1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
aliya0001 [1]
3 years ago
5

The equation for a circle is x^2 - 8x + y^2 -8 =0. what is the equation of the circle in standard form?

Mathematics
1 answer:
yKpoI14uk [10]3 years ago
8 0
You have to complete the square on this to get it into standard form of a circle.  Move the 8 over to the other side because that's part of the radius.  Group together the x terms, take half the linear term which is 8, square it and add it in to both sides.  Half of 8 is 4, 4 squared is 16, so add in 16 to both sides.  I'll show you in a sec.  You don't need to do anything to the y squared term.  This just means that the center of the circle does not move up or down, only side to side, right or left.  Here's your completing the square before we simplify it down to its perfect square binomial. ( x^{2} -8x+16)+ y^{2} =8+16.  Now break down the parenthesis into the perfect square binomial and do the addition of the right: (x-4) ^{2} + y^{2}=24.  This is the standard form of a circle that has a center of (4, 0) and a radius of \sqrt{24}
You might be interested in
If 4.2 cups equals 1 liter, how many liters equals 21 cups?
kompoz [17]
21 cups/ 4.2L per cup =5 L total
Hope this helps!!
8 0
2 years ago
Find sin(a+b) if tan(a)=7/24 where a is in the third quadrant
ludmilkaskok [199]
The complete question in the attached figure

we have that
tan a=7/24    a----> III quadrant
cos b=-12/13   b----> II quadrant
sin (a+b)=?

we know that
sin(a + b) = sin(a)cos(b) + cos(a)sin(b<span>)
</span>
step 1
find sin b
sin²b+cos²b=1------> sin²b=1-cos²b----> 1-(144/169)---> 25/169
sin b=5/13------> is positive because b belong to the II quadrant

step 2
Find sin a and cos a
tan a=7/24
tan a=sin a /cos a-------> sin a=tan a*cos a-----> sin a=(7/24)*cos a
sin a=(7/24)*cos a------> sin²a=(49/576)*cos²a-----> equation 1
sin²a=1-cos²a------> equation 2
equals 1 and 2
(49/576)*cos²a=1-cos²a---> cos²a*[1+(49/576)]=1----> cos²a*[625/576]=1
cos²a=576/625------> cos a=-24/25----> is negative because a belong to III quadrant
cos a=-24/25
sin²a=1-cos²a-----> 1-(576/625)----> sin²a=49/625
sin a=-7/25-----> is negative because a belong to III quadrant

step 3
find sin (a+b)
sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
sin a=-7/25
cos a=-24/25
sin b=5/13
cos b=-12/13
so
sin (a+b)=[-7/25]*[-12/13]+[-24/25]*[5/13]----> [84/325]+[-120/325]
sin (a+b)=-36/325

the answer is
sin (a+b)=-36/325

8 0
3 years ago
Consider a manufacturing process that is producing hypodermic needles that will be used for blood donations. These needles need
Mars2501 [29]

Answer:

\text{Average diameter is 1.65 mm and we decide that it is not 1.65 mm.}                

Step-by-step explanation:

We are given the following in the question:

The needle size should not be too big and too small.

The diameter of the needle should be 1.65 mm.

We design the null and the alternate hypothesis

H_{0}: \mu = 1.65\text{ mm}\\H_A: \mu \neq 1.65\text{ mm}

Sample size, n = 35

Sample mean, \bar{x} = 1.64 mm

Sample standard deviation, s = 0.07 mm

Type I error:

  • It is the error of rejecting the null hypothesis when it is true.
  • It is also known as false positive error.
  • It is the rejecting of a true null hypothesis.

Thus, type I error in this study would mean we reject the null hypothesis that the average diameter is 1.65 mm but actually the average diameters of the needle is 1.65 mm.

Thus, average diameter is 1.65 mm and we decide that it is not 1.65 mm.

8 0
3 years ago
Read 2 more answers
Find the equation of the line with Slope = -4 and passing through (-1,8). Write your equation in the form
Thepotemich [5.8K]

Answer:

y= -4x+4

Step-by-step explanation:

y=mx+b

where x=-1, y=8, and m=-4

8=(-4)(-1)+b

8=4+b

4=b

Thus, y= -4x+4

8 0
2 years ago
You want to buy a pair of sneakers at a shoe store and you can spend at most $80 you have a coupon for $10 off any pair of shoes
PolarNik [594]
80\geqp-20
3 0
3 years ago
Other questions:
  • Customer: "I buy the same items every week and my bill is normally $90.00. Why am I now being charged $108.00 for the exact same
    10·1 answer
  • 2x+3y+z=17<br> x-3y+2x=-8<br> 5x-2y+3z=5
    6·1 answer
  • A ladder is placed 6 feet away from a house. The ladder comes up to 8 feet on the side of the house. How long is the ladder
    12·1 answer
  • Ella and Nico had $250 altogether. If Nico spent $35, he would still have $5 more than Ella. How much money did Ella have?
    13·1 answer
  • Pls answer this yall<br> 2a-1+8b-12b+7a-12
    11·1 answer
  • A number x is between 0 and 1. Which of the following points on the number line below could be the location of −x+3 ?
    7·2 answers
  • Is there sufficient evidence to conclude that people react faster to a red stimulus? Use a = 0.1.
    9·1 answer
  • Find the common ratior for the geometric sequence and user to find the next three terms.
    5·1 answer
  • Help :( me please PLEQSE
    12·2 answers
  • X2(x−y)5−y2(x−y)5 can be rewritten as (x+y)(x−y)a. What is the value of a ?
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!