E was added).

The length of the laser beams is the addition of the segments AD to segment CB (which are equal).

We can make a rectangular triangle between points ECD. From Pythagorean theorem:

ED^2 = EC^2 + CD^2

ED = √(12^2 + 35^2)

ED = 37 ft

We can make a rectangular triangle between points AED. From Pythagorean theorem:

AD^2 = EA^2 + ED^2

AD = √(15^2 + 37^2)

AD ≈ 40

Then, there are (approximately) a total of 80 ft of laser beams.

Jacey obtains a 30-year 6/2 ARM at 4% with a 2/6 cap structure in the amount of $224,500. What is the monthly payment during the initial period?

Answers

In this case we have an ARM fixed for 6 years and adjust after the initial first 6 years every 2 years after. The basic idea behind a ARM is that the interest changes periodically, but since our ARM is fixed for 6 years, our going to calculate the monthly payment during the initial period using the formula: [tex]m= \frac{P( \frac{r}{12}) }{1-(1+ \frac{r}{12})^{-12t} } [/tex]
where
[tex]m[/tex] is the monthly payment
[tex]P[/tex] is the amount
[tex]r[/tex] is the interest rate in decimal form
[tex]t[/tex] is the number years

First we need to convert our interest rate of 4% to decimal form by dividing it by 100%:
[tex] \frac{4}{100} =0.04[/tex]
We also know from our question that [tex]P=224500[/tex] and [tex]t=30[/tex], so lets replace those values into our formula to find the monthly payment:
[tex]m= \frac{224500( \frac{0.04}{12}) }{1-(1+ \frac{0.04}{12})^{-(12)(30)} } [/tex]
[tex]m=1071.80[/tex]

We can conclude that the monthly payment during the initial period is $1071.58

help me, please............

Answers

The second choice. Because X cannot be in denominator.

B, or the second one, which is
-3/x

Kohl's sells casual shirts for $9 and polo shirts for $18.00. Total sales were $1,080, and customers bought 4 times as many casual as polo shirts. How many casual shirts did Kohl's sell?
a. 40
b. 12
c. 20
d. 60

Answers

trick question so i believe its
60
please correct e if im wrong

WILL GIVE A BRAINLEST!!!!!!!!!!

Which is true about the statements

The graph of f(x) has a vertex of (–4, 6).
The graph of f(x) is horizontally stretched.
The graph of f(x) opens upward.
The graph of f(x) has a domain of x <=–6.

Answers

the second option

hope this helps<3

Answer: B) The graph of f(x) is horizontally stretched.

Step-by-step explanation: We are given an absolute function [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex].

The standard equation of an absolute function is [tex]f(x)= a|x-h|+k[/tex].

Where (h,k) is the vertex of the absolute function.

If we compare [tex]f(x)=-\frac{2}{3} |x+4|-6[/tex] and [tex]f(x)= a|x-h|+k[/tex], we can see a=[tex]-\frac{2}{3}[/tex], h= -4 and h= -6.

Therefore, vertex of the given function is (-4,-6).Because we have value of a is a negative number so it would open down.An absolute function always have domain " All real numbers".

Therefore, first, third and fourth options are incorrect.

So, the second option would only be applicable.

B) The graph of f(x) is horizontally stretched.

If two figures are congruent, their perimeters are equal true or false?

Answers

This is true. The term congruent means that the shape is of exactly equal size. If this is true, then every side length would match for each shape. If this is true, the perimeter would also be exactly the same for each shape. Think of something that is congruent as being an exact copy of the original, with no change in size or shape.

Write an algebraic expression for the verbal description. the sum of two consecutive natural numbers, the first of which is n

Answers

I think it may be:

n + (n + 1)

hope this helps

Two consecutive natural numbers would be 1 and 2, or 5 and 6, for example.

If the first number is n and the second number is n+1, then you are writing [tex]n+(n+1)=2n+1[/tex].

PLZ HELP!!!! 43 POINTS!!!!! Koji is installing a rectangular window in an office building. The window is 8 2/3 ft wide and 5 3/4 ft high. The formula for the area of a rectangle is A=bh. What is the area of the window?

Answers

49 and 10/12
multiply 8 and 2/3 by 5 and 3/4!

A toy rocket is launched from a platform 42 feet above the ground at a speed of 91 feet per second. The height of the rocket in feet is given by the polynomial −16t^2 + 91t + 42, where t is the time in seconds. How high will the rocket be after 3 seconds? HELP ASAP!!

A. 122 feetB. 218 feetC. 93 feetD. 2570 feet

Answers

Lets get started!

height = -16t² + 91t + 42
After 3 sec means, t = 3, so we substitute t with 3

H = -16(3)² + 91(3) + 42
= -144 + 273 + 42
= 171 feet

The height of the rocket after 3 seconds is 171 feet.

What is a function?

A function is defined as a relation between the set of inputs having exactly one output each.

The height = -16t² + 91t + 42

After 3 sec means, t = 3, so we substitute t with 3

In order to find the height of the rocket after t seconds we plugin t = 3 in the function.

height H = -16t² + 91t + 42

H = -16(3)² + 91(3) + 42

= -144 + 273 + 42

= 171 feet

Thus, the height of the rocket after 3 seconds = 171 feet.

Learn more about function here:

https://brainly.com/question/2253924

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On a map, 1.5 centimeters represents a distance of 45 kilometers. If two points on the map are 0.8 centimeters apart, what is the actual distance between the two points?

Answers

Write a proportion
centimeters / kilometers
1.5 / 45 = 0.8 / x
cross multiply
(1.5 * x ) = (45 * 0.8)
1.5x = 36
divide both sides by 1.5
x = 24

The actual distance between the two points is 24 kilometers.

Hope this helps

When you add two rational numbers, each number can be written as a?

Answers

When you add two rational numbers, each number can be written as a

✔ fraction .

Step-by-step explanation:

When you add two rational numbers, each number can be written as a fraction.

What is a rational number?

A Rational number can be defined as any number which can be represented in the form of p/q where q ≠ 0. It can be made by dividing an integer by an integer.

For the given situation,

The sum of two rational numbers is rational.

The closure property of addition of rational number states that if we add two rational number, then the sum of these two rational number will also be a rational number.

Adding two rationals is the same as adding two such fractions, which will result in another fraction of this same form since integers are closed under addition and multiplication.

Hence we can conclude that when you add two rational numbers, each number can be written as a fraction.

Learn more about rational numbers here

https://brainly.com/question/13261309

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Need help ASAP WILL GIVE TEN POINTS FIVE QUESTIONS-
1

What is the solution to the inequality?

6x−5>−29

A x>−4
B x<4
C x>4
D x<−4
2

What is the solution to the inequality?

−4x−8>−20
A x>3
B x>−3
C x<−3
D x<3

3Solve.

−4.2y+2.1>−2.52

Drag and drop a number or symbol into each box to show the solution.
< > 0.1 1.1 4.62 −4.62

Y.(number) (number)

4 Solve.

−12x+13>35

Drag and drop a number or symbol into each box to show the solution.
< > −8/15 −4/15 4/15 8/15

x (number) (number)

What is the solution set?

−2.8x+5.6<8.4

Enter your answer in the box.

x (answer) plz help and ty

Answers

The answer for
1) x>-4
2)x<3
3)y<1.1
4)x<-11/6
5)x>-1
HOPE THIS HELP

Answer:

Part 1) Option A [tex]x>-4[/tex]

Part 2) Option D [tex]x<3[/tex]

Part 3) [tex]y < 1.1[/tex]

Part 4) [tex]x<-8/15[/tex]

Part 5) [tex]x>-1[/tex]

Step-by-step explanation:

Part 1) we have

[tex]6x-5>-29[/tex]

[tex]6x>-29+5[/tex]

[tex]x>-24/6[/tex]

[tex]x>-4[/tex]

Part 2) we have

[tex]-4x-8>-20[/tex]

[tex]-4x>-20+8[/tex]

[tex]-4x>-12[/tex] -----> Multiply by [tex]-1[/tex] both sides

[tex]4x<12[/tex]

[tex]x<12/4[/tex]

[tex]x<3[/tex]

Part 3) we have

[tex]-4.2y+2.1 >-2.52[/tex]

[tex]-4.2y >-2.52-2.1[/tex]

[tex]-4.2y >-4.62[/tex] ----> Multiply by [tex]-1[/tex] both sides

[tex]4.2y < 4.62[/tex]

[tex]y < 1.1[/tex]

Part 4) we have

[tex]-(1/2)x+(1/3)>3/5[/tex]

[tex]-1/2x>(3/5)-(1/3)[/tex]

[tex]-1/2x>4/15[/tex] ---> Multiply by [tex]-1[/tex] both sides

[tex]1/2x<-4/15[/tex]

[tex]x<-8/15[/tex]

Part 5) we have

[tex]-2.8x+5.6< 8.4[/tex]

[tex]-2.8x< 8.4-5.6[/tex]

[tex]-2.8x< 2.8[/tex] ---> Multiply by [tex]-1[/tex] both sides

[tex]2.8x>-2.8[/tex]

[tex]x>-2.8/2.8[/tex]

[tex]x>-1[/tex]

Find the zeros K(x) = -x²+ 2x + 15 EXPLAIN EVERY STEP!

Answers

Take out - 1
k(x) = -1(x^2 - 2x - 15) Now factor what's inside the brackets. The numbers you pick must add to - 2 and multiply to -15.
When you multiply to -15 you should note that one of the numbers is plus and the other is minus.
(x - )(x + ) is the way it looks.
They differ by 2 and the "largest" one is minus. That means your answer is -5 and +3
k(x) = - (x - 5)(x + 3)
Now for the zeros.
x - 5 can be a zero
x - 5 = 0
x = 5

x + 3 = 0
x = - 3

Use inductive reasoning to find the next term in the sequence 1, 2, 4, 7, 11, 16… what is the next term?
a. 18
b. 19
c. 22
d. 26

Answers

Hello,

[tex]u_1=1\\ u_2=2\\ u_3=4\\ u_4=7\\ u_5=11\\ u_6=16\\ u_2-u_1=2-1=1\\ u_3-u_2=4-2=2\\ u_4-u_3=7-4=3\\ u_5-u_4=11-7=4\\ u_6-u_5=16-11=5\\ ... u_n-u_{n-1}=n-1\\ \boxed{u_n=u_{n-1}+n-1}\\ u_7=u_6+(7-1)=16+6=22\\ [/tex]

Answer C

Let f(x)=x2+14x+48. What are the zeros of the function? Enter your answers in the boxes.

Answers

Remember that to find the zeroes of a quadratic expression of the form [tex]a x^{2} +bx+c[/tex] we could either factor it or use the quadratic formula. When [tex]a=1[/tex], like in our case, is often way easier and faster factor the expression than using the quadratic formula. The only thing we need to do to factor the expression is find tow number whose product is 48 and its sum is 14; those numbers are 6 and 8. [tex](6)(8)=48[/tex] and [tex]6+8=14[/tex]. Now we can factor our quadratic like follows:
[tex] x^{2} +14x+48=(x+6)(x+8)[/tex]
Since we are trying to find the zeroes of the function, we are going to set each one of our factored binomial equal to zero and solve for x:
[tex]x+6=0[/tex]
[tex]x=-6[/tex]
and
[tex]x+8=0[/tex]
[tex]x=-8[/tex]

We can conclude that the zeroes of the function [tex]f(x)= x^{2} +14x+48[/tex] are [tex]x=-6[/tex] and [tex]x=-8[/tex].

Answer:x= -6 and -8

Step-by-step explanation: I took the test

Nicholas used a $10 bill to pay for a granola bar that only costs p dollars. How much change did Nicholas receive from the cashier?

Answers

10 - p.
Nicholas would have spent $p, so he has $p less than $10!

you can subtract 10 dollars by the p then you will get your answer 10-p=10p since you can't subtract a number by a letter.

Quadrilateral ABCD is inscribed in this circle.

What is the measure of angle A?

Enter your answer in the box.

°

Answers

The answer to this is 65.

Remember that the angles opposite of each other equal to 180. So a+c=180 and b+d=180.

First, we solve for x. Since we know that b and d equal to 180, we subtract 148 from 180.
180-148=32. x=32.

Then we plug that in the expression for angle a.
2x+1 becomes 2(32)+1
2*32=64
64+1=65.
a=65

Solve the following equation. Then place the correct number in the box provided. 9(x - 6) = 8(x + 6)

x=

Answers

Hello!

9(x - 6) = 8(x + 6)

The first step to take here is to apply the Distributive Property, which is
a(b + c) = ab + ac.

9(x - 6) = 8(x + 6)
9x - 54 = 8x + 48

After this, you want to begin to eliminate terms to ultimately isolate x; you can subtract 8x from both sides first:

9x - 54 = 8x + 48
x - 54 = 48

Finally, add 54 to both sides to get x by itself:

x - 54 = 48
x = 102

Answer:
x = 102

The answer is 102.
9(x -6) = 8(x+6)
9x - 54= 8x +48
x- 54= 48
x= 102

22.6 is an outlier for which of the following sets of data?
1. 22.6, 21.5, 23.7, 22.6, 28.9, 22.6, 20.9

2. 2.4, 5.3, 3.5, 22.6, 1.8, 2.1, 4.6, 1.9

3. 20.5, 20.8, 21.6, 22.6, 23.7, 24.5, 25.1

4. 13.6, 31.7, 25.8, 22.6, 18.9, 21.6, 30.5

Answers

22.6 is an outlier for the second data set. The reason for this is that 22.6 is nowhere near the rest of the data points. Outliers are numbers that are either a lot bigger or a lot smaller than the rest of the other numbers in the set. In this case, 22.6 is a lot bigger.

Step-by-step explanation: B

equation that passes through the points (-1,0)(0,2)

Answers

1. Find the slope.

2. Plug the slope you found in step 1, one of the given points, and plug both into the point-slope formula.

The point-slope formula is:

y - y_1 = m(x - x_1)

3. Solve the point-slope formula for y.

Your final answer must be in the form

y = mx + b

WILL GIVE A BRAINLEST

What is the solution of x+4/2x-1<0 ?

Answers

To solve the inequality x + 4/2x - 1 < 0, first find the critical value x = 1/2. Then, test the intervals to determine the solution set x < 1/2.

To find the solution of the inequality x + 4/2x - 1 < 0, we can follow these steps:

First, find the critical values by setting the denominator, 2x - 1, equal to zero and solve for x. The critical value is x = 1/2.

Next, test the intervals created by the critical value in the original inequality x + 4/2x - 1 < 0. This helps determine the solution set which is x < 1/2.

In the diagram a || b. Use the diagram to answer the question. (Diagram not to scale.) Name the interior angle to 7
A. 1
B. 2
C. 6
D. 4

Answers

thats wrong it is 2 b

the distance light travels in one second (one light-second) is about 1.86 x 10^5 miles. Saturn is about 475 light-seconds from the sun. About how many miles from the sun is saturn?

Answers

the distance light travels in one second (one light second ) - 1.86 x 10^5 miles
Saturn is 475 light seconds away from the sun. Using this information we are asked to find the distance saturn is away from the sun.
1 light second - 1.86 x 10^5 miles
Therefore 475 light seconds -1.86 x 10^5 miles/light second * 475 light seconds
= 8.83 x 10^7 miles
Saturn is 8.83 x 10^7 miles away from the sun

Answer:

Step-by-step explanation:

Given that the distance light travels in one light second about

[tex]1.86(10^5) miles[/tex]

Distance of Saturn from Sun = Time taken for travel x speed

Here speed = [tex]1.86 x 10^5[/tex]

Time taken = 475 light seconds

Hence distance = [tex]1.86 x 10^5x475\\=883.5x10^5\\=8.835x10^7[/tex] miles

I need more math help, the!

Cement truck A can pour 200 cubic ft of concrete in 20 minutes. It only takes truck B 15 minutes to do the same job. If they both work together,how long will it take them to pour the 200 cubic feet?

I need help setting up the problem and solving it, thank you!

Answers

Track A takes 20 minutes
Track B takes 15 minutes
In 1 minute track be will do a fraction of 1/20, while track B will do 1/15
Both tracks in a minute = 1/20+1/15
= 35/300
Therefore the two tracks will take 300/35 minutes to fill the 200 cubic feet
That is 300/35
= 8.57 minutes
≈ 9 minutes

If p(q-r)x^2 +q(r-p)x + r(p-q) has equal roots,then, 2/q=??
a)p+ 1/r c)p+r
b) 1/p +r d) 1/p + 1/r

Answers

The answer is d) 1/p + 1/r.
Solution to this is,
[r(p-q)/p(q-r)]=1
pr-qr=pq-pr
2pr=pq+qr
2pr/pqr=(pq+qr)/pqr
2/q=1/r+1/p

What is the maximum number of distinct lines that can be drawn through 10 distinct points if no 3 of the points are collinear?

Answers

10 objects chosen 2 at a time can be chosen
.. 10*9/(2*1) = 45 ways

45 distinct lines can be drawn

Other Questions

PLEASE HELP ASAPEXTRA POINTSSheila places a 54 square inch photo behind a 12-inch-by-12-inch piece of matting.The photograph is positioned so that the matting is twice as wide at the top and bottom as the sides.Write an equation for the area of the photo in terms of x. name two ways pollination can occur A(n) _____ is a temporary endeavor undertaken to create a unique product, service, or result. Simplify 10/16 to lowest terms and find an equivalent fraction that has a denominator of 32? A rectangular garden is 6 feet long and 4 feet wide. A second rectangular garden has dimensions that are double the dimensions of the first garden. What is the percent of change in perimeter from the first garden to the second garden? The perimeter increases % from the first garden to the second garden. Compare the gill arches in marine vertebrates with the ribs in terrestrial vertebrates. What does it mean to refer to the family connection as symbolic? Which of the following changes will increase the amount of solid solute able to be dissolved in a liter of liquid water? A. increasing temperature B. increasing surface area C. decreasing temperature D. decreasing pressure After world war 11 what two forms of government began to experience conflict Which undefined term is needed to define an angle???? Janice makes 4 pizzas for dinner. There are 5 people to eat dinner. How much will each person get to eat? What role did religious festivals play in greek life? When does interest on a Direct Unsubsidized Loan begin to accrue? in the early 1600s what happen to all but 38 of the 150 english settlers in the jamesport settlement in virginia What are the dissolved particles in a solution containing a molecular solute? what are the dissolved particles in a solution containing a molecular solute? the atoms the cations the molecules the ions? need help so much ... The delivery of oxygen and nutrients to the tissues of the body is accomplished through ________ circulation. A recent news story reported that opec is expected to decrease the supply of oil next summer. summer is traditionally a time of increased demand for oil because of the many families driving and flying to vacation sites. what would be the combined effect of these two events on the summer market for gasoline? What is the GCF of 14x^2 and 4xy? A. 10x B. 28x^2y C. 2x2 D. 2x What is the central idea of the speech (First inaugural address), and how might Lincolns intended audience have shaped that idea? Cite examples of how Lincoln develops his central idea.